arXiv subjects

Xiangyu Cao

Publications and source records attributed to Xiangyu Cao.

At least 55 records · Page 3Linked to original sources

arXiv2018

Incomplete thermalization from trap-induced integrability breaking: lessons from classical hard rods

We study a one-dimensional gas of hard rods trapped in a harmonic potential, which breaks integrability of the hard-rod interaction in a non-uniform way. We explore the consequences of such broken integrability for the dynamics of a large number of particles and find three distinct regimes: initial, chaotic, and stationary. The initial regime is captured by an evolution equation for the phase-space distribution function. For any finite number of particles, this hydrodynamics breaks down and the dynamics become chaotic after a characteristic time scale determined by the inter-particle distance and scattering length. The system fails to thermalize over the time-scale studied ($10^4$ natural units), but the time-averaged ensemble is a stationary state of the hydrodynamic evolution. We close by discussing logical extensions of the results to similar systems of quantum particles.

cond-mat.stat-mech↗

arXiv2018

Operator Product Expansion in Liouville Field Theory and Seiberg type transitions in log-correlated Random Energy Models

We study transitions in log-correlated Random Energy Models (logREMs) that are related to the violation of a Seiberg bound in Liouville field theory (LFT): the binding transition and the termination point transition (a.k.a. pre-freezing). By means of LFT-logREM mapping, replica symmetry breaking and traveling-wave equation techniques, we unify both transitions in a two-parameter diagram, which describes the free energy large deviations of logREMs with a deterministic background log potential, or equivalently, the joint moments of the free energy and Gibbs measure in logREMs without background potential. Under the LFT-logREM mapping, the transitions correspond to the competition of discrete and continuous terms in a four-point correlation function. Our results provide a statistical interpretation of a peculiar non-locality of the operator product expansion in LFT. The results are re-derived by a traveling-wave equation calculation, which shows that the features of LFT responsible for the transitions are reproduced in a simple model of diffusion with absorption. We examine also the problem by a replica symmetry breaking analysis. It complements the previous methods and reveals a rich large deviation structure of the free energy of logREMs with a deterministic background log potential. Many results are verified in the integrable circular logREM, by a replica-Coulomb gas integral approach. The related problem of common length (overlap) distribution is also considered. We provide a traveling-wave equation derivation of the LFT predictions announced in a precedent work.

cond-mat.stat-mech↗

arXiv2018

Pinning by rare defects and effective mobility for elastic interfaces in high dimensions

The existence of a depinning transition for a high dimensional interface in a weakly disordered medium is controversial. Following Larkin arguments and a perturbative expansion, one expects a linear response with a renormalized mobility $μ_{\text{eff}}$ . In this paper, we compare these predictions with the exact solution of a fully connected model, which displays a finite critical force $f_c$. At small disorder, we unveil an intermediary linear regime for $f_c < f < 1$ characterized by the renormalized mobility $μ_{\text{eff}}$. Our results suggest that in high dimension the critical force is always finite and determined by the effect of rare impurities that is missed by the perturbative expansion. However, the perturbative expansion correctly describes an intermediate regime that should be visible at small disorder.

cond-mat.dis-nn↗

arXiv2017

Log-correlated Random Energy Models with extensive free energy fluctuations: pathologies caused by rare events as signatures of phase transitions

We address systematically an apparent non-physical behavior of the free energy moment generating function for several instances of the logarithmically correlated models: the Fractional Brownian Motion with Hurst index $H = 0$ (fBm0) (and its bridge version), a 1D model appearing in decaying Burgers turbulence with log-correlated initial conditions, and finally, the two-dimensional logREM introduced in [Cao et al., Phys.Rev.Lett.,118,090601] based on the 2D Gaussian free field (GFF) with background charges and directly related to the Liouville field theory. All these models share anomalously large fluctuations of the associated free energy, with a variance proportional to the log of the system size. We argue that a seemingly non-physical vanishing of the moment generating function for some values of parameters is related to the termination point transition (a.k.a pre-freezing). We study the associated universal log corrections in the frozen phase, both for log-REMs and for the standard REM, filling a gap in the literature. For the above mentioned integrable instances of logREMs, we predict the non-trivial free energy cumulants describing non-Gaussian fluctuations on the top of the Gaussian with extensive variance. Some of the predictions are tested numerically.

cond-mat.stat-mech↗

arXiv2017

Localization of soft modes at the depinning transition

We characterize the soft modes of the dynamical matrix at the depinning transition, and compare it with the properties of the Anderson model (and long--range generalizations). The density of states at the edge of the spectrum displays a universal linear tail, different from the Lifshitz tails. The eigenvectors are instead very similar in the two matrix ensembles. We focus on the ground state (soft mode), which represents the epicenter of avalanche instabilities. We expect it to be localized in all finite dimensions, and make a clear connection between its localization length and the Larkin length of the depinning model. In the fully connected model, the weak--strong pinning transition coincides with a peculiar localization transition of the ground state.

