相关论文: Convergence of Dynamics on Inductive Systems of Ba…

We survey an area of recent development, relating dynamics to theoretical computer science. We discuss the theoretical limits of simulation and computation of interesting quantities in dynamical systems. We will focus on central objects of…

Classical Bianchi-Lie, Backlund and Darboux transformations are considered. Their generalizations for the dynamical systems are discussed. For the transformation being the generalization of the normal shift the special class of dynamical…

The reduction of dynamical systems has a rich history, with many important applications related to stability, control and verification. Reduction of nonlinear systems is typically performed in an exact manner - as is the case with…

We consider non-linear evolution equations arising from mean-field limits of particle systems on discrete spaces. We investigate a notion of curvature bounds for these dynamics based on convexity of the free energy along interpolations in a…

For algorithms based on interacting particle systems that admit a mean-field description, convergence analysis is often more accessible at the mean-field level. In order to transfer convergence results obtained at the mean-field level to…

We review various bounds concerning out-of-equilibrium dynamics in few-level and many-body quantum systems. We primarily focus on closed quantum systems but will also mention some related results for open quantum systems and classical…

In this paper, we introduce generalized dichotomies for nonautonomous random linear dynamical systems acting on arbitrary Banach spaces, and obtain their complete characterization in terms of an appropriate admissibility property. These…

We review various characterizations of uniform convexity and smoothness on norm balls in finite-dimensional spaces and connect results stemming from the geometry of Banach spaces with \textit{scaling inequalities} used in analysing the…

We consider the class of quantum mechanical master equations defined on a generic Banach space, arising by projecting weakly perturbed one-parameter groups of isometries. We show that the possible semigroup approximations are far from…

The mean-field approximations of many-boson dynamics are known to be effective in many physical relevant situations. The mathematical justifications of such approximations rely generally on specific considerations which depend too much on…

Quench dynamics is an active area of study encompassing condensed matter physics and quantum information, with applications to cold-atomic gases and pump-probe spectroscopy of materials. Recent theoretical progress in studying quantum…

A formalism for studying the dynamics of quantum systems embedded in classical spin baths is introduced. The theory is based on generalized antisymmetric brackets and predicts the presence of open-path off-diagonal geometric phases in the…

We prove new characterisations of exponential stability for positive linear discrete-time systems in ordered Banach spaces, in terms of small-gain conditions. Such conditions have played an important role in the finite-dimensional systems…

We develop a generic method to compute the dynamics induced by quenches in completely connected quantum systems. These models are expected to provide a mean-field description at least of the short time dynamics of finite dimensional system.…

The article considers systems of interacting particles on networks with adaptively coupled dynamics. Such processes appear frequently in natural processes and applications. Relying on the notion of graph convergence, we prove that for large…

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…

The classical criterion for compactness in Banach spaces of functions can be reformulated into a simple tightness condition in the time-frequency domain. This description preserves more explicitly the symmetry between time and frequency…

This paper establishes limit theorems and quantitative statistical stability for a class of piecewise partially hyperbolic maps that are not necessarily continuous nor locally invertible. By employing a flexible functional-analytic…

This article deals with the realisation of constraints in underdamped Langevin dynamics via soft-constrained dynamics. Specifically, we study systems with a large (or small) parameter that controls the constraint mechanisms, e.g. the…

In this article we propose a conception of mixed limits of functional spaces as the case, when the upper limit (projective limit of inductive limits) and the lower limit (inductive limit of projective limits) coincide as topological spaces,…