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We study how the presence of correlations in physical variables contributes to the form of probability distributions. We investigate a process with correlations in the variance generated by (i) a Gaussian or (ii) a truncated L\'{e}vy…
At low temperatures and strong friction the time evolution of the density distribution in position follows a quantum Smoluchowski equation. Recently, also higher-order contributions of quantum fluctuations to drift and diffusion…
We consider a two dimensional semiconductor with carriers subject to spin-orbit interactions and scattered by randomly distributed magnetic impurities. We solve the time-dependent Schroedinger equation to investigate the relationship…
This paper develops an analytical method of truncating inequality constrained Gaussian distributed variables where the constraints are themselves described by Gaussian distributions. Existing truncation methods either assume hard…
We investigate the fluctuations of the time elapsed until the electric charge transferred through a conductor reaches a given threshold value. For this purpose, we measure the distribution of the first-passage times for the net number of…
We analyze the transport properties of a semiconductor based bilayer system under non-equilibrium conditions with special emphasis on the charge transfer statistics in the regime dominated by the exciton transport. We consider two different…
This article is the first of a trilogy that addresses various aspects of the perturbative response of general quantum systems, with possibly nontrivial ground state geometry, beyond linear order. Here, we use group theoretical…
A simplified transient energy-transport system for semiconductors subject to mixed Dirichlet-Neumann boundary conditions is analyzed. The model is formally derived from the non-isothermal hydrodynamic equations in a particular vanishing…
It is shown that the Truncated Euler Equations, i.e. a finite set of ordinary differential equations for the amplitude of the large-scale modes, can correctly describe the complex transitional dynamics that occur within the turbulent regime…
We predict the existence of an intriguing "disorder by order" phenomenon in graphene transport where higher quality (and thus more ordered) samples, while having higher mobility at high carrier density, will manifest more strongly…
This note presents conjectures on polynomial/algebraic/sub-exponential convergence of transition probabilities for $\lambda$-null recurrent and $\lambda$-transient Markov chains in continuous time. The only known positive examples are in…
We calculate the conductivity of arbitrarily stacked multilayer graphene sheets within a relaxation time approximation, considering both short-range and long-range impurities. We theoretically investigate the feasibility of identifying the…
We study the effect of disorder on the particle density evolution in a classical Hamiltonian driven lattice setup. If the disorder is localized within a finite sub-domain of the lattice, the emergence of strong tails in the density…
We investigate evolution equations for anomalous diffusion employing fractional derivatives in space and time. Linkage between the space-time variables leads to a new type of fractional derivative operator. Fractional diffusion equations…
Using the method of Krylov's estimates, we prove the existence of weak solutions of stochastic differential equations driven by purely discontinuous Levy processes satisfying an additional assumption. The diffusion coefficient is assumed to…
This paper investigates a damped stochastic wave equation driven by a non-Gaussian Levy noise. The weak solution is proved to exist and be unique. Moreover we show the existence of a unique invariant measure associated with the transition…
Charge transport in crystalline organic semiconductors is intrinsically limited by the presence of large thermal molecular motions, which are a direct consequence of the weak van der Waals inter-molecular interactions. These lead to an…
We investigate the transport properties of open quantum chaotic systems in the semiclassical limit. We show how the transmission spectrum, the conductance fluctuations, and their correlations are influenced by the underlying chaotic…
Charge transport in disordered two-dimensional (2D) systems showcases a myriad of unique phenomenologies that highlight different aspects of the underlying quantum dynamics. Electrons in such systems undergo a crossover from ballistic…
In this paper we present stochastic foundations of fractional dynamics driven by fractional material derivative of distributed order-type. Before stating our main result we present the stochastic scenario which underlies the dynamics given…