Van der Waals force derived from a quantum statistical mechanical path integral method

The main purpose of this paper is to apply the quantum statistical mechanical model for polarizable fluids, used by Høye-Stell and others, to the calculation of the van der Waals force (dispersion force) between monatomics. The results are in agreement with those obtained by quantum perturbation theory. The quantum statistical method implies considerable formal simplifications.The introductory sections of the paper show, for illustrative purposes, how the dispersion forces in limiting cases also can be obtained from macroscopic quantum electromagnetic theory when two dilute dielectric media with plane-parallel surfaces are separated by a vacuum (Casimir effect).     

Rigorous solution to a quantum statistical mechanical laser model

A quantum mechanical laser model with relaxation and pumping mechanisms is solved rigorously. A basic equation for the density matrix is derived by the damping theory and is transformed into a corresponding c-number equation for a (quasi-) probability density. This is done with the aid of the quantum phase space method. The probability density is expanded in terms of orthogonal polynomials. The expansion coefficients are solved to give a continued fraction. A complete solution is obtained, namely, time evolution of the probability density is determined as well as that for certain physical quantities. The solution is valid even for strong coupling between photons and atoms: it is free from restriction on system parameters. Detailed studies on dynamics are performed for typical values of the system parameters. This is a prototype of interacting quantum nonequilibrium systems. Relevance to systems other than a laser is briefly mentioned.     

Unified statistical method for reconstructing quantum states by purification

Mixed-state purification is used as a basis to formulate a general statistical method for reconstructing the density matrix of an arbitrary quantum state. A universal statistical distribution is obtained for the fidelity of the reconstructed quantum state. The proposed theory is supported by results of numerical simulations.     

A new quantum statistical evaluation method for time correlation functions

Considering a system ofN identical interacting particles, which obey Fermi-Dirac or Bose-Einstein statistics, we derive new formulas for correlation functions of the type (whereB _j is diagonal in the free-particle states) in the thermodynamic limit. Thereby we apply and extend a superoperator formalism, recently developed for the derivation of long-time tails in semiclassical systems. As an illustrative application, the Boltzmann equation value of the time-integrated correlation functionC(t) is derived in a straightforward manner. Due to exchange effects, the obtained t-matrix and the resulting scattering cross section, which occurs in the Boltzmann collision operator, are now functionals of the Fermi-Dirac or Bose-Einstein distribution.     

Phase diagram of a model for diluted magnetic semiconductors beyond mean-field approximations

A lattice spin-fermion model for diluted magnetic semiconductors (DMS) is investigated numerically, improving on previously used mean-field approximations. Curie temperatures are obtained varying the Mn spin x and hole n densities, and the impurity-hole exchange J in units of the hop-ping t. Optimal values are found in the subtle intermediate regime between itinerant and localized carriers. At intermediate and large J/t, a "clustered" state is observed above the Curie temperature and ferromagnetism is suppressed. Formal analogies between DMS and manganites are discussed.     

Thermal mechanics: A quantum mechanical analogue of nonequilibrium statistical thermodynamics

A formal but not conventional equivalence between stochastic processes in nonequilibrium statistical thermodynamics and Schrödinger dynamics in quantum mechanics is shown. It is found, for each stochastic process described by a stochastic differential equation of Itô type, there exists a Schrödinger-like dynamics in which the absolute square of a wavefunction gives us the same probability distribution as the original stochastic process. In utilizing this equivalence between them, that is, rewriting the stochastic differential equation by an equivalent Schrödinger equation, it is possible to obtain the notion of deterministic limit of the stochastic process as a semi-classical limit of the “Schrödinger” equation. The deterministic limit thus obtained improves the conventional deterministic approximation in the sense of Onsager-Machlup. The present approach is valid for a general class of stochastic equations where local drifts and diffusion coefficients depend on the position. Two concrete examples are given. It should be noticed that the approach in the present form has nothing to do with the conventional one where only a formal similarity between the Fokker-Planck equation and the Schrödinger equation is considered.     

Variational approximations for square lattice models in statistical mechanics

This paper concerns a square lattice, Ising-type model with interactions between the four spins at the corners of each face. These may include nearest and next-nearest-neighbor interactions, and interactions with a magnetic field. Provided the Hamiltonian is symmetric with respect to both row reversal and column reversal, a rapidly convergent sequence of variational approximations is obtained, giving the free energy and other thermodynamic properties. For the usual Ising model, the lowest such approximations are those of Bethe and of Kramers and Wannier. The method provides a new definition of corner transfer matrices.     

Radiative properties of matter based on quantum statistical method

We present the preliminary results of our code OPAQS(opacity calculation using quantum statistical model) that is based on the self consistent Hartree-Fock-Slater model for the average atom. The code is capable of performing robust calculations of average charge state, frequency-dependent and mean opacities. The accuracy of the atomic model is verified by comparing the calculations of average charge state with various published results. The monochromatic opacities for iron computed at different sets of temperatures and densities are compared with LEDCOP. The Rosseland and Planck opacities for iron and aluminum are validated with some state-of-the-art codes. The results are in good agreement with the published data.     

