Single-particle distribution function of a quantum dot system at finite temperature

In the present paper, we shall rigorously re-establish the result of the single-particle function of a quantum dot system at finite temperature. Unlike the proof given in our previous work (Phys. Rev. B 74 195414 (2006)), we take a different approach, which does not exploit the explicit expression of the Gibbs distribution function. Instead, we only assume that the statistical distribution function of the quantum dot system is thermodynamically stable. As a result, we are able to show clearly that the electronic structure in the quantum dot system is completely determined by its thermodynamic stability. Furthermore, the weaker requirements on the statistical distribution function also make it possible to apply the same method to the quantum dot systems in non-equilibrium states.     

Dynamical fluctuations in the hadronic temperature

A density two-point correlation function calculation and a power-spectrum analysis of non-statistical event-by-event fluctuations in the mean transverse momentum at large multiplicityn is performed. Good agreement with the data ofK. Braune et al. is obtained if thep _t-density function of the exponential form in the transverse mass with an event-by-event fluctuating slope is used. The pattern of the fluctuating slope is Gaussian with the mean determined by the data on \(\left\langle {\bar p_t (n)} \right\rangle \) for eachn, and the normalized standard deviation as the only free parameter taken to be 0.68. In thermodynamical models, the slope fluctuations may be interpreted as fluctuations in the temperature of the hadronic system.     

Temporal Fluctuation and Its Power Law in the Crystalline-To-Glass Transition During Electron Irradiation

Temporal nanostructural fluctuations brought about by transient metastable atom-cluster formation during radiation-induced amorphizing transformation in the intermetallic compound NiTi, observed using a combination of high-resolution high-voltage electron microscopy and molecular dynamics simulation, were characterized in terms of power-law responses of non-equilibrium energy-dissipative systems. Within the framework of the multi-Lorentzian picture, the resultant power law also describes the multirelaxation time (i.e. cluster lifetime) distribution. In addition, a unified relation for the autocorrelation functions for such fluctuation phenomena is discussed.     

Maslov distribution and formulas for the entropy

The Maslov distribution for a system of identical particles is used. The entropy and some other thermodynamical characteristics of this system are found for diverse fractal dimensions. A general formula for the entropy is established, which shows that the entropy is proportional to the derivative of the system energy with respect to the temperature. It is shown that a parastatistical parameter b, which is introduced formally, is related to the temperature of the system indeed. The nature of the phase transition in the system is studied in the two-dimensional case.     

A stochastic approach to the kinetic theory of gases

A theory of fluctuations in non-equilibrium diluted gases is presented. The velocity distribution function is treated as a stochastic variable and a master equation for its probability is derived. This evolution equation is based on two processes: binary hard sphere collisions and free flow. A mean-field approximation leads to a non-linear master equation containing explicitly a parameter which represents the spatial correlation length of the fluctuations. An infinite hierarchy of equations for the successive moments is found. If the correlation length is sufficiently short a truncation after the first equation is possible and this leads to the Boltzmann kinetic equation. The associated probability distribution is Poissonian. As to the fluctuation of the macroscopic quantities, an approximation scheme permits to recover the Langevin approach of fluctuating hydrodynamics near equilibrium and its fluctuation-dissipation relations.     

Equilibrium and non-equilibrium effects in nucleus–nucleus collisions

Local thermal and chemical equilibration is studied for central A+A collisions at 10.7–160 AGeV in the Ultrarelativistic Quantum Molecular Dynamics model (UrQMD). The UrQMD model exhibits strong deviations from local equilibrium at the high density hadron–string phase formed during the early stage of the collision. Equilibration of the hadron–resonance matter is established in the central cell of volume V=125 fm³ at later stages, t≥10 fm/c, of the resulting quasi-isentropic expansion. The thermodynamical functions in the cell and their time evolution are presented. Deviations of the UrQMD quasi-equilibrium state from the statistical mechanics equilibrium are found. They increase with energy per baryon and lead to a strong enhancement of the pion number density as compared to statistical mechanics estimates at SPS energies.     

