Quantum geometric tensor and the topological characterization of the extended Su-Schrieffer-Heeger model

We investigate the quantum metric and topological Euler number in a cyclically modulated Su-Schrieffer-Heeger(SSH)model with long-range hopping terms.By computing the quantum geometry tensor,we derive exact expressions for the quantum metric and Berry curvature of the energy band electrons,and we obtain the phase diagram of the model marked by the first Chern number.Furthermore,we also obtain the topological Euler number of the energy band based on the Gauss-Bonnet theorem on the topological characterization of the closed Bloch states manifold in the first Brillouin zone.However,some regions where the Berry curvature is identically zero in the first Brillouin zone result in the degeneracy of the quantum metric,which leads to ill-defined non-integer topological Euler numbers.Nevertheless,the non-integer"Euler number"provides valuable insights and an upper bound for the absolute values of the Chern numbers.

Physico−mathematical model of the voltage−current characteristics of light-emitting diodes with quantum wells based on the Sah−Noyce−Shockley recombination mechanism

Herein,a physical and mathematical model of the voltage−current characteristics of a p−n heterostructure with quantum wells(QWs)is prepared using the Sah−Noyce−Shockley(SNS)recombination mechanism to show the SNS recombination rate of the correction function of the distribution of QWs in the space charge region of diode configuration.A comparison of the model voltage−current characteristics(VCCs)with the experimental ones reveals their adequacy.The technological parameters of the structure of the VCC model are determined experimentally using a nondestructive capacitive approach for determining the impurity distribution profile in the active region of the diode structure with a profile depth resolution of up to 10Å.The correction function in the expression of the recombination rate shows the possibility of determining the derivative of the VCCs of structures with QWs with a nonideality factor of up to 4.

Entanglement and thermalization in the extended Bose–Hubbard model after a quantum quench: A correlation analysis

Exploring the role of entanglement in quantum nonequilibrium dynamics is important to understand the mechanism of thermalization in an isolated system. We study the relaxation dynamics in a one-dimensional extended Bose–Hubbard model after a global interaction quench by considering several observables: the local Boson numbers, the nonlocal entanglement entropy, and the momentum distribution functions. We calculate the thermalization fidelity for different quench parameters and different sizes of subsystems, and the results show that the degree of thermalization is affected by the distance from the integrable point and the size of the subsystem. We employ the Pearson coefficient as the measurement of the correlation between the entanglement entropy and thermalization fidelity, and a strong correlation is demonstrated for the quenched system.

First-order quantum phase transition and entanglement in the Jaynes-Cummings model with a squeezed light

We study the quantum phase transition and entanglement in the Jaynes-Cummings model with squeezed light,utilize a special transformation method to obtain the analytical ground state of the model within the near-resonance regime,and numerically verify the validity of the analytical ground state.It is found that the ground state exhibits a first-order quantum phase transition at the critical point linearly induced by squeezed light,and the ground state entanglement reaches its maximum when the qubit-field coupling strength is large enough at the critical point.

Quantum Fuzzy Regression Model for Uncertain Environment

In the era of big data,traditional regression models cannot deal with uncertain big data efficiently and accurately.In order to make up for this deficiency,this paper proposes a quantum fuzzy regression model,which uses fuzzy theory to describe the uncertainty in big data sets and uses quantum computing to exponentially improve the efficiency of data set preprocessing and parameter estimation.In this paper,data envelopment analysis(DEA)is used to calculate the degree of importance of each data point.Meanwhile,Harrow,Hassidim and Lloyd(HHL)algorithm and quantum swap circuits are used to improve the efficiency of high-dimensional data matrix calculation.The application of the quantum fuzzy regression model to smallscale financial data proves that its accuracy is greatly improved compared with the quantum regression model.Moreover,due to the introduction of quantum computing,the speed of dealing with high-dimensional data matrix has an exponential improvement compared with the fuzzy regression model.The quantum fuzzy regression model proposed in this paper combines the advantages of fuzzy theory and quantum computing which can efficiently calculate high-dimensional data matrix and complete parameter estimation using quantum computing while retaining the uncertainty in big data.Thus,it is a new model for efficient and accurate big data processing in uncertain environments.

GLOBAL WEAK SOLUTIONS TO A THREE-DIMENSIONAL QUANTUM KINETIC-FLUID MODEL

In this paper,we study a quantum kinetic-fluid model in a three-dimensional torus.This model is a coupling of the Vlasov-Fokker-Planck equation and the compressible quantum Navier-Stokes equations with degenerate viscosity.We establish a global weak solution to this model for arbitrarily large initial data when the pressure takes the form p(ρ)=ργ+pc(ρ),whereγ>1 is the adiabatic coefficient and pc(ρ)satisfies■for k≥4 and some constant c>0.

