Fluid moment hierarchy equations derived from quantum kinetic theory

A set of quantum hydrodynamic equations are derived from the moments of the electrostatic mean-field Wigner kinetic equation. No assumptions are made on the particular local equilibrium or on the statistical ensemble wave functions. Quantum diffraction effects appear explicitly only in the transport equation for the heat flux triad, which is the third-order moment of the Wigner pseudo-distribution. The general linear dispersion relation is derived, from which a quantum modified Bohm-Gross relation is recovered in the long wave-length limit. Nonlinear, traveling wave solutions are numerically found in the one-dimensional case. The results shed light on the relation between quantum kinetic theory, the Bohm-de Broglie-Madelung eikonal approach, and quantum fluid transport around given equilibrium distribution functions.     

Microscopic transport theory of heavy-ion collisions

Drift and diffusion coefficients for the variables of mass fragmentation and excitation energy are studied for deeply inelastic collisions. The transport coefficients are obtained in closed form as functions of the parameters of the interaction matrix elements between nucleonic states and as functions of the binding energy of the intermediate rotating quasimolecular configuration. Drift and diffusion coefficients for excitation and mass transfer are related (dissipation fluctuation theorem). In good approximation these relations take the simple form of Einstein's relation between the mobility and the diffusion coefficient of a particle in a medium. For the total mass numbers 100, 250 and 500 the results are discussed in detail. The transport coefficients are compared with experimental results. Within the uncertainties of determination from experimental data, the drift and diffusion coefficients are well described by two previously adjusted parameters of the mean interaction matrix elements. Consequences for the production of superheavy elements in deeply inelastic collisions of U on U or Cf are discussed.     

Einstein relation generalized to nonequilibrium

The Einstein relation connecting the diffusion constant and the mobility is violated beyond the linear response regime. For a colloidal particle driven along a periodic potential imposed by laser traps, we test the recent theoretical generalization of the Einstein relation to the nonequilibrium regime which involves an integral over measurable velocity correlation functions.     

Electron drift velocity and mobility in graphene

We present a theoretical study of the electric transport properties of graphene-substrate systems. The drift velocity, mobility, and temperature of the electrons are self-consistently determined using the Boltzmann equilibrium equations. It is revealed that the electronic transport exhibits a distinctly nonlinear behavior. A very high mobility is achieved with the increase of the electric fields increase. The electron velocity is not completely saturated with the increase of the electric field. The temperature of the hot electrons depends quasi-linearly on the electric field. In addition, we show that the electron velocity, mobility, and electron temperature are sensitive to the electron density. These findings could be employed for the application of graphene for high-field nano-electronic devices.     

The rich phenomenology of Brownian particles in nonlinear potential landscapes

Non-interacting Brownian particles obey Langevin equations fulfilling a fluctuation–dissipation relation between friction and thermal noise. Under a linear potential (constant force) Einstein found a relation between diffusion and transport through mobility. In nonlinear potentials this prediction is only satisfied within the limits of very small and large constant external forces. Moreover, other more interesting behaviors do appear, such as: dispersionless transport, sorting, giant diffusion, subdiffusion, superdiffusion, subtransport, etc. All these phenomena depend on the characteristics of the nonlinear potential landscape: periodic or random, the symmetries and boundary conditions. Moreover, the presence of transport is the keystone of most of this phenomenology. In this review, we present numerical simulations illustrating these facts and theoretical analysis when possible.     

Benchmark calculations for Monte Carlo simulations of electrontransport

Benchmark calculations have been performed for electron transport coefficients with an aim to produce a body of data required to verify the codes used in plasma modeling. The present code for the time resolved Monte Carlo simulation (MCS) was shown to represent properly DC transport coefficients in a purely electric field, in crossed electric and magnetic fields, and in the presence of nonconservative collisions, ionization, and attachment. In addition, we have suggested tests of the time dependent solutions. Relaxation of the initial transport coefficient may serve as an accurate test of the code as well as the input data for some fluid codes. In this paper, we show only one example, but several different sets of conditions and cross sections should be used as well. Finally, we propose application of the quasi-steady state results in RF fields. As an example we suggest calculation of the components of diffusion tensor showing anomalous longitudinal diffusion and calculations made with nonconservative collisions (ionization in this case). We also check the application of approximate formulas to determine drift velocity on the basis of total collision frequency and to determine a diffusion coefficient by using the Einstein relation. Other tests required to verify the transport data calculations are discussed as well     

