Related papers: Quantum Optimal Transport and Weak Topologies
A variant of the classical optimal transportation problem is: among all joint measures with fixed marginals and which are dominated by a given density, find the optimal one. Existence and uniqueness of solutions to this variant were…
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…
We bring together the semiclassical approximation, matrix integrals and the theory of symmetric polynomials in order to solve a long standing problem in the field of quantum chaos: to compute transport moments when tunnel barriers are…
Optimal transport is the problem of designing a joint distribution for two random variables with fixed marginals. In virtually the entire literature on this topic, the objective is to minimize expected cost. This paper is the first to study…
In the field of optimal transport, two prominent subfields face each other: (i) unregularized optimal transport, "\`a-la-Kantorovich", which leads to extremely sparse plans but with algorithms that scale poorly, and (ii)…
We study quasi-modular pseudometric spaces as asymmetric refinements of modular metric structures. To each such space we associate canonical forward and backward quasi-uniformities and the corresponding directional topologies. We introduce…
Unprecedented control over the manufacture of electronic devices on nanometer scale has allowed to perform highly controllable and fine-tuned experiments in the quantum regime where exotic effects can nowadays be measured. In quantum dot…
The theory of Monge-Kantorovich Optimal Mass Transport (OMT) has in recent years spurred a fast developing phase of research in stochastic control, control of ensemble systems, thermodynamics, data science, and several other fields in…
Klein tunneling stands as a fundamental probe of relativistic quantum transport in two-dimensional materials. We investigate this phenomenon in quadratic band-touching systems, where the Hilbert-Schmidt quantum distance plays a central role…
We show quantitative stability results for the geometric "cells" arising in semi-discrete optimal transport problems. Our results show two types of stability, the first is stability of the associated Laguerre cells in measure, without any…
This article gives an introduction to optimal transport, a mathematical theory that makes it possible to measure distances between functions (or distances between more general objects), to interpolate between objects or to enforce…
We study the Hilbert bundle description of stochastic quantum mechanics in curved spacetime developed by Prugove\v{c}ki, which gives a powerful new framework for exploring the quantum mechanical propagation of states in curved spacetime. We…
We investigate stability properties of weak supermartingale optimal transport (WSOT) problems on $\mathbb{R}$. For probability measures $\mu,\nu\in\mathcal{P}_r$ satisfying $\mu \leq_{cd} \nu$ (equivalently, $\Pi_S(\mu,\nu)\neq\emptyset$),…
Transport properties play a crucial role in several fields of science, as biology, chemistry, sociology, information science, and physics. The behavior of many dynamical processes running over complex networks is known to be closely related…
Optimal transport (OT) compares probability distributions by computing a meaningful alignment between their samples. CO-optimal transport (COOT) takes this comparison further by inferring an alignment between features as well. While this…
In this paper we introduce a theoretical framework for semi-discrete optimization using ideas from optimal transport. Our primary motivation is in the field of deep learning, and specifically in the task of neural architecture search. With…
In quantum mechanics, systems can be described in phase space in terms of the Wigner function and the star-product operation. Quantum characteristics, which appear in the Heisenberg picture as the Weyl's symbols of operators of canonical…
The exchange of information between an open quantum system and its environment, especially the backflow of information from the environment to the open system associated with quantum notions of non-Markovianity, is a widely discussed topic…
We derive nearly tight and non-asymptotic convergence bounds for solutions of entropic semi-discrete optimal transport. These bounds quantify the stability of the dual solutions of the regularized problem (sometimes called Sinkhorn…
We report a numerical study of transport properties of a quantum dot with superconducting leads. We introduce a general phenomenological model of quantum dot transport, in which electron tunnel rates are computed within the Fermi's Golden…