Related papers: Quantum and Semiquantum Pseudometrics and Applicat…
This paper presents the quantum Moebius-Escher-Penrose hypergraph, drawing inspiration from paradoxical constructs such as the Moebius strip and Penrose's `impossible objects'. The hypergraph is constructed using faithful orthogonal…
A detailed real time description of quantum tunneling in the semiclassical limit is given, using complex classical trajectories. This picture connects naturally with the ideas of post-selection and weak measurement introduced by Aharonov…
In this paper a new look on the electro-magnetic duality is presented and appropriately exploited. The duality analysis in the nonrelativistic and relativistic formulations is shown to lead to the idea the mathematical model field to be a…
We consider the problem of optimal approximation of a target measure by an atomic measure with $N$ atoms, in branched optimal transport distance. This is a new branched transport version of optimal quantization problems. New difficulties…
We show that for a metric space with an even number of points there is a 1-Lipschitz map to a tree-like space with the same matching number. This result gives the first basic version of an unoriented Kantorovich duality. The study of the…
Given a topological dynamical system $(X,T)$, we study properties of the mean orbital pseudo-metric $\bar E$ defined by \[ \bar E(x,y)= \limsup_{n\to\infty } \min_{\sigma\in S_n}\frac{1}{n}\sum_{k=0}^{n-1}d(T^k(x),T^{\sigma(k)}(y)), \]…
Electronic transport through a 2D deca-nanometer length channel with correlated and anti-correlated surfaces morphologies is studied using the Keldysh non-equilibrium Green function technique. Due to the pseudo-periodicity of these…
We analyze the behavior of quantum dynamical entropies production from sequences of quantum approximants approaching their (chaotic) classical limit. The model of the quantized hyperbolic automorphisms of the 2-torus is examined in detail…
One of the most fundamental difference between classical and quantum mechanics is observed in the particle tunneling through a localized potential: the former predicts a discontinuous transmission coefficient ($T$) as a function in incident…
In this paper we consider the semiclassical version of pseudo-differential operators on the lattice space $\hbar \mathbb{Z}^n$. The current work is an extension of a previous work and agrees with it in the limit of the parameter $\hbar…
In this paper, we introduce weak optimal entropy transport problems that cover both optimal entropy transport problems and weak optimal transport problems introduced by Liero, Mielke, and Savar\'{e} [27]; and Gozlan, Roberto, Samson and…
Canonical variables for the Poisson algebra of quantum moments are introduced here, expressing semiclassical quantum mechanics as a canonical dynamical system that extends the classical phase space. New realizations for up to fourth order…
We study the Classical Probability analogue of the dilations of a quantum dynamical semigroup in Quantum Probability. Given a (not necessarily homogeneous) Markov chain in discrete time in a finite state space E, we introduce a second…
A semiclassical Bohr-Sommerfeld approximation is derived for an N-particle, two-mode Bose-Hubbard system modeling a Bose-Einstein condensate in a double-well potential. This semiclassical description is based on the `classical' dynamics of…
We present evidence that anomalous transport in the classical standard map results in strong enhancement of fluctuations in the localization length of quasienergy states in the corresponding quantum dynamics. This generic effect occurs even…
Over the past five years, multi-marginal optimal transport, a generalization of the well known optimal transport problem of Monge and Kantorovich, has begun to attract considerable attention, due in part to a wide variety of emerging…
Using tools from the theory of optimal transport, we establish several results concerning isometric actions of amenable topological groups with potentially unbounded orbits. Specifically, suppose $d$ is a compatible left-invariant metric on…
This paper establishes a robust link between quantum dynamics and classical ones by deriving probabilistic representation for both continuous time and discrete time quantum walks. We first adapt Molchanov formula, originally employed in the…
The possibility that a classical space-time and quantum matter cohabit at the deepest level, i.e. the possibility of having a fundamental and not phenomenological semiclassical gravity, is often disregarded for lack of a good candidate…
We describe some analogy between optimal transport and the Schr\"odinger problem where the transport cost is replaced by an entropic cost with a reference path measure. A dual Kantorovich type formulation and a Benamou-Brenier type…