Related papers: Free transport for convex potentials
Gauge invariance is a fundamental principle that must be preserved in quantum transport. However, when a complex potential is incorporated into the Hamiltonian, we find that the current described by the well-established…
In machine learning and computer vision, optimal transport has had significant success in learning generative models and defining metric distances between structured and stochastic data objects, that can be cast as probability measures. The…
We explore the geometry behind the modular bootstrap and its image in the space of Taylor coefficients of the torus partition function. In the first part, we identify the geometry as an intersection of planes with the convex hull of moment…
Beyond the second-order Born approximation, we develop an improved master equation approach to quantum transport by virtue of a self-consistent Born approximation. The basic idea is replacing the free Green's function in the tunneling…
Time-independent gauge transformations are implemented in the canonical formalism by the Gauss law which is not covariant. The covariant form of Gauss law is conceptually important for studying asymptotic properties of the gauge fields. For…
We investigate linear maps between matrix algebras that remain positive under tensor powers, i.e., under tensoring with $n$ copies of themselves. Completely positive and completely co-positive maps are trivial examples of this kind. We show…
Effective transport of quantum information is an essential element of quantum computation. We consider the problem of transporting a quantum state by using a moving potential well, while maintaining the encoded quantum information. In…
We provide an explicit construction of entangled states in a noncommutative space with nonclassical states, particularly with the squeezed states. Noncommutative systems are found to be more entangled than the usual quantum mechanical…
In this work, we describe new constructions of free Stein kernels. Firstly, in dimension one, we propose a free analog to the construction of Stein kernels using moment maps as the one proposed by Fathi. This will be possible for a class of…
Quantum-state texture is a newly recognized quantum resource that has garnered attention with the advancement of quantum theory. In this work, we address several key aspects of quantum-state texture resource theory, including the…
It is well known that an exponentially localized Hamiltonian must be gapless if its ground state has algebraic correlations. We show that even certain exponentially decaying correlations can imply gaplessness. This is exemplified by the…
One way to analyze complicated non-autonomous flows is through trying to understand their transport behavior. In a quantitative, set-oriented approach to transport and mixing, finite time coherent sets play an important role. These are…
We consider a family of models having an arbitrary positive amount of mass on each site and randomly exchanging an arbitrary amount of mass with nearest neighbor sites. We restrict to the case of diffusive models. We identify a class of…
We introduce a new second order stochastic algorithm to estimate the entropically regularized optimal transport cost between two probability measures. The source measure can be arbitrary chosen, either absolutely continuous or discrete,…
We investigate the optimal mass transport problem associated to the following "ballistic" cost functional on phase space $M\times M^*$, $$ b_T(v, x):=\inf\{\langle v, \gamma (0)\rangle +\int_0^TL(\gamma (t), {\dot \gamma}(t))\, dt, \gamma…
We consider the problem of comparing several samples of stochastic processes with respect to their second-order structure, and describing the main modes of variation in this second order structure, if present. These tasks can be seen as an…
A novel class of derivative-free optimization algorithms is developed. The main idea is to utilize certain non-commutative maps in order to approximate the gradient of the objective function. Convergence properties of the novel algorithms…
We present simulations of congested traffic in circular and open systems with a non-local, gas-kinetic-based traffic model and a novel car-following model. The model parameters are all intuitive and can be easily calibrated. Micro- and…
In this paper we explore the set of linear maps sending the set of quantum Gaussian states into itself. These maps are in general not positive, a feature which can be exploited as a test to check whether a given quantum state belongs to the…
Optimal transportation distances are valuable for comparing and analyzing probability distributions, but larger-scale computational techniques for the theoretically favorable quadratic case are limited to smooth domains or regularized…