225 research outputs found
Conservation Laws in the Quantum Mechanics of Closed Systems
We investigate conservation laws in the quantum mechanics of closed systems.
We review an argument showing that exact decoherence implies the exact
conservation of quantities that commute with the Hamiltonian including the
total energy and total electric charge. However, we also show that decoherence
severely limits the alternatives which can be included in sets of histories
which assess the conservation of these quantities when they are not coupled to
a long-range field arising from a fundamental symmetry principle. We then
examine the realistic cases of electric charge coupled to the electromagnetic
field and mass coupled to spacetime curvature and show that when alternative
values of charge and mass decohere, they always decohere exactly and are
exactly conserved as a consequence of their couplings to long-range fields.
Further, while decohering histories that describe fluctuations in total charge
and mass are also subject to the limitations mentioned above, we show that
these do not, in fact, restrict {\it physical} alternatives and are therefore
not really limitations at all.Comment: 22 pages, report UCSBTH-94-4, LA-UR-94-2101, CGPG-94/10-
Decoherence and classical predictability of phase space histories
We consider the decoherence of phase space histories in a class of quantum
Brownian motion models, consisting of a particle moving in a potential
in interaction with a heat bath at temperature and dissipation gamma, in
the Markovian regime. The evolution of the density operator for this open
system is thus described by a non-unitary master equation. The phase space
histories of the system are described by a class of quasiprojectors.
Generalizing earlier results of Hagedorn and Omn\`es, we show that a phase
space projector onto a phase space cell is approximately evolved under
the master equation into another phase space projector onto the classical
dissipative evolution of , and with a certain amount of degradation due
to the noise produced by the environment. We thus show that histories of phase
space samplings approximately decohere, and that the probabilities for these
histories are peaked about classical dissipative evolution, with a width of
peaking depending on the size of the noise.Comment: 34 pages, LATEX, revised version to avoid LATEX error
Topos Theory and Consistent Histories: The Internal Logic of the Set of all Consistent Sets
A major problem in the consistent-histories approach to quantum theory is
contending with the potentially large number of consistent sets of history
propositions. One possibility is to find a scheme in which a unique set is
selected in some way. However, in this paper we consider the alternative
approach in which all consistent sets are kept, leading to a type of `many
world-views' picture of the quantum theory. It is shown that a natural way of
handling this situation is to employ the theory of varying sets (presheafs) on
the space \B of all Boolean subalgebras of the orthoalgebra \UP of history
propositions. This approach automatically includes the feature whereby
probabilistic predictions are meaningful only in the context of a consistent
set of history propositions. More strikingly, it leads to a picture in which
the `truth values', or `semantic values' of such contextual predictions are not
just two-valued (\ie true and false) but instead lie in a larger logical
algebra---a Heyting algebra---whose structure is determined by the space \B
of Boolean subalgebras of \UP.Comment: 28 pages, LaTe
A quantum trajectory description of decoherence
A complete theoretical treatment in many problems relevant to physics,
chemistry, and biology requires considering the action of the environment over
the system of interest. Usually the environment involves a relatively large
number of degrees of freedom, this making the problem numerically intractable
from a purely quantum-mechanical point of view. To overcome this drawback, a
new class of quantum trajectories is proposed. These trajectories, based on the
same grounds as Bohmian ones, are solely associated to the system reduced
density matrix, since the evolution of the environment degrees of freedom is
not considered explicitly. Within this approach, environment effects come into
play through a time-dependent damping factor that appears in the system
equations of motion. Apart from their evident computational advantage, this
type of trajectories also results very insightful to understand the system
decoherence. In particular, here we show the usefulness of these trajectories
analyzing decoherence effects in interference phenomena, taking as a working
model the well-known double-slit experiment.Comment: 8 pages, 3 figure
Decoherence of Hydrodynamic Histories: A Simple Spin Model
In the context of the decoherent histories approach to the quantum mechanics
of closed systems, Gell-Mann and Hartle have argued that the variables
typically characterizing the quasiclassical domain of a large complex system
are the integrals over small volumes of locally conserved densities --
hydrodynamic variables. The aim of this paper is to exhibit some simple models
in which approximate decoherence arises as a result of local conservation. We
derive a formula which shows the explicit connection between local conservation
and approximate decoherence. We then consider a class of models consisting of a
large number of weakly interacting components, in which the projections onto
local densities may be decomposed into projections onto one of two alternatives
of the individual components. The main example we consider is a one-dimensional
chain of locally coupled spins, and the projections are onto the total spin in
a subsection of the chain. We compute the decoherence functional for histories
of local densities, in the limit when the number of components is very large.
