1,635 research outputs found
Generalized Uncertainty Relations and Long Time Limits for Quantum Brownian Motion Models
We study the time evolution of the reduced Wigner function for a class of
quantum Brownian motion models. We derive two generalized uncertainty
relations. The first consists of a sharp lower bound on the uncertainty
function, , after evolution for time in the
presence of an environment. The second, a stronger and simpler result, consists
of a lower bound at time on a modified uncertainty function, essentially
the area enclosed by the contour of the Wigner function. In both
cases the minimizing initial state is a non-minimal Gaussian pure state. These
generalized uncertainty relations supply a measure of the comparative size of
quantum and thermal fluctuations. We prove two simple inequalites, relating
uncertainty to von Neumann entropy, and the von Neumann entropy to linear
entropy. We also prove some results on the long-time limit of the Wigner
function for arbitrary initial states. For the harmonic oscillator the Wigner
function for all initial states becomes a Gaussian at large times (often, but
not always, a thermal state). We derive the explicit forms of the long-time
limit for the free particle (which does not in general go to a Gaussian), and
also for more general potentials in the approximation of high temperature.Comment: 35 pages (plain Tex, revised to avoid corruption during file
transmission), Imperial College preprint 92-93/25 (1994
Emergence: Key physical issues for deeper philosophical inquiries
A sketch of three senses of emergence and a suggestive view on the emergence
of time and the direction of time is presented. After trying to identify which
issues philosophers interested in emergent phenomena in physics view as
important I make several observations pertaining to the concepts, methodology
and mechanisms required to understand emergence and describe a platform for its
investigation. I then identify some key physical issues which I feel need be
better appreciated by the philosophers in this pursuit. I end with some
comments on one of these issues, that of coarse-graining and persistent
structures.Comment: 16 pages. Invited Talk at the Heinz von Foerster Centenary
International Conference on Self-Organization and Emergence: Emergent Quantum
Mechanics (EmerQuM11). Nov. 10-13, 2011, Vienna, Austria. Proceedings to
appear in J. Phys. (Conf. Series
Emergence: Key physical issues for deeper philosophical inquiries
A sketch of three senses of emergence and a suggestive view on the emergence
of time and the direction of time is presented. After trying to identify which
issues philosophers interested in emergent phenomena in physics view as
important I make several observations pertaining to the concepts, methodology
and mechanisms required to understand emergence and describe a platform for its
investigation. I then identify some key physical issues which I feel need be
better appreciated by the philosophers in this pursuit. I end with some
comments on one of these issues, that of coarse-graining and persistent
structures.Comment: 16 pages. Invited Talk at the Heinz von Foerster Centenary
International Conference on Self-Organization and Emergence: Emergent Quantum
Mechanics (EmerQuM11). Nov. 10-13, 2011, Vienna, Austria. Proceedings to
appear in J. Phys. (Conf. Series
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