Related papers: Integrability in out-of-equilibrium systems

We derive a number of exact relations between equilibrium and nonequilibrium quantities for spin glasses in external fields using the Jarzynski equality and gauge symmetry. For randomly-distributed longitudinal fields, a lower bound is…

Recent years have witnessed a wave of research activities in systems science toward the study of population systems. The driving force behind this shift was geared by numerous emerging and ever-changing technologies in life and physical…

This note presents a summary and review of various conditions and characterizations for matrix stability (in particular diagonal matrix stability) and matrix stabilizability.

In a previous article [N. Delice, F.W. Nijhoff and S. Yoo-Kong, J. Phys. A: Math. Theor. 48(3) (2015), 035206] a novel class of elliptic Lax pairs for integrable lattice equations was introduced. The present article proposes a…

We address a particular problem of output regulation for multi-input multi-output nonlinear systems. Specifically, we are interested in making the stability of an equilibrium point and the regulation to zero of an output, robust to (small)…

Earlier two of us (J.L. and L.P.) considered a matrix model for a two-level system interacting with a $n\times n$ reservoir and assuming that the interaction is modelled by a random matrix. We presented there a formula for the reduced…

Motivated by the recent preprint [arXiv:2004.08412] by Ayala, Carinci, and Redig, we first provide a general framework for the study of scaling limits of higher order fields. Then, by considering the same class of infinite interacting…

Theoretical studies of nonequilibrium systems are complicated by the lack of a general framework. In this work we first show that a transformation introduced by Ao recently (J. Phys. A {\bf 37}, L25 (2004)) is related to previous works of…

The concept of structural invariance previously introduced by the authors is used to argue that the connection between random matrix theory and quantum systems with a chaotic classical counterpart is in fact largely exact in the…

In the time evolution of isolated quantum systems out of equilibrium, local observables generally relax to a long-time asymptotic value, governed by the expectation values (diagonal matrix elements) of the corresponding operator in the…

Some formulas and speculations are presented relative to integrable systems and quantum mechanics.

We present and discuss a general density-matrix description of energy-dissipation and decoherence phenomena in open quantum systems, able to overcome the intrinsic limitations of the conventional Markov approximation. In particular, the…

Basic notions regarding classical integrable systems are reviewed. An algebraic description of the classical integrable models together with the zero curvature condition description is presented. The classical r-matrix approach for discrete…

Random matrices now play a role in many parts of computational mathematics. To advance these applications, it is desirable to have tools that are flexible, easy to use, and powerful. Over the last 25 years, researchers have developed a…

An overview of recent studies of nonequilibrium bound interfaces is given. Attention is focused on Kardar-Parisi-Zhang interfaces in the presence of upper and lower walls, interacting via short-- and long--ranged potentials. A comparison…

This paper considers the problem of recovery of a low-rank matrix in the situation when most of its entries are not observed and a fraction of observed entries are corrupted. The observations are noisy realizations of the sum of a low rank…

This paper provides the best bounds to date on the number of randomly sampled entries required to reconstruct an unknown low rank matrix. These results improve on prior work by Candes and Recht, Candes and Tao, and Keshavan, Montanari, and…

In this arxiv-post I present my solutions (published or not) to Problems that appeared in Amer. Math. Monthly, Math. Magazine, Elemente der Mathematik and CRUX, that were mostly done in collaboration with Rudolf Rupp. Some of them…

Long-range interacting systems may exhibit ensemble inequivalence and can possibly attain equilibrium states under completely open conditions, for which energy, volume and number of particles simultaneously fluctuate. Here we consider a…

This paper examines the problem of state estimation in power distribution systems under low-observability conditions. The recently proposed constrained matrix completion method which combines the standard matrix completion method and power…