Long-term cyclotron dynamics of relativistic wave packets: Spontaneous collapse and revival

Abstract

In this work we study the effects of collapse and revival as well as Zitterbewegung (ZB) phenomenon, for the relativistic electron wave packets, which are a superposition of the states with quantum numbers sharply peaked around some Landau level n0 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 t = TR/2 its reshaping takes place firstly. The behavior of the wave packet containing the states of both energy bands (with En > 0 and En < 0) 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 packet-fractions. However, at t = TR 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 En > 0 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 10 8 − 10 9 T, as well as for interpretation of experiments with trapped ions.

Wave packet dynamics in monolayer MoS2 with and without a magnetic field

“…Similar expressions for velocity in the quasiclassical regime, were also obtained in Ref. [49], where they studied the dynamics of relativistic wave packets. Note that these can also be obtained by differentiating Eq.…”

“…The dynamical evolution of wave packets of a quantum system with discrete but non-equidistant energy spectrum is generally quiet complex due to quantum interference. However several well defined periodicities emerge 31,44,46,49,50 , if the initial wave packet is peaked around some large Landau level characterized by n 0 .…”

Coherent states in a magnetic field and their generalizations

“…Coherent-like superpositions of energy states for the Dirac particle in a uniform magnetic field were considered in [78], using some analogies with the famous Jaynes-Cummings model of quantum optics. The dynamics of such packets was studied also in [79].…”

Wave packet dynamics in various two-dimensional systems: A unified description

“…The quantum behavior being manifested in the form of spontaneous collapse and long term quantum revival of the wave-packet arising due to quantum interference. However well defined periodicities for quasi-classical behavior, spontaneous collapse and revival emerge [3,17,46,47], if the initial wave packet have a substantial overlap with some large Landau level denoted by n 0 .…”