相关论文: Energy statistics in disordered systems: The local…

These are notes for a mini-course on the extremes of correlated random fields which I gave in the spring 2013 in Marseille. The first chapter recalls the paradigmatic random energy models with finitely many scales introduced by B. Derrida…

We study the $\pm J$ SK model for small $N$'s up to $N=9$. We sort the $2^{N(N-1)/2}$ possible realizations of the coupling matrix into equivalence classes according to the gauge symmetry and permutation symmetry and determine the energy…

We present a simple strategy in order to show the existence and uniqueness of the infinite volume limit of thermodynamic quantities, for a large class of mean field disordered models, as for example the Sherrington-Kirkpatrick model, and…

It is shown that the infinite random Heisenberg XXZ spin-$\frac12$ chain exhibits localization phenomena, such as spectral, eigenstate, and weak dynamical localization, in an arbitrary (but fixed) energy interval in a non-trivial region of…

The four principal energy conditions (ECs) in general relativity prohibit negative energies, repulsive gravity and superluminal energy flows. One must invoke exotic matter to violate any one of these, yet $\Lambda$CDM does so quite…

We show how statistical thermodynamics can be formulated in situations in which thermodynamics applies, while equilibrium statistical mechanics does not. A typical case is, in the words of Landau and Lifshitz, that of partial (or…

We present a spectral-theoretic approach to time-average statistical mechanics for general, non-equilibrium initial conditions. We consider the statistics of bounded, local additive functionals of reversible as well as irreversible ergodic…

The emergence of statistical mechanics for isolated classical systems comes about through chaotic dynamics and ergodicity. Here we review how similar questions can be answered in quantum systems. The crucial point is that individual energy…

Since the discovery of the accelerated expansion of the Universe, the constraints on the equation of state $w_\text{DE}$ of dark energy, the stress-energy component responsible for the acceleration, have tightened significantly. These…

In this paper I introduce the probability distribution of the local overlap in spin glasses. The properties of the local overlaps are studied in details. These quantities are related to the recently proposed local version of the fluctuation…

We consider ground state energies (GSE) of multipartite $p$-spin models. Relying on partially lifted random duality theory (pl RDT) concepts we introduce an analytical mechanism that produces easy to compute lower and upper GSE bounds for…

The estimation of rare event probabilities plays a pivotal role in diverse fields. Our aim is to determine the probability of a hazard or system failure occurring when a quantity of interest exceeds a critical value. In our approach, the…

Behavior of condensed matter systems deviating from the standard equilibrium conditions is discussed. Statistical properties of coupled dynamic-stochastic systems are studied within a combination of the maximum information principle and the…

In a recent paper we conjectured that for ferromagnetic Heisenberg models the smallest eigenvalues in the invariant subspaces of fixed total spin are monotone decreasing as a function of the total spin and called this property ferromagnetic…

We discuss a generalization of the conditions of validity of the interpolation method for the density of quenched free energy of mean field spin glasses. The condition is written just in terms of the $L^2$ metric structure of the Gaussian…

Despite considerable work on the energy-level and wavefunction statistics of disordered quantum systems, numerical studies of those statistics relevant for electron-electron interactions in mesoscopic systems have been lacking. We plug this…

This paper introduces and analyses a general statistical model, termed the RARE model, of random relaxation processes in disordered systems. The model considers excitations, that are randomly scattered around a reaction center in a general…

We study the probability distribution P(E) of the ground state energy E in various Ising spin glasses. In most models, P(E) seems to become Gaussian with a variance growing as the system's volume V. Exceptions include the…

The notion of complex energy landscape underpins the intriguing dynamical behaviors in many complex systems ranging from polymers, to brain activity, to social networks and glass transitions. The spin glass state found in dilute magnetic…

Random matrix ensembles are introduced that respect the local tensor structure of Hamiltonians describing a chain of $n$ distinguishable spin-half particles with nearest-neighbour interactions. We prove a central limit theorem for the…