Showing papers in "Journal of Statistical Mechanics: Theory and Experiment in 2006"
TL;DR: A microscopic model of communicating autonomous agents performing language games without any central control is introduced and it is shown that the system undergoes a disorder/order transition, going through a sharp symmetry breaking process to reach a shared set of conventions.
Abstract: What processes can explain how very large populations are able to converge on the use of a particular word or grammatical construction without global coordination? Answering this question helps to understand why new language constructs usually propagate along an S-shaped curve with a rather sudden transition towards global agreement. It also helps to analyse and design new technologies that support or orchestrate self-organizing communication systems, such as recent social tagging systems for the web. The article introduces and studies a microscopic model of communicating autonomous agents performing language games without any central control. We show that the system undergoes a disorder/order transition, going through a sharp symmetry breaking process to reach a shared set of conventions. Before the transition, the system builds up non-trivial scale-invariant correlations, for instance in the distribution of competing synonyms, which display a Zipf-like law. These correlations make the system ready for the transition towards shared conventions, which, observed on the timescale of collective behaviours, becomes sharper and sharper with system size. This surprising result not only explains why human language can scale up to very large populations but also suggests ways to optimize artificial semiotic dynamics.
380 citations
TL;DR: In this article, the results of a bottleneck experiment with pedestrians are presented in the form of total times, fluxes, specific fluxes and time gaps, and the main aim was to find the dependence of these values on the bottleneck width.
Abstract: In this work the results of a bottleneck experiment with pedestrians are presented in the form of total times, fluxes, specific fluxes, and time gaps. A main aim was to find the dependence of these values on the bottleneck width. The results show a linear decline of the specific flux with increasing width as long as only one person at a time can pass, and a constant value for larger bottleneck widths. Differences between small (one person at a time) and wide bottlenecks (two persons at a time) were also found in the distribution of time gaps.
307 citations
TL;DR: In this paper, the authors used multifractal detrended fluctuation analysis (MF-DFA) to study sunspot number fluctuations and found that there are three crossover timescales in the fluctuation function.
Abstract: We use multifractal detrended fluctuation analysis (MF-DFA), to study sunspot number fluctuations. The result of the MF-DFA shows that there are three crossover timescales in the fluctuation function. We discuss how the existence of the crossover timescales is related to a sinusoidal trend. Using Fourier detrended fluctuation analysis, the sinusoidal trend is eliminated. The Hurst exponent of the time series without the sinusoidal trend is 0.12 ± 0.01. Also we find that these fluctuations have multifractal nature. Comparing the MF-DFA results for the remaining data set to those for shuffled and surrogate series, we conclude that its multifractal nature is almost entirely due to long range correlations.
278 citations
TL;DR: This paper shows that by choosing the temperatures with a modified version of the optimized ensemble feedback method, one can minimize the round-trip times between the lowest and highest temperatures which effectively increases the efficiency of the parallel tempering algorithm.
Abstract: We introduce an algorithm for systematically improving the efficiency of parallel tempering Monte Carlo simulations by optimizing the simulated temperature set. Our approach is closely related to a recently introduced adaptive algorithm that optimizes the simulated statistical ensemble in generalized broad-histogram Monte Carlo simulations. Conventionally, a temperature set is chosen in such a way that the acceptance rates for replica swaps between adjacent temperatures are independent of the temperature and large enough to ensure frequent swaps. In this paper, we show that by choosing the temperatures with a modified version of the optimized ensemble feedback method we can minimize the round-trip times between the lowest and highest temperatures which effectively increases the efficiency of the parallel tempering algorithm. In particular, the density of temperatures in the optimized temperature set increases at the 'bottlenecks' of the simulation, such as phase transitions. In turn, the acceptance rates are now temperature dependent in the optimized temperature ensemble. We illustrate the feedback-optimized parallel tempering algorithm by studying the two-dimensional Ising ferromagnet and the two-dimensional fully frustrated Ising model, and briefly discuss possible feedback schemes for systems that require configurational averages, such as spin glasses.
272 citations
TL;DR: In this paper, the Von Neumann entropy of a block of spins in a Heisenberg chain after a sudden quench in the anisotropy parameter was studied by means of the time dependent density matrix renormalization group algorithm.