时间反演对称和非平衡统计定常态(Ⅱ)

本文是我们从微观量子统计理论出发讨论非平衡统计定常态的时间反演对称性质的第二部份。本文应用文献的结果对非平衡统计定常态的普遍性质进行较为系统的讨论。对于具有时间反演对称的非平衡统计定常态,证明了广义(自由能)势函数的存在性;导出了涨落耗散定理的Rayleigh-Jeans极限形式;推广了局部热平衡假设下的Onsager倒易关系;导得了序参量-守恒荷密度普遍方程(TDGL)的“可逆-不可逆”运动分解形式。     

Population trapping and inversion in ultracold Fermi gases by excitation of the optical lattice: non-equilibrium Floquet–Keldysh description

A gas of ultracold interacting quantum degenerate Fermions is considered in a three-dimensional optical lattice which is externally modulated in the frequency and the amplitude. This theoretical study utilizes the Keldysh formalism to account for the system being out of thermodynamical equilibrium. A dynamical mean field theory, extended to non-equilibrium, is presented to calculate characteristic quantities such as the local density of states and the non-equilibrium distribution function. A dynamic Franz–Keldysh splitting is found which accounts for the non-equilibrium modification of the underlying bandstructure. The found characteristic Floquet-fan like bandstructure accounts for the quantized nature of the effect over all frequency space.     

Viscous Fluid Cosmology in Bianchi Type-I Space-Time

The paper presents a spatially homogeneous and anisotropic Bianchi type-I cosmological model consisting of a dissipative fluid. The field equations are solved explicitly by using a law of variation for mean Hubble parameter, which is related to average scale factor and yields a constant value for deceleration parameter. We find that the constant value of deceleration parameter describes the different phases of the evolution of universe. A barotropic equation of state (p=γ ρ) together with a linear relation between shear viscosity and expansion scalar, is assumed. It is found that the viscosity plays a key role in the process of the isotropization of the universe. The presence of viscous term does not change the fundamental nature of initial singularity. The thermodynamical properties of the solutions are studied and the entropy distribution is also given explicitly.     

A convolution formula for a phase transition of hadronic matter and the multiplicity distributions

We propose a general form for the statistical bootstrap equation by means of a convolution formula for the thermodynamical system of hadronic matter. In connection with a phase transition of hadronic matter to a state of quark liberation, we predict the negative binomial distribution with k∼1 for the multiplicity distributions in the central pseudorapidity region at high energies.     

序参量-统计格林函数耦合方程组

本文建议一个自洽求解量子统计系统中序参量和费密型元激发及序参量集体激发的能谱、耗散和准粒子分布的联立方程组,并给出系统的圈图展开方法。这一理论方法既适用于平衡态,也适用于非平衡态。 关键词：     

Nonequilibrium statistical mechanics in the general theory of relativity I. A general formalism

This is the first in a series of papers, the overall objective of which is the formulation of a new covariant approach to nonequilibrium statistical mechanics in classical general relativity. The object here is the development of a tractable theory for self-gravitating systems. It is argued that the “state” of an N-particle system may be characterized by an N-particle distribution function, defined in an 8N-dimensional phase space, which satisfies a collection of N conservation equations. by mapping the true physics onto a fictitious “background” spacetime, which may be chosen to satisfy some “average” field equations, one then obtains a useful covariant notion of “evolution” in response to a fluctuating “gravitational force.” For many cases of practical interest, one may suppose (i) that these fluctuating forces satisfy linear field equations and (ii) that they may be modeled by a direct interaction. In this case, one can use a relativistic projection operator formalism to derive exact closed equations for the evolution of such objects as an appropriately defined reduced one-particle distribution function. By capturing, in a natural way, the notion of a dilute gas, or impulse, approximation, one is then led to a comparatively simple equation for the one-particle distribution. If, furthermore, one treats the effects of the fluctuating forces as “localized” in space and time, one obtains a tractable kinetic equation which reduces, in the newtonian limit, to the standard Landau equation.     

