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We construct trace codes over $\Z_4$ by using Boolean functions and skew sets, respectively. Their Lee weight distribution is studied by using a Galois ring version of the Walsh-Hadamard transform and exponential sums. We obtain a new…
A semiclassical method of complex trajectories for the calculation of the tunneling exponent in systems with many degrees of freedom is further developed. It is supplemented with an easily implementable technique, which enables one to…
In this paper we develop a general framework for constructing and analysing coupled Markov chain Monte Carlo samplers, allowing for both (possibly degenerate) diffusion and piecewise deterministic Markov processes. For many performance…
The Boltzmann equation for d-dimensional inelastic Maxwell models is considered to analyze transport properties in spatially inhomogeneous states close to the simple shear flow. A normal solution is obtained via a Chapman--Enskog--like…
We consider the conductivity tensor for composite fermions in a close to half-filled Landau band in the temperature regime where the scattering off the potential and the trapped gauge field of random impurities dominates. The Boltzmann…
We present an analytical study of one-dimensional semiconductor superlattices in external electric fields, which may be time-dependent. A number of general results for the (quasi)energies and eigenstates are derived. An equation of motion…
We summarize semiclassical modeling methods, including drift-diffusion, kinetic transport equation and Monte Carlo simulation approaches, utilized in studies of spin dynamics and transport in semiconductor structures. As a review of the…
A general lattice Boltzmann method for simulation of fluids with tailored transport coefficients is presented. It is based on the recently introduced quasi-equilibrium kinetic models, and a general lattice Boltzmann implementation is…
Charge transport in two zinc metal-organic frameworks (MOFs) has been investigated using periodic semiempirical molecular orbital calculations with the AM1* Hamiltonian. Restricted Hartree-Fock calculations underestimate the band gap…
A set of equations is derived from the Boltzmann kinetic equation describing charge transport in semiconductors. The unknowns of these equations depend on the space-time coordinates and the electron energy. The non-parabolic and parabolic…
A prominent model for transportation networks is branched transport, which seeks the optimal transportation scheme to move material from a given initial to a final distribution. The cost of the scheme encodes a higher transport efficiency…
We discuss methods of Optimal Transportation Theory and its relations to problems in quantum mechanics. This essentially means that the cost function is some Hamiltonian $H(q,p)$ on a phase space (symplectic manifold), and the marginal…
We present a microscopic calculation of transport in strongly doped superlattices where domain formation is likely to occur. Our theoretical method is based on a current formula involving the spectral functions of the system, and thus…
For an isotropic single-band system, it is well known that the semiclassical Boltzmann transport theory within the relaxation time approximation and the Kubo formula with the vertex corrections provide the same result with the…
We apply Selberg's trace formula to solve problems in hyperbolic band theory, a recently developed extension of Bloch theory to model band structures on experimentally realized hyperbolic lattices. For this purpose we incorporate the…
The local-equilibrium approach to transport processes is related to the approach based on time-dependent correlation functions and their associated spectral functions characterizing the equilibrium fluctuations of particle, momentum and…
We compute Fourier transforms of functions expressed as a ratio of one of the Jacobi elliptic functions divided by $\sinh(\pi x)$ or $\cosh(\pi x)$. In many cases, the resulting Fourier transform remains within the same class of functions.…
Optimal Transport is a foundational mathematical theory that connects optimization, partial differential equations, and probability. It offers a powerful framework for comparing probability distributions and has recently become an important…
In this paper we consider a Boltzmann-type kinetic description of Follow-the-Leader traffic dynamics and we study the resulting asymptotic distributions, namely the counterpart of the Maxwellian distribution of the classical kinetic theory.…
We investigate electron transport through clean open quantum dots (quantum billiards). We present a semiclassical theory that allows to accurately reproduce quantum transport calculations. Quantitative agreement is reached for individual…