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arXiv2014

Holographic Entanglement Entropy for General Higher Derivative Gravity

We propose a general formula for calculating the entanglement entropy in theories dual to higher derivative gravity where the Lagrangian is a contraction of Riemann tensors. Our formula consists of Wald's formula for the black hole entropy, as well as corrections involving the extrinsic curvature. We derive these corrections by noting that they arise from naively higher order contributions to the action which are enhanced due to would-be logarithmic divergences. Our formula reproduces the Jacobson-Myers entropy in the context of Lovelock gravity, and agrees with existing results for general four-derivative gravity. We emphasize that the formula should be evaluated on a particular bulk surface whose location can in principle be determined by solving the equations of motion with conical boundary conditions. This may be difficult in practice, and an alternative method is desirable. A natural prescription is simply minimizing our formula, analogous to the Ryu-Takayanagi prescription for Einstein gravity. We show that this is correct in several examples including Lovelock and general four-derivative gravity.

hep-th↗

arXiv2018

Inverse Bootstrapping Conformal Field Theories

We propose a novel approach to study conformal field theories (CFTs) in general dimensions. In the conformal bootstrap program, one usually searches for consistent CFT data that satisfy crossing symmetry. In the new approach, we reverse the logic and interpret manifestly crossing-symmetric functions as generating functions of conformal data. Physical CFTs can be obtained by scanning the space of symmetric functions. By truncating the fusion rules, we are able to concentrate on the low-lying operators and derive some approximate relations for their conformal data. It turns out that the free scalar theory, the 2d minimal model CFTs, the $ϕ^{4}$ Wilson-Fisher CFT, the Lee-Yang CFTs and the Ising CFTs are consistent with the universal relations from the minimal fusion rule $ϕ_1\times ϕ_1=I+ϕ_2+T$, where $ϕ_1,\,ϕ_2$ are scalar operators, $I$ is the identity operator and $T$ is the stress tensor.

hep-th↗

arXiv2013

Transmission matrices in gl(N) & U_q(gl(N)) quantum spin chains

The gl(N) and U_q(gl(N)) quantum spin chains in the presence of integrable spin impurities are considered. Within the Bethe ansatz formulation, we derive the associated transmission amplitudes, and the corresponding transmission matrices -representations of the underlying quadratic algebra- that physically describe the interaction between the various particle-like excitations displayed by these models and the spin impurity.

hep-th↗

arXiv2012

Landauer-Büttiker formula and Schrödinger conjecture

We study the entropy flux in the stationary state of a finite one-dimensional sample S connected at its left and right ends to two infinitely extended reservoirs at distinct temperatures T1, T2 and chemical potentials mu1, mu2. The sample is a free lattice Fermi gas confined to a box [0, L] with energy operator -Δ+ v. The Landauer-Büttiker formula expresses the steady state entropy flux in the coupled system in terms of scattering data. We study the behavior of this steady state entropy flux in the limit L->infinity and relate persistence of transport to norm bounds on the transfer matrices of the limiting half-line Schrödinger operator h. A natural conjecture is that the set of energies at which transport persists in this limit is precisely the essential support of the absolutely continuous spectrum of h. We show that this conjecture is equivalent to the Schrödinger conjecture in spectral theory of one-dimensional Schrödinger operators, thus giving a physically appealing interpretation to the Schrödinger conjecture.

math-ph↗

arXiv2013

Fifty Years of Breakthrough Discoveries in Fluid Criticality

Fifty years ago two scientists, who celebrate their 80th birthdays in 2011, Alexander V. Voronel and Johannes V. Sengers performed breakthrough experiments that challenged the commonly accepted views on critical phenomena in fluids. Voronel discovered that the isochoric heat capacity of argon becomes infinite at the vapor-liquid critical point. Almost simultaneously, Sengers observed a similar anomaly for the thermal conductivity of near-critical carbon dioxide. The existence of these singularities was later proved to be universal for all fluids. These experiments had a profound effect on the development of the modern (scaling) theory of phase transitions, which is based on the diverging fluctuations of the order parameter. In particular, the discovery of the heat-capacity divergence at the critical point was a keystone for the formulation of static scaling theory, while the discovery of the divergence of the thermal conductivity played an important role in the formulation of dynamic scaling and mode-coupling theory. Moreover, owing to the discoveries made by Voronel and Sengers 50 years ago, critical phenomena in fluids have become an integral part of contemporary condensed-matter physics.