Abstract: By means of the time dependent density matrix renormalization group algorithm we study the zero-temperature dynamics of the Von Neumann entropy of a block of spins in a Heisenberg chain after a sudden quench in the anisotropy parameter. In the absence of any disorder the block entropy increases linearly with time and then saturates. We analyse the velocity of propagation of the entanglement as a function of the initial and final anisotropies and compare our results, wherever possible, with those obtained by means of conformal field theory. In the disordered case we find a slower (logarithmic) evolution which may signal the onset of entanglement localization.
270 citations
TL;DR: In this paper, the authors derive the two-loop Bethe ansatz for the twist operator sector of gauge theory directly from the field theory and derive an all-loop prediction for the large spin anomalous dimensions of twist 2 operators.
Abstract: We derive the two-loop Bethe ansatz for the twist operator sector of gauge theory directly from the field theory. We then analyse a recently proposed perturbative asymptotic all-loop Bethe ansatz in the limit of large spacetime spin at large but finite twist, and find a novel all-loop scaling function. This function obeys the Kotikov–Lipatov transcendentality principle and does not depend on the twist. Under the assumption that one may extrapolate back to leading twist, our result yields an all-loop prediction for the large spin anomalous dimensions of twist 2 operators. The latter also appears as an undetermined function in a recent conjecture of Bern, Dixon and Smirnov for the all-loop structure of the maximally helicity violating n-point gluon amplitudes of gauge theory. This potentially establishes a direct link between the worldsheet and the spacetime S matrix approach. A further assumption for the validity of our prediction is that perturbative BMN (Berenstein–Maldacena–Nastase) scaling does not break down at four-loop level or beyond. We also discuss how the result gets modified if BMN scaling does break down. Finally, we show that our result qualitatively agrees at strong coupling with a prediction of string theory.
270 citations
TL;DR: In this paper, a logarithmic minimal model of the planar Temperley?Lieb algebra is constructed on the strip acting on link states and its associated Hamiltonian limits.
Abstract: Working in the dense loop representation, we use the planar Temperley?Lieb algebra to build integrable lattice models called logarithmic minimal models . Specifically, we construct Yang?Baxter integrable Temperley?Lieb models on the strip acting on link states and consider their associated Hamiltonian limits. These models and their associated representations of the Temperley?Lieb algebra are inherently non-local and not (time-reversal) symmetric. We argue that, in the continuum scaling limit, they yield logarithmic conformal field theories with central charges c = 1?(6(p?p')2/pp'), where p, p' = 1, 2, ... are coprime. The first few members of the principal series are critical dense polymers (m = 1, c = ?2), critical percolation (m = 2, c = 0) and the logarithmic Ising model (m = 3, c = 1/2). For the principal series, we find an infinite family of integrable and conformal boundary conditions organized in an extended Kac table with conformal weights ?r,s = (((m+1)r?ms)2?1)/4m(m+1), r, s = 1, 2, .... The associated conformal partition functions are given in terms of Virasoro characters of highest-weight representations. Individually, these characters decompose into a finite number of characters of irreducible representations. We show with examples how indecomposable representations arise from fusion.
261 citations
TL;DR: In this article, the results of a pedestrian counterflow experiment in a corridor of width 2 meters are presented, where 67 participants were divided into two groups with varying relative and absolute size and walked in opposite directions through a corridor.
Abstract: In this work the results of a pedestrian counterflow experiment in a corridor of width 2 m are presented. 67 participants were divided into two groups with varying relative and absolute size and walked in opposite directions through a corridor. The video footage taken from the experiment was evaluated for passing times, walking speeds, fluxes and lane formation, including symmetry breaking. The results include comparatively large fluxes and speeds as well as a maximal asymmetry between left- and right-hand traffic. The sum of flow and counterflow in any case turns out to be larger than the flow in all situations without counterflow.
256 citations
TL;DR: In this paper, the authors derived the Bethe ansatz equations describing the complete spectrum of the transition matrix of the partially asymmetric exclusion process with the most general open boundary conditions.
