1,438 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
Glassy dynamics in strongly anharmonic chains of oscillators
We review the mechanism for transport in strongly anharmonic chains of
oscillators near the atomic limit where all oscillators are decoupled. In this
regime, the motion of most oscillators remains close to integrable, i.e.
quasi-periodic, on very long time scales, while a few chaotic spots move very
slowly and redistribute the energy across the system. The material acquires
several characteristic properties of dynamical glasses: intermittency, jamming
and a drastic reduction of the mobility as a function of the thermodynamical
parameters. We consider both classical and quantum systems, though with more
emphasis on the former, and we discuss also the connections with quenched
disordered systems, which display a similar physics to a large extent.Comment: Review paper. Invited submission to the CRAS (special issue on
Fourier's legacy). 16 pages, 3 figure
A Derivation of Moment Evolution Equations for Linear Open Quantum Systems
Given a linear open quantum system which is described by a Lindblad master
equation, we detail the calculation of the moment evolution equations from this
master equation. We stress that the moment evolution equations are well-known,
but their explicit derivation from the master equation cannot be found in the
literature to the best of our knowledge, and so we provide this derivation for
the interested reader
Dynamical phases for the evolution of the entanglement between two oscillators coupled to the same environment
We study the dynamics of the entanglement between two oscillators that are
initially prepared in a general two-mode Gaussian state and evolve while
coupled to the same environment. In a previous paper we showed that there are
three qualitatively different dynamical phases for the entanglement in the long
time limit: sudden death, sudden death and revival and no-sudden death [Paz &
Roncaglia, Phys. Rev. Lett. 100, 220401 (2008)]. Here we generalize and extend
those results along several directions: We analyze the fate of entanglement for
an environment with a general spectral density providing a complete
characterization of the corresponding phase diagrams for ohmic and sub--ohmic
environments (we also analyze the super-ohmic case showing that for such
environment the expected behavior is rather different). We also generalize
previous studies by considering two different models for the interaction
between the system and the environment (first we analyze the case when the
coupling is through position and then we examine the case where the coupling is
symmetric in position and momentum). Finally, we analyze (both numerically and
analytically) the case of non-resonant oscillators. In that case we show that
the final entanglement is independent of the initial state and may be non-zero
at very low temperatures. We provide a natural interpretation of our results in
terms of a simple quantum optics model.Comment: 18 pages, 13 figure
A Non-critical String (Liouville) Approach to Brain Microtubules: State Vector reduction, Memory coding and Capacity
Microtubule (MT) networks, subneural paracrystalline cytosceletal structures,
seem to play a fundamental role in the neurons. We cast here the complicated MT
dynamics in the form of a -dimensional non-critical string theory, thus
enabling us to provide a consistent quantum treatment of MTs, including
enviromental {\em friction} effects. Quantum space-time effects, as described
by non-critical string theory, trigger then an {\em organized collapse} of the
coherent states down to a specific or {\em conscious state}. The whole process
we estimate to take . The {\em microscopic arrow of
time}, endemic in non-critical string theory, and apparent here in the
self-collapse process, provides a satisfactory and simple resolution to the
age-old problem of how the, central to our feelings of awareness, sensation of
the progression of time is generated. In addition, the complete integrability
of the stringy model for MT we advocate in this work proves sufficient in
providing a satisfactory solution to memory coding and capacity. Such features
might turn out to be important for a model of the brain as a quantum computer.Comment: 70 pages Latex, 4 figures (not included), minor corrections, no
effect on conclusion
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