Search results for: Fractional Quantum Mechanics

Authors: Elias Akoury

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Nuclear Magnetic Resonance (NMR) spectroscopy is an indispensable technique used in structure determination of small and macromolecules to study their physical properties, elucidation of characteristic interactions, dynamics and thermodynamic processes. Quantum mechanics defines the theoretical description of NMR spectroscopy and treatment of the dynamics of nuclear spin systems. The phenomenon of residual dipolar coupling (RDCs) has become a routine tool for accurate structure determination by providing global orientation information of magnetic dipole-dipole interaction vectors within a common reference frame. This offers accessibility of distance-independent angular information and insights to local relaxation. The measurement of RDCs requires an anisotropic orientation medium for the molecules to partially align along the magnetic field. This can be achieved by introduction of liquid crystals or attaching a paramagnetic center. Although anisotropic paramagnetic tags continue to mark achievements in the biomolecular NMR of large proteins, its application in small organic molecules remains unspread. Here, we propose a strategy for the synthesis of a lanthanide tag and the measurement of RDCs in organic molecules using paramagnetic lanthanide complexes.

Keywords: lanthanide tags, NMR spectroscopy, residual dipolar coupling, quantum mechanics of spin dynamics

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Authors: Amit Tribedi

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Genuine Quantumness present in Quantum Systems is the resource for implementing Quantum Information and Computation Protocols which can outperform the classical counterparts. These Quantumness measures encompass non-local ones known as quantum entanglement (QE) and quantum information theoretic (QIT) ones, e.g. Quantum Discord (QD). In this paper, some well-known measures of QE and QD in some wheel-like frustrated molecular magnetic systems have been studied. One of the systems has already been synthesized using coordination chemistry, and the other is hypothetical, where the dominant interaction is the spin-spin exchange interaction. Exact analytical methods and exact numerical diagonalization methods have been used. Some counter-intuitive non-trivial features, like non-monotonicity of quantum correlations with temperature, persistence of multipartite entanglement over bipartite ones etc. indicated by the behaviour of the correlations and the QIT measures have been found. The measures, being operational ones, can be used to realize the resource of Quantumness in experiments.

Keywords: 0D Magnets, discord, entanglement, frustration

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Authors: Imen Harabi, Hanae Toura, Safa Jemai, Bernabe Mari Soucase

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A promising alternative to traditional Quantum Dots QD materials, which contain toxic heavy elements such as lead and cadmium, sheds light on indium phosphide quantum dots (InP QDs) Owing to improve the quantum yields of photoluminescence and other properties. InP, InP/ZnS core/shell and InP/ZnS/ZnS core/shell/shell Quantum Dots (QDs) were synthetized by the hot injection method. The optical and structural properties of the core InP QDs, InP/ZnS QDs, and InP/ZnS/ZnS QDs have being considered by several techniques such as X-ray diffraction, transmission electron microscopy, optical spectroscopy, and photoluminescence. The average diameter of InP, InP/ZnS, and InP/ZnS/ZnS Quantum Dots (QDs) was varying between 10 nm, 5.4 nm, and 4.10 nm. This experience revealed that the surface morphology of the Quantum Dots has a more regular spherical form with color variation of the QDs in solution. The emission peak of colloidal InP Quantum Dots was around 530 nm, while in InP/ZnS, the emission peak is displayed and located at 598 nm. whilst for InP/ZnS/ZnS is placed at 610 nm. Furthermore, an enhanced PL emission due to a passivation effect in the ZnS-covered InP QDs was obtained. Add the XRD information FWHM of the principal peak of InP QDs was 63 nm, while for InP/ZnS was 41 nm and InP/ZnS/ZnS was 33 nm. The effect of the Zinc stearate precursor concentration on the optical, structural, surface chemical of InP and InP/ZnS and InP/ZnS/ZnS QDs will be discussed.

