1,550 research outputs found
Generalized Gaussian wave packet dynamics: Integrable and Chaotic Systems
The ultimate semiclassical wave packet propagation technique is a complex,
time-dependent WBK method known as generalized Gaussian wave packet dynamics
(GGWPD). It requires overcoming many technical difficulties in order to be
carried out fully in practice. In its place roughly twenty years ago,
linearized wave packet dynamics was generalized to methods that include sets of
off-center, real trajectories for both classically integrable and chaotic
dynamical systems that completely capture the dynamical transport. The
connections between those methods and GGWPD are developed in a way that enables
a far more practical implementation of GGWPD. The generally complex saddle
point trajectories at its foundation are found using a multi-dimensional,
Newton-Raphson root search method that begins with the set of off-center, real
trajectories. This is possible because there is a one-to-one correspondence.
The neighboring trajectories associated with each off-center, real trajectory
form a path that crosses a unique saddle; there are exceptions which are
straightforward to identify. The method is applied to the kicked rotor to
demonstrate the accuracy improvement as a function of that comes with
using the saddle point trajectories.Comment: 18 pages, 9 figures, corrected a typo in Eqs. 29,3
Exact solution of the Hu-Paz-Zhang master equation
The Hu-Paz-Zhang equation is a master equation for an oscillator coupled to a
linear passive bath. It is exact within the assumption that the oscillator and
bath are initially uncoupled . Here an exact general solution is obtained in
the form of an expression for the Wigner function at time t in terms of the
initial Wigner function. The result is applied to the motion of a Gaussian wave
packet and to that of a pair of such wave packets. A serious divergence arising
from the assumption of an initially uncoupled state is found to be due to the
zero-point oscillations of the bath and not removed in a cutoff model. As a
consequence, worthwhile results for the equation can only be obtained in the
high temperature limit, where zero-point oscillations are neglected. In that
limit closed form expressions for wave packet spreading and attenuation of
coherence are obtained. These results agree within a numerical factor with
those appearing in the literature, which apply for the case of a particle at
zero temperature that is suddenly coupled to a bath at high temperature. On the
other hand very different results are obtained for the physically consistent
case in which the initial particle temperature is arranged to coincide with
that of the bath
Quantum State Diffusion, Density Matrix Diagonalization and Decoherent Histories: A Model
We analyse the quantum evolution of a particle moving in a potential in
interaction with an environment of harmonic oscillators in a thermal state,
using the quantum state diffusion (QSD) picture of Gisin and Percival, in which
one associates the usual Markovian master equation for the density operator
with a class of stochastic non-linear Schr\"odinger equations. We find
stationary solutions to the Ito equation which are Gaussians, localized around
a point in phase space undergoing classical Brownian motion. We show that every
initial state approaches these stationary solutions in the long time limit. We
recover the density operator corresponding to these solutions, and thus show,
for this particular model, that the QSD picture effectively supplies a
prescription for approximately diagonalizing the density operator in a basis of
phase space localized states. The rate of localization is related to the
decoherence time, and also to the timescale on which thermal and quantum
fluctuations become comparable. We use these results to exemplify the general
connection between the QSD picture and the decoherent histories approach.Comment: 32 pages, plain Tex
Neutrino oscillations: Entanglement, energy-momentum conservation and QFT
We consider several subtle aspects of the theory of neutrino oscillations
which have been under discussion recently. We show that the -matrix
formalism of quantum field theory can adequately describe neutrino oscillations
if correct physics conditions are imposed. This includes space-time
localization of the neutrino production and detection processes. Space-time
diagrams are introduced, which characterize this localization and illustrate
the coherence issues of neutrino oscillations. We discuss two approaches to
calculations of the transition amplitudes, which allow different physics
interpretations: (i) using configuration-space wave packets for the involved
particles, which leads to approximate conservation laws for their mean energies
and momenta; (ii) calculating first a plane-wave amplitude of the process,
which exhibits exact energy-momentum conservation, and then convoluting it with
the momentum-space wave packets of the involved particles. We show that these
two approaches are equivalent. Kinematic entanglement (which is invoked to
ensure exact energy-momentum conservation in neutrino oscillations) and
subsequent disentanglement of the neutrinos and recoiling states are in fact
irrelevant when the wave packets are considered. We demonstrate that the
contribution of the recoil particle to the oscillation phase is negligible
provided that the coherence conditions for neutrino production and detection
are satisfied. Unlike in the previous situation, the phases of both neutrinos
from decay are important, leading to a realization of the
Einstein-Podolsky-Rosen paradox.Comment: 30 pages, 3 eps figures; presentation improved, clarifications added.
To the memory of G.T. Zatsepi
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