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At least 55 records · Page 3Linked to original sources
arXiv2007

PEPS as unique ground states of local Hamiltonians

In this paper we consider projected entangled pair states (PEPS) on arbitrary lattices. We construct local parent Hamiltonians for each PEPS and isolate a condition under which the state is the unique ground state of the Hamiltonian. This condition, verified by generic PEPS and examples like the AKLT model, is an injective relation between the boundary and the bulk of any local region. While it implies the existence of an energy gap in the 1D case we will show that in certain cases (e.g., on a 2D hexagonal lattice) the parent Hamiltonian can be gapless with a critical ground state. To show this we invoke a mapping between classical and quantum models and prove that in these cases the injectivity relation between boundary and bulk solely depends on the lattice geometry.

quant-ph↗
arXiv2008

Large time asymptotics of growth models on space-like paths I: PushASEP

We consider a new interacting particle system on the one-dimensional lattice that interpolates between TASEP and Toom's model: A particle cannot jump to the right if the neighboring site is occupied, and when jumping to the left it simply pushes all the neighbors that block its way. We prove that for flat and step initial conditions, the large time fluctuations of the height function of the associated growth model along any space-like path are described by the Airy_1 and Airy_2 processes. This includes fluctuations of the height profile for a fixed time and fluctuations of a tagged particle's trajectory as special cases.

math-ph↗
arXiv2008

Phase transition in the maximum clique problem: the case of Erdos-Renyi graphs

A phase transition, like the one already found on Boolean satisfiability problem by Kirkpatrick and Selman, is found on max clique problem on ER graphs. Although number of the datapoints is limited, the transition seems to obey finite size scaling. The transition also shows concentration of the graph instances which need particularly large CPU time to solve.

cond-mat.stat-mech↗
arXiv2007

Hydrodynamical thermotransport relaxation times of semiconductor electrons via acoustic phonons

We propose a hydrodynamic model to study the thermotransport properties of semiconductor electrons. From the semiclassical Boltzmann equation a set of balance equations is built for the relevant fields. The electron density, the electron energy density, the electric current density and the heat flux density are considered as the basic fields of direct transport and cross effect fluxes. The kinetic relaxation times of the production terms are calculated by considering the electron-acoustic phonon interaction as the leading microscopic scattering process. To justify the long time thermalization regime, the Onsager symmetry relations are proved, both on the completely degenerate and non degenerate limits.

cond-mat.stat-mech↗
arXiv2007

Discontinuity in the specific heat of a weakly interacting Bose gas

We produce the discontinuity in the specific heat of a homogeneous, dilute, and weakly interacting Bose gas in a short-wavelength range with a simple statistical method. The magnitude of the discontinuity at the phase transition temperature is obtained as a function of the density and scattering length of the Bose particles.

cond-mat.stat-mech↗
arXiv2007

Polarization effects on the dielectric properties of molten AgI

The results are reported of molecular dynamics simulations of the static longitudinal dielectric and response functions for molten AgI at 923 K using two ionic models. The first one is a rigid ion model, while in the second the induced dipole moments of the anions are added to the effective pair potentials of the first. It is derived theoretically that the dielectric functions for the polarizable ion model are determined by spatial correlations of charge and dipole moment densities. The charge structure factor at long wavelengths is also studied.

cond-mat.soft↗
arXiv2007

Network Rewiring Models

Recently we showed that a simple model of network rewiring could be solved exactly for any time and any parameter value. We also showed that this model can be recast in terms of several well known models of statistical physics such as Urn model and the Voter model. We also noted that it has been applied to a wide range of problems. Here we consider various generalisations of this model and include some new exact results.

cond-mat.stat-mech↗
arXiv2007

Nonequilibrium Renormalization Theory I

In the present article we consider some general class of divergent diagrams in Keldysh diagram technique. These divergences arise for nonequilibrium matter and closely related to the divergences in the kinetic theory of gases. We suggest a scheme of renormalization of such divergences and illustrate it on some examples. In the other papers of these series we develop the general theory of renormalization of nonequilibrium diagram technique. The fact that thermal divergences in non-equilibrium diagram technique can be renormalized leads to the following consequence: to prove that the system tends to the thermal equilibrium one should to take into account the behaviour of the system on its boundary. In this paper we illustrate this fact on Bogoliubov derivation of kinetic equations.