Keywords: indium phosphide, quantum dot, nanoparticle, core-shell, multishell, luminescence

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Authors: Nisa Özge Önal, Kamil Karaçuha, Göksu Hazar Erdinç, Banu Bahar Karaçuha, Ertuğrul Karaçuha

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The study aims to use a mathematical approach with the fractional calculus which is developed to have the ability to continuously analyze the factors related to the children’s height development. Until now, tracking the development of the child is getting more important and meaningful. Knowing and determining the factors related to the physical development of the child any desired time would provide better, reliable and accurate results for childcare. In this frame, 7 groups for height percentile curve (3th, 10th, 25th, 50th, 75th, 90th, and 97th) of Turkey are used. By using discrete height data of 0-18 years old children and the least squares method, a continuous curve is developed valid for any time interval. By doing so, in any desired instant, it is possible to find the percentage and location of the child in Percentage Chart. Here, with the help of the fractional calculus theory, a mathematical model is developed. The outcomes of the proposed approach are quite promising compared to the linear and the polynomial method. The approach also yields to predict the expected values of children in the sense of height.

Keywords: children growth percentile, children physical development, fractional calculus, linear and polynomial model

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Authors: Aleksey Fedorov

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Building a scalable platform for quantum computing remains one of the most challenging tasks in quantum science and technologies. However, the implementation of most important quantum operations with qubits (quantum analogues of classical bits), such as multiqubit Toffoli gate, requires either a polynomial number of operation or a linear number of operations with the use of ancilla qubits. Therefore, the reduction of the number of operations in the presence of scalability is a crucial goal in quantum information processing. One of the most elegant ideas in this direction is to use qudits (multilevel systems) instead of qubits and rely on additional levels of qudits instead of ancillas. Although some of the already obtained results demonstrate a reduction of the number of operation, they suffer from high complexity and/or of the absence of scalability. We show a strong reduction of the number of operations for the realization of the Toffoli gate by using qudits for a scalable multi-qudit processor. This is done on the basis of a general relation between the dimensionality of qudits and their topology of connections, that we derived.

Keywords: quantum computing, qudits, Toffoli gates, gate decomposition

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Authors: Debjit Dutta, P. Roy, O. Panella

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In recent years, non Hermitian interaction in non relativistic as well as relativistic quantum mechanics have been examined from various aspect. We can observe interesting fact that for such systems a class of potentials, namely the PT symmetric and η-pseudo Hermitian admit real eigenvalues despite being non Hermitian and analogues of those system have been experimentally verified. Point to be noted that relativistic non Hermitian (PT symmetric) interactions can be realized in optical structures and also there exists photonic realization of the (1 + 1) dimensional Dirac oscillator. We have thoroughly studied generalized Dirac oscillators with non Hermitian interactions in (1 + 1) dimensions. To be more specific, we have examined η pseudo Hermitian interactions within the framework of generalized Dirac oscillator in (1 + 1) dimensions. In particular, we have obtained a class of interactions which are η-pseudo Hermitian and the metric operator η could have been also found explicitly. It is possible to have exact solutions of the generalized Dirac oscillator for some choices of the interactions. Subsequently we have employed the mapping between the generalized Dirac oscillator and the Jaynes Cummings (JC) model by spin flip to obtain a class of exactly solvable non Hermitian JC as well as anti Jaynes Cummings (AJC) type models.

Keywords: Dirac oscillator, non-Hermitian quantum system, Hermitian, relativistic

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Authors: Sadia Arshad, Yifa Tang, Dumitru Baleanu

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A fractional order mathematical model is proposed that incorporate CD8+ cells, natural killer cells, cytokines and tumor cells. The tumor cells growth in the absence of an immune response is modeled by logistic law as it was the simplest form for which predictions also agreed with the experimental data. Natural Killer Cells are our first line of defense. NK cells directly kill tumor cells through several mechanisms, including the release of cytoplasmic granules containing perforin and granzyme, expression of tumor necrosis factor (TNF) family members. The effect of the NK cells on the tumor cell population is expressed with the product term. Rational form is used to describe interaction between CD8+ cells and tumor cells. A number of cytokines are produced by NKs, including tumor necrosis factor TNF, IFN, and interleukin (IL-10). Source term for cytokines is modeled by Michaelis-Menten form to indicate the saturated effects of the immune response. Stability of the equilibrium points is discussed for biologically significant values of bifurcation parameters. We studied the treatment of fractional order system by investigating analytical conditions of tumor eradication. Numerical simulations are presented to illustrate the analytical results.