Ground-state phase diagram,symmetries,excitation spectra and finite-frequency scaling of the two-mode quantum Rabi model

We investigate the two-mode quantum Rabi model(QRM)describing the interaction between a two-level atom and a two-mode cavity field.The quantum phase transitions are found when the ratioηof transition frequency of atom to frequency of cavity field approaches infinity.We apply the Schrieffer–Wolff(SW)transformation to derive the low-energy effective Hamiltonian of the two-mode QRM,thus yielding the critical point and rich phase diagram of quantum phase transitions.The phase diagram consists of four regions:a normal phase,an electric superradiant phase,a magnetic superradiant phase and an electromagnetic superradiant phase.The quantum phase transition between the normal phase and the electric(magnetic)superradiant phase is of second order and associates with the breaking of the discrete Z_(2) symmetry.On the other hand,the phase transition between the electric superradiant phase and the magnetic superradiant phase is of first order and relates to the breaking of the continuous U(1)symmetry.Several important physical quantities,for example the excitation energy and average photon number in the four phases,are derived.We find that the excitation spectra exhibit the Nambu–Goldstone mode.We calculate analytically the higher-order correction and finite-frequency exponents of relevant quantities.To confirm the validity of the low-energy effective Hamiltonians analytically derived by us,the finite-frequency scaling relation of the averaged photon numbers is calculated by numerically diagonalizing the two-mode quantum Rabi Hamiltonian.

Leveraging Quantum Computing for the Ising Model to Simulate Two Real Systems: Magnetic Materials and Biological Neural Networks (BNNs)

Quantum computing is a field with increasing relevance as quantum hardware improves and more applications of quantum computing are discovered. In this paper, we demonstrate the feasibility of modeling Ising Model Hamiltonians on the IBM quantum computer. We developed quantum circuits to simulate these systems more efficiently for both closed and open boundary Ising models, with and without perturbations. We tested these various geometries of systems in both 1-D and 2-D space to mimic two real systems: magnetic materials and biological neural networks (BNNs). Our quantum model is more efficient than classical computers, which can struggle to simulate large, complex systems of particles.

An anti-aliasing filtering of quantum images in spatial domain using a pyramid structure

As a part of quantum image processing,quantum image filtering is a crucial technology in the development of quantum computing.Low-pass filtering can effectively achieve anti-aliasing effects on images.Currently,most quantum image filterings are based on classical domains and grayscale images,and there are relatively fewer studies on anti-aliasing in the quantum domain.This paper proposes a scheme for anti-aliasing filtering based on quantum grayscale and color image scaling in the spatial domain.It achieves the effect of anti-aliasing filtering on quantum images during the scaling process.First,we use the novel enhanced quantum representation(NEQR)and the improved quantum representation of color images(INCQI)to represent classical images.Since aliasing phenomena are more pronounced when images are scaled down,this paper focuses only on the anti-aliasing effects in the case of reduction.Subsequently,we perform anti-aliasing filtering on the quantum representation of the original image and then use bilinear interpolation to scale down the image,achieving the anti-aliasing effect.The constructed pyramid model is then used to select an appropriate image for upscaling to the original image size.Finally,the complexity of the circuit is analyzed.Compared to the images experiencing aliasing effects solely due to scaling,applying anti-aliasing filtering to the images results in smoother and clearer outputs.Additionally,the anti-aliasing filtering allows for manual intervention to select the desired level of image smoothness.

On the Cosmic Evolution of the Quantum Vacuum Using Two Variable G Models and Winterberg’s Thesis

We work within a Winterberg framework where space, i.e., the vacuum, consists of a two component superfluid/super-solid made up of a vast assembly (sea) of positive and negative mass Planck particles, called planckions. These material particles interact indirectly, and have very strong restoring forces keeping them a finite distance apart from each other within their respective species. Because of their mass compensating effect, the vacuum appears massless, charge-less, without pressure, net energy density or entropy. In addition, we consider two varying G models, where G, is Newton’s constant, and G-1, increases with an increase in cosmological time. We argue that there are at least two competing models for the quantum vacuum within such a framework. The first follows a strict extension of Winterberg’s model. This leads to nonsensible results, if G increases, going back in cosmological time, as the length scale inherent in such a model will not scale properly. The second model introduces a different length scale, which does scale properly, but keeps the mass of the Planck particle as, ± the Planck mass. Moreover we establish a connection between ordinary matter, dark matter, and dark energy, where all three mass densities within the Friedman equation must be interpreted as residual vacuum energies, which only surface, once aggregate matter has formed, at relatively low CMB temperatures. The symmetry of the vacuum will be shown to be broken, because of the different scaling laws, beginning with the formation of elementary particles. Much like waves on an ocean where positive and negative planckion mass densities effectively cancel each other out and form a zero vacuum energy density/zero vacuum pressure surface, these positive mass densities are very small perturbations (anomalies) about the mean. This greatly alleviates, i.e., minimizes the cosmological constant problem, a long standing problem associated with the vacuum.