cond-mat.dis-nn↗

arXiv2017

Liouville field theory and log-correlated Random Energy Models

An exact mapping is established between the $c\geq25$ Liouville field theory (LFT) and the Gibbs measure statistics of a thermal particle in a 2D Gaussian Free Field plus a logarithmic confining potential. The probability distribution of the position of the minimum of the energy landscape is obtained exactly by combining the conformal bootstrap and one-step replica symmetry breaking methods. Operator product expansions in LFT allow to unveil novel universal behaviours of the log-correlated Random Energy class. High precision numerical tests are given.

cond-mat.stat-mech↗

arXiv2017

Disordered statistical physics in low dimensions: extremes, glass transition, and localization

This thesis presents original results in two domains of disordered statistical physics: logarithmic correlated Random Energy Models (logREMs), and localization transitions in long-range random matrices. In the first part devoted to logREMs, we show how to characterise their common properties and model--specific data. Then we develop their replica symmetry breaking treatment, which leads to the freezing scenario of their free energy distribution and the general description of their minima process, in terms of decorated Poisson point process. We also report a series of new applications of the Jack polynomials in the exact predictions of some observables in the circular model and its variants. Finally, we present the recent progress on the exact connection between logREMs and the Liouville conformal field theory. The goal of the second part is to introduce and study a new class of banded random matrices, the broadly distributed class, which is characterid an effective sparseness. We will first study a specific model of the class, the Beta Banded random matrices, inspired by an exact mapping to a recently studied statistical model of long--range first--passage percolation/epidemics dynamics. Using analytical arguments based on the mapping and numerics, we show the existence of localization transitions with mobility edges in the "stretch--exponential" parameter--regime of the statistical models. Then, using a block--diagonalization renormalization approach, we argue that such localization transitions occur generically in the broadly distributed class.

cond-mat.dis-nn↗

arXiv2017

Genuine localisation transition in a long-range hopping model

We introduce and study a new class of Banded Random Matrix model describing sparse, long range quantum hopping in one dimension. Using a series of analytic arguments, numerical simulations, and mappings to statistical physics models, we establish the phase diagram of the model. A genuine localisation transition, with well defined mobility edges, appears as the hopping rate decreases slower than $\ell^{-2}$, where $\ell$ is the distance. Correspondingly, the decay of the localised states evolves from a standard exponential shape to a stretched exponential and finally to a novel $\exp(-C\ln^κ\ell)$ behaviour, with $κ> 1$.

cond-mat.stat-mech↗

arXiv2017

Second level semi-degenerate fields in W3 Toda theory: matrix element and differential equation

In a recent study we considered W3 Toda 4-point functions that involve matrix elements of a primary field with the highest-weight in the adjoint representation of sl3. We generalize this result by considering a semi-degenerate primary field, which has one null vector at level two. We obtain a sixth-order Fuchsian differential equation for the conformal blocks. We discuss the presence of multiplicities, the matrix elements and the fusion rules.

hep-th↗

arXiv2016

One step replica symmetry breaking and extreme order statistics of logarithmic REMs

Building upon the one-step replica symmetry breaking formalism, duly understood and ramified, we show that the sequence of ordered extreme values of a general class of Euclidean-space logarithmically correlated random energy models (logREMs) behave in the thermodynamic limit as a randomly shifted decorated exponential Poisson point process. The distribution of the random shift is determined solely by the large-distance ("infra-red", IR) limit of the model, and is equal to the free energy distribution at the critical temperature up to a translation. the decoration process is determined solely by the small-distance ("ultraviolet", UV) limit, in terms of the biased minimal process. Our approach provides connections of the replica framework to results in the probability literature and sheds further light on the freezing/duality conjecture which was the source of many previous results for log-REMs. In this way we derive the general and explicit formulae for the joint probability density of depths of the first and second minima (as well its higher-order generalizations) in terms of model-specific contributions from UV as well as IR limits. In particular, we show that the second min statistics is largely independent of details of UV data, whose influence is seen only through the mean value of the gap. For a given log-correlated field this parameter can be evaluated numerically, and we provide several numerical tests of our theory using the circular model of $1/f$-noise.

cond-mat.stat-mech↗

arXiv2016

Joint min-max distribution and Edwards-Anderson's order parameter of the circular $1 / f$-noise model

We calculate the joint min--max distribution and the Edwards-Anderson's order parameter for the circular model of $1 / f$-noise. Both quantities, as well as generalisations, are obtained exactly by combining the freezing-duality conjecture and Jack-polynomial techniques. Numerical checks come with significantly improved control of finite-size effects in the glassy phase, and the results convincingly validate the freezing-duality conjecture. Application to diffusive dynamics is discussed. We also provide a formula for the pre-factor ratio of the joint/marginal Carpentier-Le Doussal tail for minimum/maximum which applies to any logarithmic random energy model.