Keywords: cancer model, fractional calculus, numerical simulations, stability analysis

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Authors: Thomas Prevenslik

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Weakly Interacting Massive Particle (WIMP) experiments suggesting dark matter does not exist are consistent with the argument that the long-standing galaxy rotation problem may be resolved without the need for dark matter if the redshift measurements giving the higher than expected galaxy velocities are corrected for the redshift in cosmic dust. Because of the ubiquity of cosmic dust, all velocity measurements in astronomy based on redshift are most likely overstated, e.g., an accelerating Universe expansion need not exist if data showing supernovae brighter than expected based on the redshift/distance relation is corrected for the redshift in dust. Extensions of redshift corrections for cosmic dust to other historical astronomical observations are briefly discussed.

Keywords: alternative theories, cosmic dust redshift, doppler effect, quantum mechanics, quantum electrodynamics

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Authors: Georgi Bebrov, Rozalina Dimova

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In the field of quantum secure communication, there is no evaluation that characterizes quantum secure communication (QSC) protocols in a complete, general manner. The current paper addresses the problem concerning the lack of such an evaluation for QSC protocols by introducing an optimality evaluation, which is expressed as the average over the three main parameters of QSC protocols: efficiency, security, and practicality. For the efficiency evaluation, the common expression of this parameter is used, which incorporates all the classical and quantum resources (bits and qubits) utilized for transferring a certain amount of information (bits) in a secure manner. By using criteria approach whether or not certain criteria are met, an expression for the practicality evaluation is presented, which accounts for the complexity of the QSC practical realization. Based on the error rates that the common quantum attacks (Measurement and resend, Intercept and resend, probe attack, and entanglement swapping attack) induce, the security evaluation for a QSC protocol is proposed as the minimum function taken over the error rates of the mentioned quantum attacks. For the sake of clarity, an example is presented in order to show how the optimality is calculated.

Keywords: quantum cryptography, quantum secure communcation, quantum secure direct communcation security, quantum secure direct communcation efficiency, quantum secure direct communcation practicality

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Authors: K. Orozović, B. Balon

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In this paper, we take a different approach to de Broglie wavelength, as we relate it to relativistic physics. The quantum energy of the photon radiated by a body with de Broglie wavelength, as it moves with velocity v, can be defined within relativistic physics by rest energy E₀. In this way, we can show the connection between the quantum of radiation energy of the body and the rest of energy E₀ and thus combine what has been incompatible so far, namely relativistic and quantum physics. So, here we discuss the unification of relativistic and quantum physics by introducing the factor k that is analog to the Lorentz factor in Einstein's theory of relativity.

Keywords: de Brogli wavelength, relativistic physics, rest energy, quantum physics

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Authors: Jorge Gonzalez Camus, Carlos Lizama

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In this work is proved the existence of at least one globally attractive mild solution to the Cauchy problem, for fractional evolution equation of neutral type, involving the fractional derivate in Caputo sense. An almost sectorial operator on a Banach space X and a kernel belonging to a large class appears in the equation, which covers many relevant cases from physics applications, in particular, the important case of time - fractional evolution equations of neutral type. The main tool used in this work was the Hausdorff measure of noncompactness and fixed point theorems, specifically Darbo-type. Initially, the equation is a Cauchy problem, involving a fractional derivate in Caputo sense. Then, is formulated the equivalent integral version, and defining a convenient functional, using the analytic integral resolvent operator, and verifying the hypothesis of the fixed point theorem of Darbo type, give us the existence of mild solution for the initial problem. Furthermore, each mild solution is globally attractive, a property that is desired in asymptotic behavior for that solution.

Keywords: attractive mild solutions, integral Volterra equations, neutral type equations, non-local in time equations

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Authors: Ali Motalebi Saraji, Reza Zarei Lamuki

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Speed control and behavior improvement of permanent magnet synchronous motors (PMSM) that have reliable performance, low loss, and high power density, especially in industrial drives, are of great importance for researchers. Because of its importance in this paper, coefficients optimization of proportional-integrator-derivative fractional order controller is presented using Particle Swarm Optimization (PSO) algorithm in order to improve the behavior of PMSM in its speed control loop. This improvement is simulated in MATLAB software for the proposed optimized proportional-integrator-derivative fractional order controller with a Genetic algorithm and compared with a full order controller with a classic optimization method. Simulation results show the performance improvement of the proposed controller with respect to two other controllers in terms of rising time, overshoot, and settling time.

