Search results for: quantum master equation

Authors: Amit Tribedi

Abstract:

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: Y. Pala, M. O. Ertas

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In this paper, the general Riccati equation is analytically solved by a new transformation. By the method developed, looking at the transformed equation, whether or not an explicit solution can be obtained is readily determined. Since the present method does not require a proper solution for the general solution, it is especially suitable for equations whose proper solutions cannot be seen at first glance. Since the transformed second order linear equation obtained by the present transformation has the simplest form that it can have, it is immediately seen whether or not the original equation can be solved analytically. The present method is exemplified by several examples.

Keywords: Riccati equation, analytical solution, proper solution, nonlinear

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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: Jiawei Li

Abstract:

How cooperation emerges and persists in a population of selfish agents is a fundamental question in evolutionary game theory. Our research shows that Collective Strategies with Master-Slave Mechanism (CSMSM) defeat Tit-for-Tat and other well-known strategies in spatial iterated prisoner’s dilemma. A CSMSM identifies kin members by means of a handshaking mechanism. If the opponent is identified as non-kin, a CSMSM will always defect. Once two CSMSMs meet, they play master and slave roles. A mater defects and a slave cooperates in order to maximize the master’s payoff. CSMSM outperforms non-collective strategies in spatial IPD even if there is only a small cluster of CSMSMs in the population. The existence and performance of CSMSM in spatial iterated prisoner’s dilemma suggests that cooperation first appears and persists in a group of collective agents.

Keywords: Evolutionary game theory, spatial prisoners dilemma, collective strategy, master-slave mechanism

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Authors: Aleksey Fedorov

Abstract:

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: Mishack Thiza Gumbo

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The participatory action research study reported in this paper aims to explore indigenous mathematics, science, and technology to develop an indigenous Mathematics, Science and Technology Education Master’s Programme ultimately. The study is based on an ongoing collaborative project between the Mathematics, Science and Technology Education Departments of the University of South Africa, University of Botswana and Chinhoyi University of Technology. The study targets the Mathematics, Science and Technology Education Master’s students and indigenous knowledge holders in these three contexts as research participants. They will be interviewed; documents of existing Mathematics, Science and Technology Education Master’s Programmes will be analysed; mathematics, science and technology-related artefacts will also be collected and analysed. Mathematics, Science, and Technology Education are traditionally referred to as gateway subjects because the world economy revolves around them. Scores of scholars call for the indigenisation of research and methodologies so that research can suit and advance indigenous knowledge and sustainable development. There are ethnomathematics, ethnoscience and ethnotechnology which exist in indigenous contexts such as blacksmithing, woodcarving, textile-weaving and dyeing, but the current curricula and research in institutions of learning reflect the Western notions of these subjects. Indigenisation of the academic programmecontributes toward the decolonisation of education. Hence, the development of an indigenous Mathematics, Science and Technology Education Master’s Programme, which will be jointly offered by the three universities mentioned above, will contribute to the transformation of higher education in this sense.

Keywords: indigenous, mathematics, science, technology, master's program, universities, collaboration

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Authors: Sharon-Yasotha Veerayah-Mcgregor, Valipuram Manoranjan

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A backward or inverse problem is known to be an ill-posed problem due to its instability that easily emerges with any slight change within the conditions of the problem. Therefore, only a limited number of numerical approaches are available to solve a backward problem. This paper considers the Nagumo equation, an equation that describes impulse propagation in nerve axons, which also models population growth with the Allee effect. A creative operator splitting numerical scheme is constructed to solve the inverse Nagumo equation. Computational simulations are used to verify that this scheme is stable, accurate, and efficient.

Keywords: inverse/backward equation, operator-splitting, Nagumo equation, ill-posed, finite-difference

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Authors: Saeed Otarod

Abstract:

In a different simple and straight forward analysis a closed-form integral solution is found for nonhomogeneous second order linear ordinary differential equations, in terms of a particular solution of their corresponding homogeneous part. To find the particular solution of the homogeneous part, the equation is transformed into a simple Riccati equation from which the general solution of non-homogeneouecond order differential equation, in the form of a closed integral equation is inferred. The method works well in manyimportant cases, such as Schrödinger equation for hydrogen-like atoms. A non-homogenous second order linear differential equation has been solved as an extra example

Keywords: explicit, linear, differential, closed form

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Authors: Yuan Yan Tang, Lina Yang, Hong Li

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Harmonic model is a very important approximation for the image transform. The harmanic model converts an image into arbitrary shape; however, this mode cannot be described by any fixed functions in mathematics. In fact, it is represented by partial differential equation (PDE) with boundary conditions. Therefore, to develop an efficient method to solve such a PDE is extremely significant in the image transform. In this paper, a novel Integral Equation-Wavelet based method is presented, which consists of three steps: (1) The partial differential equation is converted into boundary integral equation and representation by an indirect method. (2) The boundary integral equation and representation are changed to plane integral equation and representation by boundary measure formula. (3) The plane integral equation and representation are then solved by a method we call wavelet collocation. Our approach has two main advantages, the shape of an image is arbitrary and the program code is independent of the boundary. The performance of our method is evaluated by numerical experiments.

