Related papers: Weak Adversarial Neural Pushforward Method for the…

The evolution of the discrete Wigner function is formally similar to a probabilistic process, but the transition probabilities, like the discrete Wigner function itself, can be negative. We investigate these transition probabilities, as…

We study Fokker--Planck equations with symmetric, positive definite mobility matrices capturing diffusion in heterogeneous environments. A weighted Wasserstein metric is introduced for which these equations are gradient flows. This metric…

Within the expansive domain of optical sciences, achieving the precise characterization of light beams stands as a fundamental pursuit, pivotal for various applications, including telecommunications and imaging technologies. This study…

We propose ARDO method for solving PDEs and PDE-related problems with deep learning techniques. This method uses a weak adversarial formulation but transfers the random difference operator onto the test function. The main advantage of this…

In Part I of this two-part series, the reverse perturbation method for shearing simple liquids [Phys. Rev. E 59, 4894 (1999)] was extended to systems of interacting particles with time-discrete stochastic dynamics. For verification, in this…

In semiclassical theories for chaotic systems such as Gutzwiller's periodic orbit theory the energy eigenvalues and resonances are obtained as poles of a non-convergent series g(w)=sum_n A_n exp(i s_n w). We present a general method for the…

We present an analog to classic potential theory on weighted graphs. With nodes partitioned into exterior, boundary and interior nodes and an appropriate decomposition of the Laplacian, we define discrete analogues to the trace operators,…

The transport properties of quantum dots with up to N=7 electrons ranging from the weak to the strong interacting regime are investigated via the projected Hartree-Fock technique. As interactions increase radial order develops in the dot,…

The Wigner-Liouville equation is reformulated using a spectral decomposition of the classical force field instead of the potential energy. The latter is shown to simplify the Wigner-Liouville kernel both conceptually and numerically as the…

Starting from Feynman's Lagrangian description of quantum mechanics, we propose a method to construct explicitly the propagator for the Wigner distribution function of a single system. For general quadratic Lagrangians, only the classical…

We consider the optimization problem of minimizing a functional defined over a family of probability distributions, where the objective functional is assumed to possess a variational form. Such a distributional optimization problem arises…

We advance a phase-space theory of partially coherent accelerating, non-diffracting beams employing the Wigner distribution function (WDF). We derive a general expression for the WDF of any accelerating, diffraction-free beam of arbitrary…

We obtained the Feynman propagators for a noncommutative (NC) quantum mechanics defined in the recently developed Doplicher-Fredenhagen-Roberts-Amorim (DFRA) NC background that can be considered as an alternative framework for the NC…

For the nanoscale structures, disorder scattering plays a vital role in the carriers' transport, including electrons and high-frequency phonons. The capability for effectively treating the disorders, including both diagonal and off-diagonal…

Quantum walk (QW) provides a versatile tool to study fundamental physics and also to make a variety of practical applications. We here start with the recent idea of {\it nonlinear} QW and show that introducing {\it nonlinearity} to QW can…

We consider a recent plate model obtained as a scaled limit of the three dimensional Biot system of poro-elasticity. The result is a "2.5" dimensional linear system that couples traditional Euler-Bernoulli plate dynamics to a pressure…

We have considered the problem of the influence of inhomogeneity of gravitational field on transport effects predicted by the field theory describing massless Dirac fermions in the Maxwell and dark matter background. As a model of dark…

Adversarial transferability enables black-box attacks on unknown victim deep neural networks (DNNs), rendering attacks viable in real-world scenarios. Current transferable attacks create adversarial perturbation over the entire image,…

Over the last two decades, several fast, robust, and high-order accurate methods have been developed for solving the Poisson equation in complicated geometry using potential theory. In this approach, rather than discretizing the partial…

In this work we present an application of modern deep learning methodologies to the numerical solution of partial differential equations in transport models. More specifically, we employ a supervised deep neural network that takes into…