577 research outputs found
Preferred Basis in a Measurement Process
The effect of decoherence is analysed for a free particle, interacting with
an environment via a dissipative coupling. The interaction between the particle
and the environment occurs by a coupling of the position operator of the
particle with the environmental degrees of freedom. By examining the exact
solution of the density matrix equation one finds that the density matrix
becomes completely diagonal in momentum with time while the position space
density matrix remains nonlocal. This establishes the momentum basis as the
emergent 'preferred basis' selected by the environment which is contrary to the
general expectation that position should emerge as the preferred basis since
the coupling with the environment is via the position coordinate.Comment: Standard REVTeX format, 10 pages of output. Accepted for publication
in Phys. Rev
Decoherence, Chaos, and the Second Law
We investigate implications of decoherence for quantum systems which are
classically chaotic. We show that, in open systems, the rate of von Neumann
entropy production quickly reaches an asymptotic value which is: (i)
independent of the system-environment coupling, (ii) dictated by the dynamics
of the system, and (iii) dominated by the largest Lyapunov exponent. These
results shed a new light on the correspondence between quantum and classical
dynamics as well as on the origins of the ``arrow of time.''Comment: 13 Pages, 2 Figures available upon request, Preprint LA-UR-93-, The
new version contains the text, the previous one had only the Macros: sorry
Following a "Collapsing" Wavefunction
I study the quantum mechanics of a spin interacting with an ``apparatus''.
Although the evolution of the whole system is unitary, the spin evolution is
not. The system is chosen so that the spin exhibits loss of quantum coherence,
or ``wavefunction collapse'', of the sort usually associated with a quantum
measurement. The system is analyzed from the point of view of the spin density
matrix (or ``Schmidt paths''), and also using the consistent histories
approach. These two points of view are contrasted with each other. Connections
between the results and the form of the Hamiltonian are discussed in detail.Comment: 30 pages, plain LaTex, 3 figures in a separate uuencoded fil
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
Decoherence of a Pointer by a Gas Reservoir
We study the effect of the environment on the process of the measurement of a
state of a microscopic spin half system. The measuring apparatus is a heavy
particle, whose center of mass coordinates can be considered at the end of the
measurement as approximately classical, and thus can be used as a pointer. The
state of the pointer, which is the result of its interaction with the spin, is
transformed into a mixed state by the coupling of the pointer to the
environment. The environment is considered to be a gas reservoir, whose
particles interact with the pointer. This results in a Fokker-Planck equation
for the reduced density matrix of the pointer. The solution of the equation
shows that the quantum coherences, which are characteristic to the entangled
state between the probabilities to find the pointer in one of two positions,
decays exponentially fast in time. We calculate the exponential decay function
of this decoherence effect, and express it in terms of the parameters of the
model.Comment: 41 pages, 1 figur
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
Phase Diffusion in Quantum Dissipative Systems
We study the dynamics of the quantum phase distribution associated with the
reduced density matrix of a system for a number of situations of practical
importance, as the system evolves under the influence of its environment,
interacting via a quantum nondemoliton type of coupling, such that there is
decoherence without dissipation, as well as when it interacts via a dissipative
interaction, resulting in decoherence as well as dissipation. The system is
taken to be either a two-level atom (or equivalently, a spin-1/2 system) or a
harmonic oscillator, and the environment is modeled as a bath of harmonic
oscillators, starting out in a squeezed thermal state. The impact of the
different environmental parameters on the dynamics of the quantum phase
distribution for the system starting out in various initial states, is
explicitly brought out. An interesting feature that emerges from our work is
that the relationship between squeezing and temperature effects depends on the
type of system-bath interaction. In the case of quantum nondemolition type of
interaction, squeezing and temperature work in tandem, producing a diffusive
effect on the phase distribution. In contrast, in case of a dissipative
interaction, the influence of temperature can be counteracted by squeezing,
which manifests as a resistence to randomization of phase. We make use of the
phase distributions to bring out a notion of complementarity in atomic systems.
We also study the dispersion of the phase using the phase distributions
conditioned on particular initial states of the system.Comment: Accepted for publication in Physical Review A; changes in section V;
20 pages, 12 figure
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
Decoherence at zero temperature
Most discussions of decoherence in the literature consider the
high-temperature regime but it is also known that, in the presence of
dissipation, decoherence can occur even at zero temperature. Whereas most
previous investigations all assumed initial decoupling of the quantum system
and bath, we consider that the system and environment are entangled at all
times. Here, we discuss decoherence for a free particle in an initial
Schr\"{o}dinger cat state. Memory effects are incorporated by use of the single
relaxation time model (since the oft-used Ohmic model does not give physically
correct results)
Decoherence due to three-body loss and its effect on the state of a Bose-Einstein condensate
A Born-Markov master equation is used to investigate the decoherence of the
state of a macroscopically occupied mode of a cold atom trap due to three-body
loss. In the large number limit only coherent states remain pure for times
longer than the decoherence time: the time it takes for just three atoms to be
lost from the trap. For large numbers of atoms (N>10^4) the decoherence time is
found to be much faster than the phase collapse time caused by intra-trap
atomic collisions
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