Charged Quantum Particle Research Articles

Diffraction Approach in the Scattering Problem for Three Charged Quantum Particles

Diffraction Approach in the Scattering Problem for Three Charged Quantum Particles

Effect of noise on quantum transport of a charged particle in a tight-binding lattice

We investigate diffusion of a quantum charged particle in a tight-binding lattice (TBL) under fluctuating noisy electric fields. Several closed-form expressions such as that of probability propagator, average current, and mean-squared displacement are derived. The particular effect of Gaussian noise in a 1D TBL is studied in detail and a comparison is made with the case of a telegraph noise. The Gaussian white noise and telegraph noise show up in different manifestations in the underdamped regime. On the contrary, when relaxation is rapid the noisy field averages out to zero yielding delocalization for both Gaussian and telegraphic noisy electric fields. Depending on the strength of noise and the external field one can observe different current characteristics.

Diffraction Approach in the Scattering Problem for Three Charged Quantum Particles

Diffraction Approach in the Scattering Problem for Three Charged Quantum Particles

A Quantum Charged Particle under Sudden Jumps of the Magnetic Field and Shape of Non-Circular Solenoids

We consider a quantum charged particle moving in the x y plane under the action of a time-dependent magnetic field described by means of the linear vector potential of the form A = B ( t ) − y ( 1 + β ) , x ( 1 − β ) / 2 . Such potentials with β ≠ 0 exist inside infinite solenoids with non-circular cross sections. The systems with different values of β are not equivalent for nonstationary magnetic fields or time-dependent parameters β ( t ) , due to different structures of induced electric fields. Using the approximation of the stepwise variations of parameters, we obtain explicit formulas describing the change of the mean energy and magnetic moment. The generation of squeezing with respect to the relative and guiding center coordinates is also studied. The change of magnetic moment can be twice bigger for the Landau gauge than for the circular gauge, and this change can happen without any change of the angular momentum. A strong amplification of the magnetic moment can happen even for rapidly decreasing magnetic fields.

Propagation of Waves and Particles Through Porous Structures (I)

The processes of the propagation of quantum and classical charged particles through porous films are studied. The propagation of quantum particles is analyzed by numerically calculating the Schrodinger equation. The polarization force acting on the charge is calculated within the framework of classical electrodynamics. The possibility of pore formation in the films is analyzed in the problem of the propagation of ions with large charges through ultrathin carbon films. Mathematical modeling of the film accompanied by elucidation of the most important polarization properties is carried out to understand the process more clearly. The calculations show the possibility of film perforation because of the action of ponderomotive forces generated by the strong polarization field of the wave packet of the passing ion.

Some Aspects of the Scattering Problem for a System of Three Charged Particles

The question of influence of the spectral neighborhood of an accumulative point of bound energies of a pair subsystem on the structure of eigenfunctions of the continuous spectrum for a system of three charged quantum particles is studied. The unified contribution of pair high-excited states are separated in the coordinate asymptotics of such functions.

Squeezing of Relative and Center-of-Orbit Coordinates of a Charged Particle by Step-Wise Variations of a Uniform Magnetic Field with an Arbitrary Linear Vector Potential

We consider a quantum charged particle moving in the xy plane under the action of a time-dependent magnetic field described by means of the linear vector potential A = H(t) [−y(1 + β), x(1 − β)] /2 with a fixed parameter β. The systems with different values of β are not equivalent for nonstationary magnetic fields due to different structures of induced electric fields, whose lines of force are ellipses for |β| 1. Using the approximation of the stepwise variation of the magnetic field H(t), we obtain explicit formulas describing the evolution of the principal squeezing in two pairs of noncommuting observables: the coordinates of the center of orbit and relative coordinates with respect to this center. Analysis of these formulas shows that no squeezing can arise for the circular gauge (β = 0). On the other hand, for any nonzero value of β, one can find the regimes of excitations resulting in some degree of squeezing in the both pairs. The maximum degree of squeezing can be obtained for the Landau gauge (|β| = 1) if the magnetic field is switched off and returns to the initial value after some time T, in the limit T → ∞.

Coulomb Scattering of a Slow Quantum Particle in a Space of Arbitrary Dimension

We assume that a charged quantum particle moves in a space of dimension d = 2, 3,... and is scattered by a fixed Coulomb center. We derive and study expansions of the wave function and all radial functions of such a particle in integer powers of the wave number and in Bessel functions of a real order. We prove that finite sums of such expansions are asymptotic approximations of the wave functions in the low-energy limit.

Penetration of Waves and Particles through Porous Structures

The penetration of quantum and classical charged particles through porous films is investigated. The passage of quantum particles is analyzed by numerically solving the Schrodinger equation. The force of polarization acting on a charge is calculated by means of classical electrodynamics. The possibility of perforating thin films is analyzed.

