1,523 research outputs found
Decoherence and Dissipation for a Quantum System Coupled to a Local Environment
Decoherence and dissipation in quantum systems has been studied extensively
in the context of Quantum Brownian Motion. Effective decoherence in coarse
grained quantum systems has been a central issue in recent efforts by Zurek and
by Hartle and Gell-Mann to address the Quantum Measurement Problem. Although
these models can yield very general classical phenomenology, they are incapable
of reproducing relevant characteristics expected of a local environment on a
quantum system, such as the characteristic dependence of decoherence on
environment spatial correlations. I discuss the characteristics of Quantum
Brownian Motion in a local environment by examining aspects of first
principle calculations and by the construction of phenomenological models.
Effective quantum Langevin equations and master equations are presented in a
variety of representations. Comparisons are made with standard results such as
the Caldeira-Leggett master equation.Comment: 6 Pages (LaTeX), to appear in the Proceedings of the Third
International Workshop on Squeezed States and Uncertainty Relation
Quantum Master Equation of Particle in Gas Environment
The evolution of the reduced density operator of Brownian particle is
discussed in single collision approach valid typically in low density gas
environments. This is the first succesful derivation of quantum friction caused
by {\it local} environmental interactions. We derive a Lindblad master equation
for , whose generators are calculated from differential cross section of
a single collision between Brownian and gas particles, respectively. The
existence of thermal equilibrium for is proved. Master equations
proposed earlier are shown to be particular cases of our one.Comment: 6 pages PlainTeX, 23-March-199
Models for local ohmic quantum dissipation
We construct model master equations for local quantum dissipation. The master
equations are in the form of Lindblad generators, with imposed constraints that
the dissipations be strictly linear (i.e. ohmic), isotropic and translationally
invariant. A particular form for is chosen to satisfy the constraints. The
resulting master equations are given in both the Schr\"odinger and Heisenberg
forms. We obtain fluctuation-dissipation relations, and discuss the relaxation
of average kinetic energy to effective thermal equilibrium values. We compare
our results to the Dekker and the Caldeira-Leggett master equations. These
master equations allow a more general approach to quantum dissipation and the
dynamics of quantum coherence to account for the nontrivial system-environment
coupling in a local environment.Comment: 19 pages, REVTEX, PSU/TH/12
A wall-function approach to incorporating Knudsen-layer effects in gas micro flow simulations
For gas flows in microfluidic configurations, the Knudsen layer close to the wall can comprise a substantial part of the entire flow field and has a major effect on quantities such as the mass flow rate through micro devices. The Knudsen layer itself is characterized by a highly nonlinear relationship between the viscous stress and the strain rate of the gas, so even if the Navier-Stokes equations can be used to describe the core gas flow they are certainly inappropriate for the Knudsen layer itself. In this paper we propose a "wall-function" model for the stress/strain rate relations in the Knudsen layer. The constitutive structure of the Knudsen layer has been derived from results from kinetic theory for isothermal shear flow over a planar surface. We investigate the ability of this simplified model to predict Knudsen-layer effects in a variety of configurations. We further propose a semi-empirical Knudsen-number correction to this wall function, based on high-accuracy DSMC results, to extend the predictive capabilities of the model to greater degrees of rarefaction
The usefulness of higher-order constitutive relations for describing the Knudsen layer
The Knudsen layer is an important rarefaction phenomenon in gas flows in and around microdevices. Its accurate and efficient modeling is of critical importance in the design of such systems and in predicting their performance. In this paper we investigate the potential that higher-order continuum equations may have to model the Knudsen layer, and compare their predictions to high-accuracy DSMC (direct simulation Monte Carlo) data, as well as a standard result from kinetic theory. We find that, for a benchmark case, the most common higher-order continuum equation sets (Grad's 13 moment, Burnett, and super-Burnett equations) cannot capture the Knudsen layer. Variants of these equation families have, however, been proposed and some of them can qualitatively describe the Knudsen layer structure. To make quantitative comparisons, we obtain additional boundary conditions (needed for unique solutions to the higher-order equations) from kinetic theory. However, we find the quantitative agreement with kinetic theory and DSMC data is only slight
Classical and quantum dissipation in non homogeneous environments
We generalize the oscillator model of a particle interacting with a thermal
reservoir by introducing arbitrary nonlinear couplings in the particle
coordinates.The equilibrium positions of the heat bath oscillators are promoted
to space-time functions, which are shown to represent a modulation of the
internal noise by the external forces. The model thus provides a description of
classical and quantum dissipation in non homogeneous environments. In the
classical case we derive a generalized Langevin equation with nonlinear
multiplicative noise and a position-dependent fluctuation- dissipation theorem
associated to non homogeneous dissipative forces. When time-modulation of the
noise is present, a new force term is predicted besides the dissipative and
random ones. The model is quantized to obtain the non homogenous influence
functional and master equation for the reduced density matrix of the Brownian
particle. The quantum evolution equations reproduce the correct Langevin
dynamics in the semiclassical limit. The consequences for the issues of
decoherence and localization are discussed.Comment: 17 pages, plain LaTeX [12pt,A4wide], DFPD 94/TH/2
Capturing the Knudsen layer in continuum-fluid models of non-equilibrium gas flows
In hypersonic aerodynamics and microflow device design, the momentum and energy fluxes to solid surfaces are often of critical importance. However, these depend on the characteristics of the Knudsen layer - the region of local non-equilibrium existing up to one or two molecular mean free paths from the wall in any gas flow near a surface. While the Knudsen layer has been investigated extensively using kinetic theory, the ability to capture it within a continuum-fluid formulation (in conjunction with slip boundary conditions) suitable for current computational fluid dynamics toolboxes would offer distinct and practical computational advantages
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