46 research outputs found
The grand canonical ABC model: a reflection asymmetric mean field Potts model
We investigate the phase diagram of a three-component system of particles on
a one-dimensional filled lattice, or equivalently of a one-dimensional
three-state Potts model, with reflection asymmetric mean field interactions.
The three types of particles are designated as , , and . The system is
described by a grand canonical ensemble with temperature and chemical
potentials , , and . We find that for
the system undergoes a phase transition from a
uniform density to a continuum of phases at a critical temperature . For other values of the chemical potentials the system
has a unique equilibrium state. As is the case for the canonical ensemble for
this model, the grand canonical ensemble is the stationary measure
satisfying detailed balance for a natural dynamics. We note that , where is the critical temperature for a similar transition in
the canonical ensemble at fixed equal densities .Comment: 24 pages, 3 figure
Phase diagram of the ABC model with nonconserving processes
The three species ABC model of driven particles on a ring is generalized to
include vacancies and particle-nonconserving processes. The model exhibits
phase separation at high densities. For equal average densities of the three
species, it is shown that although the dynamics is {\it local}, it obeys
detailed balance with respect to a Hamiltonian with {\it long-range
interactions}, yielding a nonadditive free energy. The phase diagrams of the
conserving and nonconserving models, corresponding to the canonical and
grand-canonical ensembles, respectively, are calculated in the thermodynamic
limit. Both models exhibit a transition from a homogeneous to a phase-separated
state, although the phase diagrams are shown to differ from each other. This
conforms with the expected inequivalence of ensembles in equilibrium systems
with long-range interactions. These results are based on a stability analysis
of the homogeneous phase and exact solution of the hydrodynamic equations of
the models. They are supported by Monte-Carlo simulations. This study may serve
as a useful starting point for analyzing the phase diagram for unequal
densities, where detailed balance is not satisfied and thus a Hamiltonian
cannot be defined.Comment: 32 page, 7 figures. The paper was presented at Statphys24, held in
Cairns, Australia, July 201
Multiple Core-Hole Coherence in X-Ray Four-Wave-Mixing Spectroscopies
Correlation-function expressions are derived for the coherent nonlinear
response of molecules to three resonant ultrafast pulses in the x-ray regime.
The ability to create two-core-hole states with controlled attosecond timing in
four-wave-mixing and pump probe techniques should open up new windows into the
response of valence electrons, which are not available from incoherent x-ray
Raman and fluorescence techniques. Closed expressions for the necessary
four-point correlation functions are derived for the electron-boson model by
using the second order cumulant expansion to describe the fluctuating
potentials. The information obtained from multidimensional nonlinear techniques
could be used to test and refine this model, and establish an anharmonic
oscillator picture for electronic excitations
Phase diagram of the ABC model with nonequal densities
The ABC model is a driven diffusive exclusion model, composed of three
species of particles that hop on a ring with local asymmetric rates. In the
weak asymmetry limit, where the asymmetry vanishes with the length of the
system, the model exhibits a phase transition between a homogenous state and a
phase separated state. We derive the exact solution for the density profiles of
the three species in the hydrodynamic limit for arbitrary average densities.
The solution yields the complete phase diagram of the model and allows the
study of the nature of the first order phase transition found for average
densities that deviate significantly from the equal densities point.Comment: 19 pages, 6 figures, submitted to J. Phys.
Ensemble Inequivalence and the Spin-Glass Transition
We report on the ensemble inequivalence in a many-body spin-glass model with
integer spin. The spin-glass phase transition is of first order for certain
values of the crystal field strength and is dependent whether it was derived in
the microcanonical or the canonical ensemble. In the limit of infinitely
many-body interactions, the model is the integer-spin equivalent of the
random-energy model, and is solved exactly. We also derive the integer-spin
equivalent of the de Almeida-Thouless line.Comment: 19 pages, 7 figure
Fluctuations in Nonequilibrium Statistical Mechanics: Models, Mathematical Theory, Physical Mechanisms
The fluctuations in nonequilibrium systems are under intense theoretical and
experimental investigation. Topical ``fluctuation relations'' describe
symmetries of the statistical properties of certain observables, in a variety
of models and phenomena. They have been derived in deterministic and, later, in
stochastic frameworks. Other results first obtained for stochastic processes,
and later considered in deterministic dynamics, describe the temporal evolution
of fluctuations. The field has grown beyond expectation: research works and
different perspectives are proposed at an ever faster pace. Indeed,
understanding fluctuations is important for the emerging theory of
nonequilibrium phenomena, as well as for applications, such as those of
nanotechnological and biophysical interest. However, the links among the
different approaches and the limitations of these approaches are not fully
understood. We focus on these issues, providing: a) analysis of the theoretical
models; b) discussion of the rigorous mathematical results; c) identification
of the physical mechanisms underlying the validity of the theoretical
predictions, for a wide range of phenomena.Comment: 44 pages, 2 figures. To appear in Nonlinearity (2007
Visual attention and action: How cueing, direct mapping, and social interactions drive orienting
Despite considerable interest in both action perception and social attention over the last 2 decades, there has been surprisingly little investigation concerning how the manual actions of other humans orient visual attention. The present review draws together studies that have measured the orienting of attention, following observation of another’s goal-directed action. Our review proposes that, in line with the literature on eye gaze, action is a particularly strong orienting cue for the visual system. However, we additionally suggest that action may orient visual attention using mechanisms, which gaze direction does not (i.e., neural direct mapping and corepresentation). Finally, we review the implications of these gaze-independent mechanisms for the study of attention to action. We suggest that our understanding of attention to action may benefit from being studied in the context of joint action paradigms, where the role of higher level action goals and social factors can be investigated