Related papers: The Shortest Path Across the Mesoscopic System
We present an analytical approach to calculating the distribution of shortest paths lengths (also called intervertex distances, or geodesic paths) between nodes in unweighted undirected networks. We obtain very accurate results for…
A recent Drude model description of the metallic regime and of a channel- averaged elastic mean free path (mfp), $\ell_0$, in an $N$-channel tight-binding wire identifies the Thouless localization length, $N\ell_0$, as a proper lower bound…
The calculation of the conductance of ballistic rings requires a theory that goes well beyond the Kubo-Drude formula. Assuming "mesoscopic" circumstance of very weak environmental relaxation, the conductance is much smaller compared with…
We report on the comprehensive numerical study of the fluctuation and correlation properties of wave functions in three-dimensional mesoscopic diffusive conductors. Several large sets of nanoscale samples with finite metallic conductance,…
Analytical study of the distribution of phase of the transmission coefficient through 1D disordered absorbing system is presented. The phase is shown to obey approximately Gaussian distribution. An explicit expression for the variance is…
Connecting optimal transport and variational inference, we present a principled and systematic framework for sampling and generative modelling centred around divergences on path space. Our work culminates in the development of the…
We present a mechanism for displaying the transmission property of the discrete Heisenberg ferromagnetic spin chain (DHF) via a geometric approach. By the aid of a discrete nonlinear Schr\"odinger-like equation which is the discrete gauge…
We perform a Bayesian parameter inference in the context of resonantly damped transverse coronal loop oscillations. The forward problem is solved in terms of parametric results for kink waves in one-dimensional flux tubes in the thin tube…
Starting from the Abrikosov-Ryzhkin formulation of the 1D random potential problem I find closed functional representations for various physical quantities. These functional integrals are calculated exactly without the use of any…
Translational diffusion coefficients are routinely estimated from molecular dynamics simulations. Linear fits to mean squared displacement (MSD) curves have become the de facto standard, from simple liquids to complex biomacromolecules.…
A fundamental process for any given chaotic flow is the deterministic point process (DPP) generated by any chaotic trajectory of the flow repeatedly crossing a canonical surface-of-section (herein referred to as a sigma-type DPP). This…
We analyze the statistics of the shortest and fastest paths on the road network between randomly sampled end points. To a good approximation, these optimal paths are found to be directed in that their lengths (at large scales) are linearly…
We present the theoretical analysis of the steady state currents and density distributions of particles moving with Langevin dynamics, under the effects of an external potential displaced at constant rate. The Dynamic Density Functional…
We introduce a model of interacting Random Walk, whose hopping amplitude depends on the number of walkers/particles on the link. The mesoscopic counterpart of such a microscopic dynamics is a diffusing system whose diffusivity depends on…
Both the porous medium equation and the system of isentropic Euler equations can be considered as steepest descents on suitable manifolds of probability measures in the framework of optimal transport theory. By discretizing these…
We revisit the variational characterization of diffusion as entropic gradient flux and provide for it a probabilistic interpretation based on stochastic calculus. It was shown by Jordan, Kinderlehrer, and Otto that, for diffusions of…
We present a scaling hypothesis for the distribution function of the shortest paths connecting any two points on a percolating cluster which accounts for {\it (i)} the effect of the finite size of the system, and {\it (ii)} the dependence…
In this paper a method of obtaining smooth analytical estimates of probability densities, radial distribution functions and potentials of mean force from sampled data in a statistically controlled fashion is presented. The approach is…
The capacitance of mesoscopic samples depends on their geometry and physical properties, described in terms of characteristic times scales. The resulting ac admittance shows sample to sample fluctuations. Their distribution is studied here…
The smoothing distribution is the conditional distribution of the diffusion process in the space of trajectories given noisy observations made continuously in time. It is generally difficult to sample from this distribution. We use the…