1,329 research outputs found
Bethe anzats derivation of the Tracy-Widom distribution for one-dimensional directed polymers
The distribution function of the free energy fluctuations in one-dimensional
directed polymers with -correlated random potential is studied by
mapping the replicated problem to a many body quantum boson system with
attractive interactions. Performing the summation over the entire spectrum of
excited states the problem is reduced to the Fredholm determinant with the Airy
kernel which is known to yield the Tracy-Widom distributionComment: 5 page
Bosonization, vicinal surfaces, and hydrodynamic fluctuation theory
Through a Euclidean path integral we establish that the density fluctuations
of a Fermi fluid in one dimension are related to vicinal surfaces and to the
stochastic dynamics of particles interacting through long range forces with
inverse distance decay. In the surface picture one easily obtains the Haldane
relation and identifies the scaling exponents governing the low energy,
Luttinger liquid behavior. For the stochastic particle model we develop a
hydrodynamic fluctuation theory, through which in some cases the large distance
Gaussian fluctuations are proved nonperturbatively
The No-Binding Regime of the Pauli-Fierz Model
The Pauli-Fierz model in nonrelativistic quantum electrodynamics
is considered. The external potential is sufficiently shallow and the
dipole approximation is assumed. It is proven that there exist constants
such that has no ground state for
, which complements an earlier result stating that there is
a ground state for . We develop a suitable extension of
the Birman-Schwinger argument. Moreover for any given examples of
potentials are provided such that .Comment: 18 pages and 1 figur
Spatial structures and dynamics of kinetically constrained models for glasses
Kob and Andersen's simple lattice models for the dynamics of structural
glasses are analyzed. Although the particles have only hard core interactions,
the imposed constraint that they cannot move if surrounded by too many others
causes slow dynamics. On Bethe lattices a dynamical transition to a partially
frozen phase occurs. In finite dimensions there exist rare mobile elements that
destroy the transition. At low vacancy density, , the spacing, ,
between mobile elements diverges exponentially or faster in . Within the
mobile elements, the dynamics is intrinsically cooperative and the
characteristic time scale diverges faster than any power of (although
slower than ). The tagged-particle diffusion coefficient vanishes roughly
as .Comment: 4 pages. Accepted for pub. in Phys. Rev. Let
On the derivation of Fourier's law in stochastic energy exchange systems
We present a detailed derivation of Fourier's law in a class of stochastic
energy exchange systems that naturally characterize two-dimensional mechanical
systems of locally confined particles in interaction. The stochastic systems
consist of an array of energy variables which can be partially exchanged among
nearest neighbours at variable rates. We provide two independent derivations of
the thermal conductivity and prove this quantity is identical to the frequency
of energy exchanges. The first derivation relies on the diffusion of the
Helfand moment, which is determined solely by static averages. The second
approach relies on a gradient expansion of the probability measure around a
non-equilibrium stationary state. The linear part of the heat current is
determined by local thermal equilibrium distributions which solve a
Boltzmann-like equation. A numerical scheme is presented with computations of
the conductivity along our two methods. The results are in excellent agreement
with our theory.Comment: 19 pages, 5 figures, to appear in Journal of Statistical Mechanics
(JSTAT
Pure Stationary States of Open Quantum Systems
Using Liouville space and superoperator formalism we consider pure stationary
states of open and dissipative quantum systems. We discuss stationary states of
open quantum systems, which coincide with stationary states of closed quantum
systems. Open quantum systems with pure stationary states of linear oscillator
are suggested. We consider stationary states for the Lindblad equation. We
discuss bifurcations of pure stationary states for open quantum systems which
are quantum analogs of classical dynamical bifurcations.Comment: 7p., REVTeX
Quantum transport through single-molecule junctions with orbital degeneracies
We consider electronic transport through a single-molecule junction where the
molecule has a degenerate spectrum. Unlike previous transport models, and
theories a rate-equations description is no longer possible, and the quantum
coherences between degenerate states have to be taken into account. We present
the derivation and application of a master equation that describes the system
in the weak-coupling limit and give an in-depth discussion of the parameter
regimes and the new phenomena due to coherent on-site dynamics
Complementarity relation for irreversible process derived from stochastic energetics
When the process of a system in contact with a heat bath is described by
classical Langevin equation, the method of stochastic energetics [K. Sekimoto,
J. Phys. Soc. Jpn. vol. 66 (1997) p.1234] enables to derive the form of
Helmholtz free energy and the dissipation function of the system. We prove that
the irreversible heat Q_irr and the time lapse $Delta t} of an isothermal
process obey the complementarity relation, Q_irr {Delta t} >= k_B T S_min,
where S_min depends on the initial and the final values of the control
parameters, but it does not depend on the pathway between these values.Comment: 3 pages. LaTeX with 6 style macro
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