3,071 research outputs found
Quantum Resonances and Regularity Islands in Quantum Maps
We study analytically as well as numerically the dynamics of a quantum map
near a quantum resonance of an order q. The map is embedded into a continuous
unitary transformation generated by a time-independent quasi-Hamiltonian. Such
a Hamiltonian generates at the very point of the resonance a local gauge
transformation described the unitary unimodular group SU(q). The resonant
energy growth of is attributed to the zero Liouville eigenmodes of the
generator in the adjoint representation of the group while the non-zero modes
yield saturating with time contribution. In a vicinity of a given resonance,
the quasi-Hamiltonian is then found in the form of power expansion with respect
to the detuning from the resonance. The problem is related in this way to the
motion along a circle in a (q^2-1)-component inhomogeneous "magnetic" field of
a quantum particle with intrinsic degrees of freedom described by the SU(q)
group. This motion is in parallel with the classical phase oscillations near a
non-linear resonance. The most important role is played by the resonances with
the orders much smaller than the typical localization length, q << l. Such
resonances master for exponentially long though finite times the motion in some
domains around them. Explicit analytical solution is possible for a few lowest
and strongest resonances.Comment: 28 pages (LaTeX), 11 ps figures, submitted to PR
Simple model - a way to integrate software development processes and project management software
Physical regularization for the spin-1/2 Aharonov-Bohm problem in conical space
We examine the bound state and scattering problem of a spin-one-half particle
undergone to an Aharonov-Bohm potential in a conical space in the
nonrelativistic limit. The crucial problem of the \delta-function singularity
coming from the Zeeman spin interaction with the magnetic flux tube is solved
through the self-adjoint extension method. Using two different approaches
already known in the literature, both based on the self-adjoint extension
method, we obtain the self-adjoint extension parameter to the bound state and
scattering scenarios in terms of the physics of the problem. It is shown that
such a parameter is the same for both situations. The method is general and is
suitable for any quantum system with a singular Hamiltonian that has bound and
scattering states.Comment: Revtex4, 5 pages, published versio
Inclusive probability to record an electron in elastic electromagnetic scattering by a spin one-half hadron wave packet
The inclusive probability to record an electron in elastic electromagnetic
scattering of an electron by a spin one-half hadron is obtained, the initial
quantum states of the electron and the hadron being described by the density
matrices of a general form. Contrary to the Rosenbluth formula for the
differential cross-section for this process, the first nontrivial contribution
to the inclusive probability turns out to be of order and not
. This contribution describes the interference between the trivial
contribution to the -matrix and the leading contribution to its connected
part. The explicit expression for this interference terms is derived. It is
shown that the same interference term arises when the electron is scattered by
the classical electromagnetic field produced by the hadron electromagnetic
current averaged with respect to the free evolving density matrix of the
hadron, even in the case of a single hadron. The interference term describes
coherent scattering of the electron by the hadron wave packet and is immune to
the quantum recoil experienced by a hadron due to scattering. The effective
electron mass operator is found on the mass-shell.Comment: 14 pp., 2 fig
Coupled phonon-ripplon modes in a single wire of electrons on the liquid-helium surface
The coupled phonon-ripplon modes of the quasi-one-dimensional electron chain
on the liquid helium sutface are studied. It is shown that the electron-ripplon
coupling leads to the splitting of the collective modes of the wire with the
appearance of low-frequency modes and high-frequency optical modes starting
from threshold frequencies. The effective masses of an electron plus the
associated dimple for low frequency modes are estimated and the values of the
threshold frequencies are calculated. The results obtained can be used in
experimental attempts to observe the phase transition of the electron wire into
a quasi-ordered phase.Comment: 5 pages, 1 figure, Physical Review (in press
CPT and Lorentz violation effects in hydrogen-like atoms
Within the framework of Lorentz-violating extended electrodynamics, the Dirac
equation for a bound electron in an external electromagnetic field is
considered assuming the interaction with a CPT-odd axial vector background
. The quasi-relativistic Hamiltonian is obtained using a -series
expansion. Relativistic Dirac eigenstates in a spherically-symmetric potential
are found accurate up to the second order in . -induced CPT-odd
corrections to the electromagnetic dipole moment operators of a bound electron
are calculated that contribute to the anapole moment of the atomic orbital and
may cause a specific asymmetry of the angular distribution of the radiation of
a hydrogen atom.Comment: 13 pages, 1 figure; (5.14) is corrected to conform to the
normalization convention for Laguerre polynomials adopted at present; minor
grammatical change
Formation of bound states of electrons in spherically symmetric oscillations of plasma
We study spherically symmetric oscillations of electrons in plasma in the
frame of classical electrodynamics. Firstly, we analyze the electromagnetic
potentials for the system of radially oscillating charged particles. Secondly,
we consider both free and forced spherically symmetric oscillations of
electrons. Finally, we discuss the interaction between radially oscillating
electrons through the exchange of ion acoustic waves. It is obtained that the
effective potential of this interaction can be attractive and can transcend the
Debye-Huckel potential. We suggest that oscillating electrons can form bound
states at the initial stages of the spherical plasma structure evolution. The
possible applications of the obtained results for the theory of natural
plasmoids are examined.Comment: 9 pages in LaTeX2e, no figures; paper was significantly modified, 2
new references added, some inessential mathematics was removed, many typos
were corrected; final variant to be published in Physica Script
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