Collisional decoherence reexamined

We re-derive the quantum master equation for the decoherence of a massive Brownian particle due to collisions with the lighter particles from a thermal environment. Our careful treatment avoids the occurrence of squares of Dirac delta functions. It leads to a decoherence rate which is smaller by a factor of 2 pi compared to previous findings. This result, which is in agreement with recent experiments, is confirmed by both a physical analysis of the problem and by a perturbative calculation in the weak coupling limit.Comment: 33 pages, 4 figure

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

Decoherence in a Talbot Lau interferometer: the influence of molecular scattering

We study the interference of C70 fullerenes in a Talbot-Lau interferometer with a large separation between the diffraction gratings. This permits the observation of recurrences of the interference contrast both as a function of the de Broglie wavelength and in dependence of the interaction with background gases. We observe an exponential decrease of the fringe visibility with increasing background pressure and find good quantitative agreement with the predictions of decoherence theory. From this we extrapolate the limits of matter wave interferometry and conclude that the influence of collisional decoherence may be well under control in future experiments with proteins and even larger objects.Comment: 8 pages, 5 figure

On the Asymptotic Dynamics of a Quantum System Composed by Heavy and Light Particles

We consider a non relativistic quantum system consisting of $K$ heavy and $N$ light particles in dimension three, where each heavy particle interacts with the light ones via a two-body potential $\alpha V$. No interaction is assumed among particles of the same kind. Choosing an initial state in a product form and assuming $\alpha$ sufficiently small we characterize the asymptotic dynamics of the system in the limit of small mass ratio, with an explicit control of the error. In the case K=1 the result is extended to arbitrary $\alpha$. The proof relies on a perturbative analysis and exploits a generalized version of the standard dispersive estimates for the Schr\"{o}dinger group. Exploiting the asymptotic formula, it is also outlined an application to the problem of the decoherence effect produced on a heavy particle by the interaction with the light ones.Comment: 38 page

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

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

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.

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

Collapses and revivals in the interference between two Bose-Einstein condensates formed in small atomic samples

We investigate the quantum interference between two Bose-Einstein condensates formed in small atomic samples composed of a few thousand atoms both by imposing Bose broken gauge symmetry from the outset and also using an explicit model of atomic detection. In the former case we show that the macroscopic wave function collapses and revives in time, and we calculate the characteristic times for current experiments. Collapses and revivals are also predicted in the interference between two Bose-Einstein condensates which are initially in Fock states, a relative phase between the condensates being established via atomic detections corresponding to uncertainty in the number difference between them.Comment: 17 pages, 3 PostScript figure, submitted to PR

A ballistic motion disrupted by quantum reflections

I study a Lindblad dynamics modeling a quantum test particle in a Dirac comb that collides with particles from a background gas. The main result is a homogenization theorem in an adiabatic limiting regime involving large initial momentum for the test particle. Over the time interval considered, the particle would exhibit essentially ballistic motion if either the singular periodic potential or the kicks from the gas were removed. However, the particle behaves diffusively when both sources of forcing are present. The conversion of the motion from ballistic to diffusive is generated by occasional quantum reflections that result when the test particle's momentum is driven through a collision near to an element of the half-spaced reciprocal lattice of the Dirac comb.Comment: 54 pages. I rewrote the introduction and simplified some of the presentatio