271 research outputs found
Master-equations for the study of decoherence
Different structures of master-equation used for the description of
decoherence of a microsystem interacting through collisions with a surrounding
environment are considered and compared. These results are connected to the
general expression of the generator of a quantum dynamical semigroup in
presence of translation invariance recently found by Holevo.Comment: 10 pages, latex, no figures, to appear in Int. J. Theor. Phy
Two Derivations of the Master Equation of Quantum Brownian Motion
Central to many discussion of decoherence is a master equation for the
reduced density matrix of a massive particle experiencing scattering from its
surrounding environment, such as that of Joos and Zeh. Such master equations
enjoy a close relationship with spontaneous localization models, like the GRW
model. This aim of this paper is to present two derivations of the master
equation. The first derivation is a pedagogical model designed to illustrate
the origins of the master equation as simply as possible, focusing on physical
principles and without the complications of S-matrix theory. This derivation
may serve as a useful tutorial example for students attempting to learn this
subject area. The second is the opposite: a very general derivation using
non-relativistic many body field theory. It reduces to the equation of the type
given by Joos and Zeh in the one-particle sector, but correcting certain
numerical factors which have recently become significant in connection with
experimental tests of decoherence. This master equation also emphasizes the
role of local number density as the ``preferred basis'' for decoherence in this
model.Comment: 19 pages, RevTe
Atom Lasers, Coherent States, and Coherence:II. Maximally Robust Ensembles of Pure States
As discussed in Wiseman and Vaccaro [quant-ph/9906125], the stationary state
of an optical or atom laser far above threshold is a mixture of coherent field
states with random phase, or, equivalently, a Poissonian mixture of number
states. We are interested in which, if either, of these descriptions of
, is more natural. In the preceding paper we concentrated upon
whether descriptions such as these are physically realizable (PR). In this
paper we investigate another relevant aspect of these ensembles, their
robustness. A robust ensemble is one for which the pure states that comprise it
survive relatively unchanged for a long time under the system evolution. We
determine numerically the most robust ensembles as a function of the parameters
in the laser model: the self-energy of the bosons in the laser mode, and
the excess phase noise . We find that these most robust ensembles are PR
ensembles, or similar to PR ensembles, for all values of these parameters. In
the ideal laser limit (), the most robust states are coherent
states. As the phase noise or phase dispersion is increased, the
most robust states become increasingly amplitude-squeezed. We find scaling laws
for these states. As the phase diffusion or dispersion becomes so large that
the laser output is no longer quantum coherent, the most robust states become
so squeezed that they cease to have a well-defined coherent amplitude. That is,
the quantum coherence of the laser output is manifest in the most robust PR
states having a well-defined coherent amplitude. This lends support to the idea
that robust PR ensembles are the most natural description of the state of the
laser mode. It also has interesting implications for atom lasers in particular,
for which phase dispersion due to self-interactions is expected to be large.Comment: 16 pages, 9 figures included. To be published in Phys. Rev. A, as
Part II of a two-part paper. The original version of quant-ph/9906125 is
shortly to be replaced by a new version which is Part I of the two-part
paper. This paper (Part II) also contains some material from the original
version of quant-ph/990612
The Post-Decoherence Density Matrix Propagator for Quantum Brownian Motion
Using the path integral representation of the density matrix propagator of
quantum Brownian motion, we derive its asymptotic form for times greater than
the localization time, (\hbar / \gamma k T )^{\half}, where is the
dissipation and the temperature of the thermal environment. The
localization time is typically greater than the decoherence time, but much
shorter than the relaxation time, . We use this result to show
that the reduced density operator rapidly evolves into a state which is
approximately diagonal in a set of generalized coherent states. We thus
reproduce, using a completely different method, a result we previously obtained
using the quantum state diffusion picture (Phys.Rev. D52, 7294 (1995)). We also
go beyond this earlier result, in that we derive an explicit expression for the
weighting of each phase space localized state in the approximately diagonal
density matrix, as a function of the initial state. For sufficiently long times
it is equal to the Wigner function, and we confirm that the Wigner function is
positive for times greater than the localization time (multiplied by a number