Statistical Physics on the Space (x, v) for Dissipative Systems and Study of an Ensemble of Harmonic Oscillators in a Weak Linear Dissipative Medium

We use the phase space position-velocity (x, v) to deal with the statistical properties of velocity dependent dynamical systems, like dissipative ones. Within this approach, we study the statistical properties of an ensemble of harmonic oscillators in a linear weak dissipative media. Using the Debye model of a crystal, we calculate at first order in the dissipative parameter the entropy, free energy, internal energy, equation of state and specific heat using the classical and quantum approaches. For the classical approach we found that the entropy, the equation of state, and the free energy depend on the dissipative parameter, but the internal energy and specific heat do not depend of it. For the quantum case, we found that all the thermodynamical quantities depend on this parameter. PACS: 05.20.Gg, 05.30.Ch, 05.20.-y, 05.30.-d     

Theoretical calculation of acoustic non-linearity parameter B/A of binary mixtures

Acoustic non-linearity parameter B/A is calculated for five binary liquid mixtures using Tong and Dong equation along with the Flory’s statistical theory. Similar to other excess thermodynamical quantities an excess non-linearity parameter (B/A)^E is defined for binary liquid mixtures. The interactions in the liquid mixtures are explained on the basis of the excess non-linearity parameter.     

Equivalence of Non-equilibrium Ensembles and Representation of Friction in Turbulent Flows: The Lorenz 96 Model

We construct different equivalent non-equilibrium statistical ensembles in a simple yet instructive \(N\) -degrees of freedom model of atmospheric turbulence, introduced by Lorenz in 1996. The vector field can be decomposed into an energy-conserving, time-reversible part, plus a non-time reversible part, including forcing and dissipation. We construct a modified version of the model where viscosity varies with time, in such a way that energy is conserved, and the resulting dynamics is fully time-reversible. For each value of the forcing, the statistical properties of the irreversible and reversible model are in excellent agreement, if in the latter the energy is kept constant at a value equal to the time-average realized with the irreversible model. In particular, the average contraction rate of the phase space of the time-reversible model agrees with that of the irreversible model, where instead it is constant by construction. We also show that the phase space contraction rate obeys the fluctuation relation, and we relate its finite time corrections to the characteristic time scales of the system. A local version of the fluctuation relation is explored and successfully checked. The equivalence between the two non-equilibrium ensembles extends to dynamical properties such as the Lyapunov exponents, which are shown to obey to a good degree of approximation a pairing rule. These results have relevance in motivating the importance of the chaotic hypothesis. in explaining that we have the freedom to model non-equilibrium systems using different but equivalent approaches, and, in particular, that using a model of a fluid where viscosity is kept constant is just one option, and not necessarily the only option, for describing accurately its statistical and dynamical properties.     

Mechanism for thermal conductivity in energetic displacement cascades

Abstract

Temperature relaxation inside and outside the energetic displacement cascade in fast neutron-irradiated metals is consistently described. The characteristic time of the energy transfer between phonons and electrons in the damaged area is calculated. The space–time temperature distribution in the cascade damaged area in Fe and Ni is presented. The electron–phonon coupling is shown to play an important role in the evolution of the damaged area due to non-equilibrium between the local phonon and electron systems at the beginning of the cooling phase of the displacement cascade.     

Non-equilibrium statistical mechanics in the general theory of relativity: II. Linear fields in a kinetic approximation

The first paper in this series introduced a new, manifestly covariant approach to non-equilibrium statistical mechanics in classical general relativity. The object of this second paper is to apply that formalism to the evolution of a collection of particles that interact via linear fields in a fixed curved background spacetime. Given the viewpoint adopted here, the fundamental objects of the theory are a many-particle distribution function, which lives in a many-particle phase space, and a many-particle conservation equation which this distribution satisfies. By viewing a composite N-particle system as interacting one- and (N ? 1)-particle subsystems, one can derive exact coupled equations for appropriately defined reduced one- and (N ? 1)-particle distribution functions. Alternatively, by treating all the particles on an identical footing, one can extract an exact closed equation involving only the one-particle distribution. The implementation of plausible assumptions, which constitute straightforward generalizations of standard non-relativistic “kinetic approximations”, then permits the formulation of an approximate kinetic equation for the one-particle distribution function. In the obvious non-relativistic limit, one recovers the well-known Vlasov-Landau equation. The explicit form for the relativistic expression is obtained for three concrete examples, namely, interactions via an electromagnetic field, a massive scalar field, and a symmetric second rank tensor field. For a large class of interactions, of which these three examples are representative, the kinetic equation will admit a relativistic Maxwellian distribution as an exact stationary solution; and, for these interactions, an H-theorem may be proved.