Structural Foundation and Geometry of the Material Singularity (and Its Quantum Entanglement)

In this paper we develop and study, as the second part of one more general development, the energy transmutation equation for the material singularity, previously obtained through the symmetrisation of a wave packet, that is, we develop the correlation between the terms of this equation, which accounts for the formation of matter from a previous vibrational state, and the different possible energy species. These energetic species are ascribed, in a simplified form, to the equation E¯ω=E¯k+E¯f, which allows us, through its associated phase factor, to gain an insight into the wave character of the kinetic energy and thus to attain the basis of the matter-wave, and all sorts of related phenomenologies, including that concerning quantum entanglement. The formation of the matter was previously identified as an energetic process, analogous to the kinetic one, in which finally the inertial mass is consolidated as a mass in a different phase, now, in addition, the mass of the material singularity is identified as a volumetric density of waves of toroidal geometry created in the process of singularisation or energy transfer between species, which makes it possible to establish the real relation or correspondence between the corpuscular and photonic energy equation (E=mc2=hν), i.e. to explain through m the intimate sense of the first equivalence, which explains what νis in the second one.

A Blind Spot in the Reframing of a Universe of Possibles: Towards a Suitable Model for Decision-Making Theory and A.I.

Bayesian inference model is an optimal processing of incomplete information that, more than other models, better captures the way in which any decision-maker learns and updates his degree of rational beliefs about possible states of nature, in order to make a better judgment while taking new evidence into account. Such a scientific model proposed for the general theory of decision-making, like all others in general, whether in statistics, economics, operations research, A.I., data science or applied mathematics, regardless of whether they are time-dependent, have in common a theoretical basis that is axiomatized by relying on related concepts of a universe of possibles, especially the so-called universe (or the world), the state of nature (or the state of the world), when formulated explicitly. The issue of where to stand as an observer or a decision-maker to reframe such a universe of possibles together with a partition structure of knowledge (i.e. semantic formalisms), including a copy of itself as it was initially while generalizing it, is not addressed. Memory being the substratum, whether human or artificial, wherein everything stands, to date, even the theoretical possibility of such an operation of self-inclusion is prohibited by pure mathematics. We make this blind spot come to light through a counter-example (namely Archimedes’ Eureka experiment) and explore novel theoretical foundations, fitting better with a quantum form than with fuzzy modeling, to deal with more than a reference universe of possibles. This could open up a new path of investigation for the general theory of decision-making, as well as for Artificial Intelligence, often considered as the science of the imitation of human abilities, while being also the science of knowledge representation and the science of concept formation and reasoning.

Refinement of Adaptive Dynamical Simulation of Quantum Mechanical Double Slit Interference Phenomenon

We applied adaptive dynamics to double slit interference phenomenon using particle model and obtained partial successful results in our previous report. The patterns qualitatively corresponded well with experiments. Several properties such as concave single slit pattern and large influence of slight displacement of the emission position were different from the experimental results. In this study we tried other slit conditions and obtained consistent patterns with experiments. We do not claim that the adaptive dynamics is the principle of quantum mechanics, but the present results support the probability of adaptive dynamics as the candidate of the basis of quantum mechanics. We discuss the advantages of the adaptive dynamical view for foundations of quantum mechanics.

Electrostatic Attraction and Repulsion Explained and Modelled Mathematically Using Classical Physics—A Detailed Mechanism Based on Particle Wave Functions

The phenomenon of electrical attraction and repulsion between charged particles is well known, and described mathematically by Coulomb’s Law, yet until now there has been no explanation for why this occurs. There has been no mechanistic explanation that reveals what causes the charged particles to accelerate, either towards or away from each other. This paper gives a detailed explanation of the phenomena of electrical attraction and repulsion based on my previous work that determined the exact wave-function solutions for both the Electron and the Positron. It is revealed that the effects are caused by wave interactions between the wave functions that result in Electromagnetic reflections of parts of the particle’s wave functions, causing a change in their momenta.

