17,193 research outputs found
The Exact Ground State of the Frenkel-Kontorova Model with Repeated Parabolic Potential: II. Numerical Treatment
A procedure is described for efficiently finding the ground state energy and
configuration for a Frenkel-Kontorova model in a periodic potential, consisting
of N parabolic segments of identical curvature in each period, through a
numerical solution of the convex minimization problem described in the
preceding paper. The key elements are the use of subdifferentials to describe
the structure of the minimization problem; an intuitive picture of how to solve
it, based on motion of quasiparticles; and a fast linear optimization method
with a reduced memory requirement. The procedure has been tested for N up to
200.Comment: 9 RevTeX pages, using AMS-Fonts (amssym.tex,amssym.def), 3 Postscript
figures, accepted by Phys.Rev.B to be published together with
cond-mat/970722
Choice of Consistent Family, and Quantum Incompatibility
In consistent history quantum theory, a description of the time development
of a quantum system requires choosing a framework or consistent family, and
then calculating probabilities for the different histories which it contains.
It is argued that the framework is chosen by the physicist constructing a
description of a quantum system on the basis of questions he wishes to address,
in a manner analogous to choosing a coarse graining of the phase space in
classical statistical mechanics. The choice of framework is not determined by
some law of nature, though it is limited by quantum incompatibility, a concept
which is discussed using a two-dimensional Hilbert space (spin half particle).
Thus certain questions of physical interest can only be addressed using
frameworks in which they make (quantum mechanical) sense. The physicist's
choice does not influence reality, nor does the presence of choices render the
theory subjective. On the contrary, predictions of the theory can, in
principle, be verified by experimental measurements. These considerations are
used to address various criticisms and possible misunderstandings of the
consistent history approach, including its predictive power, whether it
requires a new logic, whether it can be interpreted realistically, the nature
of ``quasiclassicality'', and the possibility of ``contrary'' inferences.Comment: Minor revisions to bring into conformity with published version.
Revtex 29 pages including 1 page with figure
Correlation inequalities for noninteracting Bose gases
For a noninteracting Bose gas with a fixed one-body Hamiltonian H^0
independent of the number of particles we derive the inequalities _N <
_{N+1}, _N _N _N for i\neq j, \partial
_N/\partial \beta >0 and ^+_N _N. Here N_i is the occupation
number of the ith eigenstate of H^0, \beta is the inverse temperature and the
superscript + refers to adding an extra level to those of H^0. The results
follow from the convexity of the N-particle free energy as a function of N.Comment: a further inequality adde
Quantum chaos in open systems: a quantum state diffusion analysis
Except for the universe, all quantum systems are open, and according to
quantum state diffusion theory, many systems localize to wave packets in the
neighborhood of phase space points. This is due to decoherence from the
interaction with the environment, and makes the quasiclassical limit of such
systems both more realistic and simpler in many respects than the more familiar
quasiclassical limit for closed systems. A linearized version of this theory
leads to the correct classical dynamics in the macroscopic limit, even for
nonlinear and chaotic systems. We apply the theory to the forced, damped
Duffing oscillator, comparing the numerical results of the full and linearized
equations, and argue that this can be used to make explicit calculations in the
decoherent histories formalism of quantum mechanics.Comment: 18 pages standard LaTeX + 9 figures; extensively trimmed; to appear
in J. Phys.
Ultra-fine beryllium powder by amalgam process Progress report, period ending 31 Oct. 1966
Metallurgical evaluation of beryllium powdered metal, and electron microscope studies of agglomerate particle size
Decoherence of Histories and Hydrodynamic Equations for a Linear Oscillator Chain
We investigate the decoherence of histories of local densities for linear
oscillators models. It is shown that histories of local number, momentum and
energy density are approximately decoherent, when coarse-grained over
sufficiently large volumes. Decoherence arises directly from the proximity of
these variables to exactly conserved quantities (which are exactly decoherent),
and not from environmentally-induced decoherence. We discuss the approach to
local equilibrium and the subsequent emergence of hydrodynamic equations for
the local densities.Comment: 37 pages, RevTe
Types of quantum information
Quantum, in contrast to classical, information theory, allows for different
incompatible types (or species) of information which cannot be combined with
each other. Distinguishing these incompatible types is useful in understanding
the role of the two classical bits in teleportation (or one bit in one-bit
teleportation), for discussing decoherence in information-theoretic terms, and
for giving a proper definition, in quantum terms, of ``classical information.''
Various examples (some updating earlier work) are given of theorems which
relate different incompatible kinds of information, and thus have no
counterparts in classical information theory.Comment: Minor changes so as to agree with published versio
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