We find that decoherence requires two things: the smearing volumes must be
sufficiently large to ensure approximate conservation, and the local densities
must be partitioned into sufficiently large ranges to ensure protection against
quantum fluctuations.Comment: Standard TeX, 36 pages + 3 figures (postscript) Revised abstract and
introduction. To appear in Physical Review
Probability sum rules and consistent quantum histories
An example shows that weak decoherence is more restrictive than the minimal
logical decoherence structure that allows probabilities to be used consistently
for quantum histories. The probabilities in the sum rules that define minimal
decoherence are all calculated by using a projection operator to describe each
possibility for the state at each time. Weak decoherence requires more sum
rules. They bring in additional variables, that require different measurements
and a different way to calculate probabilities, and raise questions of
operational meaning. The example shows that extending the linearly positive
probability formula from weak to minimal decoherence gives probabilities that
are different from those calculated in the usual way using the Born and von
Neumann rules and a projection operator at each time.Comment: 14 pages, 2 figures, added discussion of tensor-product histories in
response to Physics Letters A referee, corrected typ
How Phase Transitions induce classical behaviour
We continue the analysis of the onset of classical behaviour in a scalar
field after a continuous phase transition, in which the system-field, the long
wavelength order parameter of the model, interacts with an environment, of its
own short-wavelength modes and other fields, neutral and charged, with which it
is expected to interact. We compute the decoherence time for the system-field
modes from the master equation and directly from the decoherence functional
(with identical results). In simple circumstances the order parameter field is
classical by the time the transition is complete.Comment: 10 pages, 1 figure: To be published in the International Journal of
Theoretical Physics (2005) as part of the Proceedings of the "Peyresq Physics
9" meeting (2004) on "Micro and Macro structures of spacetime",ed. E.
Verdague
A model of quantum reduction with decoherence
The problem of reduction (wave packet reduction) is reexamined under two
simple conditions: Reduction is a last step completing decoherence. It acts in
commonplace circumstances and should be therefore compatible with the
mathematical frame of quantum field theory and the standard model.
These conditions lead to an essentially unique model for reduction.
Consistency with renormalization and time-reversal violation suggest however a
primary action in the vicinity of Planck's length. The inclusion of quantum
gravity and the uniqueness of space-time point moreover to generalized quantum
theory, first proposed by Gell-Mann and Hartle, as a convenient framework for
developing this model into a more complete theory.Comment: 20 pages. To be published in Physical Review
Tests of Basic Quantum Mechanics in Oscillation Experiments
According to standard quantum theory, the time evolution operator of a
quantum system is independent of the state of the system. One can, however,
consider systems in which this is not the case: the evolution operator may
depend on the density operator itself. The presence of such modifications of
quantum theory can be tested in long baseline oscillation experiments.Comment: 8 pages, LaTeX; no macros neede
Unitarity and Causality in Generalized Quantum Mechanics for Non-Chronal Spacetimes
Spacetime must be foliable by spacelike surfaces for the quantum mechanics of
matter fields to be formulated in terms of a unitarily evolving state vector
defined on spacelike surfaces. When a spacetime cannot be foliated by spacelike
surfaces, as in the case of spacetimes with closed timelike curves, a more
general formulation of quantum mechanics is required. In such generalizations
the transition matrix between alternatives in regions of spacetime where states
{\it can} be defined may be non-unitary. This paper describes a generalized
quantum mechanics whose probabilities consistently obey the rules of
probability theory even in the presence of such non-unitarity. The usual notion
of state on a spacelike surface is lost in this generalization and familiar
notions of causality are modified. There is no signaling outside the light
cone, no non-conservation of energy, no ``Everett phones'', and probabilities
of present events do not depend on particular alternatives of the future.
However, the generalization is acausal in the sense that the existence of
non-chronal regions of spacetime in the future can affect the probabilities of
alternatives today. The detectability of non-unitary evolution and violations
of causality in measurement situations are briefly considered. The evolution of
information in non-chronal spacetimes is described.Comment: 40pages, UCSBTH92-0
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