cond-mat.stat-mech↗

arXiv2015

Extreme value statistics of 2d Gaussian Free Field: effect of finite domains

We study minima statistics of the 2d Gaussian Free Field on circles in the unit disk with Dirichlet boundary condition. Free energy distributions of the associated Random Energy models are exactly calculated in the high temperature phase, and shown to satisfy the duality property, which enables us to predict the minima distribution by assuming the freezing scenario. Numerical tests are provided. Related questions concerning the GFF on a sphere are also considered.

cond-mat.stat-mech↗

arXiv2015

Conformal invariance of loop ensembles under Kardar-Parisi-Zhang dynamics

We study scaling properties of the honeycomb fully packed loop ensemble associated with a lozenge tiling model of rough surface, when the latter is driven out of equilibrium by Kardar-Parisi-Zhang (KPZ) type dynamics. We show numerically that conformal invariance and signatures of critical percolation appear in the stationary KPZ state. In terms of the two-component Coulomb gas description of the Edwards-Wilkinson stationary state, our finding is understood as the invariance of one component under the effect of the non-linear KPZ term. On the other hand, we show a breaking of conformal invariance when the level lines of the other component are considered.

cond-mat.stat-mech↗

arXiv2015

Black hole spectroscopy from Loop Quantum Gravity models

Using Monte Carlo simulations, we compute the integrated emission spectra of black holes in the framework of Loop Quantum Gravity (LQG). The black hole emission rates are governed by the entropy whose value, in recent holographic loop quantum gravity models, was shown to agree at leading order with the Bekenstein-Hawking entropy. Quantum corrections depend on the Barbero-Immirzi parameter $γ$. Starting with black holes of initial horizon area $A \sim 10^2$ in Planck units, we present the spectra for different values of $γ$. Each spectrum clearly decomposes in two distinct parts: a continuous background which corresponds to the semi-classical stages of the evaporation and a series of discrete peaks which constitutes a signature of the deep quantum structure of the black hole. We show that $γ$ has an effect on both parts that we analyze in details. Finally, we estimate the number of black holes and the instrumental resolution required to experimentally distinguish between the considered models.

gr-qc↗

arXiv2014

TASEP and Planar Binary Trees: A Combinatorial Approach

We give a simple explanation why the stationary state of the 1D TASEP model with open boundaries is related to the Catalan numbers. Our construction is based on planar binary trees and provides a combinatorial solution of the stationary state. We discuss the relation to Catalan tableaux approaches in an appendix.

math.CO↗

arXiv2011

Probing Loop Quantum Gravity with Evaporating Black Holes

This letter aims at showing that the observation of evaporating black holes should allow distinguishing between the usual Hawking behavior and Loop Quantum Gravity (LQG) expectations. We present a full Monte-Carlo simulation of the evaporation in LQG and statistical tests that discriminate between competing models. We conclude that contrarily to what was commonly thought, the discreteness of the area in LQG leads to characteristic features that qualify evaporating black holes as objects that could reveal quantum gravity footprints.

gr-qc↗

arXiv2011

The entropy of large black holes in loop quantum gravity: A combinatorics/analysis approach

The issue of a possible damping of the entropy periodicity for large black holes in Loop Quantum Gravity is highly debated. Using a combinatorics/analysis approach, we give strong arguments in favor of this damping, at least for prescriptions where the projection constraint is not fully implemented. This means that black holes in loop gravity exhibit an asymptotic Bekenstein-Hawking behavior, provided that a consistent choice of the Immirzi constant is made.

gr-qc↗

arXiv2011

Cohomological rigidity and the number of homeomorphism types for small covers over prisms

In this paper, based upon the basic theory for glued manifolds in M.W. Hirsch (1976) \cite[Chapter 8, §2 Gluing Manifolds Together]{h}, we give a method of constructing homeomorphisms between two small covers over simple convex polytopes. As a result we classify, up to homeomorphism, all small covers over a 3-dimensional prism $P^3(m)$ with $m\geq 3$. We introduce two invariants from colored prisms and other two invariants from ordinary cohomology rings with ${\Bbb Z}_2$-coefficients of small covers. These invariants can form a complete invariant system of homeomorphism types of all small covers over a prism in most cases. Then we show that the cohomological rigidity holds for all small covers over a prism $P^3(m)$ (i.e., cohomology rings with ${\Bbb Z}_2$-coefficients of all small covers over a $P^3(m)$ determine their homeomorphism types). In addition, we also calculate the number of homeomorphism types of all small covers over $P^3(m)$.

math.GT↗