arXiv subjects

Jorge A. Lizarraga

Publications and source records attributed to Jorge A. Lizarraga.

6 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↗

arXiv2025

Time-dependent conserved operators for autonomous systems and quantization of resistance

Two systems for a charged particle are studied, the first one when it is under the effect of a constant electric field, and the second one when it is under the effect of a constant electromagnetic field. For both systems, it is possible to find time-dependent conserved operators that can be used to derive time-dependent wave functions to the complete Schrödinger equation, such that the time variable is not separable from the space coordinates. At the same time, these conserved operators are used to build up a unitary operators, which define the symmetries of the systems. Then, it is shown that the invariance of the wave function under the action of these unitary operators leads to the quantization of resistance as integer multiples of the Klitzing's constant.

quant-ph↗

arXiv2024

Constants of motion and quantum non-relativistic motion of a charged particle on a flat surface with transversal magnetic field

The motion of a charged particle moving on a flat surface is studied through the constants of motion associated to the system, given the magnetic gauge. The usual Landau' solution and the non separable solution for the Landau's gauge are found, and new non separable solution for the symmetric gauge is given. As a consequence of this, the quantization of the magnetic flux results from the invariance of the solutions under the unitary transformations which arise from the operators constants of motion.

quant-ph↗

arXiv2024

Canonical transformations applied to the non-free Landau electron

The method previously used to solve Schrödinger equation by a unitary transformation for a electron under the influence of a constant magnetic field is used to obtain a non-free Landau electron wave function. The physical meaning of this wave function is discussed based on the conserved properties of the transformed Hamiltonian.

quant-ph↗

arXiv2024

Quantization of resistivity as consequence of symmetry invariance

The Schrödinger equation for an electron under the influence of an electromagnetic field is analyzed based on the conserved operators of the system when the magnetic field is described by Landau's gauge. It is shown that the Lorentz force can be recovered only if two conserved generalized momentum operators are considered: one along the $x$-axis and the second one along $y$-axis; otherwise, the system cannot be fully described. Based on the general solution found, a ground state is built which has the characteristic of having quantized resistivity proportional to integer multiples of the von Klitzing's constant when it is invariant under a unitary transform.

quant-ph↗

arXiv2020

Charged particle in a flat box with static electromagnetic field and Landau's levels

We study the quantization of the motion of a charged particle without spin inside a flat box under a static electromagnetic field. Contrary to Landau's solution with constant magnetic field transverse to the box, we found a non separable variables solution for the wave function, and this fact remains when static electric field is added. However, the Landau's Levels appear in all cases.

physics.gen-ph↗