124 research outputs found
Quenched and Negative Hall Effect in Periodic Media: Application to Antidot Superlattices
We find the counterintuitive result that electrons move in OPPOSITE direction
to the free electron E x B - drift when subject to a two-dimensional periodic
potential. We show that this phenomenon arises from chaotic channeling
trajectories and by a subtle mechanism leads to a NEGATIVE value of the Hall
resistivity for small magnetic fields. The effect is present also in
experimentally recorded Hall curves in antidot arrays on semiconductor
heterojunctions but so far has remained unexplained.Comment: 10 pages, 4 figs on request, RevTeX3.0, Europhysics Letters, in pres
Generation of scalar-tensor gravity effects in equilibrium state boson stars
Boson stars in zero-, one-, and two-node equilibrium states are modeled
numerically within the framework of Scalar-Tensor Gravity. The complex scalar
field is taken to be both massive and self-interacting. Configurations are
formed in the case of a linear gravitational scalar coupling (the Brans-Dicke
case) and a quadratic coupling which has been used previously in a cosmological
context. The coupling parameters and asymptotic value for the gravitational
scalar field are chosen so that the known observational constraints on
Scalar-Tensor Gravity are satisfied. It is found that the constraints are so
restrictive that the field equations of General Relativity and Scalar-Tensor
gravity yield virtually identical solutions. We then use catastrophe theory to
determine the dynamically stable configurations. It is found that the maximum
mass allowed for a stable state in Scalar-Tensor gravity in the present
cosmological era is essentially unchanged from that of General Relativity. We
also construct boson star configurations appropriate to earlier cosmological
eras and find that the maximum mass for stable states is smaller than that
predicted by General Relativity, and the more so for earlier eras. However, our
results also show that if the cosmological era is early enough then only states
with positive binding energy can be constructed.Comment: 20 pages, RevTeX, 11 figures, to appear in Class. Quantum Grav.,
comments added, refs update
Geometry of the energy landscape of the self-gravitating ring
We study the global geometry of the energy landscape of a simple model of a
self-gravitating system, the self-gravitating ring (SGR). This is done by
endowing the configuration space with a metric such that the dynamical
trajectories are identified with geodesics. The average curvature and curvature
fluctuations of the energy landscape are computed by means of Monte Carlo
simulations and, when possible, of a mean-field method, showing that these
global geometric quantities provide a clear geometric characterization of the
collapse phase transition occurring in the SGR as the transition from a flat
landscape at high energies to a landscape with mainly positive but fluctuating
curvature in the collapsed phase. Moreover, curvature fluctuations show a
maximum in correspondence with the energy of a possible further transition,
occurring at lower energies than the collapse one, whose existence had been
previously conjectured on the basis of a local analysis of the energy landscape
and whose effect on the usual thermodynamic quantities, if any, is extremely
weak. We also estimate the largest Lyapunov exponent of the SGR using
the geometric observables. The geometric estimate always gives the correct
order of magnitude of and is also quantitatively correct at small
energy densities and, in the limit , in the whole homogeneous
phase.Comment: 20 pages, 12 figure
Mixmaster universe in Horava-Lifshitz gravity
We consider spatially homogeneous (but generally non-isotropic) cosmologies
in the recently proposed Horava-Lifshitz gravity and compare them to those of
general relativity using Hamiltonian methods. In all cases, the problem is
described by an effective point particle moving in a potential well with
exponentially steep walls. Focusing on the closed-space cosmological model
(Bianchi type IX), the mixmaster dynamics is now completely dominated by the
quadratic Cotton tensor potential term for very small volume of the universe.