Keywords: speed control loop of permanent magnet synchronous motor, fractional and full order proportional-integrator-derivative controller, coefficients optimization, particle swarm optimization, improvement of behavior

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Authors: Hoang Van Ngoc, Nguyen Thu Huong, Nguyen Quang Bau

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Using the quantum kinetic equation for electrons interacting with acoustic phonon, the density of the constant current associated with the drag of charge carriers in cylindrical quantum wire by a linearly polarized electromagnetic wave, a DC electric field and a laser radiation field is calculated. The density of the constant current is studied as a function of the frequency of electromagnetic wave, as well as the frequency of laser field and the basic elements of quantum wire with a parabolic potential. The analytic expression of the constant current density is numerically evaluated and plotted for a specific quantum wires GaAs/AlGaAs to show the dependence of the constant current density on above parameters. All these results of quantum wire compared with bulk semiconductors and superlattices to show the difference.

Keywords: The photon-drag effect, the constant current density, quantum wire, parabolic potential

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Authors: Sadia Nasrin Tisha, Mushfika Sharmin Rahman, Javier Orduz

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Machine learning is applied in a variety of fields throughout the world. The healthcare sector has benefited enormously from it. One of the most effective approaches for predicting human heart diseases is to use machine learning applications to classify data and predict the outcome as a classification. However, with the rapid advancement of quantum technology, quantum computing has emerged as a potential game-changer for many applications. Quantum algorithms have the potential to execute substantially faster than their classical equivalents, which can lead to significant improvements in computational performance and efficiency. In this study, we applied quantum machine learning concepts to predict coronary heart diseases from text data. We experimented thrice with three different features; and three feature sets. The data set consisted of 100 data points. We pursue to do a comparative analysis of the two approaches, highlighting the potential benefits of quantum machine learning for predicting heart diseases.

Keywords: quantum machine learning, SVM, QSVM, matrix product state

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Authors: Prashant Pandey

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In the present article, an effective Laguerre collocation method is used to obtain the approximate solution of a system of coupled fractional-order non-linear reaction-advection-diffusion equation with prescribed initial and boundary conditions. In the proposed scheme, Laguerre polynomials are used together with an operational matrix and collocation method to obtain approximate solutions of the coupled system, so that our proposed model is converted into a system of algebraic equations which can be solved employing the Newton method. The solution profiles of the coupled system are presented graphically for different particular cases. The salient feature of the present article is finding the stability analysis of the proposed method and also the demonstration of the lower variation of solute concentrations with respect to the column length in the fractional-order system compared to the integer-order system. To show the higher efficiency, reliability, and accuracy of the proposed scheme, a comparison between the numerical results of Burger’s coupled system and its existing analytical result is reported. There are high compatibility and consistency between the approximate solution and its exact solution to a higher order of accuracy. The exhibition of error analysis for each case through tables and graphs confirms the super-linearly convergence rate of the proposed method.

Keywords: fractional coupled PDE, stability and convergence analysis, diffusion equation, Laguerre polynomials, spectral method

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Authors: Hector Carcel Luis Alberiko Gil-Alana

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This paper examines the time series behavior of three variables (GDP, Price level of Consumption and Population) in the eight countries that belong to the West African Economic and Monetary Union (WAEMU), which are Benin, Burkina Faso, Côte d’Ivoire, Guinea-Bissau, Mali, Niger, Senegal and Togo. The reason for carrying out this study lies in the considerable heterogeneity that can be perceived in the data from these countries. We conduct a long memory and fractional integration modeling framework and we also identify potential breaks in the data. The aim of the study is to perceive up to which degree the eight West African countries that belong to the same monetary union follow the same economic patterns of stability. Testing for mean reversion, we only found strong evidence of it in the case of Senegal for the Price level of Consumption, and in the cases of Benin, Burkina Faso and Senegal for GDP.

