5,222 research outputs found
Dynamics and Lax-Phillips scattering for generalized Lamb models
This paper treats the dynamics and scattering of a model of coupled
oscillating systems, a finite dimensional one and a wave field on the half
line. The coupling is realized producing the family of selfadjoint extensions
of the suitably restricted self-adjoint operator describing the uncoupled
dynamics. The spectral theory of the family is studied and the associated
quadratic forms constructed. The dynamics turns out to be Hamiltonian and the
Hamiltonian is described, including the case in which the finite dimensional
systems comprises nonlinear oscillators; in this case the dynamics is shown to
exist as well. In the linear case the system is equivalent, on a dense
subspace, to a wave equation on the half line with higher order boundary
conditions, described by a differential polynomial explicitely
related to the model parameters. In terms of such structure the Lax-Phillips
scattering of the system is studied. In particular we determine the incoming
and outgoing translation representations, the scattering operator, which turns
out to be unitarily equivalent to the multiplication operator given by the
rational function , and the Lax-Phillips semigroup,
which describes the evolution of the states which are neither incoming in the
past nor outgoing in the future
Boltzmann-conserving classical dynamics in quantum time-correlation functions: "Matsubara dynamics".
We show that a single change in the derivation of the linearized semiclassical-initial value representation (LSC-IVR or "classical Wigner approximation") results in a classical dynamics which conserves the quantum Boltzmann distribution. We rederive the (standard) LSC-IVR approach by writing the (exact) quantum time-correlation function in terms of the normal modes of a free ring-polymer (i.e., a discrete imaginary-time Feynman path), taking the limit that the number of polymer beads N → ∞, such that the lowest normal-mode frequencies take their "Matsubara" values. The change we propose is to truncate the quantum Liouvillian, not explicitly in powers of ħ(2) at ħ(0) (which gives back the standard LSC-IVR approximation), but in the normal-mode derivatives corresponding to the lowest Matsubara frequencies. The resulting "Matsubara" dynamics is inherently classical (since all terms O(ħ(2)) disappear from the Matsubara Liouvillian in the limit N → ∞) and conserves the quantum Boltzmann distribution because the Matsubara Hamiltonian is symmetric with respect to imaginary-time translation. Numerical tests show that the Matsubara approximation to the quantum time-correlation function converges with respect to the number of modes and gives better agreement than LSC-IVR with the exact quantum result. Matsubara dynamics is too computationally expensive to be applied to complex systems, but its further approximation may lead to practical methods.T.J.H.H., M.J.W., and S.C.A. acknowledge funding from the U.K. Engineering and Physical Sciences Research Council. A.M. acknowledges the European Lifelong Learning Programme (LLP) for an Erasmus student placement scholarship. T.J.H.H. also acknowledges a Research Fellowship from Jesus College, Cambridge and helpful discussions with Dr. Adam Harper.This is the author accepted manuscript. The final version is available from AIP via http://dx.doi.org/10.1063/1.491631
Energy landscape of a Lennard-Jones liquid: Statistics of stationary points
Molecular dynamics simulations are used to generate an ensemble of saddles of
the potential energy of a Lennard-Jones liquid. Classifying all extrema by
their potential energy u and number of unstable directions k, a well defined
relation k(u) is revealed. The degree of instability of typical stationary
points vanishes at a threshold potential energy, which lies above the energy of
the lowest glassy minima of the system. The energies of the inherent states, as
obtained by the Stillinger-Weber method, approach the threshold energy at a
temperature close to the mode-coupling transition temperature Tc.Comment: 4 RevTeX pages, 6 eps figures. Revised versio
Geometric approach to the dynamic glass transition
We numerically study the potential energy landscape of a fragile glassy
system and find that the dynamic crossover corresponding to the glass
transition is actually the effect of an underlying geometric transition caused
by a qualitative change in the topological properties of the landscape.
Furthermore, we show that the potential energy barriers connecting local glassy
minima increase with decreasing energy of the minima, and we relate this
behaviour to the fragility of the system. Finally, we analyze the real space
structure of activated processes by studying the distribution of particle
displacements for local minima connected by simple saddles
Constraining the expansion rate of the Universe using low-redshift ellipticals as cosmic chronometers
We present a new methodology to determine the expansion history of the
Universe analyzing the spectral properties of early type galaxies (ETG). We
found that for these galaxies the 4000\AA break is a spectral feature that
correlates with the relative ages of ETGs. In this paper we describe the
method, explore its robustness using theoretical synthetic stellar population
models, and apply it using a SDSS sample of 14 000 ETGs. Our motivation
to look for a new technique has been to minimise the dependence of the cosmic
chronometer method on systematic errors. In particular, as a test of our
method, we derive the value of the Hubble constant (stat)
(syst) (68% confidence), which is not only fully compatible with the
value derived from the Hubble key project, but also with a comparable error
budget. Using the SDSS, we also derive, assuming w=constant, a value for the
dark energy equation of state parameter (stat)
(syst). Given the fact that the SDSS ETG sample only reaches , this
result shows the potential of the method. In future papers we will present
results using the high-redshift universe, to yield a determination of H(z) up
to .Comment: 25 pages, 17 figures, JCAP accepte
Non-extremal Black Hole Microstates: Fuzzballs of Fire or Fuzzballs of Fuzz ?
We construct the first family of microstate geometries of near-extremal black
holes, by placing metastable supertubes inside certain scaling supersymmetric
smooth microstate geometries. These fuzzballs differ from the classical black
hole solution macroscopically at the horizon scale, and for certain probes the
fluctuations between various fuzzballs will be visible as thermal noise far
away from the horizon. We discuss whether these fuzzballs appear to infalling
observers as fuzzballs of fuzz or as fuzzballs of fire. The existence of these
solutions suggests that the singularity of non-extremal black holes is resolved
all the way to the outer horizon and this "backwards in time" singularity
resolution can shed light on the resolution of spacelike cosmological
singularities.Comment: 34 pages, 10 figure
Entropy Crisis, Ideal Glass Transition and Polymer Melting: Exact Solution on a Husimi Cactus
We introduce an extension of the lattice model of melting of semiflexible
polymers originally proposed by Flory. Along with a bending penalty, present in
the original model and involving three sites of the lattice, we introduce an
interaction energy that corresponds to the presence of a pair of parallel bonds
and a second interaction energy associated with the presence of a hairpin turn.
Both these new terms represent four-site interactions. The model is solved
exactly on a Husimi cactus, which approximates a square lattice. We study the
phase diagram of the system as a function of the energies. For a proper choice
of the interaction energies, the model exhibits a first-order melting
transition between a liquid and a crystalline phase. The continuation of the
liquid phase below this temperature gives rise to a supercooled liquid, which
turns continuously into a new low-temperature phase, called metastable liquid.
This liquid-liquid transition seems to have some features that are
characteristic of the critical transition predicted by the mode-coupling
theory.Comment: To be published in Physical Review E, 68 (2) (2003
- …