Quantum Master Equation of Particle in Gas Environment

The evolution of the reduced density operator $\rho$ 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 $\rho$, whose generators are calculated from differential cross section of a single collision between Brownian and gas particles, respectively. The existence of thermal equilibrium for $\rho$ 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

Exact solution of Riemann--Hilbert problem for a correlation function of the XY spin chain

A correlation function of the XY spin chain is studied at zero temperature. This is called the Emptiness Formation Probability (EFP) and is expressed by the Fredholm determinant in the thermodynamic limit. We formulate the associated Riemann--Hilbert problem and solve it exactly. The EFP is shown to decay in Gaussian.Comment: 7 pages, to be published in J. Phys. Soc. Jp

Deconstructing Decoherence

The study of environmentally induced superselection and of the process of decoherence was originally motivated by the search for the emergence of classical behavior out of the quantum substrate, in the macroscopic limit. This limit, and other simplifying assumptions, have allowed the derivation of several simple results characterizing the onset of environmentally induced superselection; but these results are increasingly often regarded as a complete phenomenological characterization of decoherence in any regime. This is not necessarily the case: The examples presented in this paper counteract this impression by violating several of the simple ``rules of thumb''. This is relevant because decoherence is now beginning to be tested experimentally, and one may anticipate that, in at least some of the proposed applications (e.g., quantum computers), only the basic principle of ``monitoring by the environment'' will survive. The phenomenology of decoherence may turn out to be significantly different.Comment: 13 two-column pages, 3 embedded figure

Quantum open systems and turbulence

We show that the problem of non conservation of energy found in the spontaneous localization model developed by Ghirardi, Rimini and Weber is very similar to the inconsistency between the stochastic models for turbulence and the Navier-Stokes equation. This sort of analogy may be useful in the development of both areas.Comment: to appear in Physical Review

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

Signatures of non-locality in the first-order coherence of the scattered light

The spatial coherence of an atomic wavepacket can be detected in the scattered photons, even when the center-of-mass motion is in the quantum coherent superposition of two distant, non-overlapping wave packets. Spatial coherence manifests itself in the power spectrum of the emitted photons, whose spectral components can exhibit interference fringes as a function of the emission angle. The contrast and the phase of this interference pattern provide information about the quantum state of the center of mass of the scattering atom.Comment: 5 pages, one figure, submitted to Laser Physics, special issue in memory of Herbert Walthe

Decoherence produces coherent states: an explicit proof for harmonic chains

We study the behavior of infinite systems of coupled harmonic oscillators as t->infinity, and generalize the Central Limit Theorem (CLT) to show that their reduced Wigner distributions become Gaussian under quite general conditions. This shows that generalized coherent states tend to be produced naturally. A sufficient condition for this to happen is shown to be that the spectral function is analytic and nonlinear. For a rectangular lattice of coupled oscillators, the nonlinearity requirement means that waves must be dispersive, so that localized wave-packets become suppressed. Virtually all harmonic heat-bath models in the literature satisfy this constraint, and we have good reason to believe that coherent states and their generalizations are not merely a useful analytical tool, but that nature is indeed full of them. Standard proofs of the CLT rely heavily on the fact that probability densities are non-negative. Although the CLT generally fails if the probability densities are allowed to take negative values, we show that a CLT does indeed hold for a special class of such functions. We find that, intriguingly, nature has arranged things so that all Wigner functions belong to this class.Comment: Final published version. 17 pages, Plain TeX, no figures. Online at http://astro.berkeley.edu/~max/gaussians.html (faster from the US), from http://www.mpa-garching.mpg.de/~max/gaussians.html (faster from Europe) or from [email protected]

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