On the Significance of Density of an Electrically Charged Quantum Particle

On the Significance of Density of an Electrically Charged Quantum Particle

The “Forgotten” Pseudomomenta and Gauge Changes in Generalized Landau Level Problems: Spatially Nonuniform Magnetic and Temporally Varying Electric Fields

By perceiving gauge invariance as an analytical tool in order to get insight into the states of the "generalized Landau problem" (a charged quantum particle moving inside a magnetic, and possibly electric field), and motivated by an early article that correctly warns against a naive use of gauge transformation procedures in the usual Landau problem (i.e. with the magnetic field being static and uniform), we first show how to bypass the complications pointed out in that article by solving the problem in full generality through gauge transformation techniques in a more appropriate manner. Our solution provides in simple and closed analytical forms all Landau Level-wavefunctions without the need to specify a particular vector potential. This we do by proper handling of the so-called pseudomomentum K (or of a quantity that we term pseudoangular momentum Lz), a method that is crucially different from the old warning argument, but also from standard treatments in textbooks and in research literature (where the usual Landau wavefunctions are employed - labeled with canonical momenta quantum numbers). Most importantly, we go further by showing that a similar procedure can be followed in the more difficult case of spatially-nonuniform magnetic fields: in such case we define K and Lz as plausible generalizations of the previous ordinary case, namely as appropriate line integrals of the inhomogeneous magnetic field - our method providing closed analytical expressions for all stationary state wavefunctions.. (see paper) ... also provide explicit Berry's phase calculations and their connection to probability currents and ...issues in elementary Quantum Mechanics and Condensed Matter Physics. As an added feature, we also show how the possible presence of an additional electric field can be treated through a further generalization of pseudomomenta and their proper handling.

The quantum charged particle self-interaction problem within the Fock many temporal and Feynman proper time paradigms

A quantum fermionic massless charged particle self-intercating with its own self-generated bosonic electromagnetic field is reanalyzed in the framework of the Fock many-temporal and Feynman proper time approaches. The self-interaction phenomenon structure is discussed within the renormalized quantum Fock space. The quantum electromagnetic charged particle mass origin is suggested.

Two-dimensional Coulomb scattering of a quantum particle: Low-energy asymptotic behavior

We consider a charged quantum particle moving in a two-dimensional plane in the three-dimensional coordinate space and scattering on an immovable Coulomb center in the same plane. We derive and investigate expansions of the wave function and of all radial wave functions of the particle in integer powers of the wave number and in Bessel functions of a real order. We prove that finite sums of such expansions are asymptotic in the low-energy limit.

Spectral Properties of Magnetic Chain Graphs

We discuss spectral properties of a charged quantum particle confined to a chain graph consisting of an infinite array of rings under influence of a magnetic field assuming a $\delta$-coupling at the points where the rings touch. We start with the situation when the system has a translational symmetry and analyze spectral consequences of perturbations of various kind, such as a local change of the magnetic field, of the coupling constant, or of a ring circumference. A particular attention is paid to weak perturbations, both local and periodic; for the latter we prove a version of Saxon-Hutner conjecture.

Two-dimensional Coulomb scattering of a quantum particle: Wave functions and Green’s functions

We solve the problem of the propagation of a charged quantum particle in a two-dimensional plane embedded in the three-dimensional coordinate space. We consider scattering of this particle by a stable Coulomb center situated in the same plane. We study the wave function of this particle, its Green’s function, and all radial components of these functions. We derive uniform majorant bounds on absolute values of these functions and find the wave function representation in terms of regular radial Coulomb functions and the scattering amplitude representation via partial phases. We obtain integral representations of the Greens’s function and all its radial components.

Two-dimensional Coulomb scattering of a quantum particle: Construction of radial wave functions

We prove that radial wave functions of a charged quantum particle moving in a two-dimensional plane of the three-dimensional coordinate space and scattering by a Coulomb center at rest in the same plane are governed by the Coulomb equation with a half-integer index. We investigate the structure of these functions and consider three physically interesting limits: the non-Coulomb limit and high- and low-energy limits. We explicate the basic differences between two- and three-dimensional Coulomb scattering.

Black hole horizons and quantum charged particles

We point out a structural similarity between the characterization of black hole apparent horizons as stable, marginally outer trapped surfaces (MOTS) and the quantum description of a non-relativistic charged particle moving in given magnetic and electric fields on a closed surface. Specifically, the spectral problem of the MOTS-stability operator corresponds to a stationary quantum particle with a formal fine-structure constant α of negative sign. We discuss how such analogy enriches both problems, illustrating this with the insights into the MOTS-spectral problem gained from the analysis of the spectrum of the quantum charged particle Hamiltonian.

Black hole horizons and quantum charged particles

Black hole horizons and quantum charged particles

A perspective on Black Hole Horizons from the Quantum Charged Particle

Black hole apparent horizons possess a natural notion of stability, whose spectral characterization can be related to the problem of the stationary quantum charged particle. Such mathematical relation leads to an “analyticity conjecture” on the dependence of the spectral properties on a complex “fine-structure-constant” parameter, that can reduce the study of the spectrum of the (non-selfadjoint) MOTS-stability operator to that of the (selfadjoint) Hamiltonian of the quantum charged particle. Moreover, this perspective might open an avenue to the spinorialtreatment of apparent horizon (MOTS-)stability and to the introduction of semiclassicaltools to explore some of the qualitative aspects of this black hole spectral problem.

Generation of uniform synthetic magnetic fields by split driving of an optical lattice

We describe a method to generate a synthetic gauge potential for ultracold atoms held in an optical lattice. Our approach uses a time-periodic driving potential based on two quickly alternating signals to engineer the appropriate Aharonov-Bohm phases, and permits the simulation of a uniform tunable magnetic field. We explicitly demonstrate that our split driving scheme reproduces the behavior of a charged quantum particle in a magnetic field over the complete range of field strengths, and obtain the Hofstadter butterfly band-structure for the Floquet quasienergies at high fluxes.