1,451 research outputs found
Matrix-valued Quantum Lattice Boltzmann Method
We devise a lattice Boltzmann method (LBM) for a matrix-valued quantum
Boltzmann equation, with the classical Maxwell distribution replaced by
Fermi-Dirac functions. To accommodate the spin density matrix, the distribution
functions become 2 x 2 matrix-valued. From an analytic perspective, the
efficient, commonly used BGK approximation of the collision operator is valid
in the present setting. The numerical scheme could leverage the principles of
LBM for simulating complex spin systems, with applications to spintronics.Comment: 18 page
Coherent States Formulation of Polymer Field Theory
We introduce a stable and efficient complex Langevin (CL) scheme to enable
the first numerical simulations of the coherent-states (CS) formulation of
polymer field theory. In contrast with Edwards' well known auxiliary-field (AF)
framework, the CS formulation does not contain an embedded non-linear,
non-local functional of the auxiliary fields, and the action of the field
theory has a fully explicit, finite-order and semi-local polynomial character.
In the context of a polymer solution model, we demonstrate that the new CS-CL
dynamical scheme for sampling fluctuations in the space of coherent states
yields results in good agreement with now-standard AF simulations. The
formalism is potentially applicable to a broad range of polymer architectures
and may facilitate systematic generation of trial actions for use in
coarse-graining and numerical renormalization-group studies.Comment: 14pages 8 figure
On low temperature kinetic theory; spin diffusion, Bose Einstein condensates, anyons
The paper considers some typical problems for kinetic models evolving through
pair-collisions at temperatures not far from absolute zero, which illustrate
specific quantum behaviours. Based on these examples, a number of differences
between quantum and classical Boltzmann theory is then discussed in more
general terms.Comment: 25 pages, minor updates of previous versio
Non-Equilibrium Quantum Fields in the Large N Expansion
An effective action technique for the time evolution of a closed system
consisting of one or more mean fields interacting with their quantum
fluctuations is presented. By marrying large expansion methods to the
Schwinger-Keldysh closed time path (CTP) formulation of the quantum effective
action, causality of the resulting equations of motion is ensured and a
systematic, energy conserving and gauge invariant expansion about the
quasi-classical mean field(s) in powers of developed. The general method
is exposed in two specific examples, symmetric scalar \l\F^4 theory
and Quantum Electrodynamics (QED) with fermion fields. The \l\F^4 case is
well suited to the numerical study of the real time dynamics of phase
transitions characterized by a scalar order parameter. In QED the technique may
be used to study the quantum non-equilibrium effects of pair creation in strong
electric fields and the scattering and transport processes in a relativistic
plasma. A simple renormalization scheme that makes practical the
numerical solution of the equations of motion of these and other field theories
is described.Comment: 43 pages, LA-UR-94-783 (PRD, in press), uuencoded PostScrip
The phonon Boltzmann equation, properties and link to weakly anharmonic lattice dynamics
For low density gases the validity of the Boltzmann transport equation is
well established. The central object is the one-particle distribution function,
, which in the Boltzmann-Grad limit satisfies the Boltzmann equation. Grad
and, much refined, Cercignani argue for the existence of this limit on the
basis of the BBGKY hierarchy for hard spheres. At least for a short kinetic
time span, the argument can be made mathematically precise following the
seminal work of Lanford. In this article a corresponding programme is
undertaken for weakly nonlinear, both discrete and continuum, wave equations.
Our working example is the harmonic lattice with a weakly nonquadratic on-site
potential. We argue that the role of the Boltzmann -function is taken over
by the Wigner function, which is a very convenient device to filter the slow
degrees of freedom. The Wigner function, so to speak, labels locally the
covariances of dynamically almost stationary measures. One route to the phonon
Boltzmann equation is a Gaussian decoupling, which is based on the fact that
the purely harmonic dynamics has very good mixing properties. As a further
approach the expansion in terms of Feynman diagrams is outlined. Both methods
are extended to the quantized version of the weakly nonlinear wave equation.
The resulting phonon Boltzmann equation has been hardly studied on a rigorous
level. As one novel contribution we establish that the spatially homogeneous
stationary solutions are precisely the thermal Wigner functions. For three
phonon processes such a result requires extra conditions on the dispersion law.
We also outline the reasoning leading to Fourier's law for heat conduction.Comment: special issue on "Kinetic Theory", Journal of Statistical Physics,
improved versio
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