Number-resolved master equation approach to quantum transport under the self-consistent Born approximation

We construct a particle-number(n)-resolved master equation(ME) approach under the self-consistent Born approximation(SCBA) for quantum transport through mesoscopic systems.The formulation is essentially non-Markovian and incorporates the interplay of the multi-tunneling processes and many-body correlations.The proposed n-SCBA-ME goes beyond the scope of the BornMarkov master equation,being applicable to transport under small bias voltage,in non-Markovian regime and with strong Coulomb correlations.For steady state,it can recover not only the exact result of noninteracting transport under arbitrary voltages,but also the challenging nonequilibrium Kondo efect.Moreover,the n-SCBA-ME approach is efcient for the study of shot noise.We demonstrate the application by a couple of representative examples,including particularly the nonequilibrium Kondo system.     

A relation between cumulants of a thermodynamic variable and the state equation

A general relation between the cumulant of any order of a thermal variable and the thermal equilibrium state equation is pointed out. This relation has particular importance near the critical point of a phase transtion. This is discussed for standard examples.     

A convenient expansion of the master equation

We present a simple and very convenient expansion of the master equation.     

A master equation description of local fluctuations

A theory of fluctuations of macrovariables in nonequilibrium systems based on a nonlinear master equation is outlined. This equation takes into account, via a “mean field” type of approximation, the effect of the spatial extension of fluctuations. A comparison with the birth and death formalism reveals several unsatisfactory features of the latter.     

General-dyne unravelling of a thermal master equation

We analyze the unravelling of the quantum optical master equation at finite temperature due to direct, continuous, general-dyne detection of the environment. We first express the general-dyne Positive Operator Valued Measure (POVM) in terms of the eigenstates of a non-Hermitian operator associated to the general-dyne measurement. Then we derive the stochastic master equation obtained by considering the interaction between the system and a reservoir at thermal equilibrium, which is measured according to the POVM previously determined. Finally, we present a feasible measurement scheme, which reproduces general-dyne detection for any value of the parameter characterizing the stochastic master equation.     

A comparison of master equation and Fokker-Planck equation in the thermodynamic limit

The master equation and the Fokker-Planck equation are compared thoroughly in both of the stationary and the time-dependent cases for a one-dimensional system. The comparison includes the master equation without detailed balance.     

A new mixed self-consistent field procedure

A new approach for the calculation of three-centre electronic repulsion integrals (ERIs) is developed, implemented and benchmarked in the framework of auxiliary density functional theory (ADFT). The so-called mixed self-consistent field (mixed SCF) divides the computationally costly ERIs in two sets: far-field and near-field. Far-field ERIs are calculated using the newly developed double asymptotic expansion as in the direct SCF scheme. Near-field ERIs are calculated only once prior to the SCF procedure and stored in memory, as in the conventional SCF scheme. Hence the name, mixed SCF. The implementation is particularly powerful when used in parallel architectures, since all RAM available are used for near-field ERI storage. In addition, the efficient distribution algorithm performs minimal intercommunication operations between processors, avoiding a potential bottleneck. One-, two- and three-dimensional systems are used for benchmarking, showing substantial time reduction in the ERI calculation for all of them. A Born–Oppenheimer molecular dynamics calculation for the Na⁺₅₅ cluster is also shown in order to demonstrate the speed-up for small systems achievable with the mixed SCF.     

Conservation laws and self-consistent sources for a super-CKdV equation hierarchy

From the super-matrix Lie algebras, we consider a super-extension of the CKdV equation hierarchy in the present Letter, and propose the super-CKdV hierarchy with self-consistent sources. Furthermore, we establish the infinitely many conservation laws for the integrable super-CKdV hierarchy.     

Quantum fluctuations,master equation and Fokker-Planck equation

In order to describe quantum fluctuations a general method is developed, which also may be applied to nonstationary systems as well as to states far from thermodynamic equilibrium. After a concise derivation of the master equation quantum mechanically determined dissipation and fluctuation coefficients are introduced, for which several theorems and relations are given. By using these coefficients there is set up a general Fokker-Planck equation for the diffusion of the statistical operator due to quantum fluctuations.     

A stochastic master equation representation of statistical mechanics

A functional master equation for a probability density of the velocity distribution function is presented. This constitutes a representation of statistical mechanics which is equivalent to the BBGKY hierarchy but makes alternative approximation schemes available.     

Equivalence of the master equation and the Langevin equation

It is shown that the random force in the Langevin equation for a nonlinear system may be chosen in such a way that the resulting equation is mathematically equivalent to the master equation.     

Study of decoherence with a generalized master equation

The behavior of macroscopic system is investigated with a generalized master equation. Making use of a coarse-grained position operator based on the SO(3,1), we can derive that the macroscopic nature of this operator induces decoherence leading to classical behavior.     

A master equation for spontaneous emission from a system of harmonic oscillators

An exact equation is derived for the evolution of the density operator in the coherent state representation describing spontaneous emission from a system of harmonic oscillators.     

A Markoffian master equation for high-field electron transport

The high-field electron transport problem is reanalyzed in the frame of a Markoffian (i.e. memoryless) master equation proposed by Hashitsume et al. for the reduced density matrix. It is shown that a Markoffian high-field transport equation for the velocity distribution can be established, which considerably simplifies the usual (non-Markoffian) approaches of hot electron transport.     

Integration of the nonlinear Schroedinger equation with a self-consistent source

It is shown that the nonlinear Schroedinger equation with a self-consistent source admits investigation by the inverse scattering method for the Dirac operator. The conditions are found under which the solutions of the nonlinear Schroedinger equation with a self-consistent source describe the creation and annihilation of solitons.     

新型旋转液体实验——介绍一个研究性物理实验

介绍一种新型旋转液体实验，可以观察离心力现象，测量重力加速度，研究由旋转液体表面所形成的光学系统中焦距与角速度ω的关系，并观察该系统成像与转速的关系。     

Exact master equation for a noncommutative Brownian particle

We derive the Hu-Paz-Zhang master equation for a Brownian particle linearly coupled to a bath of harmonic oscillators on the plane with spatial noncommutativity. The results obtained are exact to all orders in the noncommutative parameter. As a by-product we derive some miscellaneous results such as the equilibrium Wigner distribution for the reservoir of noncommutative oscillators, the weak coupling limit of the master equation and a set of sufficient conditions for strict purity decrease of the Brownian particle. Finally, we consider a high-temperature Ohmic model and obtain an estimate for the time scale of the transition from noncommutative to ordinary quantum mechanics. This scale is considerably smaller than the decoherence scale.     

A master equation description of coupled systems. II

Dynamical correlations between two coupled systems are described by means of an infinite hierarchy of equations. The condition for a consistent truncation of the hierarchy is given. It allows to derive a closed equation describing the dynamics of one system. The structure of the equations for the stationary and non-stationary case is discussed and a comparison with other approaches is made.     

A master equation description of open systems. III

In this paper the results of previous work on the dynamics of coupled systems are generalized. A closed equation for the reduced density operator of the relevant subsystem is derived without assumptions on the behaviour of the irrelevant one. Equations relating the expectation values of observables of the two subsystems are given. They allow to reconstruct the dynamics of one subsystem once that of the other is known.