Related papers: The Shortest Path Across the Mesoscopic System
We investigate the transport of electrons in disordered and pristine graphene devices. Fano shot noise, a standard metric to assess the mechanism for electronic transport in mesoscopic devices, has been shown to produce almost the same…
Because of a close blood relationship between directed percolation & directed polymers in random media, the latter's journey to asymptotic scaling can be greatly retarded by an uninformed choice of departure point; i.e., the bare-bond PDF…
Random processes play a crucial role in scientific research, often characterized by distribution functions or probability density functions (PDFs). These PDFs serve as essential approximations of the actual and frequently undisclosed…
Computing a minimum path cover (MPC) of a directed acyclic graph (DAG) is a fundamental problem with a myriad of applications, including reachability. Although it is known how to solve the problem by a simple reduction to minimum flow,…
We consider the distribution of free path lengths, or the distance between consecutive bounces of random particles, in an n-dimensional rectangular box. If each particle travels a distance R, then, as R tends to infinity the free path…
We report a scattering matrix theory for dynamic and nonlinear transport in coherent mesoscopic conductors. In general this theory allows predictions of low frequency linear dynamic conductance, as well as weakly nonlinear DC conductance.…
Despite a long history and a clear overall understanding of properties of random walks on an incipient infinite cluster in percolation, some important information on it seems to be missing in the literature. In the present work, we revisit…
An arrangement of mesoscopic experiments is considered when the conductance of a mesoscopic normal metal sample is governed not only by the magnetic flux threading the sample but by the supercurrent inside the superconductor coupled to the…
We introduce a Monte Carlo algorithm to efficiently compute transport properties of chaotic dynamical systems. Our method exploits the importance sampling technique that favors trajectories in the tail of the distribution of displacements,…
Distribution-dependent stochastic dynamical systems arise widely in engineering and science. We consider a class of such systems which model the limit behaviors of interacting particles moving in a vector field with random fluctuations. We…
Mesoscopic theory for soft-matter systems that combines density functional and statistical field theory is derived from the microscopic theory by a systematic coarse-graining procedure. Within the framework of this theory we obtain the…
Statistics of closed paths in two-dimensional (2D) systems, which just determines the interference quantum correction to conductivity and anomalous magnetoconductance, has been studied by computer simulation of a particle motion over the…
We study some mesoscopic properties of electron transport by employing one-dimensional chains and Anderson tight-binding model. Principal attention is paid to the resistance of finite-length chains with disordered white-noise potential. We…
We demonstrate a new near-analytical path to the threshold-size of random-lasing for the case of a uniform and isotropic-scattering sphere. We assess a geometric-distribution-probability (GDP) weighted integration of the diffusion-equation…
Measurements have been made of the probability distribution of total transmission of microwave radiation in waveguides filled with randomly positioned scatterers which would have values of the dimensionless conductance g near unity. The…
The path probability of a particle undergoing stochastic motion is studied by the use of functional technique, and the general formula is derived for the path probability distribution functional. The probability of finding paths inside a…
The correspondence between the telegraph random process and transport within a binary stochastic Markovian mixture is established. This equivalence is used to derive the distribution function for the transit length, defined as the distance…
Minimum flow decomposition (MFD) is the NP-hard problem of finding a smallest decomposition of a network flow/circulation $X$ on a directed graph $G$ into weighted source-to-sink paths whose superposition equals $X$. We show that, for…
For diffusive stochastic dynamics, the probability to observe any individual trajectory is vanishingly small, making it unclear how to experimentally validate theoretical results for ratios of path probabilities. We provide the missing link…
We prove precise almost sure lower path regularity results for a wide class of stochastic processes in all space dimensions $d\geq 1$. Examples include Gaussian processes, in particular, fractional Brownian motions with Hurst index $H\in…