Keywords: West Africa, Monetary Union, fractional integration, economic patterns

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Authors: Nikolaos Petropoulos, Elena Blokhina, Andrii Sokolov, Andrii Semenov, Panagiotis Giounanlis, Xutong Wu, Dmytro Mishagli, Eugene Koskin, Robert Bogdan Staszewski, Dirk Leipold

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We investigate entanglement and quantum information scrambling (QIS) by the example of a many-body Extended and spinless effective Fermi-Hubbard Model (EFHM and e-FHM, respectively) that describes a special type of quantum dot array provided by Equal1 labs silicon-based quantum computer. The concept of QIS is used in the framework of quantum information processing by quantum circuits and quantum channels. In general, QIS is manifest as the de-localization of quantum information over the entire quantum system; more compactly, information about the input cannot be obtained by local measurements of the output of the quantum system. In our work, we will first make an introduction to the concept of quantum information scrambling and its connection with the 4-point out-of-time-order (OTO) correlators. In order to have a quantitative measure of QIS we use the tripartite mutual information, in similar lines to previous works, that measures the mutual information between 4 different spacetime partitions of the system and study the Transverse Field Ising (TFI) model; this is used to quantify the dynamical spreading of quantum entanglement and information in the system. Then, we investigate scrambling in the quantum many-body Extended Hubbard Model with external magnetic field Bz and spin-spin coupling J for both uniform and thermal quantum channel inputs and show that it scrambles for specific external tuning parameters (e.g., tunneling amplitudes, on-site potentials, magnetic field). In addition, we compare different Hilbert space sizes (different number of qubits) and show the qualitative and quantitative differences in quantum scrambling as we increase the number of quantum degrees of freedom in the system. Moreover, we find a "scrambling phase transition" for a threshold temperature in the thermal case, that is, the temperature of the model that the channel starts to scramble quantum information. Finally, we make comparisons to the TFI model and highlight the key physical differences between the two systems and mention some future directions of research.

Keywords: condensed matter physics, quantum computing, quantum information theory, quantum physics

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Authors: Constantin Z. Leshan

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Hole Vacuum theory is based on discontinuous spacetime that contains vacuum holes. Vacuum holes can explain gravitation, some laws of quantum mechanics and allow teleportation of matter. All massive bodies emit a flux of holes which curve the spacetime; if we increase the concentration of holes, it leads to length contraction and time dilation because the holes do not have the properties of extension and duration. In the limited case when space consists of holes only, the distance between every two points is equal to zero and time stops - outside of the Universe, the extension and duration properties do not exist. For this reason, the vacuum hole is the only particle in physics capable of describing gravitation using its own properties only. All microscopic particles must 'jump' continually and 'vibrate' due to the appearance of holes (impassable microscopic 'walls' in space), and it is the cause of the quantum behavior. Vacuum holes can explain the entanglement, non-locality, wave properties of matter, tunneling, uncertainty principle and so on. Particles do not have trajectories because spacetime is discontinuous and has impassable microscopic 'walls' due to the simple mechanical motion is impossible at small scale distances; it is impossible to 'trace' a straight line in the discontinuous spacetime because it contains the impassable holes. Spacetime 'boils' continually due to the appearance of the vacuum holes. For teleportation to be possible, we must send a body outside of the Universe by enveloping it with a closed surface consisting of vacuum holes. Since a material body cannot exist outside of the Universe, it reappears instantaneously in a random point of the Universe. Since a body disappears in one volume and reappears in another random volume without traversing the physical space between them, such a transportation method can be called teleportation (or Hole Teleportation). It is shown that Hole Teleportation does not violate causality and special relativity due to its random nature and other properties. Although Hole Teleportation has a random nature, it can be used for colonization of extrasolar planets by the help of the method called 'random jumps': after a large number of random teleportation jumps, there is a probability that the spaceship may appear near a habitable planet. We can create vacuum holes experimentally using the method proposed by Descartes: we must remove a body from the vessel without permitting another body to occupy this volume.

Keywords: border of the Universe, causality violation, perfect isolation, quantum jumps

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Authors: Kwang-Ho Kim, Kwan-Hong Min, Pyungwoo Jang, Chisup Jung, Kyu Seomoon

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By restricting the dimensions of silicon to less than Bohr radius of bulk crystalline silicon (∼5 nm), quantum confinement causes its effective bandgap to increase. Therefore, silicon quantum wells (QWs) using these quantum phenomena could be a good candidate to achieve high performance silicon solar cells. The Al2O3/Si QW structures were fabricated by using the successive deposition technique, as a quantum confinement device to increase the effective energy bandgap and passivation effect in Si surface for the 3rd generation solar cell applications. In Si/Al2O3 QWs, the thicknesses of Si layers and Al2O3 layers were varied between 1 to 5 nm, respectively. The roughness of deposited Si on Al2O3 was less than 4 Å in the thickness of 2 nm. By using the Al2O3/Si QW structures on Si surfaces, the lifetime measured by u-PCD technique increased as a result of passivated surface effects. The discussion about the other properties such as electrical and optical properties of the QWs structures as well as the fabricated solar cells will be presented in this paper.