Quantum statistical effects in nuclear reactions,fission, and open quantum systems

Quantum diffusion equations with time-dependent transport coefficients are derived from generalized non-Markovian Langevin equations. Generalized fluctuation-dissipation relations and analytical formulas for calculating friction and diffusion coefficients in nuclear processes are obtained. The asymptotics of the transport coefficients and of the correlation functions are investigated. The problem of correlation decay in quantum dissipative systems is studied. A comparative analysis of diffusion coefficients for the harmonic and inverted oscillators is performed. The role of quantum statistical effects during passage through a parabolic potential barrier is investigated. Sets of diffusion coefficient assuring the purity of states at any time instant are found in cases of non-Markovian dynamics. The influence of different sets of transport coefficients on the rate of decay from a metastable state is studied in the framework of the master equation for reduced density matrices describing open quantum systems. The approach developed is applied to investigation of fission processes and the processes of projectile-nuclei capture by target nuclei for bombarding energies in the vicinity of the Coulomb barrier. The influence of dissipation and fluctuation on these processes is taken into account in a self-consistent way. The evaporation residue cross sections for asymmetric fusion reactions are calculated from the derived capture probabilities averaged over all orientations of the deformed projectile and target nuclei.     

探讨黑洞Hawking辐射的新方法——量子统计法

将黑洞看作由裸黑洞和二维热力学面(黑洞的视界)组成的正则系综,利用量子统计方法给出黑洞Hawking 辐射的能量谱.找到黑洞辐射温度与熵的关系. 关键词： Hawking辐射 正则系统 量子统计     

A Peierls-Hubbard model: Exact quantum mechanical results and a variational method

The energy for the ground- and excited states of a system of two electrons interacting with two lattice sites is calculated exactly as a function of the electronic onsite- and intersite-correlation strength. A satisfactory agreement with the results of a variational method proposed recently is found. Results for systems up to 24 particles are presented.     

Capture into resonance: a method for efficient control

To achieve large changes in adiabatic invariants using small control input, a conservative dynamical system must possess an internal resonance. Capture into resonance is an inherently probabilistic process. We propose a control method to make it more structured. We study the motion of charged particles in an electromagnetic field as an example of such a system. When the nominal dynamics brings particles close to a resonance surface, a short control pulse forces the capture of a particle into the resonance with the wave. A captured particle is transported by the wave across the energy levels. The second pulse releases a particle from the resonance when the desired energy level is achieved. We discuss the distribution of energy achieved by the method.     

Variational quantum simulation of thermal statistical states on a superconducting quantum processer

Quantum computers promise to solve finite-temperature properties of quantum many-body systems, which is generally challenging for classical computers due to high computational complexities. Here, we report experimental preparations of Gibbs states and excited states of Heisenberg $XX$ and $XXZ$ models by using a 5-qubit programmable superconducting processor. In the experiments, we apply a hybrid quantum-classical algorithm to generate finite temperature states with classical probability models and variational quantum circuits. We reveal that the Hamiltonians can be fully diagonalized with optimized quantum circuits, which enable us to prepare excited states at arbitrary energy density. We demonstrate that the approach has a self-verifying feature and can estimate fundamental thermal observables with a small statistical error. Based on numerical results, we further show that the time complexity of our approach scales polynomially in the number of qubits, revealing its potential in solving large-scale problems.     

Nonequilibrium statistical mechanical formulation for grain growth

A nonequilibrium statistical mechanical theory for grain growth is presented in this paper. The fluctuation of grain growth is determined from the self similarity of grain size distribution. The grain size distribution scaled by the averaged size is derived under the condition that the volume of specimen is strictly conserved. The growth law of grain is also derived. The scaled grain size distribution are compared with the associating lognormal distribution which is usually used in the analysis of the experimental results. It has been found that the theoretical results is in good agreement with experimental results.     

Nonequilibrium statistical mechanical formulation for grain growth

A nonequilibrium statistical mechanical theory for grain growth is presented in this paper. The fluctuation of grain growth is determined from the self similarity of grain size distribution. The grain size distribution scaled by the averaged size is derived under the condition that the volume of specimen is strictly conserved. The growth law of grain is also derived. The scaled grain size distribution are compared with the associating lognormal distribution which is usually used in the analysis of the experimental results. It has been found that the theoretical results is in good agreement with experimental results.     

Numerical approximations for fractional diffusion equations via a Chebyshev spectral-tau method

In this paper, a class of fractional diffusion equations with variable coefficients is considered. An accurate and efficient spectral tau technique for solving the fractional diffusion equations numerically is proposed. This method is based upon Chebyshev tau approximation together with Chebyshev operational matrix of Caputo fractional differentiation. Such approach has the advantage of reducing the problem to the solution of a system of algebraic equations, which may then be solved by any standard numerical technique. We apply this general method to solve four specific examples. In each of the examples considered, the numerical results show that the proposed method is of high accuracy and is efficient for solving the time-dependent fractional diffusion equations.     

Entanglement and statistical independence for mixed quantum states

We show that three conditions associated with “entanglement,”viz., non-locality, non-factorisability and statistical dependence, are equivalent for pure states, and that non-factorisability and statistical dependence are equivalent for mixed states. Discussion then reinforces the generally held view that the key condition for mixed states is nonseparability.     

A one-dimensional lattice model for a quantum mechanical free particle

Two types of particles, A and B with their corresponding antiparticles, are defined in a onedimensional cyclic lattice with an odd number of sites. In each step of time evolution, each particle acts as a source for the polarization field of the other type of particle with nonlocal action but with an effect decreasing with the distance: . It is shown that the combined distribution of these particles obeys the time evolution of a free particle as given by quantum mechanics.