32 research outputs found
Entropy and Time
The emergence of a direction of time in statistical mechanics from an
underlying time-reversal-invariant dynamics is explained by examining a simple
model. The manner in which time-reversal symmetry is preserved and the role of
initial conditions are emphasized. An extension of the model to finite
temperatures is also discussed.Comment: 9 pages, 8eps figures. To appear in the theme issue of the American
Journal of Physics on Statistical Physic
Width and Magnetic Field Dependence of Transition Temperature in Ultranarrow Superconducting Wires
We calculate the transition temperature in ultranarrow superconducting wires
as a function of wire width, resistance and applied magnetic field. We compare
the results of first-order perturbation theory and the non-perturbative
resummation technique developed by Oreg and Finkel'stein. The latter technique
is found to be superior as it is valid even in the strong disorder limit. In
both cases the predicted additional suppression of the transition temperature
due to the reduced dimensionality is strongly dependent upon the boundary
conditions used. When we use the correct (zero-gradient) boundary conditions,
we find that theory and experiment are consistent, although more experimental
data is required to verify this systematically. We calculate the magnetic field
dependence of the transition temperature for different wire widths and
resistances in the hope that this will be measured in future experiments. The
predicted results have a rich structure - in particular we find a dimensional
crossover which can be tuned by varying either the width of the wire or its
resistance per square.Comment: 12 pages, 1 table, 7 figures. The changes made to the paper are ones
of emphasis. The comparison between theory and experiment has been altered,
and detailed comparisons of various approximations have been omitted,
although the results are summarised in the paper. Much more emphasis has been
placed on the new predictions of the effect of an applied magnetic field on
transition temperature in wires (Figs. 5-7
Decoherence without dissipation?
In a recent article, Ford, Lewis and O'Connell (PRA 64, 032101 (2001))
discuss a thought experiment in which a Brownian particle is subjected to a
double-slit measurement. Analyzing the decay of the emerging interference
pattern, they derive a decoherence rate that is much faster than previous
results and even persists in the limit of vanishing dissipation. This result is
based on the definition of a certain attenuation factor, which they analyze for
short times. In this note, we point out that this attenuation factor captures
the physics of decoherence only for times larger than a certain time t_mix,
which is the time it takes until the two emerging wave packets begin to
overlap. Therefore, the strategy of Ford et al of extracting the decoherence
time from the regime t < t_mix is in our opinion not meaningful. If one
analyzes the attenuation factor for t > t_mix, one recovers familiar behaviour
for the decoherence time; in particular, no decoherence is seen in the absence
of dissipation. The latter conclusion is confirmed with a simple calculation of
the off-diagonal elements of the reduced density matrix.Comment: 8 pages, 4 figure
Estimating errors reliably in Monte Carlo simulations of the Ehrenfest model
Using the Ehrenfest urn model we illustrate the subtleties of error
estimation in Monte Carlo simulations. We discuss how the smooth results of
correlated sampling in Markov chains can fool one's perception of the accuracy
of the data, and show (via numerical and analytical methods) how to obtain
reliable error estimates from correlated samples
The 2-channel Kondo model I: review of experimental evidence for its realization in metal nanoconstrictions
Decoherence in weak localization II: Bethe-Salpeter calculation of Cooperon
This is the second in a series of two papers (I and II) on the problem of
decoherence in weak localization. In paper I, we discussed how the Pauli
principle could be incorporated into an influence functional approach for
calculating the Cooperon propagator and the magnetoconductivity. In the present
paper II, we check and confirm the results so obtained by diagrammatically
setting up a Bethe-Salpeter equation for the Cooperon, which includes
self-energy and vertex terms on an equal footing and is free from both infrared
and ultraviolet divergencies. We then approximately solve this Bethe-Salpeter
equation by the Ansatz C(t) = C^0 (t) e^{-F(t)}, where the decay function F(t)
determines the decoherence rate. We show that in order to obtain a
divergence-free expression for the decay function F(t), it is sufficient to
calculate C^1 (t), the Cooperon in the position-time representation to first
order in the interaction. Paper II is independent of paper I and can be read
without detailed knowledge of the latter.Comment: 18 pages, 3 figures. This is the second of a series of two papers on
decoherence. The first introduces an influence functional approach, the
second obtains equivalent results using a diagrammatic Bethe-Salpeter
equation. For a concise summary of the main results and conclusions, see
Section II of the first pape
The 2-channel Kondo model II: CFT calculation of non-equilibrium conductance through a nanoconstriction containing 2-channel Kondo impurities
Effect of Magnetic Impurities on Suppression of the Transition Temperature in Disordered Superconductors
We calculate the first-order perturbative correction to the transition
temperature in a superconductor with both non-magnetic and magnetic
impurities. We do this by first evaluating the correction to the effective
potential, , and then obtain the first-order correction to the
order parameter, , by finding the minimum of . Setting
finally allows to be evaluated. is now a function of
both the resistance per square, , a measure of the non-magnetic
disorder, and the spin-flip scattering rate, , a measure of the
magnetic disorder. We find that the effective pair-breaking rate per magnetic
impurity is virtually independent of the resistance per square of the film, in
agreement with an experiment of Chervenak and Valles. This conclusion is
supported by both the perturbative calculation, and by a non-perturbative
re-summation technique.Comment: 29 pages, 9 figure