arXiv subjects

A. D. Levin

Publications and source records attributed to A. D. Levin.

45 records · Page 3Linked to original sources

arXiv2013

Quantum Hall effect in n-p-n and n-2D Topological Insulator-n junctions

We have studied quantized transport in HgTe wells with inverted band structure corresponding to the two-dimensional topological insulator phase (2D TI) with locally-controlled density allowing n-p-n and n-2D TI-n junctions. The resistance reveals the fractional plateau $2h/e^{2}$ in n-p-n regime in the presence of the strong perpendicular magnetic field. We found that in n-2D TI-n regime the plateaux in resistance in not universal and results from the edge state equilibration at the interface between chiral and helical edge modes. We provided the simple model describing the resistance quantization in n-2D TI-n regime.

cond-mat.mes-hall↗

arXiv2012

Nonlocal transport near the charge neutrality point in a two-dimensional electron-hole system

Nonlocal resistance is studied in a two-dimensional system with a simultaneous presence of electrons and holes in a 20 nm HgTe quantum well. A large nonlocal electric response is found near the charge neutrality point (CNP) in the presence of a perpendicular magnetic field. We attribute the observed nonlocality to the edge state transport via counter propagating chiral modes similar to the quantum spin Hall effect at zero magnetic field and graphene near Landau filling factor $ν=0$

cond-mat.mes-hall↗

arXiv2012

Electronic Structure of Superheavy Atoms. Revisited

The electronic structure of an atom with Z <= 137 can be described by the Dirac equation with the Coulomb field of a point charge Ze. It was believed that the Dirac equation with Z > 137 is inconsistent and physically meaningless because the formula for the lower energy level of the Dirac Hamiltonian formally gives imaginary eigenvalues. But a strict mathematical consideration shows that difficulties with the electronic spectrum for Z > 137 do not arise if the Dirac Hamiltonian is correctly defined as a self-adjoint operator, see [1]. In this article, we brie y summarize the main physical results of that consideration in a form suitable for physicists with some additional new details and numerical calculations of the electronic spectra. [1] B.L. Voronov, D.M. Gitman, and I.V. Tyutin, Theor. Math. Phys. 150(1) (2007) 34

math-ph↗

arXiv2012

Coherent states and related quantizations for unbounded motions

We build coherent states (CS) for unbounded motions along two different procedures. In the first one we adapt the Malkin-Manko construction for quadratic Hamiltonians to the motion of a particle in a linear potential. A generalization to arbitrary potentials is discussed. The second one extends to continuous spectrum previous constructions of action-angle coherent states in view of a consistent energy quantization.

quant-ph↗

arXiv2011

Quantum deformation of the angular distributions of synchrotron radiation. Emission of particles in the first excited state

The exact expressions for the characteristics of synchrotron radiation of charged particles in the first excited state are obtained in analytical form using quantum theory methods. We performed a detailed analysis of the angular distribution structure of radiation power and its polarization for particles with spin 0 and 1/2. It is shown that the exact quantum calculations lead to results that differ substantially from the predictions of classical theory.

quant-ph↗

arXiv2011

Quantum motion in superposition of Aharonov-Bohm with some additional electromagnetic fields

The structure of additional electromagnetic fields to the Aharonov-Bohm field, for which the Schrödinger, Klein-Gordon, and Dirac equations can be solved exactly are described and the corresponding exact solutions are found. It is demonstrated that aside from the known cases (a constant and uniform magnetic field that is parallel to the Aharonov-Bohm solenoid, a static spherically symmetrical electric field, and the field of a magnetic monopole), there are broad classes of additional fields. Among these new additional fields we have physically interesting electric fields acting during a finite time, or localized in a restricted region of space. There are additional time-dependent uniform and isotropic electric fields that allow exact solutions of the Schrodinger equation. In the relativistic case there are additional electric fields propagating along the Aharonov-Bohm solenoid with arbitrary electric pulse shape.

quant-ph↗

arXiv2010

Two and four-level systems in magnetic fields restricted in time

We describe some new exact solutions for two- and four-level systems. In all the cases, external fields have a restricted behavior in time. First, we consider two types of new solutions for one-spin equation, one of them is in a external magnetic field that acts during a finite time interval. A new solution for two interacting spins is found in the case when the field difference between the external fields in each spin vary adiabatically, vanishing on the time infinity. The latter system can be identified with a quantum gate realized by two coupled quantum dots. The probability of the Swap operation for such a gate can be explicitly expressed in terms of special functions. Using the obtained expressions, we construct plots for the Swap operation for some parameters of the external magnetic field and interaction function.

quant-ph↗

arXiv2006

Two interacting spins in external fields. Four-level systems

In the present article, we consider the so-called two-spin equation that describes four-level quantum systems. Recently, these systems attract attention due to their relation to the problem of quantum computation. We study general properties of the two-spin equation and show that the problem for certain external backgrounds can be identified with the problem of one spin in an appropriate background. This allows one to generate a number of exact solutions for two-spin equations on the basis of already known exact solutions of the one-spin equation. Besides, we present some exact solutions for the two-spin equation with an external background different for each spin but having the same direction. We study the eigenvalue problem for a time-independent spin interaction and a time-independent external background. A possible analogue of the Rabi problem for the two-spin equation is defined. We present its exact solution and demonstrate the existence of magnetic resonances in two specific frequencies, one of them coinciding with the Rabi frequency, and the other depending on the rotating field magnitude. The resonance that corresponds to the second frequency is suppressed with respect to the first one.

quant-ph↗

arXiv2005

Spin equation and its solutions

The aim of the present article is to study in detail the so-called spin equation (SE) and present both the methods of generating new solution and a new set of exact solutions. We recall that the SE with a real external field can be treated as a reduction of the Pauli equation to the (0+1)-dimensional case. Two-level systems can be described by an SE with a particular form of the external field. In this article, we also consider associated equations that are equivalent or (in one way or another) related to the SE. We describe the general solution of the SE and solve the inverse problem for this equation. We construct the evolution operator for the SE and consider methods of generating new sets of exact solutions. Finally, we find a new set of exact solutions of the SE.

quant-ph↗