303 research outputs found
General Approach to the Quantum Kicked Particle in a Magnetic Field: Quantum-Antiresonance Transition
The quantum kicked particle in a magnetic field is studied in a weak-chaos
regime under realistic conditions, i.e., for {\em general} values of the
conserved coordinate of the cyclotron orbit center. The system
exhibits spectral structures [``Hofstadter butterflies'' (HBs)] and quantum
diffusion depending sensitively on . Most significant changes take
place when approaches the value at which quantum antiresonance
(exactly periodic recurrences) can occur: the HB essentially ``doubles'' and
the quantum-diffusion coefficient is strongly reduced. An
explanation of these phenomena, including an approximate formula for in a class of wave packets, is given on the basis of an effective
Hamiltonian which is derived as a power expansion in a small parameter. The
global quantum diffusion of a two-dimensional wave packet for all
is briefly considered.Comment: Revised Version, publishe
General approach to potentials with two known levels
We present the general form of potentials with two given energy levels
, and find corresponding wave functions. These entities are
expressed in terms of one function and one parameter -. We show how the quantum numbers of both levels depend on
properties of the function . Our approach does not need resorting to
the technique of supersymmetric (SUSY) quantum mechanics but automatically
generates both the potential and superpotential.Comment: 14 pages, REVTeX 3.0. In v.2 misprints and inaccuracies in
presentation corrected, discussion of 3-dim. case added. In v.3 misprint in
eq. 41, several typos and inaccuracies in English corrected. To be published
in J. of Phys. A: Math. Ge
Quasi-exactly solvable quartic Bose Hamiltonians
We consider Hamiltonians, which are even polynomials of the forth order with
the respect to Bose operators. We find subspaces, preserved by the action of
Hamiltonian These subspaces, being finite-dimensional, include, nonetheless,
states with an \QTR{it}{infinite} number of quasi-particles, corresponding to
the original Bose operators. The basis functions look rather simple in the
coherent state representation and are expressed in terms of the degenerate
hypergeometric function with respect to the complex variable labeling the
representation. In some particular degenerate cases they turn (up to the power
factor) into the trigonometric or hyperbolic functions, Bessel functions or
combinations of the exponent and Hermit polynomials. We find explicitly the
relationship between coefficients at different powers of Bose operators that
ensure quasi-exact solvability of Hamiltonian.Comment: 21 pages, REVTeX 3.0, no figures. In v.2 couple of misprints in
English corrected. To be published in J. Phys. A: Math. Ge
Coherent Acceleration of Material Wavepackets
We study the quantum dynamics of a material wavepacket bouncing off a
modulated atomic mirror in the presence of a gravitational field. We find the
occurrence of coherent accelerated dynamics for atoms. The acceleration takes
place for certain initial phase space data and within specific windows of
modulation strengths. The realization of the proposed acceleration scheme is
within the range of present day experimental possibilities.Comment: 6 pages, 3 figures, NASA "Quantum-to-Cosmos" conference proceedings
to be published in IJMP
Modelling by maps of two-frequency microwave ionization of hydrogen atoms
Mapping equations of motion of the highly exited classical atom in a
monochromatic field are generalized for the two-frequency microwave field.
Analysis of the obtained equations indicates to the weak sensitivity of the
position of the recently observed ionization peak near the main resonance to
the frequency and amplitude of the additional microwave field. In the high
frequency region, however, the sensitivity of the enhanced ionization peaks on
the additional field frequency is predicted.Comment: LaTex, 3 PostScript figure
Entropy of Quantum Fields for Nonextreme Black Holes in the Extreme Limit
Nonextreme black hole in a cavity within the framework of the canonical or
grand canonical ensemble can approach the extreme limit with a finite
temperature measured on a boundary located at a finite proper distance from the
horizon. In spite of this finite temperature, it is shown that the one-loop
contribution of quantum fields to the thermodynamic entropy due
to equilibrium Hawking radiation vanishes in the limit under consideration. The
same is true for the finite temperature version of the Bertotti-Robinson
spacetime into which a classical Reissner-Nordstr\"{o}m black hole turns in the
extreme limit. The result is attributed to the nature of a horizon
for the Bertotti-Robinson spacetime.Comment: 11 pages, ReVTeX, no figures. New references added, discussion
expanded, presentation and English improved. Accepted for publication in
Phys. Rev.
Near-extremal and extremal quantum-corrected two-dimensional charged black holes
We consider charged black holes within dilaton gravity with
exponential-linear dependence of action coefficients on dilaton and minimal
coupling to quantum scalar fields. This includes, in particular, CGHS and RST
black holes in the uncharged limit. For non-extremal configuration quantum
correction to the total mass, Hawking temperature, electric potential and
metric are found explicitly and shown to obey the first generalized law. We
also demonstrate that quantum-corrected extremal black holes in these theories
do exist and correspond to the classically forbidden region of parameters in
the sense that the total mass ( is a charge). We show that in
the limit (where is the Hawking temperature) the mass and
geometry of non-extremal configuration go smoothly to those of the extremal
one, except from the narrow near-horizon region. In the vicinity of the horizon
the quantum-corrected geometry (however small quantum the coupling parameter
would be) of a non-extremal configuration tends to not the
quantum-corrected extremal one but to the special branch of solutions with the
constant dilaton (2D analog of the Bertotti-Robinson metric) instead.
Meanwhile, if exactly, the near-extremal configuration tends to the
extremal one. We also consider the dilaton theory which corresponds classically
to the spherically-symmetrical reduction from 4D case and show that for the
quantum-corrected extremal black hole .Comment: 25 pages. Typos corrected. To appear in Class. Quant. Gra
Phase transition between quantum and classical regimes for the escape rate of a biaxial spin system
Employing the method of mapping the spin problem onto a particle one, we have
derived the particle Hamiltonian for a biaxial spin system with a transverse or
longitudinal magnetic field. Using the Hamiltonian and introducing the
parameter where (U_{min})
corresponds to the top (bottom) of the potential and is the energy of the
particle, we have studied the first- or second-order transition around the
crossover temperature between thermal and quantum regimes for the escape rate,
depending on the anisotropy constant and the external magnetic field. It is
shown that the phase boundary separating the first- and second-order transition
and its crossover temperature are greatly influenced by the transverse
anisotropy constant as well as the transverse or longitudinal magnetic field.Comment: 5 pages + 3 figures, to be published in Phys. Rev.
Coherent acceleration of material wavepackets in modulated optical fields
We study the quantum dynamics of a material wavepacket bouncing off a
modulated atomic mirror in the presence of a gravitational field. We find the
occurrence of coherent accelerated dynamics for atoms beyond the familiar
regime of dynamical localization. The acceleration takes place for certain
initial phase space data and within specific windows of modulation strengths.
The realization of the proposed acceleration scheme is within the range of
present day experimental possibilities
Extremal limit of the regular charged black holes in nonlinear electrodynamics
The near horizon limit of the extreme nonlinear black hole is investigated.
It is shown that resulting geometry belongs to the AdS2xS2 class with different
modules of curvatures of subspaces and could be described in terms of the
Lambert functions. It is demonstrated that the considered class of Lagrangians
does not admit solutions of the Bertotti-Robinson type
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