arXiv subjects

A. Matulis

Publications and source records attributed to A. Matulis.

At least 19 recordsLinked to original sources

arXiv2020

Negative flow of energy in a mechanical wave

A classical system, which is analogous to the quantum one with a backflow of probability, is proposed. The system consists of a chain of masses interconnected by springs, as well attached by other springs to fixed supports. Thanks to the last springs the cutoff frequency and dispersion appears in the spectrum of waves propagating along the chain. It is shown that this dispersion contributes to the appearance of a backflow of energy. In the case of the interference of the two waves, the magnitude of this backflow is an order of magnitude higher than the value of the probability backflow in the mentioned quantum problem. The equation of Green's function is considered, and it is shown that the backflow of energy is also possible when the system is excited by two consecutive short pulses. This classical backflow phenomenon is explained by the branching of energy flow to local modes, what is confirmed by the results for the forced damped oscillator. It is shown that even in such a simple system the backflow of energy takes place (both an instantaneous and on average) and the energy comes back to external force.

physics.class-ph↗

arXiv2019

Classical analog to the Airy wave packet

The solution of the Liouville equation for the ensemble of free particles is presented and the classical analog to the quantum accelerating Airy wave packet is constructed and discussed. Considering the motion of various classical packets -- with an infinite and restricted distribution of velocities of particles -- and also the motion of their fronts, we demonstrate in the simplest and most definite way why the packet can display a more sophisticated behavior (even acceleration) as compared with a free individual particle that moves at a fixed velocity. A comparison of this classical solution with the quantum one in the Wigner representation of quantum mechanics which provides the closest analogy is also presented.

physics.gen-ph↗

arXiv2012

Scattering of a Dirac electron on a mass barrier

The interaction of a wave packet (and in particular the wave front) with a mass barrier is investigated in one dimension. We discuss the main features of the wave packet that are inherent to two-dimensional wave packets, such as compression during reflection, penetration in the case when the energy is lower than the height of the barrier, waving tails, precursors, and the retardation of the reflected and penetrated wave packets. These features depend on the wave-packet envelope function which we demonstrate by considering the case of a rectangular wave packet with sharp front and trailing edges and a smooth Gaussian wave packet. The method of Fourier integral for obtaining the nonstationary solutions is used.

cond-mat.mes-hall↗

arXiv2011

Scattering of Dirac electrons by circular mass barriers: valley filter and resonant scattering

The scattering of two-dimensional (2D) massless Dirac electrons is investigated in the presence of a random array of circular mass barriers. The inverse momentum relaxation time and the Hall factor are calculated and used to obtain parallel and perpendicular resistivity components within linear transport theory. We found a non zero perpendicular resistivity component which has opposite sign for electrons in the different K and K' valleys. This property can be used for valley filter purposes. The total cross-section for scattering on penetrable barriers exhibit resonances due to the presence of quasi-bound states in the barriers that show up as sharp gaps in the cross-section while for Schrödinger electrons they appear as peaks.

cond-mat.mes-hall↗

arXiv2009

Quasi-bound states of Schrodinger and Dirac electrons in magnetic quantum dot

The properties of a two-dimensional electron are investigated in the presence of a circular step magnetic field profile. Both electrons with parabolic dispersion as well as Dirac electrons with linear dispersion are studied. We found that in such a magnetic quantum dot no electrons can be confined. Nevertheless close to the Landau levels quasi-bound states can exist with a rather long life time.

cond-mat.mes-hall↗

arXiv2007

Quasi-bound states of quantum dots in single and bilayer graphene

Dirac fermions interacting with a cylindrically symmetric quantum dot potential created in single and bilayer graphene are not confined but form quasi-bound states. The broadening of these quasi-bound states (i. e. the inverse of their lifetimes) decreases (increases) with the orbital momentum of the electron in the case of graphene (bilayer). Quasi-bound states with energy below (above) the barrier height are dominantly electron(hole)-like. A remarkable decrease of the energy level broadening is predicted for electron energies close to the barrier height, which are a consequence of the total internal reflection of the electronic wave at the dot edge.

cond-mat.mes-hall↗

arXiv2007

Schrodinger-equation formalism for a dissipative quantum system

We consider a model dissipative quantum-mechanical system realized by coupling a quantum oscillator to a semi-infinite classical string which serves as a means of energy transfer from the oscillator to the infinity and thus plays the role of a dissipative element. The coupling between the two -- quantum and classical -- parts of the compound system is treated in the spirit of the mean-field approximation and justification of the validity of such an approach is given. The equations of motion of the classical subsystem are solved explicitly and an effective dissipative Schrodinger equation for the quantum subsystem is obtained. The proposed formalism is illustrated by its application to two basic problems: the decay of the quasi-stationary state and the calculation of the nonlinear resonance line shape.

cond-mat.other↗

arXiv2007

Enhanced Weiss oscillations in graphene

The magneto-conductivity of a single graphene layer where the electrons are described by the Dirac Hamiltonian weakly modulated by a periodic potential is calculated. It is shown that Weiss oscillations periodic in the inverse magnetic field appear, that are more pronounced and less damped with the increment of temperature as compared with the same oscillations in a typical two-dimensional electron system with a standard parabolic energy spectrum.

cond-mat.mes-hall↗

arXiv2004

Power-law dependence of the angular momentum transition fields in few-electron quantum dots

We show that the critical magnetic fields at which a few-electron quantum dot undergoes transitions between successive values of its angular momentum (M), for large M values follow a very simple power-law dependence on the effective inter-electron interaction strength. We obtain this power law analytically from a quasi-classical treatment and demonstrate its nearly-universal validity by comparison with the results of exact diagonalization.