Keywords: harmonic model, partial differential equation (PDE), integral equation, integral representation, boundary measure formula, wavelet collocation

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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: Sun Ailu, Zhao Wanmin

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Since the reform and opening, the urbanization process of China has entered a rapid development period. In recent years, the authors participated in some projects of urban master planning in China and found a phenomenon that the rapid urbanization area of China is experiencing frequent adjustment process of urban master planning. This phenomenon is not the natural process of urbanization development. It may be caused by different government roles from different levels. Through the methods of investigation, data comparison and case study, this paper aims to explore the reason why the rapid urbanization area is experiencing frequent adjustment of master planning and give some solution strategies. Firstly, taking Changshou district of Chongqing city as an example, this paper wants to introduce the phenomenon about frequent adjustment process in China. And then, discuss distinct roles in the process between national government, provincial government and local government of China. At last, put forward preliminary solutions strategies for this area in China from the aspects of land use, intergovernmental cooperation and so on.

Keywords: urban master planning, frequent adjustment, urbanization development, problems and strategies, China

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Authors: Tadas Telksnys, Zenonas Navickas, Minvydas Ragulskis

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Necessary and sufficient conditions for the existence of second order solitary solutions to the Hodgkin-Huxley equation are derived in this paper. The generalized multiplicative operator of differentiation helps not only to construct closed-form solitary solutions but also automatically generates conditions of their existence in the space of the equation's parameters and initial conditions. It is demonstrated that bright, kink-type solitons and solitary solutions with singularities can exist in the Hodgkin-Huxley equation.

Keywords: Hodgkin-Huxley equation, solitary solution, existence condition, operator method

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Authors: Mohd Radzi Hilmi, Khairidzan Mohd Kamal, Che Azemin Mohd Zulfaezal, Ariffin Azrin Esmady

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Purpose: Corneal curvature (CC) is an important anterior segment parameter. This study compared CC measurements conducted with two optical devices in phakic eyes. Methods: Sixty phakic eyes of 30 patients were enrolled in this study. CC was measured three times with the optical biometer and topography-keratometer Tomey AO-2000 (Tomey Corporation, Nagoya, Japan), then with the standard partial optical coherence interferometry (PCI) IOL Master (Carl Zeiss Meditec, Dublin, CA) and data were statistically analysed. Results: The measurements resulted in a mean CC of 43.86 ± 1.57 D with Tomey AO-2000 and 43.84 ± 1.55 D with IOL Master. Distribution of data is normal, and no significance difference in CC values was detected (P = 0.952) between the two devices. Correlation between CC measurements was highly significant (r = 0. 99; P < 0.0001). The mean difference of CC values between devices was 0.017 D and 95% limit of agreement was -0.088 to 0.12. Duration taken for measurements with the standard biometer IOL Master was longer (55.17 ± 2.24 seconds) than with Tomey AO-2000 (39.88 ± 2.38 seconds) in automatic mode. Duration of manual measurement with Tomey AO-2000 in manual mode was the shortest (28.57 ± 2.71 seconds). Conclusion: In phakic eyes, CC measured with Tomey AO-2000 and IOL Master showed similar values, and high correlation was observed between these two devices. This shows that both devices can be used interchangeably. Tomey AO-2000 is better in terms of faster to operate and has its own topography systems.

Keywords: corneal topography, corneal curvature, IOL Master, Tomey AO2000

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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: Nara Guimarães, Marcelo Aquino Martorano, Douglas Gouvêa

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An investigation into Cahn-Hilliard equation was carried out through numerical simulation to identify a possible phase separation for one and two dimensional domains. It was observed that this equation can reproduce important mass fluxes necessary for phase separation within the miscibility gap and for coalescence of particles.

Keywords: Cahn-Hilliard equation, miscibility gap, phase separation, dimensional domains

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Authors: Sayor Ajfar Aaron, Md. Mushfiqur Rahman, Sajjat Hossain Abir, Ashif Newaz

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This paper examines the transformative potential of quantum computing in the field of cybersecurity, with a focus on advanced penetration testing and forensics. It explores how quantum technologies can be leveraged to identify and exploit vulnerabilities more efficiently than traditional methods and how they can enhance the forensic analysis of cyber-attacks. Through theoretical analysis and practical simulations, this study highlights the enhanced capabilities of quantum algorithms in detecting and responding to sophisticated cyber threats, providing a pathway for developing more resilient cybersecurity infrastructures.

