Operator equality on entropy production in quantum Markovian master equations

An operator equality on the entropy production for general quantum Markovian master equations is derived without resorting quantum stochastic trajectory and priori quantum definition of entropy production. We find that, the equality can be still interpreted as a consequence of time-reversal asymmetry of the nonequilibrium processes of the systems. In contrast with the classical case, however, the first order expansion of the equality does not directly related to the mean entropy production, which arises from noncommute property of operators in quantum physics.Comment: 5 pages, 1 figur

Equivalence of two Bochkov-Kuzovlev equalities in quantum two-level systems

We present two kinds of Bochkov-Kuzovlev work equalities in a two-level system that is described by a quantum Markovian master equation. One is based on multiple time correlation functions and the other is based on the quantum trajectory viewpoint. We show that these two equalities are indeed equivalent. Importantly, this equivalence provides us a way to calculate the probability density function of the quantum work by solving the evolution equation for its characteristic function. We use a numerical model to verify these results.Comment: 9 pages, 1 figure. Phys. Rev. E, in pres

Calculating work in adiabatic two-level quantum Markovian master equations: A characteristic function method

We present a characteristic function method to calculate the probability density functions of the inclusive work in the adiabatic two-level quantum Markovian master equations. These systems are steered by some slowly varying parameters and the dissipations may depend on time. Our theory is based on the interpretation of the quantum jump for the master equations. In addition to the calculation, we also find that the fluctuation properties of the work can be described by the symmetry of the characteristic functions, which is exactly the same as the case of the isolated systems. A periodically driven two-level model is used to show the method.Comment: 2 figure

Calculating work in weakly driven quantum master equations: backward and forward equations

I present a technical report indicating that the two methods used for calculating characteristic functions for the work distribution in weakly driven quantum master equations are equivalent. One involves applying the notion of quantum jump trajectory [Phys. Rev. E 89, 042122 (2014)], while the other is based on two energy measurements on the combined system and reservoir [Silaev, et al., Phys. Rev. E 90, 022103 (2014)]. These represent backward and forward methods, respectively, which adopt a very similar approach to that of the Kolmogorov backward and forward equations used in classical stochastic theory. The microscopic basis for the former method is also clarified. In addition, a previously unnoticed equality related to the heat is also revealed.Comment: 1 figur

Heat and work in Markovian quantum master equations: concepts, fluctuation theorems, and computations

Markovian quantum master equations (MQMEs) were established nearly half a century ago. They have often been used in the study of irreversible thermodynamics. However, the previous results were mainly concerned about ensemble averages; the stochastic thermodynamics of these systems went unnoticed for a very long time. This situation remained unchanged until a variety of fluctuation theorems in classical and quantum regimes were found in the past two decades. In this paper, we systematically summarize the current understanding on the stochastic heat and work in MQMEs using two distinct strategies. One strategy is to treat the system and its surrounding heat bath as a closed quantum system, to suppose that the evolution of the composite system is unitary under a time-dependent total Hamiltonian and to define the heat and work as the changes in energy by applying two energy measurements scheme to the composite system. The other strategy is to unravel these MQMEs into random quantum jump trajectories (QJTs) and to define the stochastic heat and work along the individual trajectories. Many important physical concepts, mathematical techniques, and fluctuation theorems at different descriptive levels are given in as detailed a manner as possible. We also use concrete models to illustrate these results.Comment: 6 figure

Quantum corrections of work statistics in closed quantum systems

We investigate quantum corrections to the classical work characteristic function (CF) as a semiclassical approximation to the full quantum work CF. In addition to explicitly establishing the quantum-classical correspondence of the Feynman-Kac formula, we find that these quantum corrections must be in even powers of $\hbar$. Exact formulas of the lowest corrections ($\hbar^2$) are proposed, and their physical origins are clarified. We calculate the work CFs for a forced harmonic oscillator and a forced quartic oscillator respectively to illustrate our results.Comment: Phys.Rev.E, in pres

Comments on Lattice Calculations of Proton Spin Components

Comments on the recent lattice QCD calculations of the flavor-singlet axial coupling constant $g_A^0$ and individual quark and gluon spin contributions to the proton spin is given. I point out the physics learned from these calculations as well as some of the lessons and pitfalls.Comment: 11-page Latex file, no figures, Report for the workshop on ``Future Physics at HERA'', Sept. 25 - 26, 199

From Nuclear Structure to Nucleon Structure

Similarities between nuclear structure study with many-body theory approach and nucleon structure calculations with lattice QCD are pointed out. We will give an example of how to obtain the connected sea partons from a combination of the experimental data, a global fit of parton distribution functions and a lattice calculation. We also present a complete calculation of the quark and glue decomposition of the proton momentum and angular momentum in the quenched approximation. It is found that the quark orbital angular momentum constitutes about 50% of the proton spin.Comment: 16 pages, 11 figures, to be published in the Gerry Brown Memorial issue of Nucl. Phys. A (2014

Nucleon Structure from Lattice QCD

We report results on the nucleon structure obtained from the lattice quantum chromodynamics calculation. These include the axial, electromagnetic, $\pi NN$, and scalar form factors. The calculation is carried out at $\beta = 6$ on a $16^3 \times 24$ lattice with 24 quenched gauge configurations. The chiral limit results are extrapolated from several light quark cases. For the disconnected insertion (sea-quark contribution), we used the stochastic estimation with the $Z_2$ noise to calculate the diagonal and off-diagonal traces of the inverse matrices with a size of $10^6 \times 10^6$. It is found that the $Z_2$ noise is the optimal choice and its comparison with the Gaussian noise for our quark matrix is given. For the sea-quark contribution, we report results on the strange condensate in the nucleon and the $\pi N \sigma$ term.Comment: 9 pages, 4 figures (uuencoded), UK/94-02. (A missing factor of 4 is included in the calculation of the disconnected insertion of the $\pi N \sigma$ term and the strange condensate in the nucleon.

A Unified Stochastic Particle Bhatnagar-Gross-Krook Method for Multiscale Gas Flows

The stochastic particle method based on Bhatnagar-Gross-Krook (BGK) or ellipsoidal statistical BGK (ESBGK) model approximates the pairwise collisions in the Boltzmann equation using a relaxation process. Therefore, it is more efficient to simulate gas flows at small Knudsen numbers than the counterparts based on the original Boltzmann equation, such as the Direct Simulation Monte Carlo (DSMC) method. However, the traditional stochastic particle BGK method decouples the molecular motions and collisions in analogy to the DSMC method, and hence its transport properties deviate from physical values as the time step increases. This defect significantly affects its computational accuracy and efficiency for the simulation of multiscale flows, especially when the transport processes in the continuum regime is important. In the present paper, we propose a unified stochastic particle ESBGK (USP-ESBGK) method by combining the molecular convection and collision effects. In the continuum regime, the proposed method can be applied using large temporal-spatial discretization and approaches to the Navier-Stokes solutions accurately. Furthermore, it is capable to simulate both the small scale non-equilibrium flows and large scale continuum flows within a unified framework efficiently and accurately. The applications of USP-ESBGK method to a variety of benchmark problems, including Couette flow, thermal Couette flow, Poiseuille flow, Sod tube flow, cavity flow, and flow through a slit, demonstrated that it is a promising tool to simulate multiscale gas flows ranging from rarefied to continuum regime.Comment: submitted to J. Comput. Phys. on 2018/5/1