3,038 research outputs found
Melting of an Ising Quadrant
We consider an Ising ferromagnet endowed with zero-temperature spin-flip
dynamics and examine the evolution of the Ising quadrant, namely the spin
configuration when the minority phase initially occupies a quadrant while the
majority phase occupies three remaining quadrants. The two phases are then
always separated by a single interface which generically recedes into the
minority phase in a self-similar diffusive manner. The area of the invaded
region grows (on average) linearly with time and exhibits non-trivial
fluctuations. We map the interface separating the two phases onto the
one-dimensional symmetric simple exclusion process and utilize this isomorphism
to compute basic cumulants of the area. First, we determine the variance via an
exact microscopic analysis (the Bethe ansatz). Then we turn to a continuum
treatment by recasting the underlying exclusion process into the framework of
the macroscopic fluctuation theory. This provides a systematic way of analyzing
the statistics of the invaded area and allows us to determine the asymptotic
behaviors of the first four cumulants of the area.Comment: 28 pages, 3 figures, submitted to J. Phys.
Generalized Exclusion Processes: Transport Coefficients
A class of generalized exclusion processes parametrized by the maximal
occupancy, , is investigated. For these processes with symmetric
nearest-neighbor hopping, we compute the diffusion coefficient and show that it
is independent on the spatial dimension. In the extreme cases of (simple
symmetric exclusion process) and (non-interacting symmetric random
walks) the diffusion coefficient is constant; for , the
diffusion coefficient depends on the density and the maximal occupancy . We
also study the evolution of a tagged particle. It exhibits a diffusive behavior
which is characterized by the coefficient of self-diffusion which we probe
numerically.Comment: v1: 9 pages, 6 figures. v2: + 2 references. v3: 10 pages, 7 figures,
published versio
Tagged particle in single-file diffusion
Single-file diffusion is a one-dimensional interacting infinite-particle
system in which the order of particles never changes. An intriguing feature of
single-file diffusion is that the mean-square displacement of a tagged particle
exhibits an anomalously slow sub-diffusive growth. We study the full statistics
of the displacement using a macroscopic fluctuation theory. For the simplest
single-file system of impenetrable Brownian particles we compute the large
deviation function and provide an independent verification using an exact
solution based on the microscopic dynamics. For an arbitrary single-file
system, we apply perturbation techniques and derive an explicit formula for the
variance in terms of the transport coefficients. The same method also allows us
to compute the fourth cumulant of the tagged particle displacement for the
symmetric exclusion process.Comment: 34 pages, to appear in Journal of Statistical Physics (2015
Reply to "Comment on Generalized Exclusion Processes: Transport Coefficients"
We reply to the comment of Becker, Nelissen, Cleuren, Partoens, and Van den
Broeck, Phys. Rev. E 93, 046101 (2016) on our article, Phys. Rev. E 90, 052108
(2014) about transport properties of a class of generalized exclusion
processes.Comment: 2 pages, 1 figur
Large Deviations in Single File Diffusion
We apply macroscopic fluctuation theory to study the diffusion of a tracer in
a one-dimensional interacting particle system with excluded mutual passage,
known as single-file diffusion. In the case of Brownian point particles with
hard-core repulsion, we derive the cumulant generating function of the tracer
position and its large deviation function. In the general case of arbitrary
inter-particle interactions, we express the variance of the tracer position in
terms of the collective transport properties, viz. the diffusion coefficient
and the mobility. Our analysis applies both for fluctuating (annealed) and
fixed (quenched) initial configurations.Comment: Revised version with few corrections. Accepted for publication in
Phys. Rev. Let
Dynamical properties of single-file diffusion
We study the statistics of a tagged particle in single-file diffusion, a
one-dimensional interacting infinite-particle system in which the order of
particles never changes. We compute the two-time correlation function for the
displacement of the tagged particle for an arbitrary single-file system. We
also discuss single-file analogs of the arcsine law and the law of the iterated
logarithm characterizing the behavior of Brownian motion. Using a macroscopic
fluctuation theory we devise a formalism giving the cumulant generating
functional. In principle, this functional contains the full statistics of the
tagged particle trajectory---the full single-time statistics, all multiple-time
correlation functions, etc. are merely special cases.Comment: 20 pages, 1 figur
Interacting quantum walkers: Two-body bosonic and fermionic bound states
We investigate the dynamics of bound states of two interacting particles,
either bosons or fermions, performing a continuous-time quantum walk on a
one-dimensional lattice. We consider the situation where the distance between
both particles has a hard bound, and the richer situation where the particles
are bound by a smooth confining potential. The main emphasis is on the velocity
characterizing the ballistic spreading of these bound states, and on the
structure of the asymptotic distribution profile of their center-of-mass
coordinate. The latter profile generically exhibits many internal fronts.Comment: 31 pages, 14 figure
Survival of classical and quantum particles in the presence of traps
We present a detailed comparison of the motion of a classical and of a
quantum particle in the presence of trapping sites, within the framework of
continuous-time classical and quantum random walk. The main emphasis is on the
qualitative differences in the temporal behavior of the survival probabilities
of both kinds of particles. As a general rule, static traps are far less
efficient to absorb quantum particles than classical ones. Several lattice
geometries are successively considered: an infinite chain with a single trap, a
finite ring with a single trap, a finite ring with several traps, and an
infinite chain and a higher-dimensional lattice with a random distribution of
traps with a given density. For the latter disordered systems, the classical
and the quantum survival probabilities obey a stretched exponential asymptotic
decay, albeit with different exponents. These results confirm earlier
predictions, and the corresponding amplitudes are evaluated. In the
one-dimensional geometry of the infinite chain, we obtain a full analytical
prediction for the amplitude of the quantum problem, including its dependence
on the trap density and strength.Comment: 35 pages, 10 figures, 2 tables. Minor update
Return probability of fermions released from a 1D confining potential
We consider non-interacting fermions prepared in the ground state of a 1D
confining potential and submitted to an instantaneous quench consisting in
releasing the trapping potential. We show that the quantum return probability
of finding the fermions in their initial state at a later time falls off as a
power law in the long-time regime, with a universal exponent depending only on
and on whether the free fermions expand over the full line or over a
half-line. In both geometries the amplitudes of this power-law decay are
expressed in terms of finite determinants of moments of the one-body
bound-state wavefunctions in the potential. These amplitudes are worked out
explicitly for the harmonic and square-well potentials. At large fermion
numbers they obey scaling laws involving the Fermi energy of the initial state.
The use of the Selberg-Mehta integrals stemming from random matrix theory has
been instrumental in the derivation of these results.Comment: 24 pages, 1 tabl
Asymmetric Exclusion Process with Global Hopping
We study a one-dimensional totally asymmetric simple exclusion process with
one special site from which particles fly to any empty site (not just to the
neighboring site). The system attains a non-trivial stationary state with
density profile varying over the spatial extent of the system. The density
profile undergoes a non-equilibrium phase transition when the average density
passes through the critical value 1-1/[4(1-ln 2)]=0.185277..., viz. in addition
to the discontinuity in the vicinity of the special site, a shock wave is
formed in the bulk of the system when the density exceeds the critical density.Comment: Published version (v2
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