Keywords: cybersecurity, cyber forensics, penetration testing, quantum computing

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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: Hesamoddin Abdollahpour, Roghayeh Abdollahpour, Elham Rahgozar

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This paper we deal with an analysis of the free vibrations of the governing partial differential equation that it is Danel equation in the shells. The problem considered represents the governing equation of the nonlinear, large amplitude free vibrations of the hinged shell. A new implementation of the new method is presented to obtain natural frequency and corresponding displacement on the shell. Our purpose is to enhance the ability to solve the mentioned complicated partial differential equation (PDE) with a simple and innovative approach. The results reveal that this new method to solve Danel equation is very effective and simple, and can be applied to other nonlinear partial differential equations. It is necessary to mention that there are some valuable advantages in this way of solving nonlinear differential equations and also most of the sets of partial differential equations can be answered in this manner which in the other methods they have not had acceptable solutions up to now. We can solve equation(s), and consequently, there is no need to utilize similarity solutions which make the solution procedure a time-consuming task.

Keywords: large amplitude, free vibrations, analytical solution, Danell Equation, diagram of phase plane

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Authors: Nisarg A. Patel, Hiren B. Patel

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Quantum cryptography is described as a point-to-point secure key generation technology that has emerged in recent times in providing absolute security. Researchers have started studying new innovative approaches to exploit the security of Quantum Key Distribution (QKD) for a large-scale communication system. A number of approaches and models for utilization of QKD for secure communication have been developed. The uncertainty principle in quantum mechanics created a new paradigm for QKD. One of the approaches for use of QKD involved network fashioned security. The main goal was point-to-point Quantum network that exploited QKD technology for end-to-end network security via high speed QKD. Other approaches and models equipped with QKD in network fashion are introduced in the literature as. A different approach that this paper deals with is using QKD in existing protocols, which are widely used on the Internet to enhance security with main objective of unconditional security. Our work is towards the analysis of the QKD in Mobile ad-hoc network (MANET).

Keywords: cryptography, networking, quantum, encryption and decryption

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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: S. Mousavian, F. Mousavian, V. Nikkhah Rashidabad

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Cubic equations of state like Redlich–Kwong (RK) EOS have been proved to be very reliable tools in the prediction of phase behavior. Despite their good performance in compositional calculations, they usually suffer from weaknesses in the predictions of saturated liquid density. In this research, RK equation was modified. The result of this study shows that modified equation has good agreement with experimental data.

Keywords: equation of state, modification, ammonia, genetic algorithm

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Authors: Muna Alghabshi, Edmana Krishnan

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A nonlinear Schrodinger equation has been considered for solving by mapping methods in terms of Jacobi elliptic functions (JEFs). The equation under consideration has a linear evolution term, linear and nonlinear dispersion terms, the Kerr law nonlinearity term and three terms representing the contribution of meta materials. This equation which has applications in optical fibers is found to have soliton solutions, shock wave solutions, and singular wave solutions when the modulus of the JEFs approach 1 which is the infinite period limit. The equation with special values of the parameters has also been solved using the tanh method.

Keywords: Jacobi elliptic function, mapping methods, nonlinear Schrodinger Equation, tanh method

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Authors: Benedict Barnes, Anthony Y. Aidoo

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A Divergence Regularization Method (DRM) is used to regularize the ill-posed Helmholtz equation where the boundary deflection is inhomogeneous in a Hilbert space H. The DRM incorporates a positive integer scaler which homogenizes the inhomogeneous boundary deflection in Cauchy problem of the Helmholtz equation. This ensures the existence, as well as, uniqueness of solution for the equation. The DRM restores all the three conditions of well-posedness in the sense of Hadamard.

Keywords: divergence regularization method, Helmholtz equation, ill-posed inhomogeneous Cauchy boundary conditions

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Authors: William Chung

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This paper is to study the use of multiple subproblems in Dantzig-Wolfe decomposition of linear programming (DW-LP). Traditionally, the decomposed LP consists of one LP master problem and one LP subproblem. The master problem and the subproblem is solved alternatively by exchanging the dual prices of the master problem and the proposals of the subproblem until the LP is solved. It is well known that convergence is slow with a long tail of near-optimal solutions (asymptotic convergence). Hence, the performance of DW-LP highly depends upon the number of decomposition steps. If the decomposition steps can be greatly reduced, the performance of DW-LP can be improved significantly. To reduce the number of decomposition steps, one of the methods is to increase the number of proposals from the subproblem to the master problem. To do so, we propose to add a quadratic approximation function to the LP subproblem in order to develop a set of approximate-LP subproblems (multiple subproblems). Consequently, in each decomposition step, multiple subproblems are solved for providing multiple proposals to the master problem. The number of decomposition steps can be reduced greatly. Note that each approximate-LP subproblem is nonlinear programming, and solving the LP subproblem must faster than solving the nonlinear multiple subproblems. Hence, using multiple subproblems in DW-LP is the tradeoff between the number of approximate-LP subproblems being formed and the decomposition steps. In this paper, we derive the corresponding algorithms and provide some simple computational results. Some properties of the resulting algorithms are also given.

