Derivation of Effective Evolution Equations from Microscopic Quantum Dynamics
نویسنده
چکیده
2 Derivation of the Hartree Equation in the Mean Field Limit 5 2.1 Mean Field Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Derivation of the Hartree Equation for Bounded Potentials . . . . . . . . . . . . . . . 7 2.3 Another Proof of Theorem 2.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.4 Derivation of the Hartree Equation for a Coulomb Potential . . . . . . . . . . . . . . . 14
منابع مشابه
Microscopic derivation of rate equations for quantum transport.
It is shown that under certain conditions the resonant transport in meso-scopic systems can be described by modified (quantum) rate equations, which resemble the optical Bloch equations with some additional terms. Detailed microscopic derivation from the many-body Schrödinger equation is presented. Special attention is paid to the Coulomb blockade and quantum coherence effects in coupled quantu...
متن کاملDerivation of an Effective Evolution Equation for a Strongly Coupled Polaron
1.1. Setting of the problem. In this paper we are interested in the dynamics of a strongly coupled polaron. A polaron is a model of an electron in an ionic lattice interacting with its surrounding polarization field. In 1937 Fröhlich [8] proposed a quantum-mechanical Hamiltonian, given in (1.1) below, in order to describe the dynamics of a polaron. In this model the phonon field is treated as a...
متن کاملThe Quantum Statistical Mechanical Theory of Transport Processes
A new derivation of the quantum Boltzmann transport equation for the Fermion system from the quantum time evolution equation for the wigner distribution function is presented. The method exhibits the origin of the time - irreversibility of the Boltzmann equation. In the present work, the spin dependent and indistinguishibility of particles are also considered.
متن کاملEquation-free, Coarse-grained Multiscale Computation: Enabling Microscopic Simulators to Perform System-level Analysis∗
We present and discuss a framework for computer-aided multiscale analysis, which enables models at a fine (microscopic/stochastic) level of description to perform modeling tasks at a coarse (macroscopic, systems) level. These macroscopic modeling tasks, yielding information over long time and large space scales, are accomplished through appropriately initialized calls to the microscopic simulat...
متن کاملHeuristic derivation of continuum kinetic equations from microscopic dynamics.
We present an approximate and heuristic scheme for the derivation of continuum kinetic equations from microscopic dynamics for stochastic, interacting systems. The method consists of a mean-field-type, decoupled approximation of the master equation followed by the "naive" continuum limit. The Ising model and driven diffusive systems are used as illustrations. The equations derived are in agreem...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008