physics.hist-ph↗

arXiv2011

Dynamic Critical Behavior of the Chayes-Machta Algorithm for the Random-Cluster Model. I. Two Dimensions

We study, via Monte Carlo simulation, the dynamic critical behavior of the Chayes-Machta dynamics for the Fortuin-Kasteleyn random-cluster model, which generalizes the Swendsen-Wang dynamics for the q-state Potts ferromagnet to non-integer q \ge 1. We consider spatial dimension d=2 and 1.25 \le q \le 4 in steps of 0.25, on lattices up to 1024^2, and obtain estimates for the dynamic critical exponent z_{CM}. We present evidence that when 1 \le q \lesssim 1.95 the Ossola-Sokal conjecture z_{CM} \ge β/νis violated, though we also present plausible fits compatible with this conjecture. We show that the Li-Sokal bound z_{CM} \ge α/νis close to being sharp over the entire range 1 \le q \le 4, but is probably non-sharp by a power. As a byproduct of our work, we also obtain evidence concerning the corrections to scaling in static observables.

cond-mat.stat-mech↗

arXiv2013

Additional Invariants and Statistical Equilibria for the 2D Euler Equations on a spherical domain

The role of the domain geometry for the statistical mechanics of 2D Euler flows is investigated. It is shown that for a spherical domain, there exists invariant subspaces in phase space which yield additional angular momentum, energy and enstrophy invariants. The microcanonical measure taking into account these invariants is built and a mean-field, Robert-Sommeria-Miller theory is developed in the simple case of the energy-enstrophy measure. The variational problem is solved analytically and a partial energy condensation is obtained. The thermodynamic properties of the system are also discussed.

cond-mat.stat-mech↗

arXiv2013

Complex Network Structure of Flocks in the Standard Vicsek Model

In flocking models, the collective motion of self-driven individuals leads to the formation of complex spatiotemporal patterns. The Standard Vicsek Model (SVM) considers individuals that tend to adopt the direction of movement of their neighbors under the influence of noise. By performing an extensive complex network characterization of the structure of SVM flocks, we show that flocks are highly clustered, assortative, and non-hierarchical networks with short-tailed degree distributions. Moreover, we also find that the SVM dynamics leads to the formation of complex structures with an effective dimension higher than that of the space where the actual displacements take place. Furthermore, we show that these structures are capable of sustaining mean-field-like orientationally ordered states when the displacements are suppressed, thus suggesting a linkage between the onset of order and the enhanced dimensionality of SVM flocks.

cond-mat.stat-mech↗

arXiv2013

Geometrical Excess Entropy Production in Nonequilibrium Quantum Systems

For open systems described by the quantum Markovian master equation, we study a possible extension of the Clausius equality to quasistatic operations between nonequilibrium steady states (NESSs). We investigate the excess heat divided by temperature (i.e., excess entropy production) which is transferred into the system during the operations. We derive a geometrical expression for the excess entropy production, which is analogous to the Berry phase in unitary evolution. Our result implies that in general one cannot define a scalar potential whose difference coincides with the excess entropy production in a thermodynamic process, and that a vector potential plays a crucial role in the thermodynamics for NESSs. In the weakly nonequilibrium regime, we show that the geometrical expression reduces to the extended Clausius equality derived by Saito and Tasaki (J. Stat. Phys. {\bf 145}, 1275 (2011)). As an example, we investigate a spinless electron system in quantum dots. We find that one can define a scalar potential when the parameters of only one of the reservoirs are modified in a non-interacting system, but this is no longer the case for an interacting system.

