arXiv subjects

Kenan Uriostegui

Publications and source records attributed to Kenan Uriostegui.

3 recordsLinked to original sources

arXiv2025

Non-Hermitian linear perturbation to a Hamiltonian with a constant electromagnetic field and Hall conductivity

The stationary Schrödinger equation for an electron in a constant electromagnetic field with a non-Hermitian linear perturbation is studied. The wave function and the spectrum of the system are derived analytically, with the spectrum consisting of Landau levels modified by an additional term associated with the linear Stark effect, proportional to a complex constant $λ$. It is shown that this constant arises from an operator $\hatΠ$ that commutes with the Hamiltonian, i.e., $\hatΠ$ is a symmetry of the system. Finally, the Hall conductivity for the lowest Landau level is calculated, showing that it remains exactly equal to the inverse of Klitzing's constant despite the perturbation.

cond-mat.mes-hall↗

arXiv2021

Discrete Bessel and Mathieu functions

The two-dimensional Helmholtz equation separates in elliptic coordinates based on two distinct foci, a limit case of which includes polar coordinate systems when the two foci coalesce. This equation is invariant under the Euclidean group of translations and orthogonal transformations; we replace the latter by the discrete dihedral group of N discrete rotations and reflections. The separation of variables in polar and elliptic coordinates is then used to define discrete Bessel and Mathieu functions, as approximants to the well-known continuous Bessel and Mathieu functions, as N-point Fourier transforms approximate the Fourier transform over the circle, with integrals replaced by finite sums. We find that these 'discrete' functions approximate the numerical values of their continuous counterparts very closely and preserve some key special function relations.

math-ph↗

arXiv2020

Discrete Bessel functions and transform

We present a straightforward discretization of the Bessel functions $J_n(x)$ to discrete counterparts $B^{(N)}_n(x_m)$, of $N$ integer orders $n$ on $N$ integer points $x_m \equiv m$, that we call discrete Bessel functions. These are built from a Bessel integral generating function, restricting the Fourier transform over the circle to $N$ points. We show that the discrete Bessel functions satisfy several linear and quadratic relations, particularly Graf's product-displacement formulas, that are exact analogues of well-known relations between the continuous functions. It is noteworthy that these discrete Bessel functions approximate very closely the values of the continuous functions in ranges $n + |m| < N$. For fixed $N$, this provides an $N$-point transform between functions of order and of position,$f_n$ and $\widetilde{f}_m$, which is efficient for the Fourier analysis of finite decaying signals.

math-ph↗