Abstract: We derive the Bethe ansatz equations describing the complete spectrum of the transition matrix of the partially asymmetric exclusion process with the most general open boundary conditions. By analysing these equations in detail for the cases of totally asymmetric and symmetric diffusion, we calculate the finite-size scaling of the spectral gap, which characterizes the approach to stationarity at large times. In the totally asymmetric case we observe boundary induced crossovers between massive, diffusive and KPZ (Kardar–Parisi–Zhang) scaling regimes. We further study higher excitations, and demonstrate the absence of oscillatory behaviour at large times on the 'coexistence line', which separates the massive low and high density phases. In the maximum current phase, oscillations are present on the KPZ scale . While independent of the boundary parameters, the spectral gap as well as the oscillation frequency in the maximum current phase have different values compared to the totally asymmetric exclusion process with periodic boundary conditions. We discuss a possible interpretation of our results in terms of an effective domain wall theory.
217 citations
TL;DR: The derivation details, logic, and motivation for the three loop calculus introduced in Chertkov and Chernyak (2006) are presented and local gauge symmetry transformations that clarify an important invariant feature of the BP solution are revealed.
Abstract: In this paper we present the derivation details, logic, and motivation for the three loop calculus introduced in Chertkov and Chernyak (2006 Phys. Rev. E 73 065102(R)). Generating functions for each of the three interrelated discrete statistical models are expressed in terms of a finite series. The first term in the series corresponds to the Bethe–Peierls belief–propagation (BP) contribution; the other terms are labelled by loops on the factor graph. All loop contributions are simple rational functions of spin correlation functions calculated within the BP approach. We discuss two alternative derivations of the loop series. One approach implements a set of local auxiliary integrations over continuous fields with the BP contribution corresponding to an integrand saddle-point value. The integrals are replaced by sums in the complementary approach, briefly explained in Chertkov and Chernyak (2006 Phys. Rev. E 73 065102(R)). Local gauge symmetry transformations that clarify an important invariant feature of the BP solution are revealed in both approaches. The individual terms change under the gauge transformation while the partition function remains invariant. The requirement for all individual terms to be nonzero only for closed loops in the factor graph (as opposed to paths with loose ends) is equivalent to fixing the first term in the series to be exactly equal to the BP contribution. Further applications of the loop calculus to problems in statistical physics, computer and information sciences are discussed.
212 citations
TL;DR: In this article, the effects of non-conservative forces that violate detailed balance and non-autonomous dynamics arising from the variation of an external parameter were examined under the unifying framework of Langevin dynamics.
Abstract: We examine classical, transient fluctuation theorems within the unifying framework of Langevin dynamics. We explicitly distinguish between the effects of non-conservative forces that violate detailed balance, and non-autonomous dynamics arising from the variation of an external parameter. When both these sources of nonequilibrium behaviour are present, there naturally arise two distinct fluctuation theorems.
TL;DR: In this article, the authors proposed a modification of the algorithm proposed by Newman for community detection (Phys. Rev. E 69 066133) which treats communities of different sizes on an equal footing, and show that it outperforms the original algorithm while retaining its speed.
Abstract: Identifying community structure can be a potent tool in the analysis and understanding of the structure of complex networks. Up to now, methods for evaluating the performance of identification algorithms use ad-hoc networks with communities of equal size. We show that inhomogeneities in community sizes can and do affect the performance of algorithms considerably, and propose an alternative method which takes these factors into account. Furthermore, we propose a simple modification of the algorithm proposed by Newman for community detection (Phys. Rev. E 69 066133) which treats communities of different sizes on an equal footing, and show that it outperforms the original algorithm while retaining its speed.
TL;DR: In this paper, the empirical constitutive laws and their interpretation using dimensional analysis are presented, and the results of different flow configurations are discussed based on comparison with recent studies, where the successes and limits of the approach are discussed.
Abstract: Recent experiments and numerical simulations of dry granular flows suggest that a simple rheological description in terms of a friction coefficient varying both with shear rate and pressure through a dimensionless inertial number may be sufficient to capture the major properties of granular flows. In this paper we first present the empirical constitutive laws and their interpretation using dimensional analysis, before analysing the prediction for different flow configurations. The successes and limits of the approach are discussed based on comparison with recent studies.