Mathematical Wave Functions and 3D Finite Element Modelling of the Electron and Positron

The wave/particle duality of particles in Physics is well known. Particles have properties that uniquely characterize them from one another, such as mass, charge and spin. Charged particles have associated Electric and Magnetic fields. Also, every moving particle has a De Broglie wavelength determined by its mass and velocity. This paper shows that all of these properties of a particle can be derived from a single wave function equation for that particle. Wave functions for the Electron and the Positron are presented and principles are provided that can be used to calculate the wave functions of all the fundamental particles in Physics. Fundamental particles such as electrons and positrons are considered to be point particles in the Standard Model of Physics and are not considered to have a structure. This paper demonstrates that they do indeed have structure and that this structure extends into the space around the particle’s center (in fact, they have infinite extent), but with rapidly diminishing energy density with the distance from that center. The particles are formed from Electromagnetic standing waves, which are stable solutions to the Schrödinger and Classical wave equations. This stable structure therefore accounts for both the wave and particle nature of these particles. In fact, all of their properties such as mass, spin and electric charge, can be accounted for from this structure. These particle properties appear to originate from a single point at the center of the wave function structure, in the same sort of way that the Shell theorem of gravity causes the gravity of a body to appear to all originate from a central point. This paper represents the first two fully characterized fundamental particles, with a complete description of their structure and properties, built up from the underlying Electromagnetic waves that comprise these and all fundamental particles.

The queueing model for quantum key distribution network

This paper develops a QKD （quantum key distribution）-based queueing model to investigate the data delay on QKD link and network, especially that based on trusted relays. It shows the mean packet delay performance of the QKD system. Furthermore, it proposes a key buffering policy which could effectively improve the delay performance in practice. The results will be helpful for quality of service in practical QKD systems.

Quantum correlation dynamics in a two-qubit Heisenberg XY Z model with decoherence

Quantum correlation dynamics in an anisotropic Heisenberg XYZ model under decoherence is investigated by making use of concurrence C and quantum discord （QD）. Firstly, we show that both the concurrence and QD exhibit oscillation with time whereas a remarkable difference between them is presented： there is an ＂entanglement intermittently sudden death＂ phenomenon in the concurrence but not in the QD, which is valid for all the initial states of this system. Also, the interval time of entanglement sudden death is found to be strongly dependent on the initial states, the inhomogeneous magnetic field b and the anisotropic parameter △. Then, it implies that the steady concurrence and QD can be obtained in the long-time limit, which means that the environmental decoherence cannot entirely destroy the quantum correlation, the variation of the uniform magnetic field B and the anisotropic parameter can change the magnitude of the steady concurrence and QD evidently whereas the parameter b cannot. In addition, based on the analysis of the steady concurrence and QD with t →∞, we give the reason why the magnitude of the steady concurrence and QD is so complicated with the change of the parameters B and .4, whereas the parameter b is independent of the steady concurrence and QD.

Thermal quantum discord in Heisenberg models with Dzyaloshinski-Moriya interaction

We study the quantum discord of the bipartite Heisenberg model with the Dzyaloshinski-Moriya （DM） interaction in thermal equilibrium state and discuss the effect of the DM interaction on the quantum discord. The quantum entanglement of the system is also discussed and compared with quantum discord. Our results show that the quantum discord may reveal more properties of the system than quantum entanglement and the DM interaction may play an important role in the Heisenberg model.

Single-atom entropy squeezing and quantum entanglement in Tavis-Cummings model with atomic motion

We examine the single-atom entropy squeezing and the atom-field entanglement in a system of two moving twolevel atoms interacting with a single-mode coherent field in a lossless resonant cavity. Our numerical calculations indicate that the squeezing period, the squeezing time and the maximM squeezing can be controlled by appropriately choosing the atomic motion and the field-mode structure. The atomic motion leads to a periodical time evolution of entanglement between the two-atom and the field. Moreover, there exists corresponding relation between the time evolution properties of the atomic entropy squeezing and that of the entanglement between the two atoms and the field.

Establishing formal state space models via quantization forquantum control systems

Formal state space models of quantum control systems are deduced and a scheme to establish formal state space models via quantization could been obtained for quantum control systems is proposed. State evolution of quantum control systems must accord with Schrdinger equations, so it is foremost to obtain Hamiltonian operators of systems. There are corresponding relations between operators of quantum systems and corresponding physical quantities of classical systems, such as momentum, energy and Hamiltonian, so Schrdinger equation models of corresponding quantum control systems via quantization could been obtained from classical control systems, and then establish formal state space models through the suitable transformation from Schrdinger equations for these quantum control systems. This method provides a new kind of path for modeling in quantum control.