of order 1).Comment: 17 pages, plain Tex, submitted to Physical Review
Completely Positive Quantum Dissipation
A completely positive master equation describing quantum dissipation for a
Brownian particle is derived starting from microphysical collisions, exploiting
a recently introduced approach to subdynamics of a macrosystem. The obtained
equation can be cast into Lindblad form with a single generator for each
Cartesian direction. Temperature dependent friction and diffusion coefficients
for both position and momentum are expressed in terms of the collision
cross-section.Comment: 8 pages, revtex, no figure
Simulations of Aerodynamic Damping for MEMS Resonators
Aerodynamic damping for MEMS resonators is studied based on the numerical solution of Boltzmann-ESBGK equation. A compact model is then developed based on numerical simulations for a wide range of Knudsen numbers. The damping predictions are compared with both Reynold equation based models and several sets of experimental data. It has been found that the structural damping is dominant at low pressures (high Knudsen numbers). For cases with small length-to-width ratios and large vibration amplitudes, the threedimensionality effects must be taken into account. Finally, an uncertainty quantification approach based on the probability transformation method has been applied to assess the influence of pressure and geometric uncertainties. The output probability density functions (PDF) of the damping ratio has been studied for various input PDF of beam geometry and ambient pressure
Positive Quantum Brownian Evolution
Using the independent oscillator model with an arbitrary system potential, we
derive a quantum Brownian equation assuming a correlated total initial state.
Although not of Lindblad form, the equation preserves positivity of the density
operator on a restricted set of initial states
Non-Newtonian Couette-Poiseuille flow of a dilute gas
The steady state of a dilute gas enclosed between two infinite parallel
plates in relative motion and under the action of a uniform body force parallel
to the plates is considered. The Bhatnagar-Gross-Krook model kinetic equation
is analytically solved for this Couette-Poiseuille flow to first order in the
force and for arbitrary values of the Knudsen number associated with the shear
rate. This allows us to investigate the influence of the external force on the
non-Newtonian properties of the Couette flow. Moreover, the Couette-Poiseuille
flow is analyzed when the shear-rate Knudsen number and the scaled force are of
the same order and terms up to second order are retained. In this way, the
transition from the bimodal temperature profile characteristic of the pure
force-driven Poiseuille flow to the parabolic profile characteristic of the
pure Couette flow through several intermediate stages in the Couette-Poiseuille
flow are described. A critical comparison with the Navier-Stokes solution of
the problem is carried out.Comment: 24 pages, 5 figures; v2: discussion on boundary conditions added; 10
additional references. Published in a special issue of the journal "Kinetic
and Related Models" dedicated to the memory of Carlo Cercignan
Apparent wave function collapse caused by scattering
Some experimental implications of the recent progress on wave function
collapse are calculated. Exact results are derived for the center-of-mass wave
function collapse caused by random scatterings and applied to a range of
specific examples. The results show that recently proposed experiments to
measure the GRW effect are likely to fail, since the effect of naturally
occurring scatterings is of the same form as the GRW effect but generally much
stronger. The same goes for attempts to measure the collapse caused by quantum
gravity as suggested by Hawking and others. The results also indicate that
macroscopic systems tend to be found in states with (Delta-x)(Delta-p) =
hbar/sqrt(2), but microscopic systems in highly tiltedly squeezed states with
(Delta-x)(Delta-p) >> hbar.Comment: Final published version. 20 pages, Plain TeX, no figures. Online at
http://astro.berkeley.edu/~max/collapse.html (faster from the US), from
http://www.mpa-garching.mpg.de/~max/collapse.html (faster from Europe) or
from [email protected]
Diffusive limit for a quantum linear Boltzmann dynamics
In this article, I study the diffusive behavior for a quantum test particle
interacting with a dilute background gas. The model I begin with is a reduced
picture for the test particle dynamics given by a quantum linear Boltzmann
equation in which the gas particle scattering is assumed to occur through a
hard-sphere interaction. The state of the particle is represented by a density
matrix that evolves according to a translation-covariant Lindblad equation. The
main result is a proof that the particle's position distribution converges to a
Gaussian under diffusive rescaling.Comment: 51 pages. I have restructured Sections 2-4 from the previous version
and corrected an error in the proof of Proposition 7.
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