Transnational Quantum: Quantum Physics in India through the Lens of Satyendranath Bose

This paper traces the social and cultural dimensions of quantum physics in colonial India where Satyendranath Bose worked. By focusing on Bose’s approach towards the quantum and his collaboration with Albert Einstein, I argue that his physics displayed both the localities of doing science in early twentieth century India as well as a cosmopolitan dimension. He transformed the fundamental new concept of the light quantum developed by Einstein in 1905 within the social and political context of colonial India. This cross-pollination of the local with the global is termed here as the locally rooted cosmopolitan nature of Bose’s science. The production of new knowledge through quantum statistics by Bose show the co-constructed nature of physics and the transnational nature of the quantum.     

输运过程的红外发散理论

本文基于低频涨落、耗散和弛豫现象的普适理论所提供的物理图象,探讨了非Markov过程的输运特点。发现:1.由于红外发散的影响、扩散系数、迁移率与粘滞系数以及它们之间所存在的广义Nernst-Einstein关系(以下简称MD关系)和广义DV关系(以下简称DV关系)一般说来都是色散的,色散的程度与表征物质内部结构差异的一个单参数——红外发散指数n有关。如果n=0,则所有的结果立即化为经典形式。2.在所讨论的模型中,按假设条件MV关系不依赖过程的性质和过程的结构。3.广义扩散系数与广义迁移率和MV,DV关系具 关键词：     

A continued-fraction expansion for flux limiters

A hierarchy of evolution equations for higher-order moments of the velocity distribution function is generalized by including the effects of an external field. The use of continued-fraction techniques yields generalized transport coefficients including not only memory effects but also non-linear effects leading to a saturation in the corresponding flux. The ensuing corrections to the Einstein transport relation far from equilibrium are also studied.     

Nonlinear Theory of Quantum Brownian Motion

A nonlinear theory of quantum Brownian motion in classical environment is developed based on a thermodynamically enhanced nonlinear Schrödinger equation. The latter is transformed via the Madelung transformation into a nonlinear quantum Smoluchowski-like equation, which is proven to reproduce key results from the quantum and classical physics. The application of the theory to a free quantum Brownian particle results in a nonlinear dependence of the position dispersion on time, being quantum generalization of the Einstein law of Brownian motion. It is shown that the time of decoherence from quantum to classical diffusion is proportional to the square of the thermal de Broglie wavelength divided by the classical Einstein diffusion constant.     

One-Dimensional Steady Transport by Molecular Dynamics Simulation：Non-Boltzmann Position Distribution and Non-Arrhenius Dynamical Behavior

A non-equilibrium steady state can be characterized by a nonzero but stationary flux driven by a static external force. Under a weak external force, the drift velocity is difficult to detect because the drift motion is feeble and submerged in the intense thermal diffusion. In this article, we employ an accurate method in molecular dynamics simulation to determine the drift velocity of a particle driven by a weak external force in a one-dimensional periodic potential. With the calculated drift velocity, we found that the mobility and diffusion of the particle obey the Einstein relation, whereas their temperature dependences deviate from the Arrhenius law. A microscopic hopping mechanism was proposed to explain the non-Arrhenius behavior. Moreover, the position distribution of the particle in the potential well was found to deviate from the Boltzmann equation in a non-equilibrium steady state. The non-Boltzmann behavior may be attributed to the thermostat which introduces an effective "viscous" drag opposite to the drift direction of the particle.     

Transport in a ratchet with spatial disorder and time-delayed feedback

A Brownian motor with Gaussian short-range correlated spatial disorder and time-delayed feedback is investigated. The effects of disorder intensity, correlation strength and delay time on the transport properties of an overdamped periodic ratchet are discussed for different driving force. For small driving force, the disorder intensity can induce a peak in the drift motion and a linear increasing function in diffusion motion. For large driving force, the disorder intensity can suppress the drift motion but enhance the diffusion motion. For both small and large driving forces, the correlation strength of the spatial disorder can enhance the drift motion but suppress the diffusion motion. While the delay time can reduce the drift motion to a small value and enhance the diffusion motion to a large value. The drift motion increases as the driving force increases. However, the diffusion motion is either decreases or only increases slightly when the driving force increases.     

