187 research outputs found
Large deviations in the alternating mass harmonic chain
We extend the work of Kannan et al. and derive the cumulant generating
function for the alternating mass harmonic chain consisting of N particles and
driven by heat reservoirs. The main result is a closed expression for the
cumulant generating function in the thermodynamic large N limit. This
expression is independent of N but depends on whether the chain consists of an
even or an odd number of particles, in accordance with the results obtained by
Kannan el al. for the heat current. This result is in accordance with the
absence of local thermodynamic equilibrium in a linear system.Comment: 19 pages latex, 6 figures, final version, appeared in J. Phys. A:
Math. Theor 47, 325003 (2014
Morphology and scaling in the noisy Burgers equation: Soliton approach to the strong coupling fixed point
The morphology and scaling properties of the noisy Burgers equation in one
dimension are treated by means of a nonlinear soliton approach based on the
Martin-Siggia-Rose technique. In a canonical formulation the strong coupling
fixed point is accessed by means of a principle of least action in the
asymptotic nonperturbative weak noise limit. The strong coupling scaling
behaviour and the growth morphology are described by a gas of nonlinear soliton
modes with a gapless dispersion law and a superposed gas of linear diffusive
modes with a gap. The dynamic exponent is determined by the gapless soliton
dispersion law, whereas the roughness exponent and a heuristic expression for
the scaling function are given by the form factor in a spectral representation
of the interface slope correlation function. The scaling function has the form
of a Levy flight distribution.Comment: 5 pages, Revtex file, submitted to Phys. Rev. Let
Heat fluctuations and fluctuation theorems in the case of multiple reservoirs
We consider heat fluctuations and fluctuation theorems for systems driven by
multiple reservoirs. We establish a fundamental symmetry obeyed by the joint
probability distribution for the heat transfers and system coordinates. The
symmetry leads to a generalisation of the asymptotic fluctuation theorem for
large deviations at large times. As a result the presence of multiple
reservoirs influence the tails in the heat distribution. The symmetry,
moreover, allows for a simple derivation of a recent exact fluctuation theorem
valid at all times. Including a time dependent work protocol we also present a
derivation of the integral fluctuation theorem.Comment: 27 pages, 1 figure, new extended version, to appear in J. Stat. Mech,
(2014
Towards a strong coupling theory for the KPZ equation
After a brief introduction we review the nonperturbative weak noise approach
to the KPZ equation in one dimension. We argue that the strong coupling aspects
of the KPZ equation are related to the existence of localized propagating
domain walls or solitons representing the growth modes; the statistical weight
of the excitations is governed by a dynamical action representing the
generalization of the Boltzmann factor to kinetics. This picture is not limited
to one dimension. We thus attempt a generalization to higher dimensions where
the strong coupling aspects presumably are associated with a cellular network
of domain walls. Based on this picture we present arguments for the Wolf-Kertez
expression z= (2d+1)/(d+1) for the dynamical exponent.Comment: 10 pages, 4 figures, "Horizons in Complex Systems", Messina, December
2001 (H. E. Stanley, 60th birthday
Energetics and efficiency of a molecular motor model
The energetics and efficiency of a linear molecular motor model proposed by
Mogilner et al. (Phys. Lett. 237, 297 (1998)) is analyzed from an analytical
point of view. The model which is based on protein friction with a track is
described by coupled Langevin equations for the motion in combination with
coupled master equations for the ATP hydrolysis. Here the energetics and
efficiency of the motor is addressed using a many body scheme with focus on the
efficiency at maximum power (EMP). It is found that the EMP is reduced from
about 10 pct in a heuristic description of the motor to about 1 per mille when
incorporating the full motor dynamics, owing to the strong dissipation
associated with the motor action.Comment: 23 pages, 6 figures, final version, appeared in J. Stat. Mech. P12001
(2013
Nonequilibrium dynamics of a growing interface
A growing interface subject to noise is described by the Kardar-Parisi-Zhang
equation or, equivalently, the noisy Burgers equation. In one dimension this
equation is analyzed by means of a weak noise canonical phase space approach
applied to the associated Fokker-Planck equation. The growth morphology is
characterized by a gas of nonlinear soliton modes with superimposed linear
diffusive modes. We also discuss the ensuing scaling properties.Comment: 14 pages, 11 figures, conference proceeding; a few corrections have
been adde
Bound particle coupled to two thermostats
We consider a harmonically bound Brownian particle coupled to two distinct
heat reservoirs at different temperatures. We show that the presence of a
harmonic trap does not change the large deviation function from the case of a
free Brownian particle discussed by Derrida and Brunet and Visco. Likewise, the
Gallavotti-Cohen fluctuation theorem related to the entropy production at the
heat sources remains in force. We support the analytical results with numerical
simulations
Scaling function for the noisy Burgers equation in the soliton approximation
We derive the scaling function for the one dimensional noisy Burgers equation
in the two-soliton approximation within the weak noise canonical phase space
approach. The result is in agreement with an earlier heuristic expression and
exhibits the correct scaling properties. The calculation presents the first
step in a many body treatment of the correlations in the Burgers equation.Comment: Replacement: Several corrections, 4 pages, Revtex file, 3 figures. To
appear in Europhysics Letter
Solitons in the noisy Burgers equation
We investigate numerically the coupled diffusion-advective type field
equations originating from the canonical phase space approach to the noisy
Burgers equation or the equivalent Kardar-Parisi-Zhang equation in one spatial
dimension. The equations support stable right hand and left hand solitons and
in the low viscosity limit a long-lived soliton pair excitation. We find that
two identical pair excitations scatter transparently subject to a size
dependent phase shift and that identical solitons scatter on a static soliton
transparently without a phase shift. The soliton pair excitation and the
scattering configurations are interpreted in terms of growing step and
nucleation events in the interface growth profile. In the asymmetrical case the
soliton scattering modes are unstable presumably toward multi soliton
production and extended diffusive modes, signalling the general
non-integrability of the coupled field equations. Finally, we have shown that
growing steps perform anomalous random walk with dynamic exponent z=3/2 and
that the nucleation of a tip is stochastically suppressed with respect to
plateau formation.Comment: 11 pages Revtex file, including 15 postscript-figure
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