Keywords: Al2O3/Si quantum well, quantum confinement, solar cells, third generation, successive deposition technique

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Authors: Bello Yusuf Idi

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The Gongola arm of the Upper Banue Trough, Northeastern Nigeria is predominantly covered by the outcrops of Limestone-bearing rocks in form of Sandstone with intercalation of carbonate clay, shale, basaltic, felsphatic and migmatide rocks at subpixel dimension. In this work, subpixel classification algorithm was used to classify the data acquired from landsat 7 Enhance Thematic Mapper (ETM+) satellite system with the aim of producing fractional distribution image for three most economically important solid minerals of the area: Limestone, Basalt and Migmatide. Linear Spectral Unmixing (LSU) algorithm was used to produce fractional distribution image of abundance of the three mineral resources within a 100Km2 portion of the area. The results show that the minerals occur at different proportion all over the area. The fractional map could therefore serve as a guide to the ongoing reconnaissance for the economic potentiality of the formation.

Keywords: linear spectral un-mixing, upper benue trough, gongola arm, geological engineering

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Authors: Aquil Ahmed, Srikant Gupta, Irfan Ali

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In this paper, we study a multi-objective capacitated transportation problem (MOCTP) with mixed constraints. This paper is comprised of the modelling and optimisation of an MOCTP in a fuzzy environment in which some goals are fractional and some are linear. In real life application of the fuzzy goal programming (FGP) problem with multiple objectives, it is difficult for the decision maker(s) to determine the goal value of each objective precisely as the goal values are imprecise or uncertain. Also, we developed the concept of linearization of fractional goal for solving the MOCTP. In this paper, imprecision of the parameter is handled by the concept of fuzzy set theory by considering these parameters as a trapezoidal fuzzy number. α-cut approach is used to get the crisp value of the parameters. Numerical examples are used to illustrate the method for solving MOCTP.

Keywords: capacitated transportation problem, multi objective linear programming, multi-objective fractional programming, fuzzy goal programming, fuzzy sets, trapezoidal fuzzy number

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Authors: R. Rama Kishore, Sunesh Malik

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Development in the usage of internet for different purposes in recent times creates great threat for the copy right protection of the digital images. Digital watermarking is the best way to rescue from the said problem. This paper presents detailed review of the different watermarking techniques, latest trends in the field and categorized like spatial and transform domain, blind and non-blind methods, visible and non visible techniques etc. It also discusses the different optimization techniques used in the field of watermarking in order to improve the robustness and imperceptibility of the method. Different measures are discussed to evaluate the performance of the watermarking algorithm. At the end, this paper proposes a watermarking algorithm using (k.n) shares of halftone visual cryptography (HVC) instead of (2, 2) share cryptography. (k,n) shares visual cryptography improves the security of the watermark. As halftone is a method of reprographic, it helps in improving the visual quality of watermark image. The proposed method uses fractional transformation to improve the robustness of the copyright protection of the method.

Keywords: digital watermarking, fractional transform, halftone, visual cryptography

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Authors: Valeria Bondarenko

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In this paper, we propose two problems related to fractal Brownian motion. First problem is simultaneous estimation of two parameters, Hurst exponent and the volatility, that describe this random process. Numerical tests for the simulated fBm provided an efficient method. Second problem is approximation of the increments of the observed time series by a power function by increments from the fractional Brownian motion. Approximation and estimation are shown on the example of real data, daily deposit interest rates.

