19,971 research outputs found
Spreading and localization of wavepackets in disordered wires in a magnetic field
We study the diffusive and localization properties of wavepackets in
disordered wires in a magnetic field. In contrast to a recent supersymmetry
approach our numerical results show that the decay rate of the steady state
changes {\em smoothly} at the crossover from preserved to broken time-reversal
symmetry. Scaling and fluctuation properties are also analyzed and a formula,
which was derived analytically only in the pure symmetry cases is shown to
describe also the steady state wavefunction at the crossover regime. Finally,
we present a scaling for the variance of the packet which shows again a smooth
transition due to the magnetic field.Comment: 4 pages, 4 figure
Importance Sampling Simulation of Population Overflow in Two-node Tandem Networks
In this paper we consider the application of importance sampling in simulations of Markovian tandem networks in order to estimate the probability of rare events, such as network population overflow. We propose a heuristic methodology to obtain a good approximation to the 'optimal' state-dependent change of measure (importance sampling distribution). Extensive experimental results on 2-node tandem networks are very encouraging, yielding asymptotically efficient estimates (with bounded relative error) where no other state-independent importance sampling techniques are known to be efficient The methodology avoids the costly optimization involved in other recently proposed approaches to approximate the 'optimal' state-dependent change of measure. Moreover, the insight drawn from the heuristic promises its applicability to larger networks and more general topologies
Entropy production and fluctuation theorems under feedback control: the molecular refrigerator model revisited
We revisit the model of a Brownian particle in a heat bath submitted to an
actively controlled force proportional to the velocity that leads to thermal
noise reduction (cold damping). We investigate the influence of the continuous
feedback on the fluctuations of the total entropy production and show that the
explicit expression of the detailed fluctuation theorem involves different
dynamics and observables in the forward and backward processes. As an
illustration, we study the analytically solvable case of a harmonic oscillator
and calculate the characteristic function of the entropy production in a
nonequilibrium steady state. We then determine the corresponding large
deviation function which results from an unusual interplay between 'boundary'
and 'bulk' contributions.Comment: 16 pages, 5 figures. References 9,10,13,14,15 added. A few changes in
the text. Accepted for publication in J. Stat. Mec
Heat fluctuations of Brownian oscillators in nonstationary processes: fluctuation theorem and condensation transition
We study analytically the probability distribution of the heat released by an
ensemble of harmonic oscillators to the thermal bath, in the nonequilibrium
relaxation process following a temperature quench. We focus on the asymmetry
properties of the heat distribution in the nonstationary dynamics, in order to
study the forms taken by the Fluctuation Theorem as the number of degrees of
freedom is varied. After analysing in great detail the cases of one and two
oscillators, we consider the limit of a large number of oscillators, where the
behavior of fluctuations is enriched by a condensation transition with a
nontrivial phase diagram, characterized by reentrant behavior. Numerical
simulations confirm our analytical findings. We also discuss and highlight how
concepts borrowed from the study of fluctuations in equilibrium under symmetry
breaking conditions [Gaspard, J. Stat. Mech. P08021 (2012)] turn out to be
quite useful in understanding the deviations from the standard Fluctuation
Theorem.Comment: 16 pages, 7 figure
Symmetrized importance samplers for stochastic differential equations
We study a class of importance sampling methods for stochastic differential
equations (SDEs). A small-noise analysis is performed, and the results suggest
that a simple symmetrization procedure can significantly improve the
performance of our importance sampling schemes when the noise is not too large.
We demonstrate that this is indeed the case for a number of linear and
nonlinear examples. Potential applications, e.g., data assimilation, are
discussed.Comment: Added brief discussion of Hamilton-Jacobi equation. Also made various
minor corrections. To appear in Communciations in Applied Mathematics and
Computational Scienc
PT-Symmetric Quantum Mechanics
This paper proposes to broaden the canonical formulation of quantum
mechanics. Ordinarily, one imposes the condition on the
Hamiltonian, where represents the mathematical operation of complex
conjugation and matrix transposition. This conventional Hermiticity condition
is sufficient to ensure that the Hamiltonian has a real spectrum. However,
replacing this mathematical condition by the weaker and more physical
requirement , where represents combined parity reflection
and time reversal , one obtains new classes of complex Hamiltonians
whose spectra are still real and positive. This generalization of Hermiticity
is investigated using a complex deformation of the
harmonic oscillator Hamiltonian, where is a real parameter. The
system exhibits two phases: When , the energy spectrum of is
real and positive as a consequence of symmetry. However, when
, the spectrum contains an infinite number of complex
eigenvalues and a finite number of real, positive eigenvalues because symmetry is spontaneously broken. The phase transition that occurs at
manifests itself in both the quantum-mechanical system and the
underlying classical system. Similar qualitative features are exhibited by
complex deformations of other standard real Hamiltonians
with integer and ; each of these
complex Hamiltonians exhibits a phase transition at . These -symmetric theories may be viewed as analytic continuations of conventional
theories from real to complex phase space.Comment: 20 pages RevTex, 23 ps-figure
Asymptotic behavior of the conductance in disordered wires with perfectly conducting channels
We study the conductance of disordered wires with unitary symmetry focusing
on the case in which perfectly conducting channels are present due to the
channel-number imbalance between two-propagating directions. Using the exact
solution of the Dorokhov-Mello-Pereyra-Kumar (DMPK) equation for transmission
eigenvalues, we obtain the average and second moment of the conductance in the
long-wire regime. For comparison, we employ the three-edge Chalker-Coddington
model as the simplest example of channel-number-imbalanced systems with , and obtain the average and second moment of the conductance by using a
supersymmetry approach. We show that the result for the Chalker-Coddington
model is identical to that obtained from the DMPK equation.Comment: 20 pages, 1 figur
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