Steady-state and transient electron transport within bulk wurtzite zinc oxide

We study the steady-state and transient electron transport that occurs within bulk wurtzite zinc oxide using an ensemble semi-classical three-valley Monte Carlo simulation approach. We find that for electric field strengths in excess of 180 kV/cm, the steady-state electron drift velocity associated with bulk wurtzite zinc oxide exceeds that associated with bulk wurtzite gallium nitride. We also present evidence to suggest that the negative differential mobility exhibited by the velocity-field characteristic associated with bulk wurtzite zinc oxide is not related to transitions to the upper valleys. The transient electron transport that occurs within bulk wurtzite zinc oxide is studied by examining how electrons, initially in thermal equilibrium, respond to the sudden application of a constant electric field. From these transient electron transport results, we conclude that for devices with dimensions smaller than 0.1 μm, gallium nitride based devices will offer the advantage, owing to their superior transient electron transport, while for devices with dimensions greater than 0.1 μm, zinc oxide based devices will offer the advantage, owing to their superior high-field steady-state electron transport.     

水-气-颗粒固体三相混合系统的流体动力学

按照经典物理中处理混合物的一般热力学方法, 将近年来报道的颗粒固体流体动力 学进一步推广到孔隙被水和气填充的情形, 建立了其自由能的初步模型. 水-气-颗粒三相体系是与岩土工程和地质灾害密切相关的材料, 但其经典宏观物理基础却一直未能全面澄清.目前用于分析这类混合物力学行为的基本工程理论含Darcy渗流定律、Terzaghi有效应力及其运动方程(即本构方程)等内容. 通过与经典物理对比, 本文澄清了渗流对应于不同相之间的质量扩散, 有效应力与这类材料特有的体积填充形式自由能有关, 这两部分内容工程与物理是一致的.目前的分歧具体体现在材料建模对象上, 前者认为是本构方程, 而后者是自由能和迁移系数. 该分歧的解决将是建立这类材料的连续介质物理基础、突破本构方法面临的困境的一个关键. 关键词： 颗粒物质 混合物 应力 流体动力学     

Quantum Transport of Particles and Entropy

A unified view on macroscopic thermodynamics and quantum transport is presented. Thermodynamic processes with an exchange of energy between two systems necessarily involve the flow of other balancable quantities. These flows are first analyzed using a simple drift-diffusion model, which includes the thermoelectric effects, and connects the various transport coefficients to certain thermodynamic susceptibilities and a diffusion coefficient. In the second part of the paper, the connection between macroscopic thermodynamics and quantum statistics is discussed. It is proposed to employ not particles, but elementary Fermi- or Bose-systems as the elementary building blocks of ideal quantum gases. In this way, the transport not only of particles but also of entropy can be derived in a concise way, and is illustrated both for ballistic quantum wires, and for diffusive conductors. In particular, the quantum interference of entropy flow is in close correspondence to that of electric current.     

Dissipative quantum dynamics in a multiwell system

We investigate the dynamics of a quantum particle moving in a tight-binding lattice and coupled to a heat bath environment. Using the Feynman-Vernon influence functional method, we obtain an exact series representation in powers of the tunneling matrix for the generating functional of moments of the probability distribution which is valid for arbitrary temperatures and linear dissipation. We prove that the Einstein relation between the linear mobility and the diffusion coefficient holds to any order of the expansion for Ohmic, and for a restricted region of super-Ohmic dissipation. We also compute in the Ohmic case the mobility in certain regions of the parameter space. In particular, we find that the low temperature correction to the zero temperature mobility behaves asT ², and we also determine the prefactor. Finally, the exact solution of the dynamics for any times, temperatures and bias is presented for a particular value of the damping strength in the case of strict Ohmic dissipation.     

Nonlinear relativistic and quantum equations with a common type of solution

Generalizations of the three main equations of quantum physics, namely, the Schr?dinger, Klein-Gordon, and Dirac equations, are proposed. Nonlinear terms, characterized by exponents depending on an index q, are considered in such a way that the standard linear equations are recovered in the limit q→1. Interestingly, these equations present a common, solitonlike, traveling solution, which is written in terms of the q-exponential function that naturally emerges within nonextensive statistical mechanics. In all cases, the well-known Einstein energy-momentum relation is preserved for arbitrary values of q.