Related papers: Weyl's problem: A computational approach
We investigate the confined states and transport of three-dimensional Weyl electrons around a one-dimensional external rectangular electrostatic potential. Confined states with finite transverse wave vector exist at energies higher than the…
Wigner functions play a central role in the phase space formulation of quantum mechanics. Although closely related to classical Liouville densities, Wigner functions are not positive definite and may take negative values on subregions of…
The Wigner-Weyl transform and phase space formulation of a density matrix approach are applied to a non-Hermitian model which is quadratic in positions and momenta. We show that in the presence of a quantum environment or reservoir, mean…
The beam-plasma instability, i.e. the response of the plasma bulk to the injection of supra thermal charged-particle beams, results to be appropriately characterized by a long-range interaction system. This physical system hosts a number of…
Equation of state with quantum statistics corrections is derived for systems of the Fermi and Bose particles by using their van der Waals (vdW) and effective density-dependent Skyrme mean-field interactions. First few orders of these…
Weyl semimetal showing open-arc surface states is a prominent example of topological quantum matter in three dimensions. With the bulk-boundary correspondence present, nontrivial surface-bulk hybridization is inevitable but less understood.…
We design and implement a three dimensional acoustic Weyl metamaterial hosting robust modes bound to a one-dimensional topological lattice defect. The modes are related to topological features of the bulk bands, and carry nonzero orbital…
Noticing that really the fermions of the Standard Model are best thought of as Weyl - rather than Dirac - particles (relative to fundamental scales located at some presumably very high energies) it becomes interesting that the experimental…
This thesis is concerned with dynamics of conservative nonlinear waves on bounded domains. In general, there are two scenarios of evolution. Either the solution behaves in an oscillatory, quasiperiodic manner or the nonlinear effects cause…
The paper considers the wave equation, with constant or variable coefficients in $\R^n$, with odd $n\geq 3$. We study the asymptotics of the distribution $\mu_t$ of the random solution at time $t\in\R$ as $t\to\infty$. It is assumed that…
The Laughlin states for $N$ interacting electrons at the plateaus of the fractional Hall effect are studied in the thermodynamic limit of large $N$. It is shown that this limit leads to the semiclassical regime for these states, thereby…
We study collective phenomena of self-propagating particles using the nonlinear Kramers equation. A solitary wave state appears from an instability of the spatially uniform ordered state with nonzero average velocity. Two solitary waves…
We analyse the problem of finding sets of quantum states that can be deterministically discriminated. From a geometric point of view this problem is equivalent to that of embedding a simplex of points whose distances are maximal with…
Wavelength determines the length scale of the cross section when electromagnetic waves are scattered by an electrically small object. The cross section diverges for resonant scattering, and diminishes for non-resonant scattering, when…
A functional integral representation is given for a large class of quantum mechanical models with a non--L2 ground state. As a prototype the particle in a periodic potential is discussed: a unique ground state is shown to exist as a state…
Weyl fermions are shown to exist inside a parabolic band, where the kinetic energy of carriers is given by the non-relativistic Schroedinger equation. There are Fermi arcs as a direct consequence of the folding of a ring shaped Fermi…
We study a special kind of semiclassical limit of quantum dynamics on a circle and in a box (infinite potential well with hard walls) as the Planck constant tends to zero and time tends to infinity. The results give detailed information…
We obtain a closed system of equations for scalar perturbations in a multi-component braneworld. Our braneworld possesses a phantom-like equation of state at late times, $w_{\rm eff} < -1$, but no big-rip future singularity. In addition to…
We study particular classes of states on the Weyl algebra $\mathcal{W}$ associated with a symplectic vector space $S$ and on the von Neumann algebras generated in representations of $\mathcal{W}$. Applications in quantum physics require an…
We use variable transformation from the real line to finite or semi-infinite spaces where we expand the regular solution of the 1D time-independent Schrodinger equation in terms of square integrable bases. We also require that the basis…