1,755 research outputs found
Zero-Range Processes with Multiple Condensates: Statics and Dynamics
The steady-state distributions and dynamical behaviour of Zero Range
Processes with hopping rates which are non-monotonic functions of the site
occupation are studied. We consider two classes of non-monotonic hopping rates.
The first results in a condensed phase containing a large (but subextensive)
number of mesocondensates each containing a subextensive number of particles.
The second results in a condensed phase containing a finite number of extensive
condensates. We study the scaling behaviour of the peak in the distribution
function corresponding to the condensates in both cases. In studying the
dynamics of the condensate we identify two timescales: one for creation, the
other for evaporation of condensates at a given site. The scaling behaviour of
these timescales is studied within the Arrhenius law approach and by numerical
simulations.Comment: 25 pages, 18 figure
Density profiles, dynamics, and condensation in the ZRP conditioned on an atypical current
We study the asymmetric zero-range process (ZRP) with L sites and open
boundaries, conditioned to carry an atypical current. Using a generalized Doob
h-transform we compute explicitly the transition rates of an effective process
for which the conditioned dynamics are typical. This effective process is a
zero-range process with renormalized hopping rates, which are space dependent
even when the original rates are constant. This leads to non-trivial density
profiles in the steady state of the conditioned dynamics, and, under generic
conditions on the jump rates of the unconditioned ZRP, to an intriguing
supercritical bulk region where condensates can grow. These results provide a
microscopic perspective on macroscopic fluctuation theory (MFT) for the weakly
asymmetric case: It turns out that the predictions of MFT remain valid in the
non-rigorous limit of finite asymmetry. In addition, the microscopic results
yield the correct scaling factor for the asymmetry that MFT cannot predict.Comment: 26 pages, 4 figure
Robustness of spontaneous symmetry breaking in a bridge model
A simple two-species asymmetric exclusion model in one dimension with bulk
and boundary exchanges of particles is investigated for the existence of
spontaneous symmetry breaking. The model is a generalization of the bridge
model for which earlier studies have confirmed the existence of symmetry-broken
phases, and the motivation here is to check the robustness of the observed
symmetry breaking with respect to additional dynamical moves, in particular,
the boundary exchange of the two species of particles. Our analysis, based on
general considerations, mean-field approximation and numerical simulations,
shows that the symmetry breaking in the bridge model is sustained for a range
of values of the boundary exchange rate. Moreover, the mechanism through which
symmetry is broken is similar to that in the bridge model. Our analysis allows
us to plot the complete phase diagram of the model, demarcating regions of
symmetric and symmetry-broken phases.Comment: 26 pages, 12 figures, v2: minor changes with an added appendix,
published versio
Diffusion in a logarithmic potential: scaling and selection in the approach to equilibrium
The equation which describes a particle diffusing in a logarithmic potential
arises in diverse physical problems such as momentum diffusion of atoms in
optical traps, condensation processes, and denaturation of DNA molecules. A
detailed study of the approach of such systems to equilibrium via a scaling
analysis is carried out, revealing three surprising features: (i) the solution
is given by two distinct scaling forms, corresponding to a diffusive (x ~
\sqrt{t}) and a subdiffusive (x >> \sqrt{t}) length scales, respectively; (ii)
the scaling exponents and scaling functions corresponding to both regimes are
selected by the initial condition; and (iii) this dependence on the initial
condition manifests a "phase transition" from a regime in which the scaling
solution depends on the initial condition to a regime in which it is
independent of it. The selection mechanism which is found has many similarities
to the marginal stability mechanism which has been widely studied in the
context of fronts propagating into unstable states. The general scaling forms
are presented and their practical and theoretical applications are discussed.Comment: 42 page
Condensation and coexistence in a two-species driven model
Condensation transition in two-species driven systems in a ring geometry is
studied in the case where current-density relation of a domain of particles
exhibits two degenerate maxima. It is found that the two maximal current phases
coexist both in the fluctuating domains of the fluid and in the condensate,
when it exists. This has a profound effect on the steady state properties of
the model. In particular, phase separation becomes more favorable, as compared
with the case of a single maximum in the current-density relation. Moreover, a
selection mechanism imposes equal currents flowing out of the condensate,
resulting in a neutral fluid even when the total number of particles of the two
species are not equal. In this case the particle imbalance shows up only in the
condensate
Coarsening of a Class of Driven Striped Structures
The coarsening process in a class of driven systems exhibiting striped
structures is studied. The dynamics is governed by the motion of the driven
interfaces between the stripes. When two interfaces meet they coalesce thus
giving rise to a coarsening process in which l(t), the average width of a
stripe, grows with time. This is a generalization of the reaction-diffusion
process A + A -> A to the case of extended coalescing objects, namely, the
interfaces. Scaling arguments which relate the coarsening process to the
evolution of a single driven interface are given, yielding growth laws for
l(t), for both short and long time. We introduce a simple microscopic model for
this process. Numerical simulations of the model confirm the scaling picture
and growth laws. The results are compared to the case where the stripes are not
driven and different growth laws arise
Slow Coarsening in a Class of Driven Systems
The coarsening process in a class of driven systems is studied. These systems
have previously been shown to exhibit phase separation and slow coarsening in
one dimension. We consider generalizations of this class of models to higher
dimensions. In particular we study a system of three types of particles that
diffuse under local conserving dynamics in two dimensions. Arguments and
numerical studies are presented indicating that the coarsening process in any
number of dimensions is logarithmically slow in time. A key feature of this
behavior is that the interfaces separating the various growing domains are
smooth (well approximated by a Fermi function). This implies that the
coarsening mechanism in one dimension is readily extendible to higher
dimensions.Comment: submitted to EPJB, 13 page
Modelling one-dimensional driven diffusive systems by the Zero-Range Process
The recently introduced correspondence between one-dimensional two-species
driven models and the Zero-Range Process is extended to study the case where
the densities of the two species need not be equal. The correspondence is
formulated through the length dependence of the current emitted from a particle
domain. A direct numerical method for evaluating this current is introduced,
and used to test the assumptions underlying this approach. In addition, a model
for isolated domain dynamics is introduced, which provides a simple way to
calculate the current also for the non-equal density case. This approach is
demonstrated and applied to a particular two-species model, where a phase
separation transition line is calculated
Interaction-induced harmonic frequency mixing in quantum dots
We show that harmonic frequency mixing in quantum dots coupled to two leads
under the influence of time-dependent voltages of different frequency is
dominated by interaction effects. This offers a unique and direct spectroscopic
tool to access correlations, and holds promise for efficient frequency mixing
in nano-devices. Explicit results are provided for an Anderson dot and for a
molecular level with phonon-mediated interactions.Comment: 4 pages, 2 figures, accepted for publication in Phys.Rev.Let
Sum-over-states vs quasiparticle pictures of coherent correlation spectroscopy of excitons in semiconductors; femtosecond analogues of multidimensional NMR
Two-dimensional correlation spectroscopy (2DCS) based on the nonlinear
optical response of excitons to sequences of ultrafast pulses, has the
potential to provide some unique insights into carrier dynamics in
semiconductors. The most prominent feature of 2DCS, cross peaks, can best be
understood using a sum-over-states picture involving the many-body eigenstates.
However, the optical response of semiconductors is usually calculated by
solving truncated equations of motion for dynamical variables, which result in
a quasiparticle picture. In this work we derive Green's function expressions
for the four wave mixing signals generated in various phase-matching directions
and use them to establish the connection between the two pictures. The formal
connection with Frenkel excitons (hard-core bosons) and vibrational excitons
(soft-core bosons) is pointed out.Comment: Accepted to Phys. Rev.
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