777 research outputs found
Wave packet dynamics in a monolayer graphene
The dynamics of charge particles described by Gaussian wave packet in
monolayer graphene is studied analytically and numerically. We demonstrate that
the shape of wave packet at arbitrary time depends on correlation between the
initial electron amplitudes and on the
sublattices and correspondingly (i.e. pseudospin polarization). For the
transverse pseudospin polarization the motion of the center of wave packet
occurs in the direction perpendicular to the average momentum . Moreover, in this case the initial wave packet splits
into two parts moving with opposite velocities along . If the
initial direction of pseudospin coincides with average momentum the splitting
is absent and the center of wave packet is displaced at along the same
direction. The results of our calculations show that all types of motion
experience {\it zitterbewegung}. Besides, depending on initial polarization the
velocity of the packet center may have the constant component ,
where is the Fermi velocity and is a function of
the parameter ( is the initial width of wave packet). As a result,
the direction of the packet motion is determined not only by the orientation of
the average momentum, but mainly by the phase difference between the up- and
low- components of the wave functions. Similar peculiarities of the dynamics of
2D electron wave packet connected with initial spin polarization should take
place in the semiconductor quantum well under the influence of the Rashba
spin-orbit coupling.Comment: 7 pages, 8 figures, to be published in Phys. Rev.
Wave packet dynamics in hole Luttinger systems
For hole systems with an effective spin 3/2 we analyzed analytically and
numerically the evolution of wave packets with the different initial
polarizations. The dynamics of such systems is determined by the
Luttinger Hamiltonian. We work in the space of arbitrary superposition of
light- and heavy-hole states of the "one-particle system". For 2D packets we
obtained the analytical solution for the components of wave function and
analyzed the space-time dependence of probability densities as well as angular
momentum densities. Depending on the value of the parameter ( is
the average momentum vector and is the packet width) two scenarios of
evolution are realized. For the initial wave packet splits into two
parts and the coordinates of packet center experience the transient
oscillations or {\it Zitterbewegung} (ZB) as for other two-band systems. In the
case when remains
almost cylindrically symmetric and the ripples arise at the circumference of
wave packet. The ZB in this case is absent. We evaluated and visualized for
different values of parameter the space-time dependence of angular momentum
densities, which have the multipole structure. It was shown that the average
momentum components can precess in the absence of external or effective
magnetic fields due to the interference of the light- and heavy hole states.
For localized initial states this precession has a transient character.Comment: 9 pages, 8 gigur
Graphene superlattice with periodically modulated Dirac gap
Graphene-based superlattice (SL) formed by a periodic gap modulation is
studied theoretically using a Dirac-type Hamiltonian. Analyzing the dispersion
relation we have found that new Dirac points arise in the electronic spectrum
under certain conditions. As a result, the gap between conduction and valence
minibands disappears. The expressions for the position of these Dirac points in
-space and threshold value of the potential for their emergence were
obtained. At some parameters of the system, we have revealed interface states
which form the top of the valence miniband.Comment: 5 pages, 4 figures, accepted to Physical Review
The long-term cyclotron dynamics of relativistic wave packets: spontaneous collapse and revival
In this work we study the effects of collapse and revival as well as {\it
Zitterbewegung} (ZB) phenomenon, for the relativistic electron wave packets,
which are a superposition of the states with quantum numbers sharply peaked
around some level of the order of few tens. The probability densities as
well as average velocities of the packet center and the average spin components
were calculated analytically and visualized. Our computations demonstrate that
due to dephasing of the states for times larger than the cyclotron period the
initial wave packet (which includes the states with the positive energy only)
loses the spatial localization so that the evolution can no longer be described
classically. However, at the half-revival time its reshaping takes
place firstly. The behavior of the wave packet containing the states of both
energy bands (with and ) is more complicated. At short times of
a few classical periods such packet splits into two parts which rotate with
cyclotron frequency in the opposite directions and meet each other every
one-half of the cyclotron period. At these moments their wave functions have
significant overlap that leads to ZB. At the time of fractional revival each of
two sub-packets is decomposed into few packets-fractions. However, at
each of the two sub-packets (with positive or negative energy) restores at
various points of the cyclotron orbit, that makes it impossible reshaping of
initial wave packet entirely unlike the wave packet which consists of states
with energies only. Obtained results can be useful for the description
of electromagnetic radiation and absorption in relativistic plasma on
astrophysics objects, where super high magnetic field has the value of the
order T, as well as for interpretation of experiments with trapped
ions
Effect of humidity on characteristics of hydrogen sensors based on nanocrystalline SnO2 thin films with various catalysts
Space-time evolution of Dirac wave packets
In this work we study the dynamics of free 3D relativistic Gaussian wave
packets with different spin polarization. We analyze the connection between the
symmetry of initial state and the dynamical characteristics of moving particle.
The corresponding solutions of Dirac equation having different types of
symmetry were evaluated analytically and numerically and after that the
electron probability densities, as well as, the spin densities were visualized.
The average values of velocity of the packet center and the average spin were
calculated analytically, and the parameters of transient Zitterbewegung in
different directions were obtained. These results can be useful for the
interpretation of future experiments with trapped ions.Comment: 10 pages, 7 figure
Stability of characteristics of resistive hydrogen sensors based on thin tin dioxide films with deposited catalysts Pt and Pd
Simulation of Thermal Surface Waves in a Protoplanetary Disk in a Two-Dimensional Approximation
Theoretical models predict that the obscuration of stellar radiation by
irregularities on the surface of a protoplanetary disk can cause
self-generating waves traveling towards the star. However, this process is
traditionally simulated using the 1+1D approach, the key approximations of
which - vertical hydrostatic equilibrium of the disk and vertical diffusion of
IR radiation - can distort the picture. This article presents a two-dimensional
radiative hydrodynamic model of the evolution of an axially symmetric gas and
dust disk. Within this model, but using simplified assumptions from 1+1D
models, we have reproduced the spontaneous generation and propagation of
thermal surface waves. The key conclusion of our work is that taking into
account two-dimensional hydrodynamics and diffusion of IR radiation suppresses
the spontaneous generation and development of thermal waves observed in the
1+1D approximation. The search for the possibility of the existence of surface
thermal waves should be continued by studying the problem for various
parameters of protoplanetary disks.Comment: Accepted for publication in Astronomy Reports (2022
Application of computational fluid dynamics methods to intensify reactor operation in the catalytic cracking process
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