437 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
Acceleration of particles by rotating black holes: near-horizon geometry and kinematics
Nowadays, the effect of infinite energy in the centre of mass frame due to
near-horizon collisions attracts much attention.We show generality of the
effect combining two seemingly completely different approaches based on
properties of a particle with respect to its local light cone and calculating
its velocity in the locally nonrotaing frame directly. In doing so, we do not
assume that particles move along geodesics. Usually, a particle reaches a
horizon having the velocity equals that of light. However, there is also case
of "critical" particles for which this is not so. It is just the pair of usual
and critical particles that leads to the effect under discussion. The similar
analysis is carried out for massless particles. Then, critical particles are
distinguishable due to the finiteness of local frequency. Thus, both approach
based on geometrical and kinematic properties of particles moving near the
horizon, reveal the universal character of the effect.Comment: 8 page
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
Traversable wormholes: minimum violation of null energy condition revisited
It was argued in literature that traversable wormholes can exist with
arbitrarily small violation of null energy conditions. We show that if the
amount of exotic material near the wormhole throat tends to zero, either this
leads to a horn instead of a wormhole or the throat approaches the horizon in
such a way that infnitely large stresses develop on the throat.Comment: 12 pages. To appear in PR
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
Entropy of an extremal electrically charged thin shell and the extremal black hole
There is a debate as to what is the value of the the entropy of extremal
black holes. There are approaches that yield zero entropy , while there
are others that yield the Bekenstein-Hawking entropy , in Planck
units. There are still other approaches that give that is proportional to
or even that is a generic well-behaved function of . Here
is the black hole horizon radius and is its horizon area.
Using a spherically symmetric thin matter shell with extremal electric charge,
we find the entropy expression for the extremal thin shell spacetime. When the
shell's radius approaches its own gravitational radius, and thus turns into an
extremal black hole, we encounter that the entropy is , i.e., the
entropy of an extremal black hole is a function of alone. We speculate
that the range of values for an extremal black hole is .Comment: 11 pages, minor changes, added references, matches the published
versio
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
Truly naked spherically-symmetric and distorted black holes
We demonstrate the existence of spherically-symmetric truly naked black holes
(TNBH) for which the Kretschmann scalar is finite on the horizon but some
curvature components including those responsible for tidal forces as well as
the energy density measured by a free-falling observer are
infinite. We choose a rather generic power-like asymptotics for the metric
functions and analyze possible types of a horizon depending on the behavior of
curvature components in the free-falling frame. It is also shown in a general
case of distorted black holes that and tidal forces are either
both finite or both infinite. The general approach developed in the article
includes previously found examples and, in particular, TNBHs with an infinite
area of a horizon. The fact that the detection of singularity depends on a
frame may be relevant for a more accurate definition of the cosmic censorship
conjecture. TNBHs may be considered as a new example of so-called non-scalar
singularities for which the scalar curvature invariants are finite but some
components of the Riemann tensor may diverge in certain frames.Comment: 18 pages. 2 last sentences on quantum backreaction modified. Typos
corrected. To appear in PR
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