20,262 research outputs found
Conductance calculations for quantum wires and interfaces: mode matching and Green functions
Landauer's formula relates the conductance of a quantum wire or interface to
transmission probabilities. Total transmission probabilities are frequently
calculated using Green function techniques and an expression first derived by
Caroli. Alternatively, partial transmission probabilities can be calculated
from the scattering wave functions that are obtained by matching the wave
functions in the scattering region to the Bloch modes of ideal bulk leads. An
elegant technique for doing this, formulated originally by Ando, is here
generalized to any Hamiltonian that can be represented in tight-binding form. A
more compact expression for the transmission matrix elements is derived and it
is shown how all the Green function results can be derived from the mode
matching technique. We illustrate this for a simple model which can be studied
analytically, and for an Fe|vacuum|Fe tunnel junction which we study using
first-principles calculations.Comment: 14 pages, 5 figure
A coincidence point theorem for multi-valued contractions
A coincidence point theorem for two pairs of mappings is proved
Thermodynamic properties of spin-1/2 transverse XY chain with Dzyaloshinskii-Moriya interaction: Exact solution for correlated Lorentzian disorder
We extend the consideration of the spin-1/2 transverse XY chain with
correlated Lorentzian disorder (Phys. Rev. B {\bf 55,} 14298 (1997)) for the
case of additional Dzyaloshinskii-Moriya interspin interaction. It is shown how
the averaged density of states can be calculated exactly. Results are presented
for the density of states and the transverse magnetization.Comment: 2 figure
Localization of thermal packets and metastable states in Sinai model
We consider the Sinai model describing a particle diffusing in a 1D random
force field. As shown by Golosov, this model exhibits a strong localization
phenomenon for the thermal packet: the disorder average of the thermal
distribution of the relative distance y=x-m(t), with respect to the
(disorder-dependent) most probable position m(t), converges in the limit of
infinite time towards a distribution P(y). In this paper, we revisit this
question of the localization of the thermal packet. We first generalize the
result of Golosov by computing explicitly the joint asymptotic distribution of
relative position y=x(t)-m(t) and relative energy u=U(x(t))-U(m(t)) for the
thermal packet. Next, we compute in the infinite-time limit the localization
parameters Y_k, representing the disorder-averaged probabilities that k
particles of the thermal packet are at the same place, and the correlation
function C(l) representing the disorder-averaged probability that two particles
of the thermal packet are at a distance l from each other. We moreover prove
that our results for Y_k and C(l) exactly coincide with the thermodynamic limit
of the analog quantities computed for independent particles at equilibrium in a
finite sample of length L. Finally, we discuss the properties of the
finite-time metastable states that are responsible for the localization
phenomenon and compare with the general theory of metastable states in glassy
systems, in particular as a test of the Edwards conjecture.Comment: 17 page
Depinning with dynamic stress overshoots: A hybrid of critical and pseudohysteretic behavior
A model of an elastic manifold driven through a random medium by an applied
force F is studied focussing on the effects of inertia and elastic waves, in
particular {\it stress overshoots} in which motion of one segment of the
manifold causes a temporary stress on its neighboring segments in addition to
the static stress. Such stress overshoots decrease the critical force for
depinning and make the depinning transition hysteretic. We find that the steady
state velocity of the moving phase is nevertheless history independent and the
critical behavior as the force is decreased is in the same universality class
as in the absence of stress overshoots: the dissipative limit which has been
studied analytically. To reach this conclusion, finite-size scaling analyses of
a variety of quantities have been supplemented by heuristic arguments.
If the force is increased slowly from zero, the spectrum of avalanche sizes
that occurs appears to be quite different from the dissipative limit. After
stopping from the moving phase, the restarting involves both fractal and
bubble-like nucleation. Hysteresis loops can be understood in terms of a
depletion layer caused by the stress overshoots, but surprisingly, in the limit
of very large samples the hysteresis loops vanish. We argue that, although
there can be striking differences over a wide range of length scales, the
universality class governing this pseudohysteresis is again that of the
dissipative limit. Consequences of this picture for the statistics and dynamics
of earthquakes on geological faults are briefly discussed.Comment: 43 pages, 57 figures (yes, that's a five followed by a seven), revte
Quantum Collective Creep: a Quasiclassical Langevin Equation Approach
The dynamics of an elastic medium driven through a random medium by a small
applied force is investigated in the low-temperature limit where quantum
fluctuations dominate. The motion proceeds via tunneling of segments of the
manifold through barriers whose size grows with decreasing driving force .
In the limit of small drive, at zero-temperature the average velocity has the
form . For strongly
dissipative dynamics, there is a wide range of forces where the dissipation
dominates and the velocity--force characteristics takes the form
, with the
action for a typical tunneling event, the force dependence being determined by
the roughness exponent of the -dimensional manifold. This result
agrees with the one obtained via simple scaling considerations. Surprisingly,
for asymptotically low forces or for the case when the massive dynamics is
dominant, the resulting quantum creep law is {\it not} of the usual form with a
rate proportional to ; rather we find corresponding to and , with the naive scaling exponent for massive
dynamics. Our analysis is based on the quasi-classical Langevin approximation
with a noise obeying the quantum fluctuation--dissipation theorem. The many
space and time scales involved in the dynamics are treated via a functional
renormalization group analysis related to that used previously to treat the
classical dynamics of such systems. Various potential difficulties with these
approaches to the multi-scale dynamics -- both classical and quantum -- are
raised and questions about the validity of the results are discussed.Comment: RevTeX, 30 pages, 8 figures inserte
Gas-liquid critical point in ionic fluids
Based on the method of collective variables we develop the statistical field
theory for the study of a simple charge-asymmetric primitive model (SPM).
It is shown that the well-known approximations for the free energy, in
particular DHLL and ORPA, can be obtained within the framework of this theory.
In order to study the gas-liquid critical point of SPM we propose the method
for the calculation of chemical potential conjugate to the total number density
which allows us to take into account the higher order fluctuation effects. As a
result, the gas-liquid phase diagrams are calculated for . The results
demonstrate the qualitative agreement with MC simulation data: critical
temperature decreases when increases and critical density increases rapidly
with .Comment: 18 pages, 1 figur
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