Unlike general relativity, where the evolution towards the initial singularity
always exhibits chaotic behavior with alternating Kasner epochs, the
anisotropic universe in Horava-Lifshitz gravity (with parameter lambda > 1/3)
is described by a particle moving in a frozen potential well with fixed (but
arbitrary) energy E. Alternating Kasner epochs still provide a good description
of the early universe for very large E, but the evolution appears to be
non-ergodic. For very small E there are harmonic oscillations around the fully
isotropic model. The question of chaos remains open for intermediate energy
levels.Comment: 1+35 pages, 4 figure
Resonances in a spring-pendulum: algorithms for equivariant singularity theory
A spring-pendulum in resonance is a time-independent Hamiltonian model system for formal reduction to one degree of freedom, where some symmetry (reversibility) is maintained. The reduction is handled by equivariant singularity theory with a distinguished parameter, yielding an integrable approximation of the Poincaré map. This makes a concise description of certain bifurcations possible. The computation of reparametrizations from normal form to the actual system is performed by Gröbner basis techniques.
Adiabatically coupled systems and fractional monodromy
We present a 1-parameter family of systems with fractional monodromy and
adiabatic separation of motion. We relate the presence of monodromy to a
redistribution of states both in the quantum and semi-quantum spectrum. We show
how the fractional monodromy arises from the non diagonal action of the
dynamical symmetry of the system and manifests itself as a generic property of
an important subclass of adiabatically coupled systems
Third-order perturbative solutions in the Lagrangian perturbation theory with pressure
Lagrangian perturbation theory for cosmological fluid describes structure
formation in the quasi-nonlinear stage well. We present a third-order
perturbative equation for Lagrangian perturbation with pressure in both the
longitudinal and transverse modes. Then we derive the perturbative solution for
simplest case.Comment: 11 pages, 1 figure; accepted for publication in Physical Review
Morse index and causal continuity. A criterion for topology change in quantum gravity
Studies in 1+1 dimensions suggest that causally discontinuous topology
changing spacetimes are suppressed in quantum gravity. Borde and Sorkin have
conjectured that causal discontinuities are associated precisely with index 1
or n-1 Morse points in topology changing spacetimes built from Morse functions.
We establish a weaker form of this conjecture. Namely, if a Morse function f on
a compact cobordism has critical points of index 1 or n-1, then all the Morse
geometries associated with f are causally discontinuous, while if f has no
critical points of index 1 or n-1, then there exist associated Morse geometries
which are causally continuous.Comment: Latex, 20 pages, 3 figure
Manifestation of the Arnol'd Diffusion in Quantum Systems
We study an analog of the classical Arnol'd diffusion in a quantum system of
two coupled non-linear oscillators one of which is governed by an external
periodic force with two frequencies. In the classical model this very weak
diffusion happens in a narrow stochastic layer along the coupling resonance,
and leads to an increase of total energy of the system. We show that the
quantum dynamics of wave packets mimics, up to some extent, global properties
of the classical Arnol'd diffusion. This specific diffusion represents a new
type of quantum dynamics, and may be observed, for example, in 2D semiconductor
structures (quantum billiards) perturbed by time-periodic external fields.Comment: RevTex, 4 pages including 7 ps-figures, corrected forma
The Phoenix Project: Master Constraint Programme for Loop Quantum Gravity
The Hamiltonian constraint remains the major unsolved problem in Loop Quantum
Gravity (LQG). Seven years ago a mathematically consistent candidate
Hamiltonian constraint has been proposed but there are still several unsettled
questions which concern the algebra of commutators among smeared Hamiltonian
constraints which must be faced in order to make progress. In this paper we
propose a solution to this set of problems based on the so-called {\bf Master
Constraint} which combines the smeared Hamiltonian constraints for all smearing
functions into a single constraint. If certain mathematical conditions, which
still have to be proved, hold, then not only the problems with the commutator
algebra could disappear, also chances are good that one can control the
solution space and the (quantum) Dirac observables of LQG. Even a decision on
whether the theory has the correct classical limit and a connection with the
path integral (or spin foam) formulation could be in reach. While these are
exciting possibilities, we should warn the reader from the outset that, since
the proposal is, to the best of our knowledge, completely new and has been
barely tested in solvable models, there might be caveats which we are presently
unaware of and render the whole {\bf Master Constraint Programme} obsolete.
Thus, this paper should really be viewed as a proposal only, rather than a
presentation of hard results, which however we intend to supply in future
submissions.Comment: LATEX, uses AMSTE
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