TL;DR: In this paper, a numerical optimization algorithm was proposed to obtain the maximum synchronizability and fast random walk spreading for a particular type of extremely homogeneous regular networks, with long loops and poor modular structure, called entangled networks.
Abstract: We report on some recent developments in the search for optimal network topologies First we review some basic concepts on spectral graph theory, including adjacency and Laplacian matrices, paying special attention to the topological implications of having large spectral gaps We also introduce related concepts such as 'expanders', Ramanujan, and Cage graphs Afterwards, we discuss two different dynamical features of Networks, synchronizability and flow of random walkers, so that they are optimized if the corresponding Laplacian matrix has a large spectral gap From this, we show, by developing a numerical optimization algorithm, that maximum synchronizability and fast random walk spreading are obtained for a particular type of extremely homogeneous regular networks, with long loops and poor modular structure, that we call entangled networks These turn out to be related to Ramanujan and Cage graphs We argue also that these graphs are very good finite-size approximations to Bethe lattices, and provide optimal or almost optimal solutions to many other problems, for instance searchability in the presence of congestion or performance of neural networks Finally, we study how these results are modified when studying dynamical processes controlled by a normalized (weighted and directed) dynamics; much more heterogeneous graphs are optimal in this case Finally, a critical discussion of the limitations and possible extensions of this work is presented
TL;DR: In this article, the authors study the cost of a network, as represented by the total length of all its edges, and its efficiency in terms of the directness of routes from point to point.
Abstract: We study spatial networks that are designed to distribute or collect a commodity, such as gas pipelines or train tracks. We focus on the cost of a network, as represented by the total length of all its edges, and its efficiency in terms of the directness of routes from point to point. Using data for several real-world examples, we find that distribution networks appear remarkably close to optimal where both these properties are concerned. We propose two models of network growth that offer explanations of how this situation might arise.
TL;DR: In this paper, the authors investigated continuous separation and size sorting of particles and blood cells suspended in a microchannel flow due to an acoustic force both numerically and experimentally, and found good agreement in the measured particle trajectories in the micro channel flow subjected to the acoustic force with those obtained by the numerical simulations up to the fitting parameter.
Abstract: Continuous separation and size sorting of particles and blood cells suspended in a microchannel flow due to an acoustic force are investigated both numerically and experimentally. Good agreement in the measured particle trajectories in a microchannel flow subjected to the acoustic force with those obtained by the numerical simulations up to the fitting parameter is found. High separation efficiency, particularly in a three-stage microdevice (up to 99.975%), for particles and blood cells leads us to believe that the device can be developed into commercially useful set-up. The novel particle size sorting microdevice provides an opportunity to replace rather expensive existing devices based on specific chemical bonding with an ultrasound cell size sorter that can be considerably improved by adding many stages for multistage size sorting.
TL;DR: This work derives an algorithm to compute the leading order of the logarithm of the number of solutions, of matchings with a given size, and an analytic result for the entropy in regular and Erd?s?R?nyi random graph ensembles.
Abstract: We study matchings on sparse random graphs by means of the cavity method. We first show how the method reproduces several known results about maximum and perfect matchings in regular and Erd?s?R?nyi random graphs. Our main new result is the computation of the entropy, i.e.?the leading order of the logarithm of the number of solutions, of matchings with a given size. We derive both an algorithm to compute this entropy for an arbitrary graph with a girth that diverges in the large size limit, and an analytic result for the entropy in regular and Erd?s?R?nyi random graph ensembles.
TL;DR: In this article, the authors consider the XXX-type and Gaudin quantum integrable models associated with the Lie algebra and show that the Bethe vectors for these models are eigenvectors of higher transfer matrices and compute the corresponding eigenvalues.
Abstract: We consider the XXX-type and Gaudin quantum integrable models associated with the Lie algebra . The models are defined on a tensor product of irreducible -modules. For each model, there exist N one-parameter families of commuting operators on , called the transfer matrices. We show that the Bethe vectors for these models, given by the algebraic nested Bethe ansatz, are eigenvectors of higher transfer matrices and compute the corresponding eigenvalues.
