1,394 research outputs found
Topological Schr\"odinger cats: Non-local quantum superpositions of topological defects
Topological defects (such as monopoles, vortex lines, or domain walls) mark
locations where disparate choices of a broken symmetry vacuum elsewhere in the
system lead to irreconcilable differences. They are energetically costly (the
energy density in their core reaches that of the prior symmetric vacuum) but
topologically stable (the whole manifold would have to be rearranged to get rid
of the defect). We show how, in a paradigmatic model of a quantum phase
transition, a topological defect can be put in a non-local superposition, so
that - in a region large compared to the size of its core - the order parameter
of the system is "undecided" by being in a quantum superposition of conflicting
choices of the broken symmetry. We demonstrate how to exhibit such a
"Schr\"odinger kink" by devising a version of a double-slit experiment suitable
for topological defects. Coherence detectable in such experiments will be
suppressed as a consequence of interaction with the environment. We analyze
environment-induced decoherence and discuss its role in symmetry breaking.Comment: 7 pages, 4 figure
Finite-Time Disentanglement via Spontaneous Emission
We show that under the influence of pure vacuum noise two entangled qubits
become completely disentangled in a finite time, and in a specific example we
find the time to be given by times the
usual spontaneous lifetime.Comment: revtex, 4 pages, 2 figure
Decoherence and the rate of entropy production in chaotic quantum systems
We show that for an open quantum system which is classically chaotic (a
quartic double well with harmonic driving coupled to a sea of harmonic
oscillators) the rate of entropy production has, as a function of time, two
relevant regimes: For short times it is proportional to the diffusion
coefficient (fixed by the system--environment coupling strength). For longer
times (but before equilibration) there is a regime where the entropy production
rate is fixed by the Lyapunov exponent. The nature of the transition time
between both regimes is investigated.Comment: Revtex, 4 pages, 3 figures include
A Stepwise Planned Approach to the Solution of Hilbert's Sixth Problem. III : Measurements and von Neumann Projection/Collapse Rule
Supmech, the universal mechanics developed in the previous two papers,
accommodates both quantum and classical mechanics as subdisciplines (a brief
outline is included for completeness); this feature facilitates, in a supmech
based treatment of quantum measurements, an unambiguous treatment of the
apparatus as a quantum system approximated well by a classical one. Taking
explicitly into consideration the fact that observations on the apparatus are
made when it has `settled down after the measurement interaction' and are
restricted to macroscopically distinguishable pointer readings, the unwanted
superpositions of (system + apparatus) states are shown to be suppressed; this
provides a genuinely physics based justification for the (traditionally
\emph{postulated}) von Neumann projection/collapse rule. The decoherence
mechanism brought into play by the stated observational constraints is free
from the objections against the traditional decoherence program.Comment: 29 pages; one section and two references added; results unchange
Multiplicative Noise: Applications in Cosmology and Field Theory
Physical situations involving multiplicative noise arise generically in
cosmology and field theory. In this paper, the focus is first on exact
nonlinear Langevin equations, appropriate in a cosmologica setting, for a
system with one degree of freedom. The Langevin equations are derived using an
appropriate time-dependent generalization of a model due to Zwanzig. These
models are then extended to field theories and the generation of multiplicative
noise in such a context is discussed. Important issues in both the cosmological
and field theoretic cases are the fluctuation-dissipation relations and the
relaxation time scale. Of some importance in cosmology is the fact that
multiplicative noise can substantially reduce the relaxation time. In the field
theoretic context such a noise can lead to a significant enhancement in the
nucleation rate of topological defects.Comment: 21 pages, LaTex, LA-UR-93-210
Oscillating Superfluidity of Bosons in Optical Lattices
We follow up on a recent suggestion by C. Orzel et. al., Science, 291, 2386
(2001), whereby bosons in an optical lattice would be subjected to a sudden
parameter change from the Mott to the superfluid phase. We analyze the Bose
Hubbard model with a modified coherent states path integral which can escribe -
both - phases. The saddle point theory yields collective oscillations of the
uniform superfluid order parameter. These would be seen in time resolved
interference patterns made by the released gas. We calculate the collective
oscillation's damping rate by phason pair emission. In two dimensions the
overdamped region largely overlaps with the quantum critical region.
Measurements of critical dynamics on the Mott side are proposed.Comment: 4 pages 1 eps figures; Final version as appears in PRL. Added
discussion on spontaneous generation of vortice
Parameter scaling in the decoherent quantum-classical transition for chaotic systems
The quantum to classical transition has been shown to depend on a number of
parameters. Key among these are a scale length for the action, , a
measure of the coupling between a system and its environment, , and, for
chaotic systems, the classical Lyapunov exponent, . We propose
computing a measure, reflecting the proximity of quantum and classical
evolutions, as a multivariate function of and searching for
transformations that collapse this hyper-surface into a function of a composite
parameter . We report results
for the quantum Cat Map, showing extremely accurate scaling behavior over a
wide range of parameters and suggest that, in general, the technique may be
effective in constructing universality classes in this transition.Comment: Submitte
Decoherence, Chaos, and the Correspondence Principle
We present evidence that decoherence can produce a smooth
quantum-to-classical transition in nonlinear dynamical systems. High-resolution
tracking of quantum and classical evolutions reveals differences in expectation
values of corresponding observables. Solutions of master equations demonstrate
that decoherence destroys quantum interference in Wigner distributions and
washes out fine structure in classical distributions bringing the two closer
together. Correspondence between quantum and classical expectation values is
also re-established.Comment: 4 pages, 2 figures (color figures embedded at low resolution), uses
RevTeX plus macro (included). Phys. Rev. Lett. (in press
Entropy and Wigner Functions
The properties of an alternative definition of quantum entropy, based on
Wigner functions, are discussed. Such definition emerges naturally from the
Wigner representation of quantum mechanics, and can easily quantify the amount
of entanglement of a quantum state. It is shown that smoothing of the Wigner
function induces an increase in entropy. This fact is used to derive some
simple rules to construct positive definite probability distributions which are
also admissible Wigner functionsComment: 18 page
Objective properties from subjective quantum states: Environment as a witness
We study the emergence of objective properties in open quantum systems. In
our analysis, the environment is promoted from a passive role of reservoir
selectively destroying quantum coherence, to an active role of amplifier
selectively proliferating information about the system. We show that only
preferred pointer states of the system can leave a redundant and therefore
easily detectable imprint on the environment. Observers who--as it is almost
always the case--discover the state of the system indirectly (by probing a
fraction of its environment) will find out only about the corresponding pointer
observable. Many observers can act in this fashion independently and without
perturbing the system: they will agree about the state of the system. In this
operational sense, preferred pointer states exist objectively.Comment: 5 pages, 1 figure, extensive changes, presentation improve
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