123 research outputs found
On gauge invariance and the path integral
Using a gauge covariant operator technique we deduce the path integral for a
charged particle in a stationary magnetic field, verifying the "midpoint rule"
for the discrete form of the interaction term with the vector potential.Comment: 4 pages, Latex, IF-UFRJ-9
Violation of the zeroth law of thermodynamics for a non-ergodic interaction
The phenomenon described by our title should surprise no one. What may be
surprising though is how easy it is to produce a quantum system with this
feature; moreover, that system is one that is often used for the purpose of
showing how systems equilibrate. The violation can be variously manifested. In
our detailed example, bringing a detuned 2-level system into contact with a
monochromatic reservoir does not cause it to relax to the reservoir
temperature; rather, the system acquires the reservoir's
level-occupation-ratio
Clusters from higher order correlations
Given a set of variables and the correlations among them, we develop a method
for finding clustering among the variables. The method takes advantage of
information implicit in higher-order (not just pairwise) correlations. The idea
is to define a Potts model whose energy is based on the correlations. Each
state of this model is a partition of the variables and a Monte Carlo method is
used to identify states of lowest energy, those most consistent with the
correlations. A set of the 100 or so lowest such partitions is then used to
construct a stochastic dynamics (using the adjacency matrix of each partition)
whose observable representation gives the clustering. Three examples are
studied. For two of them the 3 order correlations are significant
for getting the clusters right. The last of these is a toy model of a
biological system in which the joint action of several genes or proteins is
necessary to accomplish a given process
Berry phase from a quantum Zeno effect
We exhibit a specific implementation of the creation of geometrical phase
through the state-space evolution generated by the dynamic quantum Zeno effect.
That is, a system is guided through a closed loop in Hilbert space by means a
sequence of closely spaced projections leading to a phase difference with
respect to the original state. Our goal is the proposal of a specific
experimental setup in which this phase could be created and observed. To this
end we study the case of neutron spin, examine the practical aspects of
realizing the "projections," and estimate the difference between the idealized
projections and the experimental implementation.Comment: 13 pages, 2 figure
Structure and time-dependence of quantum breathers
Quantum states of a discrete breather are studied in two ways. One method
involves numerical diagonalization of the Hamiltonian, the other uses the path
integral to examine correlations in the eigenstates. In both cases only the
central nonlinearity is retained. To reduce truncation effects in the numerical
diagonalization, a basis is used that involves a quadratic local mode. A
similar device is used in the path integral method for deducing localization.
Both approaches lead to the conclusion that aside from quantum tunneling the
quantized discrete breather is stable.Comment: 33 pages, 20 figures, to appear in J. Chem. Phy
Wave-Packet Scattering Without Kinematic Entanglement: Convergence of Expectation Values
A feynman path integral representation for elastic wave scattering by anisotropic weakly perturbations
We write a space-time Feynman path integral representation for scattered
elastic wave fields from a weakly compact supported anisotropic
non-homogeneity.Replacement by a new version where We (I!) propose a new
tomographic inversion methodology based solely in the wave sampling of the Ray
paths through Monte Carlo path integral sampling Holding thus great
potentiality for Navy's advanced Sonar detection .Comment: 8 page
Spectral properties of zero temperature dynamics in a model of a compacting granular column
The compacting of a column of grains has been studied using a one-dimensional
Ising model with long range directed interactions in which down and up spins
represent orientations of the grain having or not having an associated void.
When the column is not shaken (zero 'temperature') the motion becomes highly
constrained and under most circumstances we find that the generator of the
stochastic dynamics assumes an unusual form: many eigenvalues become
degenerate, but the associated multi-dimensional invariant spaces have but a
single eigenvector. There is no spectral expansion and a Jordan form must be
used. Many properties of the dynamics are established here analytically; some
are not. General issues associated with the Jordan form are also taken up.Comment: 34 pages, 4 figures, 3 table
"Explicit Time-Dependent Schrödinger Propagators" by Bernard Gaveau and Lawrence S. Schulman
Does a Computer have an Arrow of Time?
In [Sch05a], it is argued that Boltzmann's intuition, that the psychological
arrow of time is necessarily aligned with the thermodynamic arrow, is correct.
Schulman gives an explicit physical mechanism for this connection, based on the
brain being representable as a computer, together with certain thermodynamic
properties of computational processes. [Haw94] presents similar, if briefer,
arguments. The purpose of this paper is to critically examine the support for
the link between thermodynamics and an arrow of time for computers. The
principal arguments put forward by Schulman and Hawking will be shown to fail.
It will be shown that any computational process that can take place in an
entropy increasing universe, can equally take place in an entropy decreasing
universe. This conclusion does not automatically imply a psychological arrow
can run counter to the thermodynamic arrow. Some alternative possible explana-
tions for the alignment of the two arrows will be briefly discussed.Comment: 31 pages, no figures, publication versio
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