TL;DR: The analysis of weighted properties shows that centrality driven attacks are capable of shattering the network's communication or transport properties even at a very low level of damage in the connectivity pattern and the inclusion of weight and traffic provides evidence for the extreme vulnerability of complex networks to any targeted strategy.
Abstract: In real networks complex topological features are often associated with a diversity of interactions as measured by the weights of the links. Moreover, spatial constraints may also play an important role, resulting in a complex interplay between topology, weight, and geography. In order to study the vulnerability of such networks to intentional attacks, these attributes must therefore be considered along with the topological quantities. In order to tackle this issue, we consider the case of the worldwide airport network, which is a weighted heterogeneous network whose evolution and structure are influenced by traffic and geographical constraints. We first characterize relevant topological and weighted centrality measures and then use these quantities as selection criteria for the removal of vertices. We consider different attack strategies and different measures of the damage achieved in the network. The analysis of weighted properties shows that centrality driven attacks are capable of shattering the network's communication or transport properties even at a very low level of damage in the connectivity pattern. The inclusion of weight and traffic therefore provides evidence for the extreme vulnerability of complex networks to any targeted strategy and the need for them to be considered as key features in the finding and development of defensive strategies.
TL;DR: In this article, a junction of three quantum wires enclosing a magnetic flux is modeled as spinless spinless Tomonaga-Luttinger liquids, where the wires are modelled as single-channel spinless TLCs.
Abstract: We study a junction of three quantum wires enclosing a magnetic flux. The wires are modelled as single-channel spinless Tomonaga–Luttinger liquids. This is the simplest problem of a quantum junction between Tomonaga–Luttinger liquids in which Fermi statistics enter in a non-trivial way. We study the problem using a mapping onto the dissipative Hofstadter model, describing a single particle moving on a plane in a magnetic field and a periodic potential coupled to a harmonic oscillator bath. Alternatively we study the problem by identifying boundary conditions corresponding to the low energy fixed points. We obtain a rich phase diagram including a chiral fixed point in which the asymmetric current flow is highly sensitive to the sign of the flux and a phase in which electron pair tunnelling dominates. We also study the effects on the conductance tensor of the junction of contacting the three quantum wires to Fermi liquid reservoirs.
TL;DR: In this article, the authors explicitly determine the large deviation function of the energy flow of a Brownian particle coupled to two heat baths at different temperatures, based on the toy model introduced by Derrida and Brunet.
Abstract: We explicitly determine the large deviation function of the energy flow of a Brownian particle coupled to two heat baths at different temperatures. This toy model, initially introduced by Derrida and Brunet (2005, Einstein aujourd'hui (Les Ulis: EDP Sciences)), not only allows us to sort out the influence of initial conditions on large deviation functions but also allows us to pinpoint various restrictions bearing upon the range of validity of the Fluctuation Relation.
TL;DR: In this paper, the authors derived the Hamiltonian and corresponding asymptotic Bethe ansatz at the leading four perturbative orders with several free parameters and identified the moduli of the integrable system.
Abstract: Quantum spin chains arise naturally from perturbative large-N field theories and matrix models. The Hamiltonian of such a model is a long-range deformation of nearest-neighbor type interactions. Here, we study the most general long-range integrable spin chain with spins transforming in the fundamental representation of gl(n). We derive the Hamiltonian and the corresponding asymptotic Bethe ansatz at the leading four perturbative orders with several free parameters. Furthermore, we propose Bethe equations for all orders and identify the moduli of the integrable system. We finally apply our results to plane-wave matrix theory and show that the Hamiltonian in a closed sector is not of this form and therefore not integrable beyond the first perturbative order. This also implies that the complete model is not integrable.
TL;DR: In this article, the exact S-matrix and the Bethe ansatz solution for three sigma models arise as subsectors of string theory in AdS(5)xS (5): Landau-Lifshitz model (non-relativistic sigma-model on S(2), Alday-Arutyunov-Frolov model (fermionic sigma model with su(1|1) symmetry), and Faddeev-Reshetikhin model (string Sigma model on S (3)x
Abstract: We compute the exact S-matrix and give the Bethe ansatz solution for three sigma-models which arise as subsectors of string theory in AdS(5)xS(5): Landau-Lifshitz model (non-relativistic sigma-model on S(2)), Alday-Arutyunov-Frolov model (fermionic sigma-model with su(1|1) symmetry), and Faddeev-Reshetikhin model (string sigma-model on S(3)xR).
