40,056 research outputs found
Metastability in stochastic dynamics of disordered mean-field models
We study a class of Markov chains that describe reversible stochastic
dynamics of a large class of disordered mean field models at low temperatures.
Our main purpose is to give a precise relation between the metastable time
scales in the problem to the properties of the rate functions of the
corresponding Gibbs measures. We derive the analog of the Wentzell-Freidlin
theory in this case, showing that any transition can be decomposed, with
probability exponentially close to one, into a deterministic sequence of
``admissible transitions''. For these admissible transitions we give upper and
lower bounds on the expected transition times that differ only by a constant.
The distribution rescaled transition times are shown to converge to the
exponential distribution. We exemplify our results in the context of the random
field Curie-Weiss model.Comment: 73pp, AMSTE
Metastability and low lying spectra in reversible Markov chains
We study a large class of reversible Markov chains with discrete state space
and transition matrix . We define the notion of a set of {\it metastable
points} as a subset of the state space \G_N such that (i) this set is reached
from any point x\in \G_N without return to x with probability at least ,
while (ii) for any two point x,y in the metastable set, the probability
to reach y from x without return to x is smaller than
. Under some additional non-degeneracy assumption, we show
that in such a situation: \item{(i)} To each metastable point corresponds a
metastable state, whose mean exit time can be computed precisely. \item{(ii)}
To each metastable point corresponds one simple eigenvalue of which is
essentially equal to the inverse mean exit time from this state. The
corresponding eigenfunctions are close to the indicator function of the support
of the metastable state. Moreover, these results imply very sharp uniform
control of the deviation of the probability distribution of metastable exit
times from the exponential distribution.Comment: 44pp, AMSTe
Quantum theory of large amplitude collective motion and the Born-Oppenheimer method
We study the quantum foundations of a theory of large amplitude collective
motion for a Hamiltonian expressed in terms of canonical variables. In previous
work the separation into slow and fast (collective and non-collective)
variables was carried out without the explicit intervention of the Born
Oppenheimer approach. The addition of the Born Oppenheimer assumption not only
provides support for the results found previously in leading approximation, but
also facilitates an extension of the theory to include an approximate
description of the fast variables and their interaction with the slow ones.
Among other corrections, one encounters the Berry vector and scalar potential.
The formalism is illustrated with the aid of some simple examples, where the
potentials in question are actually evaluated and where the accuracy of the
Born Oppenheimer approximation is tested. Variational formulations of both
Hamiltonian and Lagrangian type are described for the equations of motion for
the slow variables.Comment: 29 pages, 1 postscript figure, preprint no UPR-0085NT. Latex + epsf
styl
Quantitative MRFM characterization of the autonomous and forced dynamics in a spin transfer nano-oscillator
Using a magnetic resonance force microscope (MRFM), the power emitted by a
spin transfer nano-oscillator consisting of a normally magnetized PyCuPy
circular nanopillar is measured both in the autonomous and forced regimes. From
the power behavior in the subcritical region of the autonomous dynamics, one
obtains a quantitative measurement of the threshold current and of the noise
level. Their field dependence directly yields both the spin torque efficiency
acting on the thin layer and the nature of the mode which first
auto-oscillates: the lowest energy, spatially most uniform spin-wave mode. From
the MRFM behavior in the forced dynamics, it is then demonstrated that in order
to phase-lock this auto-oscillating mode, the external source must have the
same spatial symmetry as the mode profile, i.e., a uniform microwave field must
be used rather than a microwave current flowing through the nanopillar
Photoinduced Fano-resonance of coherent phonons in zinc
Utilizing femtosecond optical pump-probe technique, we have studied transient
Fano-resonance in zinc. At high excitation levels the Fourier spectrum of the
coherent E phonon exhibits strongly asymmetric line shape, which is well
modeled by the Fano function. The Fano parameter (1/Q) was found to be strongly
excitation fluence dependent while depending weakly on the initial lattice
temperature. We attribute the origin of the Fano-resonance to the coupling of
coherent phonon to the electronic continuum, with their transition
probabilities strongly renormalized in the vicinity of the photoinduced
structural transition.Comment: 5 pages, 3 figures, to be published in Physical Review
Transient Nucleation near the Mean-Field Spinodal
Nucleation is considered near the pseudospinodal in a one-dimensional
model with a non-conserved order parameter and long-range
interactions. For a sufficiently large system or a system with slow relaxation
to metastable equilibrium, there is a non-negligible probability of nucleation
occurring before reaching metastable equilibrium. This process is referred to
as transient nucleation. The critical droplet is defined to be the
configuration of maximum likelihood that is dynamically balanced between the
metastable and stable wells. Time-dependent droplet profiles and nucleation
rates are derived, and theoretical results are compared to computer simulation.
The analysis reveals a distribution of nucleation times with a distinct peak
characteristic of a nonstationary nucleation rate. Under the quench conditions
employed, transient critical droplets are more compact than the droplets found
in metastable equilibrium simulations and theoretical predictions.Comment: 7 Pages, 5 Figure
A unitarized model of inclusive and diffractive DIS with Q2-evolution
We discuss the interplay of low-x physics and QCD scaling violations by
extending the unified approach describing inclusive structure functions and
diffractive production in interactions proposed in previous papers,
to large values of Q2. We describe the procedure of extracting, from the
non-perturbative model, initial conditions for the QCD evolution that respect
unitarity. Assuming Regge factorization of the diffractive structure function,
a similar procedure is proposed for the calculation of hard diffraction. The
results are in good agreement with experimental data on the proton structure
function and the most recent data on the reduced diffractive cross
section, x_P \sigma_r^{\D(3)}. Predictions for both and are
presented in a wide kinematical range and compared to calculations within
high-energy QCD.Comment: 22 pages, 12 figure
Antivortices due to competing orbital and paramagnetic pair-breaking effects
Thermodynamically stable vortex-antivortex structures in a
quasi-two-dimensional superconductor in a tilted magnetic field are predicted.
For this geometry, both orbital and spin pair-breaking effects exist, with
their relative strength depending on the tilt angle \Theta. The spectrum of
possible states contains as limits the ordinary vortex state (for large \Theta)
and the Fulde-Ferrell-Larkin-Ovchinnikov state (for \Theta=0). The
quasiclassical equations are solved near H_{c2} for arbitrary \Theta and it is
shown that stable states with coexisting vortices and antivortices exist in a
small interval close to \Theta=0. The results are compared with recent
predictions of antivortices in mesoscopic samples.Comment: 11 pages, 3 figure
Non-resonant Raman response of inhomogeneous structures in the electron doped Hubbard model
We calculate the non-resonant Raman response, the single particle spectra and
the charge-spin configuration for the electron doped Hubbard model using
unrestricted Hartree-Fock calculations. We discuss the similarities and
differences in the response of homogeneous versus inhomogeneous structures.
Metallic antiferromagnetism dominates in a large region of the phase
diagram but at high values of the on-site interaction and for intermediate
doping values, inhomogeneous configurations are found with lower energy. This
result is in contrast with the case of hole doped cuprates where
inhomogeneities are found already at very low doping. The inhomogeneities found
are in-phase stripes compatible with inelastic neutron scattering experiments.
They give an incoherent background in the Raman response. The signal
can show a quasiparticle-like component even when no Fermi surface is found in
the nodal direction.Comment: 8 pages, 10 figures, accepted for publication in Phys. Rev.
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