Related papers: The Lanczos Algorithm for extensive Many-Body Syst…
We describe a strategy for attacking the canonical nuclear structure problem ---bound-state properties of a system of point nucleons interacting via a two-body potential---which involves an expansion in the number of particles scattering at…
It is argued that a typical many body energy eigenstate has a well defined thermodynamic entropy and that individual eigenstates possess thermodynamic characteristics analogous to those of generic isolated systems. We examine large systems…
The minimal set of thermodynamic control parameters consists of a statistical (thermal) and a mechanical one. These suffice to introduce all the pertinent thermodynamic variables; thermodynamic processes can then be defined as paths on this…
In a previous paper, we have developed a general theory of thermodynamic limits. We apply it here to three different Coulomb quantum systems, for which we prove the convergence of the free energy per unit volume. The first system is the…
We reconsider some general aspects about the mean field thermodynamical description of the astrophysical systems based on the microcanonical ensemble. Starting from these basis, we devote a special attention to the analysis of the scaling…
We propose an approach to statistical systems on lattices with sphere-like topology. Focusing on the Ising model, we consider the thermodynamic limit along a sequence of lattices which preserve the {\em fixed} large scale geometry. The…
Considering the standard abelian sandpile model in one dimension, we construct an infinite volume Markov process corresponding to its thermodynamic (infinite volume) limit. The main difficulty we overcome is the strong non-locality of the…
Quantum observables of generic many-body systems exhibit a universal pattern of growth in the Krylov space of operators. This pattern becomes particularly manifest in the Lanczos basis, where the evolution superoperator assumes the…
Ordinary differential equations obtained as limits of Markov processes appear in many settings. They may arise by scaling large systems, or by averaging rapidly fluctuating systems, or in systems involving multiple time-scales, by a…
We analyze the Lanczos method for matrix function approximation (Lanczos-FA), an iterative algorithm for computing $f(\mathbf{A}) \mathbf{b}$ when $\mathbf{A}$ is a Hermitian matrix and $\mathbf{b}$ is a given vector. Assuming that $f :…
There is presently considerable interest in accurately simulating the evolution of open systems for which Markovian master equations fail. Examples are systems that are time-dependent and/or strongly damped. A number of elegant methods have…
The two-body potential of systems with long-range interactions decays at large distances as $V(r)\sim 1/r^\alpha$, with $\alpha\leq d$, where $d$ is the space dimension. Examples are: gravitational systems, two-dimensional hydrodynamics,…
In order to provide a formally correct thermodynamical description of inhomogeneous fluids valid on all length scales down to the classical limit we postulate that all extensive quantities have locally extensive analogues. We derive local…
We propose a novel framework to characterize the thermalization of many-body dynamical systems close to integrable limits using the scaling properties of the full Lyapunov spectrum. We use a classical unitary map model to investigate…
We describe quantum many--body systems in terms of projected entangled--pair states, which naturally extend matrix product states to two and more dimensions. We present an algorithm to determine correlation functions in an efficient way. We…
The characterization of quantum critical phenomena is pivotal for the understanding and harnessing of quantum many-body physics. However, their complexity makes the inference of such fundamental processes difficult. Thus, efficient and…
By combining different ideas, a general and efficient protocol to deal with discontinuous phase transitions at low temperatures is proposed. For small $T$'s, it is possible to derive a generic analytic expression for appropriate order…
The paper discusses a family of Markov processes that represent many particle systems, and their limiting behaviour when the number of particles go to infinity. The first part concerns model of biological systems: a model for sympatric…
Estimating the steady-state properties of open many-body quantum systems is a fundamental challenge in quantum science and technologies. In this work, we present a scalable approach based on semi-definite programming to derive certified…
This paper presents an in-depth analysis of the anatomy of both thermodynamics and statistical mechanics, together with the relationships between their constituent parts. Based on this analysis, using the renormalization group and…