cond-mat.mes-hall↗

arXiv2004

Currents in a many-particle parabolic quantum dot under a strong magnetic field

Currents in a few-electron parabolic quantum dot placed into a perpendicular magnetic field are considered. We show that traditional ways of investigating the Wigner crystallization by studying the charge density correlation function can be supplemented by the examination of the density-current correlator. However, care must be exercised when constructing the correct projection of the multi-dimensional wave function space. The interplay between the magnetic field and Euler-liquid-like behavior of the electron liquid gives rise to persistent and local currents in quantum dots. We demonstrate these phenomena by collating a quasi-classical theory valid in high magnetic fields and an exact numerical solution of the many-body problem.

cond-mat.mes-hall↗

arXiv2002

Magnetic edge states of impenetrable stripe

The electron motion in a strong perpendicular magnetic field close to the impenetrable stripe is considered by making use of the singular integral equation technique. The energy spectrum is calculated and compared with the energy spectrum of the round antidot.

cond-mat.mes-hall↗

arXiv2002

Structure and correlations in two-dimensional Coulomb confined classical artificial atoms

The ordering of N equally charged particles (-e) moving in two dimensions and confined by a Coulomb potential, resulting from a displaced positive charge Ze is discussed. This is a classical model system for atoms. We obtain the configurations of the charged particles which, depending on the value of N and Z, may result in ring structures, hexagonal-type configurations and for N/Z~1 in an inner structure of particles which is separated by an outer ring of particles. For N/Z<<1 the Hamiltonian of the parabolic confinement case is recovered. For N/Z~1 the configurations are very different from those found in the case of a parabolic confinement potential. A hydrodynamic analysis is presented in order to highlight the correlations effects.

cond-mat.str-el↗

arXiv2002

Quantum Dots in a Strong Magnetic Field. Quasi-classical Consideration

The electron motion in rather strong magnetic fields (when only the lowest Landau level is populated) is considered. In this case the electron kinetic energy is frozen out and the electrons are guided by slowly varied potential. Using the adiabatic procedure and expansion in magnetic length series the approximate description is developed. In zero order this approximation leads to the classical equations of motion describing the Larmor circle drift in the potential gradient. In the second order the special quantum mechanical description where the electron potential energy plays the role of the total Hamiltonian is constructed. Simple examples of a single and two electrons in the parabolic dot demonstrates that the proposed approximate description gives the main features of the electron system spectrum and the collective phenomena.

cond-mat.mes-hall↗

arXiv2001

Confined magnetic guiding orbit states

We show how snake-orbit states which run along a magnetic edge can be confined electrically. We consider a two-dimensional electron gas (2DEG) confined into a quantum wire, subjected to a strong perpendicular and steplike magnetic field $B/-B$. Close to this magnetic step new, spatially confined bound states arise as a result of the lateral confinement and the magnetic field step. The number of states, with energy below the first Landau level, increases as $B$ becomes stronger or as the wire width becomes larger. These bound states can be understood as an interference between two counter-propagating one-dimensional snake-orbit states.

cond-mat.mes-hall↗

arXiv2001

Electron scattering on circular symmetric magnetic profiles in a two-dimensional electron gas

The quasi-bound and scattered states in a 2DEG subjected to a circular symmetric steplike magnetic profile with zero average magnetic field are studied. We calculate the effect of a random distribution of such identical profiles on the transport properties of a 2DEG. We show that a nonzero Hall resistance can be obtained, although $ =0$, and that in some cases it can even change sign as function of the Fermi energy or the magnetic field strength. The Hall and magnetoresistance show pronounced resonances apart from the Landau states of the inner core, corresponding to the so-called quasi-bound snake orbit states.

cond-mat.mes-hall↗

arXiv2000

Fine structure of excitons in a quantum well in the presence of a nonhomogeneous magnetic field

The trapping of excitons in a semiconductor quantum well due to a circular symmetric nonhomogeneous magnetic field is studied. The effect of the spin state of the exciton on its trapping energy is analyzed, and the importance of the interaction of the orbital and spin Zeeman effect as compared to the diamagnetic term in the exciton Hamiltonian is emphasized. Magnetic field profiles are considered, which can experimentally be created through the deposition of ferromagnetic disks on top of a semiconductor heterostructure. This setup gives rise to a magnetic dipole type of profile in the $xy$ plane of the exciton motion. We find that the spin direction of the exciton influences its localization by changing the confinement region in the effective potential. The exciton confinement increases with magnetic field intensity, and this is more pronounced when the exciton g-factor is different from zero. The numerical calculations are performed for GaAs/Al$_{x}$Ga$_{1-x}$As quantum wells and we show that it open up a new realistic path for experiments designed to probe exciton trapping in semiconductors.

cond-mat↗

arXiv2000

Wigner crystallization in the two electron quantum dot

Wigner crystallization can be induced in a quantum dot by increasing the effective electron-electron interaction through a decrease of the electron density or by the application of a strong magnetic field. We show that the ground state in both cases is very similar but the energy scales are very different and therefore also the dynamics.

cond-mat.mes-hall↗

arXiv2000

Confinement of two-dimensional excitons in a non-homogeneous magnetic field

The effective Hamiltonian describing the motion of an exciton in an external non-homogeneous magnetic field is derived. The magnetic field plays the role of an effective potential for the exciton motion, results into an increment of the exciton mass and modifies the exciton kinetic energy operator. In contrast to the homogeneous field case, the exciton in a non-homogeneous magnetic field can also be trapped in the low field region and the field gradient increases the exciton confinement. The trapping energy and wave function of the exciton in a GaAs two-dimensional electron gas for specific circular magnetic field configurations are calculated. The results show than excitons can be trapped by non-homogeneous magnetic fields, and that the trapping energy is strongly correlated with the shape and strength of the non-homogeneous magnetic field profile.

cond-mat↗