Related papers: Radial Dunkl processes associated with Dihedral sy…
A recently developed formula for the Hall coefficient [A. Auerbach, Phys. Rev. Lett. 121, 66601 (2018)] is applied to nodal line and Weyl semimetals (including graphene), and to spin-orbit split semiconductor bands in two and three…
The effect of the Kerr nonlinearity on linear non-diffractive Bessel beams is investigated analytically and numerically using the nonlinear Schr\"odinger equation. The nonlinearity is shown to primarily affect the central parts of the…
We study the counting function of the eigenvalues for tensor products of operators, and their perturbations, in the context of Shubin classes and closed manifolds. We emphasize connections with problems of analytic number theory, concerning…
At high energies, Drell-Yan (DY) dilepton production viewed in the target rest frame should be interpreted as bremsstrahlung and can be expressed in terms of the same color dipole cross section as DIS. We compute DY cross sections on a…
We consider the gap probability for the Generalized Bessel process in the single-time and multi-time case. We prove that the scalar and matrix Fredholm determinants of such process can be expressed in terms of determinants of…
Weyl semimetals and nodal line semimetals are characterized by linear band touching at zero-dimensional points and one-dimensional lines, respectively. We predict that a circularly polarized light drives nodal line semimetals into Weyl…
We characterize the set of rectangular Weyl matrix functions corresponding to Dirac systems with locally square-integrable potentials on a semi-axis and demonstrate a new way to recover the locally square-integrable potential from the Weyl…
The semiclassical kinetic theory of Dirac particles in the presence of external electromagnetic fields and global rotation is established. To provide the Hamiltonian formulation of Dirac particles a symplectic two-form which is a matrix in…
Multivariate Bessel processes $(X_{t,k})_{t\ge0}$ describe interacting particle systems of Calogero-Moser-Sutherland type and are related with $\beta$-Hermite and $\beta$-Laguerre ensembles. They depend on a root system and a multiplicity…
Weyl semimetals are a new paradigmatic topological phase of matter featuring a gapless spectrum. One of its most distinctive features is the presence of Fermi arc surface states. Here, we report on atomistic simulations of the dc…
One object of interest in random matrix theory is a family of point ensembles (random point configurations) related to various systems of classical orthogonal polynomials. The paper deals with a one--parametric deformation of these…
Through the theory of Jack polynomials we give an iterative method for integral formula of Dunkl-Bessel functions of type $A_{N-1}$ and a partial product formula for it.
Recently, the gapless Dirac/Weyl nodal semimetals with linear dispersion and topologically protected modes degeneracy are rapidly growing frontiers of topological physics. Especially, type-I, type-II, and critical type-III nodal semimetals…
We study dynamical mass generation and the resultant helical spin orders in topological Dirac and Weyl semimetals, including the edge states of quantum spin Hall insulators, the surface states of weak topological insulators, and the bulk…
In Random Matrix Theory the local correlations of the Laguerre and Jacobi Unitary Ensemble in the hard edge scaling limit can be described in terms of the Bessel kernel (containing a parameter $\alpha$). In particular, the so-called hard…
We introduce fractional diffusion Bessel process with Hurst index $H\in(0,\frac12)$, derive a stochastic differential equation for it, and study the asymptotic properties of its sample paths.
This is a PhD dissertation. Ignited by the chiral anomaly of recently discovered Weyl (semi-)metals, we study the chiral magnetic effect and the natural optical activity of noncentrosymmetric metals. Both phenomena are related to the…
We report the discovery of a time-reversal symmetric Weyl semimetal obtained by modifying a model Hamiltonian describing the electronic properties of conventional alkali metals. The artificially generated Weyl semimetal features four…
The order derivatives of the modified Bessel function of the second kind at s = .5 are obtained as finite expressions of integrals that generalize the exponential integral appearing in the first derivative (Theorem 1.) The derivatives arise…
We classify all possible gap-closing procedures which can be achieved in two-dimensional time-reversal invariant noncentrosymmetric systems. For exhaustive classification, we examine the space group symmetries of all 49 layer groups lacking…