cond-mat.stat-mech↗

arXiv2013

Entropy production in continuous phase space systems

We propose an alternative method to compute the entropy production of a classical underdamped nonequilibrium system in a continuous phase space. This approach has the advantage that it is not necessary to distinguish between even and odd-parity variables. We show that the method leads to the same local entropy production as in previous studies while the differential entropy production along a stochastic trajectory turns out to be different. This demonstrates that the differential entropy production in continuous phase space systems is not uniquely defined.

cond-mat.stat-mech↗

arXiv2014

Quantitative universality for a class of weakly chaotic systems

We consider a general class of intermittent maps designed to be weakly chaotic, i.e., for which the separation of trajectories of nearby initial conditions is weaker than exponential. We show that all its spatio and temporal properties, hitherto regarded independently in the literature, can be represented by a single characteristic function $ϕ$. A universal criterion for the choice of $ϕ$ is obtained within the Feigenbaum's renormalization-group approach. We find a general expression for the dispersion rate $ζ(t)$ of initially nearby trajectories and we show that the instability scenario for weakly chaotic systems is more general than that originally proposed by Gaspard and Wang [Proc. Natl. Acad. Sci. USA {\bf 85}, 4591 (1988)]. We also consider a spatially extended version of such class of maps, which leads to anomalous diffusion, and we show that the mean squared displacement satisfies $σ^{2}(t)\simζ(t)$. To illustrate our results, some examples are discussed in detail.

nlin.CD↗

arXiv2018

The hydrodynamic limit for local mean-field dynamics with unbounded spins

We consider the dynamics of a class of spin systems with unbounded spins interacting with local mean field interactions. We proof convergence of the empirical measure to the solution of a McKean-Vlasov equation in the hydrodynamic limit and propagation of chaos. This extends earlier results of Gärtner, Comets and others for bounded spins or strict mean field interactions.

math.PR↗

arXiv2013

Anomalous scaling in statistical models of passively advected vector fields

The field theoretic renormalization group and the operator product expansion are applied to the stochastic model of passively advected vector field with the most general form of the nonlinear term allowed by the Galilean symmetry. The advecting turbulent velocity field is governed by the stochastic Navier--Stokes equation. It is shown that the correlation functions of the passive vector field in the inertial range exhibit anomalous scaling behaviour. The corresponding anomalous exponents are determined by the critical dimensions of tensor composite fields (operators) built solely of the passive vector field. They are calculated (including the anisotropic sectors) in the leading order of the expansion in $y$, the exponent entering the correlator of the stirring force in the Navier--Stokes equation (one-loop approximation of the renormalization group). The anomalous exponents exhibit an hierarchy related to the degree of anisotropy: the less is the rank of the tensor operator, the less is its dimension. Thus the leading terms, determined by scalar operators, are the same as in the isotropic case, in agreement with the Kolmogorov's hypothesis of the local isotropy restoration.

cond-mat.stat-mech↗

arXiv2013

An Efficient Self-optimized Sampling Method for Rare Events in Nonequilibrium Systems

Rare events such as nucleation processes are of ubiquitous importance in real systems. The most popular method for nonequilibrium systems, forward flux sampling (FFS), samples rare events by using interfaces to partition the whole transition process into sequence of steps along an order parameter connecting the initial and final states. FFS usually suffers from two main difficulties: low computational efficiency due to bad interface locations and even being not applicable when trapping into unknown intermediate metastable states. In the present work, we propose an approach to overcome these difficulties, by self-adaptively locating the interfaces on the fly in an optimized manner. Contrary to the conventional FFS which set the interfaces with euqal distance of the order parameter, our approach determines the interfaces with equal transition probability which is shown to satisfy the optimization condition. This is done by firstly running long local trajectories starting from the current interface $ł_i$ to get the conditional probability distribution $P_c$, and then determining $ł_{i+1}$ by equalling $P_c$ to a give value $p_0$. With these optimized interfaces, FFS can be run in a much efficient way. In addition, our approach can conveniently find the intermediate metastable states by monitoring some special long trajectories that nither end at the initial state nor reach the next interface, the number of which will increase sharply from zero if such metastable states are encountered. We apply our approach to a model two-state system and a two-dimensional lattice gas Ising model. Our approach is shown to be much more efficient than the conventional FFS method without losing accuracy, and it can also well reproduce the two-step nucleation scenario of the Ising model with easy identification of the intermidiate metastable state.