Keywords: fractional Brownian motion, Gausssian processes, approximation, time series, estimation of properties of the model

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Authors: Debasis Mondal, Chandan Datta, S. K. Sazim

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Quantum coherence is a key resource like entanglement and discord in quantum information theory. Wigner- Yanase skew information, which was shown to be the quantum part of the uncertainty, has recently been projected as an observable measure of quantum coherence. On the other hand, the quantum speed limit has been established as an important notion for developing the ultra-speed quantum computer and communication channel. Here, we show that both of these quantities are related. Thus, cast coherence as a resource to control the speed of quantum communication. In this work, we address three basic and fundamental questions. There have been rigorous attempts to achieve more and tighter evolution time bounds and to generalize them for mixed states. However, we are yet to know (i) what is the ultimate limit of quantum speed? (ii) Can we measure this speed of quantum evolution in the interferometry by measuring a physically realizable quantity? Most of the bounds in the literature are either not measurable in the interference experiments or not tight enough. As a result, cannot be effectively used in the experiments on quantum metrology, quantum thermodynamics, and quantum communication and especially in Unruh effect detection et cetera, where a small fluctuation in a parameter is needed to be detected. Therefore, a search for the tightest yet experimentally realisable bound is a need of the hour. It will be much more interesting if one can relate various properties of the states or operations, such as coherence, asymmetry, dimension, quantum correlations et cetera and QSL. Although, these understandings may help us to control and manipulate the speed of communication, apart from the particular cases like the Josephson junction and multipartite scenario, there has been a little advancement in this direction. Therefore, the third question we ask: (iii) Can we relate such quantities with QSL? In this paper, we address these fundamental questions and show that quantum coherence or asymmetry plays an important role in setting the QSL. An important question in the study of quantum speed limit may be how it behaves under classical mixing and partial elimination of states. This is because this may help us to choose properly a state or evolution operator to control the speed limit. In this paper, we try to address this question and show that the product of the time bound of the evolution and the quantum part of the uncertainty in energy or quantum coherence or asymmetry of the state with respect to the evolution operator decreases under classical mixing and partial elimination of states.

Keywords: completely positive trace preserving maps, quantum coherence, quantum speed limit, Wigner-Yanase Skew information

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Authors: Mohammed Abdulhameed, Sagir M. Abdullahi

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In this paper, based on the applications of nanoparticle, the blood flow along with nanoparticles through stenosed artery is studied. The blood is acted by periodic body acceleration, an oscillating pressure gradient and an external magnetic field. The mathematical formulation is based on Caputo-Fabrizio fractional derivative without singular kernel. The model of ordinary blood, corresponding to time-derivatives of integer order, is obtained as a limiting case. Analytical solutions of the blood velocity and temperature distribution are obtained by means of the Hankel and Laplace transforms. Effects of the order of Caputo-Fabrizio time-fractional derivatives and three different nanoparticles i.e. Fe3O4, TiO4 and Cu are studied. The results highlights that, models with fractional derivatives bring significant differences compared to the ordinary model. It is observed that the addition of Fe3O4 nanoparticle reduced the resistance impedance of the blood flow and temperature distribution through bell shape stenosed arteries as compared to TiO4 and Cu nanoparticles. On entering in the stenosed area, blood temperature increases slightly, but, increases considerably and reaches its maximum value in the stenosis throat. The shears stress has variation from a constant in the area without stenosis and higher in the layers located far to the longitudinal axis of the artery. This fact can be an important for some clinical applications in therapeutic procedures.

Keywords: nanoparticles, blood flow, stenosed artery, mathematical models

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Authors: Sebastian Töpfer, Jorge Fuenzalida, Marta Gilaberte Basset, Juan P. Torres, Markus Gräfe

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This work presents an experimental and theoretical study about the noise resilience of quantum holography with undetected photons. Quantum imaging has become an important research topic in the recent years after its first publication in 2014. Following this research, advances towards different spectral ranges in detection and different optical geometries have been made. Especially an interest in the field of near infrared to mid infrared measurements has developed, because of the unique characteristic, that allows to sample a probe with photons in a different wavelength than the photons arriving at the detector. This promising effect can be used for medical applications, to measure in the so-called molecule fingerprint region, while using broadly available detectors for the visible spectral range. Further advance the development of quantum imaging methods have been made by new measurement and detection schemes. One of which is quantum holography with undetected light. It combines digital phase shifting holography with quantum imaging to extent the obtainable sample information, by measuring not only the object transmission, but also its influence on the phase shift experienced by the transmitted light. This work will present extended research for the quantum holography with undetected light scheme regarding the influence of external noise. It is shown experimentally and theoretically that the samples information can still be at noise levels of 250 times higher than the signal level, because of its information being transmitted by the interferometric pattern. A detailed theoretic explanation is also provided.