TL;DR: In this article, the shape of macroscopic rods has been investigated to investigate the effect of shape on the nonequilibrium phase behavior of a horizontal monolayer of rods, and the shape plays an important role in determining the nature of the orientational ordering at high packing fraction.
Abstract: We study experimentally the nonequilibrium phase behaviour of a horizontal monolayer of macroscopic rods. The motion of the rods in two dimensions is driven by vibrations in the vertical direction. In addition to varying packing fraction and aspect ratio as in most studies on hard-particle systems, we take advantage of our ability to vary the precise shape of these macroscopic particles to investigate the effect of shape on their nonequilibrium steady states. We find that the shape plays an important role in determining the nature of the orientational ordering at high packing fraction. Cylindrical particles show substantial tetratic correlations over a range of aspect ratios where spherocylinders have previously been shown to undergo transitions between isotropic and nematic phases. Particles that are thinner at the ends (rolling pins or bails) show nematic ordering over the same range of aspect ratios, with a well established nematic phase at large aspect ratio and a defect-ridden nematic state with large-scale swirling motion at small aspect ratios. Finally, long-grain, basmati rice, whose geometry is intermediate between the two shapes above, shows phases with strong indications of smectic order.
TL;DR: In this article, the exact four-spinon contribution to the zero-temperature dynamical structure factor of the spin-1/2 Heisenberg isotropic antiferromagnet in zero magnetic field, directly in the thermodynamic limit, was computed.
Abstract: We compute the exact four-spinon contribution to the zero-temperature dynamical structure factor of the spin-1/2 Heisenberg isotropic antiferromagnet in zero magnetic field, directly in the thermodynamic limit. We make use of the expressions for matrix elements of local spin operators obtained by Jimbo and Miwa using the quantum affine symmetry of the model, and of their adaptation to the isotropic case by Abada, Bougourzi and Si-Lakhal (correcting some overall factors). The four-spinon contribution to the first frequency moment sum rule at fixed momentum is calculated. This shows, as expected, that most of the remaining correlation weight above the known two-spinon part is carried by four-spinon states. Our results therefore provide an extremely accurate description of the exact structure factor.
TL;DR: In this article, the authors examine the properties of force chains and the force chain network as they evolve during the course of the deformation and find that increasing interparticle friction, packing density and degree of polydispersity promote the formation of straighter chains and a greater degree of branching in the network.
Abstract: Interparticle contact friction, packing density and polydispersity are known to be major contributors to the macroscopic strength of particulate assemblies, that is, their bulk resistance to deformation. For example, when a solid object penetrates a particulate material, the penetration resistance (i.e. the force opposing the object) increases concomitantly with an increase in the degree of polydispersity, packing density and interparticle friction. To establish the underlying mechanisms by which these properties govern the macroscopic response, we characterize quantitatively force propagation at length scales beyond that of the interparticle contact region. Using data derived from discrete element simulations of a two-dimensional granular assembly subject to indentation by a rigid flat punch, we examine the properties of force chains and the force chain network as they evolve during the course of the deformation. Findings indicate that increasing interparticle friction, packing density and degree of polydispersity promotes the formation of straighter chains and a greater degree of branching in the force chain network. Although the force chain length appears to be independent of friction and polydispersity, on average, denser systems tend to favour shorter chains. Thus, straighter and shorter force chains, combined with a greater degree of branching in the force chain network, result in a macroscopically stronger granular material.
TL;DR: In this article, a general model of weighted networks via an optimization principle is proposed, and the topology of the optimal network turns out to be a spanning tree that minimizes a combination of topological and metric quantities.