stat.ME↗

arXiv2013

Simultaneous analysis of three-dimensional percolation models

We simulate the bond and site percolation models on several three-dimensional lattices, including the diamond, body-centered cubic, and face-centered cubic lattices. As on the simple-cubic lattice [Phys. Rev. E, \textbf{87} 052107 (2013)], it is observed that in comparison with dimensionless ratios based on cluster-size distribution, certain wrapping probabilities exhibit weaker finite-size corrections and are more sensitive to the deviation from percolation threshold $p_c$, and thus provide a powerful means for determining $p_c$. We analyze the numerical data of the wrapping probabilities simultaneously such that universal parameters are shared by the aforementioned models, and thus significantly improved estimates of $p_c$ are obtained.

cond-mat.stat-mech↗

arXiv2013

Collective behavior and evolutionary games - An introduction

This is an introduction to the special issue titled "Collective behavior and evolutionary games" that is in the making at Chaos, Solitons & Fractals. The term collective behavior covers many different phenomena in nature and society. From bird flocks and fish swarms to social movements and herding effects, it is the lack of a central planner that makes the spontaneous emergence of sometimes beautifully ordered and seemingly meticulously designed behavior all the more sensational and intriguing. The goal of the special issue is to attract submissions that identify unifying principles that describe the essential aspects of collective behavior, and which thus allow for a better interpretation and foster the understanding of the complexity arising in such systems. As the title of the special issue suggests, the later may come from the realm of evolutionary games, but this is certainly not a necessity, neither for this special issue, and certainly not in general. Interdisciplinary work on all aspects of collective behavior, regardless of background and motivation, and including synchronization and human cognition, is very welcome.

physics.soc-ph↗

arXiv2013

Evolutionary games with facilitators: When does selection favor cooperation?

We study the combined influence of selection and random fluctuations on the evolutionary dynamics of two-strategy ("cooperation" and "defection") games in populations comprising cooperation facilitators. The latter are individuals that support cooperation by enhancing the reproductive potential of cooperators relative to the fitness of defectors. By computing the fixation probability of a single cooperator in finite and well-mixed populations that include a fixed number of facilitators, and by using mean field analysis, we determine when selection promotes cooperation in the important classes of prisoner's dilemma, snowdrift and stag-hunt games. In particular, we identify the circumstances under which selection favors the replacement and invasion of defection by cooperation. Our findings, corroborated by stochastic simulations, show that the spread of cooperation can be promoted through various scenarios when the density of facilitators exceeds a critical value whose dependence on the population size and selection strength is analyzed. We also determine under which conditions cooperation is more likely to replace defection than vice versa. Keywords: Evolutionary games; dynamics of cooperation; social dilemmas; fixation; population dynamics.

q-bio.PE↗

arXiv2013

Contagion spreading on complex networks with local deterministic dynamics

Typically, contagion strength is modeled by a transmission rate $λ$, whereby all nodes in a network are treated uniformly in a mean-field approximation. However, local agents react differently to the same contagion based on their local characteristics. Following our recent work [EPL \textbf{99}, 58002 (2012)], we investigate contagion spreading models with local dynamics on complex networks. We therefore quantify contagions by their quality, $0 \leq α\leq 1$, and follow their spreading as their transmission condition (fitness) is evaluated by local agents. We choose various deterministic local rules. Initial spreading with exponential quality-dependent time scales is followed by a stationary state with a prevalence depending on the quality of the contagion. We also observe various interesting phenomena, for example, high prevalence without the participation of the hubs. This is in sharp contrast with the general belief that hubs play a central role in a typical spreading process. We further study the role of network topology in various models and find that as long as small-world effect exists, the underlying topology does not contribute to the final stationary state but only affects the initial spreading velocity.

physics.soc-ph↗