cond-mat.stat-mech↗
arXiv2008

Soret Motion of a Charged Spherical Colloid

The thermophoretic motion of a charged spherical colloidal particle and its accompanying cloud of counterions and co-ions in a temperature gradient is studied theoretically. Using the Debye-Huckel approximation, the Soret drift velocity of a weakly charged colloid is calculated analytically. For highly charged colloids, the nonlinear system of electrokinetic equations is solved numerically, and the effects of high surface potential, dielectrophoresis, and convection are examined. Our results are in good agreement with some of the recent experiments on highly charged colloids without using adjustable parameters.

cond-mat.soft↗
arXiv2008

Potts models on hierarchical lattices and Renormalization Group dynamics

We prove that the generator of the renormalization group of Potts models on hierarchical lattices can be represented by a rational map acting on a finite-dimensional product of complex projective spaces. In this framework we can also consider models with an applied external magnetic field and multiple-spin interactions. We use recent results regarding iteration of rational maps in several complex variables to show that, for some class of hierarchical lattices, Lee-Yang and Fisher zeros belong to the unstable set of the renormalization map.

cond-mat.stat-mech↗
arXiv2009

A variant of the Recoil Growth algorithm to generate multi-polymer systems

The Recoil Growth algorithm, proposed in 1999 by Consta et al., is one of the most efficient algorithm available in the literature to sample from a multi-polymer system. Such problems are closely related to the generation of self-avoiding paths. In this paper, we study a variant of the original Recoil Growth algorithm, where we constrain the generation of a new polymer to take place on a specific class of graphs. This makes it possible to make a fine trade-off between computational cost and success rate. We moreover give a simple proof for a lower bound on the irreducibility of this new algorithm, which applies to the original algorithm as well.

cs.CE↗
arXiv2010

Optimal Causal Inference: Estimating Stored Information and Approximating Causal Architecture

We introduce an approach to inferring the causal architecture of stochastic dynamical systems that extends rate distortion theory to use causal shielding---a natural principle of learning. We study two distinct cases of causal inference: optimal causal filtering and optimal causal estimation. Filtering corresponds to the ideal case in which the probability distribution of measurement sequences is known, giving a principled method to approximate a system's causal structure at a desired level of representation. We show that, in the limit in which a model complexity constraint is relaxed, filtering finds the exact causal architecture of a stochastic dynamical system, known as the causal-state partition. From this, one can estimate the amount of historical information the process stores. More generally, causal filtering finds a graded model-complexity hierarchy of approximations to the causal architecture. Abrupt changes in the hierarchy, as a function of approximation, capture distinct scales of structural organization. For nonideal cases with finite data, we show how the correct number of underlying causal states can be found by optimal causal estimation. A previously derived model complexity control term allows us to correct for the effect of statistical fluctuations in probability estimates and thereby avoid over-fitting.

cs.IT↗
arXiv2007

Active elastic dimers: self-propulsion and current reversal on a featureless track

We present a Brownian inchworm model of a self-propelled elastic dimer in the absence of an external potential. Nonequilibrium noise together with a stretch-dependent damping form the propulsion mechanism. Our model connects three key nonequilibrium features -- position-velocity correlations, a nonzero mean internal force, and a drift velocity. Our analytical results, including striking current reversals, compare very well with numerical simulations. The model unifies the propulsion mechanisms of DNA helicases, polar rods on a vibrated surface, crawling keratocytes and Myosin VI. We suggest experimental realizations and tests of the model.

cond-mat.stat-mech↗
arXiv2007

On the equivalence of the microcanonical and the canonical ensembles: a geometrical approach

In this paper, we consider the volume enclosed by the microcanonical ensemble in phase space as a statistical ensemble. This can be interpreted as an intermediate image between the microcanonical and the canonical pictures. By maintaining the ergodic hypothesis over this ensemble, that is, the equiprobability of all its accessible states, the equivalence of this ensemble in the thermodynamic limit with the microcanonical and the canonical ensembles is suggested by means of geometrical arguments. The Maxwellian and the Boltzmann-Gibbs distributions are obtained from this formalism. In the appendix, the derivation of the Boltzmann factor from a new microcanonical image of the canonical ensemble is also given.

nlin.CD↗
arXiv2008

On the dynamics of point vortices in a quantum gas confined in an annular region

The dynamics of one and two pointlike vortices in a planar quantum gas of spin-0 particles confined in an annular region is considered. New analytical and numerical solutions are found. The concept of stationarity radius, related to the doubly connected nature of the annulus, is defined. It is seen that the existence of these radii has great impact on the behaviour of the vortices. It is shown that, because of the existence of the stationarity radii, vortices exhibit similar behaviour regardless of the sign of their winding number. The energetically stable vortex solutions are studied qualitatively.

cond-mat.stat-mech↗