Abstract: Inspired by studies on the airports' network and the physical Internet, we propose a general model of weighted networks via an optimization principle. The topology of the optimal network turns out to be a spanning tree that minimizes a combination of topological and metric quantities. It is characterized by strongly heterogeneous traffic, non-trivial correlations between distance and traffic and a broadly distributed centrality. A clear spatial hierarchical organization, with local hubs distributing traffic in smaller regions, emerges as a result of the optimization. Varying the parameters of the cost function, different classes of trees are recovered, including in particular the minimum spanning tree and the shortest path tree. These results suggest that a variational approach represents an alternative and possibly very meaningful path to the study of the structure of complex weighted networks.
TL;DR: In this paper, the lattice 1-site probabilities of the four height variables in the two-dimensional Abelian sandpile model were computed and compared with the predictions of a logarithmic conformal theory with central charge c=-2.
Abstract: We compute the lattice 1-site probabilities, on the upper half-plane, of the four height variables in the two-dimensional Abelian sandpile model. We find their exact scaling form when the insertion point is far from the boundary, and when the boundary is either open or closed. Comparing with the predictions of a logarithmic conformal theory with central charge c=-2, we find a full compatibility with the following field assignments: the heights 2, 3 and 4 behave like (an unusual realization of) the logarithmic partner of a primary field with scaling dimension 2, the primary field itself being associated with the height 1 variable. Finite size corrections are also computed and successfully compared with numerical simulations. Relying on these field assignments, we formulate a conjecture for the scaling form of the lattice 2-point correlations of the height variables on the plane, which remain as yet unknown. The way conformal invariance is realized in this system points to a local field theory with c=-2 which is different from the triplet theory. Comment: 68 pages, 17 figures; v2: published version (minor corrections, one comment added)
TL;DR: The fluctuation theorem for currents is applied to several mesoscopic systems on the basis of Schnakenberg's network theory, which allows one to verify its conditions of validity as mentioned in this paper.
Abstract: The fluctuation theorem for currents is applied to several mesoscopic systems on the basis of Schnakenberg's network theory, which allows one to verify its conditions of validity. A graph is associated with the master equation ruling the random process and its cycles can be used to obtain the thermodynamic forces or affinities corresponding to the nonequilibrium constraints. This provides a method of defining the independent currents crossing the system in nonequilibrium steady states and to formulate the fluctuation theorem for the currents. This result is applied to out-of-equilibrium diffusion in a chain, to a biophysical model of ion channels in a membrane, and to electronic transport in mesoscopic circuits made of several tunnel junctions. In this latter, we show that the generalizations of Onsager's reciprocity relations to the nonlinear response coefficients also hold.
TL;DR: In this article, the authors analyzed the symmetries and the self-consistent perturbative approaches of dynamical field theories for glass-forming liquids and obtained symmetry-preserving mode-coupling equations and discussed their advantages and drawbacks.
Abstract: We analyse the symmetries and the self-consistent perturbative approaches of dynamical field theories for glass-forming liquids. In particular, we focus on the time-reversal symmetry, which is crucial to obtain fluctuation–dissipation relations (FDRs). Previous field theoretical treatment violated this symmetry, whereas others pointed out that constructing symmetry-preserving perturbation theories is a crucial and open issue. In this work we solve this problem and then apply our results to the mode-coupling theory of the glass transition (MCT). We show that in the context of dynamical field theories for glass-forming liquids time-reversal symmetry is expressed as a nonlinear field transformation that leaves the action invariant. Because of this nonlinearity, standard perturbation theories generically do not preserve time-reversal symmetry and in particular fluctuation–dissipation relations. We show how one can cure this problem and set up symmetry preserving perturbation theories by introducing some auxiliary fields. As an outcome we obtain Schwinger–Dyson dynamical equations that automatically preserve FDR and that serve as a basis for carrying out symmetry-preserving approximations. We apply our results to the mode-coupling theory of the glass transition, revisiting previous field theory derivations of MCT equations and showing that they generically violate FDR. We obtain symmetry-preserving mode-coupling equations and discuss their advantages and drawbacks. Furthermore, we show, contrary to previous works, that the structure of the dynamic equations is such that the ideal glass transition is not cut off at any finite order of perturbation theory, even in the presence of coupling between current and density. The opposite results found in previous field theoretical works, such as the ones based on nonlinear fluctuating hydrodynamics, were only due to an incorrect treatment of time-reversal symmetry.