相关论文: Dynamics and Quantum Optimal Transport: Three lect…
These notes are based on the lectures given by the second author at the School on Optimal Transport on Quantum Structures at Erd\"os Center in September 2022. The focus of the exposition is on two recently introduced approaches on quantum…
This text is a set of lecture notes for a 4.5-hour course given at the Erd\"os Center (R\'enyi Institute, Budapest) during the Summer School "Optimal Transport on Quantum Structures" (September 19th-23rd, 2023). Lecture I introduces the…
These notes are based on a series of three lectures given at the Les Houches summer school on 'Integrability in Atomic and Condensed Matter Physics' in August 2018. They provide an introduction into the unusual transport properties of…
This survey has been written in occasion of the School and Workshop about Optimal Transport on Quantum Structures at Erd\"os Center in September 2022. We discuss some recent results on noncommutative entropic optimal transport problems and…
In this Chapter, we present recent theoretical developments on the finite temperature transport of one dimensional electronic and magnetic quantum systems as described by a variety of prototype models. In particular, we discuss the…
A unified view on macroscopic thermodynamics and quantum transport is presented. Thermodynamic processes with an exchange of energy between two systems necessarily involve the flow of other balanceable quantities. These flows are first…
The theory of optimal transport of probability measures has wide-ranging applications across a number of different fields, including concentration of measure, machine learning, Markov chains, and economics. The generalisation of optimal…
Quantum transport across discrete structures is a relevant topic of solid state physics and quantum information science, which can be suitably studied in the context of continuous-time quantum walks. The addition of phases degrees of…
Notes of five lectures given at the 2003 European School of High-Energy Physics, Tsakhkadzor, Armenia, September 2003
Recently, Optimal Transport has been proposed as a probabilistic framework in Machine Learning for comparing and manipulating probability distributions. This is rooted in its rich history and theory, and has offered new solutions to…
These lecture notes present the quantitative harmonic approximation result for quadratic optimal transport and general measures obtained by Goldman and Otto. The aim is to give a clear presentation of the proof of the main theorem with more…
This paper collects and extends the lectures I gave at the "XXIV International Fall Workshop on Geometry and Physics" held in Zaragoza (Spain) August 31 - September 4, 2015. Within these lectures I review the formulation of Quantum…
Notes of a 8h course given at the University of G\"oteborg during an Erasmus exchange visit, June 11-15, 2018. It is intended for PhD and graduate students familiar with $C^*$-algebras but not specializing in quantum groups. The proofs, if…
We discuss methods of Optimal Transportation Theory and its relations to problems in quantum mechanics. This essentially means that the cost function is some Hamiltonian $H(q,p)$ on a phase space (symplectic manifold), and the marginal…
In this series of lectures we introduce the Monge-Kantorovich problem of optimally transporting one distribution of mass onto another, where optimality is measured against a cost function c(x,y). Connections to geometry, inequalities, and…
This article introduces a new notion of optimal transport (OT) between tensor fields, which are measures whose values are positive semidefinite (PSD) matrices. This "quantum" formulation of OT (Q-OT) corresponds to a relaxed version of the…
We discuss recent developments in the study of quantum wavefunctions and transport in classically ergodic systems. Surprisingly, short-time classical dynamics leaves permanent imprints on long-time and stationary quantum behavior, which are…
These lecture notes provide an elementary introduction, within the framework of finite quantum systems, to recent developments in the theory of entropic fluctuations.
I. Introduction (Preface, Nanostructures in Si Inversion Layers, Nanostructures in GaAs-AlGaAs Heterostructures, Basic Properties). II. Diffusive and Quasi-Ballistic Transport (Classical Size Effects, Weak Localization, Conductance…
I briefly review some of the recent progress in quantum field theory in curved spacetime and other aspects of semiclassical gravity, as reported at the D3 Workshop at GR15.