Equilibrium Time Correlation Functions in the Low-Density Limit
نویسنده
چکیده
We consider a system of hard spheres in thermal equilibrium. Using Lanford's result about the convergence of the solutions of the BBGKY hierarchy to the solutions of the Boltzmann hierarchy, we show that in the low-density limit (Boltzmann-Grad limit): (i) the total time correlation function is governed by the linearized Boltzmann equation (proved to be valid for short times), (ii) the self time correlation function, equivalently the distribution of a tagged particle in an equilibrium fluid, is governed by the Rayleigh-Boltzmann equation (proved to be valid for all times). In the latter case the fluid (not including the tagged particle) is to zeroth order in thermal equilibrium and to first order its distribution is governed by a combination of the Rayleigh-Boltzmann equation and the linearized Boltzmann equation (proved to be valid for short times).
منابع مشابه
A Proposed Modeling Method in Finite Element Slope Stability Analysis
Limit-equilibrium method (LEM) and finite element method (FEM) with strength reduction method (SRM) techniques are the most widely used analysis tools in slope stability assessment. Recently, researchers have reported that both factor of safety (FOS) values and failure surfaces obtained from LEM and FEM are generally in good agreement, except in some particular cases. In this paper, the FOS and...
متن کاملCharge and Current Sum Rules in Quantum Media Coupled to Radiation
This paper concerns the equilibrium bulk charge and current density correlation functions in quantum media, conductors and dielectrics, fully coupled to the radiation (the retarded regime). A sequence of static and timedependent sum rules, which fix the values of certain moments of the charge and current density correlation functions, is obtained by using Rytov’s fluctuational electrodynamics. ...
متن کاملAn exact stochastic field method for the interacting Bose gas at thermal equilibrium
We present a new exact method to numerically compute the thermodynamical properties of an interacting Bose gas in the canonical ensemble. As in our previous paper (Phys. Rev. A 63 023606 (2001)), we write the density operator ρ as an average of Hartree dyadics |N : φ 1 N : φ 2 | and we find stochastic evolution equations for the wave functions φ 1,2 such that the exact imaginary-time evolution ...
متن کاملQuantum-classical limit of quantum correlation functions.
A quantum-classical limit of the canonical equilibrium time correlation function for a quantum system is derived. The quantum-classical limit for the dynamics is obtained for quantum systems comprising a subsystem of light particles in a bath of heavy quantum particles. In this limit the time evolution of operators is determined by a quantum-classical Liouville operator, but the full equilibriu...
متن کاملTime-dependent analysis of carrier density and potential energy in spherical centered defect InGaAs/AlGaAs quantum dot (SCDQD)
Interaction and correlation effects in quantum dots play a fundamental role in defining both their equilibrium and transport properties. Numerical methods are commonly employed to study such systems. In this paper we investigate the numerical calculation of quantum transport of electrons in spherical centered defect InGaAs/AlGaAs quantum dot (SCDQD). The simulation is based on the imaginary time...
متن کامل