595 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
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
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
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