Keywords: distillation, quantum holography, quantum imaging, quantum metrology

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Authors: N. Q. Bau, N. V. Nghia

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The acoustomagnetoelectric (AME) field in a rectangular quantum wire with an infinite potential (RQWIP) is calculated in the presence of an external magnetic field (EMF) by using the quantum kinetic equation for the distribution function of electrons system interacting with external phonons and electrons scattering with internal acoustic phonon in a RQWIP. We obtained ananalytic expression for the AME field in the RQWIP in the presence of the EMF. The dependence of AME field on the frequency of external acoustic wave, the temperature T of system, the cyclotron frequency of the EMF and the intensity of the EMF is obtained. Theoretical results for the AME field are numerically evaluated, plotted and discussed for a specific RQWIP GaAs/GaAsAl. This result has shown that the dependence of the AME field on intensity of the EMF is nonlinearly and it is many distinct maxima in the quantized magnetic region. We also compared received fields with those for normal bulk semiconductors, quantum well and quantum wire to show the difference. The influence of an EMF on AME field in a RQWIP is newly developed.

Keywords: rectangular quantum wire, acoustomagnetoelectric field, electron-phonon interaction, kinetic equation method

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Authors: Anwar H. Jarndal, Ahmed S. Elwakil

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In this paper, a fraction-order model for pad parasitic effect of GaN HEMT on Si substrate is developed and validated. Open de-embedding structure is used to characterize and de-embed substrate loading parasitic effects. Unbiased device measurements are implemented to extract parasitic inductances and resistances. The model shows very good simulation for S-parameter measurements under different bias conditions. It has been found that this approach can improve the simulation of intrinsic part of the transistor, which is very important for small- and large-signal modeling process.

Keywords: fractional-order modeling, GaNHEMT, si-substrate, open de-embedding structure

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Authors: Omar Alzeley, Sergey Utev

Abstract:

Minimizing a constrained multivariate function is the fundamental of Machine learning, and these algorithms are at the core of data mining and data visualization techniques. The decision function that maps input points to output points is based on the result of optimization. This optimization is the central of learning theory. One approach to complex systems where the dynamics of the system is inferred by a statistical analysis of the fluctuations in time of some associated observable is time series analysis. The purpose of this paper is a mathematical transition from the autoregressive model of classical time series to the matrix formalization of quantum theory. Firstly, we have proposed a quantum time series model (QTS). Although Hamiltonian technique becomes an established tool to detect a deterministic chaos, other approaches emerge. The quantum probabilistic technique is used to motivate the construction of our QTS model. The QTS model resembles the quantum dynamic model which was applied to financial data. Secondly, various statistical methods, including machine learning algorithms such as the Kalman filter algorithm, are applied to estimate and analyses the unknown parameters of the model. Finally, simulation techniques such as Markov chain Monte Carlo have been used to support our investigations. The proposed model has been examined by using real and simulated data. We establish the relation between quantum statistical machine and quantum time series via random matrix theory. It is interesting to note that the primary focus of the application of QTS in the field of quantum chaos was to find a model that explain chaotic behaviour. Maybe this model will reveal another insight into quantum chaos.

Keywords: machine learning, simulation techniques, quantum probability, tensor product, time series

Procedia PDF Downloads 428

Authors: Yogesh D. Bansod, Jiri Bursa

Abstract:

The quantitative study of cell mechanics is of paramount interest since it regulates the behavior of the living cells in response to the myriad of extracellular and intracellular mechanical stimuli. The novel experimental techniques together with robust computational approaches have given rise to new theories and models, which describe cell mechanics as a combination of biomechanical and biochemical processes. This review paper encapsulates the existing continuum-based computational approaches that have been developed for interpreting the mechanical responses of living cells under different loading and boundary conditions. The salient features and drawbacks of each model are discussed from both structural and biological points of view. This discussion can contribute to the development of even more precise and realistic computational models of cell mechanics based on continuum approaches or on their combination with microstructural approaches, which in turn may provide a better understanding of mechanotransduction in living cells.

Keywords: cell mechanics, computational models, continuum approach, mechanical models

Procedia PDF Downloads 329