Keywords: approximate subproblem, Dantzig-Wolfe decomposition, large-scale models, multiple subproblems

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Authors: A. Clementking, C. Jothi Venkateswaran

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Mathematical and computational functionalities such as descriptive mining, optimization, and predictions are espoused to resolve natural resource planning. The water quality prediction and its attributes influence determinations are adopted optimization techniques. The water properties are tainted while merging water resource one with another. This work aimed to predict influencing water resource distribution connectivity in accordance to water quality and sediment using an innovative proposed master-slave neural network back-propagation model. The experiment results are arrived through collecting water quality attributes, computation of water quality index, design and development of neural network model to determine water quality and sediment, master–slave back propagation neural network back-propagation model to determine variations on water quality and sediment attributes between the water resources and the recommendation for connectivity. The homogeneous and parallel biochemical reactions are influences water quality and sediment while distributing water from one location to another. Therefore, an innovative master-slave neural network model [M (9:9:2)::S(9:9:2)] designed and developed to predict the attribute variations. The result of training dataset given as an input to master model and its maximum weights are assigned as an input to the slave model to predict the water quality. The developed master-slave model is predicted physicochemical attributes weight variations for 85 % to 90% of water quality as a target values.The sediment level variations also predicated from 0.01 to 0.05% of each water quality percentage. The model produced the significant variations on physiochemical attribute weights. According to the predicated experimental weight variation on training data set, effective recommendations are made to connect different resources.

Keywords: master-slave back propagation neural network model(MSBPNNM), water quality analysis, multivariate analysis, environmental mining

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Authors: F. U. Rahman, R. Q. Zhang

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This work aims to develop a systematic numerical technique which can be easily extended to many-body problem. The Lippmann Schwinger equation (integral form of the Schrodinger wave equation) is solved for the nonrelativistic radial wave of hydrogen atom using iterative integration scheme. As the unknown wave function appears on both sides of the Lippmann Schwinger equation, therefore an approximate wave function is used in order to solve the equation. The Green’s function is obtained by the method of Laplace transform for the radial wave equation with excluded potential term. Using the Lippmann Schwinger equation, the product of approximate wave function, the Green’s function and the potential term is integrated iteratively. Finally, the wave function is normalized and plotted against the standard radial wave for comparison. The outcome wave function converges to the standard wave function with the increasing number of iteration. Results are verified for the first fifteen states of hydrogen atom. The method is efficient and consistent and can be applied to complex systems in future.

Keywords: Green’s function, hydrogen atom, Lippmann Schwinger equation, radial wave

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Authors: Ayaz Ahmad

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In this work, we present the effect of noise on the solution of a partial differential equation (PDE) in three different setting. We shall first consider random initial condition for two nonlinear dispersive PDE the non linear Schrodinger equation and the Kortteweg –de vries equation and analyse their effect on some special solution , the soliton solutions.The second case considered a linear partial differential equation , the wave equation with random initial conditions allow to substantially decrease the computational and data storage costs of an algorithm to solve the inverse problem based on the boundary measurements of the solution of this equation. Finally, the third example considered is that of the linear transport equation with a singular drift term, when we shall show that the addition of a multiplicative noise term forbids the blow up of solutions under a very weak hypothesis for which we have finite time blow up of a solution in the deterministic case. Here we consider the problem of wave propagation, which is modelled by a nonlinear dispersive equation with noisy initial condition .As observed noise can also be introduced directly in the equations.

Keywords: drift term, finite time blow up, inverse problem, soliton solution

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Authors: Praveen Kumar, R. Uma, R. P. Sharma

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This study investigates the generation of turbulence in a deep-fluid environment using a damped 1D-modified nonlinear Schrödinger equation model. The well-known damped modified nonlinear Schrödinger equation (d-MNLS) is solved using numerical methods. Artificial damping is added to the MNLS equation, and turbulence generation is investigated through a numerical simulation. The numerical simulation employs a finite difference method for temporal evolution and a pseudo-spectral approach to characterize spatial patterns. The results reveal a recurring periodic pattern in both space and time when the nonlinear Schrödinger equation is considered. Additionally, the study shows that the modified nonlinear Schrödinger equation disrupts the localization of structure and the recurrence of the Fermi-Pasta-Ulam (FPU) phenomenon. The energy spectrum exhibits a power-law behavior, closely following Kolmogorov's spectra steeper than k⁻⁵/³ in the inertial sub-range.

Keywords: water waves, modulation instability, hydrodynamics, nonlinear Schrödinger's equation

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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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