27,391 research outputs found
Point interactions in acoustics: one dimensional models
A one dimensional system made up of a compressible fluid and several
mechanical oscillators, coupled to the acoustic field in the fluid, is analyzed
for different settings of the oscillators array. The dynamical models are
formulated in terms of singular perturbations of the decoupled dynamics of the
acoustic field and the mechanical oscillators. Detailed spectral properties of
the generators of the dynamics are given for each model we consider. In the
case of a periodic array of mechanical oscillators it is shown that the energy
spectrum presents a band structure.Comment: revised version, 30 pages, 2 figure
Spectral Properties and Linear Stability of Self-Similar Wave Maps
We study co--rotational wave maps from --Minkowski space to the
three--sphere . It is known that there exists a countable family
of self--similar solutions. We investigate their stability under linear
perturbations by operator theoretic methods. To this end we study the spectra
of the perturbation operators, prove well--posedness of the corresponding
linear Cauchy problem and deduce a growth estimate for solutions. Finally, we
study perturbations of the limiting solution which is obtained from by
letting .Comment: Some extensions added to match the published versio
Jahn-Teller effect versus Hund's rule coupling in C60N-
We propose variational states for the ground state and the low-energy
collective rotator excitations in negatively charged C60N- ions (N=1...5). The
approach includes the linear electron-phonon coupling and the Coulomb
interaction on the same level. The electron-phonon coupling is treated within
the effective mode approximation (EMA) which yields the linear t_{1u} x H_g
Jahn-Teller problem whereas the Coulomb interaction gives rise to Hund's rule
coupling for N=2,3,4. The Hamiltonian has accidental SO(3) symmetry which
allows an elegant formulation in terms of angular momenta. Trial states are
constructed from coherent states and using projection operators onto angular
momentum subspaces which results in good variational states for the complete
parameter range. The evaluation of the corresponding energies is to a large
extent analytical. We use the approach for a detailed analysis of the
competition between Jahn-Teller effect and Hund's rule coupling, which
determines the spin state for N=2,3,4. We calculate the low-spin/high-spin gap
for N=2,3,4 as a function of the Hund's rule coupling constant J. We find that
the experimentally measured gaps suggest a coupling constant in the range
J=60-80meV. Using a finite value for J, we recalculate the ground state
energies of the C60N- ions and find that the Jahn-Teller energy gain is partly
counterbalanced by the Hund's rule coupling. In particular, the ground state
energies for N=2,3,4 are almost equal
Static and dynamic Jahn-Teller effect in the alkali metal fulleride salts A4C60 (A = K, Rb, Cs)
We report the temperature dependent mid- and near-infrared spectra of K4C60,
Rb4C60 and Cs4C60. The splitting of the vibrational and electronic transitions
indicates a molecular symmetry change of C604- which brings the fulleride anion
from D2h to either a D3d or a D5d distortion. In contrast to Cs4C60, low
temperature neutron diffraction measurements did not reveal a structural phase
transition in either K4C60 and Rb4C60. This proves that the molecular
transition is driven by the molecular Jahn-Teller effect, which overrides the
distorting potential field of the surrounding cations at high temperature. In
K4C60 and Rb4C60 we suggest a transition from a static to a dynamic Jahn-Teller
state without changing the average structure. We studied the librations of
these two fullerides by temperature dependent inelastic neutron scattering and
conclude that both pseudorotation and jump reorientation are present in the
dynamic Jahn-Teller state.Comment: 13 pages, 10 figures, to be published in Phys. Rev.
Multiple classical limits in relativistic and nonrelativistic quantum mechanics
The existence of a classical limit describing interacting particles in a
second-quantized theory of identical particles with bosonic symmetry is proved.
This limit exists in addition to a previously established classical limit with
a classical field behavior, showing that the limit of the theory
is not unique. An analogous result is valid for a free massive scalar field:
two distinct classical limits are proved to exist, describing a system of
particles or a classical field. The introduction of local operators in order to
represent kinematical properties of interest is shown to break the permutation
symmetry under some localizability conditions, allowing the study of individual
particle properties.Comment: 13 page
Local energy decay of massive Dirac fields in the 5D Myers-Perry metric
We consider massive Dirac fields evolving in the exterior region of a
5-dimensional Myers-Perry black hole and study their propagation properties.
Our main result states that the local energy of such fields decays in a weak
sense at late times. We obtain this result in two steps: first, using the
separability of the Dirac equation, we prove the absence of a pure point
spectrum for the corresponding Dirac operator; second, using a new form of the
equation adapted to the local rotations of the black hole, we show by a Mourre
theory argument that the spectrum is absolutely continuous. This leads directly
to our main result.Comment: 40 page
Cosmic recall and the scattering picture of Loop Quantum Cosmology
The global dynamics of a homogeneous universe in Loop Quantum Cosmology is
viewed as a scattering process of its geometrodynamical equivalent. This
picture is applied to build a flexible (easy to generalize) and not restricted
just to exactly solvable models method of verifying the preservation of the
semiclassicality through the bounce. The devised method is next applied to two
simple examples: (i) the isotropic Friedman Robertson Walker universe, and (ii)
the isotropic sector of the Bianchi I model. For both of them we show, that the
dispersions in the logarithm of the volume ln(v) and scalar field momentum
ln(p_phi) in the distant future and past are related via strong triangle
inequalities. This implies in particular a strict preservation of the
semiclassicality (in considered degrees of freedom) in both the cases (i) and
(ii). Derived inequalities are general: valid for all the physical states
within the considered models.Comment: RevTex4, 19 pages, 3 figure
Singular factorizations, self-adjoint extensions, and applications to quantum many-body physics
We study self-adjoint operators defined by factorizing second order
differential operators in first order ones. We discuss examples where such
factorizations introduce singular interactions into simple quantum mechanical
models like the harmonic oscillator or the free particle on the circle. The
generalization of these examples to the many-body case yields quantum models of
distinguishable and interacting particles in one dimensions which can be solved
explicitly and by simple means. Our considerations lead us to a simple method
to construct exactly solvable quantum many-body systems of Calogero-Sutherland
type.Comment: 17 pages, LaTe
Quantum healing of classical singularities in power-law spacetimes
We study a broad class of spacetimes whose metric coefficients reduce to
powers of a radius r in the limit of small r. Among these four-parameter
"power-law" metrics we identify those parameters for which the spacetimes have
classical singularities as r approaches 0. We show that a large set of such
classically singular spacetimes is nevertheless nonsingular quantum
mechanically, in that the Hamiltonian operator is essentially self-adjoint, so
that the evolution of quantum wave packets lacks the ambiguity associated with
scattering off singularities. Using these metrics, the broadest class yet
studied to compare classical with quantum singularities, we explore the
physical reasons why some that are singular classically are "healed" quantum
mechanically, while others are not. We show that most (but not all) of the
remaining quantum-mechanically singular spacetimes can be excluded if either
the weak energy condition or the dominant energy condition is invoked, and we
briefly discuss the effect of this work on the strong cosmic censorship
hypothesis.Comment: 14 pages, 1 figure; extensive revision
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