4,585 research outputs found
A discrete Schrodinger spectral problem and associated evolution equations
A recently proposed discrete version of the Schrodinger spectral problem is
considered. The whole hierarchy of differential-difference nonlinear evolution
equations associated to this spectral problem is derived. It is shown that a
discrete version of the KdV, sine-Gordon and Liouville equations are included
and that the so called `inverse' class in the hierarchy is local. The whole
class of related Darboux and Backlund transformations is also exhibited.Comment: 14 pages, LaTeX2
Berry Phase Quantum Thermometer
We show how Berry phase can be used to construct an ultra-high precision
quantum thermometer. An important advantage of our scheme is that there is no
need for the thermometer to acquire thermal equilibrium with the sample. This
reduces measurement times and avoids precision limitations.Comment: Updated to published version. I. Fuentes previously published as I.
Fuentes-Guridi and I. Fuentes-Schulle
A discrete time relativistic Toda lattice
Four integrable symplectic maps approximating two Hamiltonian flows from the
relativistic Toda hierarchy are introduced. They are demostrated to belong to
the same hierarchy and to examplify the general scheme for symplectic maps on
groups equiped with quadratic Poisson brackets. The initial value problem for
the difference equations is solved in terms of a factorization problem in a
group. Interpolating Hamiltonian flows are found for all the maps.Comment: 32 pages, LaTe
Cellular Automata and Ultra-Discrete Painlev\'e Equations
Starting from integrable cellular automata we present a novel form of
Painlev\'e equations. These equations are discrete in both the independent
variable and the dependent one. We show that they capture the essence of the
behavior of the Painlev\'e equations organizing themselves into a coalescence
cascade and possessing special solutions. A necessary condition for the
integrability of cellular automata is also presented.Comment: 8 pages, plainTeX, 2 figure
Phenomenology of a light scalar: the dilaton
We make use of the language of non-linear realizations to analyze
electro-weak symmetry breaking scenarios in which a light dilaton emerges from
the breaking of a nearly conformal strong dynamics, and compare the
phenomenology of the dilaton to that of the well motivated light composite
Higgs scenario. We argue that -- in addition to departures in the
decay/production rates into massless gauge bosons mediated by the conformal
anomaly -- characterizing features of the light dilaton scenario (as well as
other scenarios admitting a light CP-even scalar not directly related to the
breaking of the electro-weak symmetry) are off-shell events at high invariant
mass involving two longitudinally polarized vector bosons and a dilaton, and
tree-level flavor violating processes. Accommodating both electro-weak
precision measurements and flavor constraints appears especially challenging in
the ambiguous scenario in which the Higgs and the dilaton fields strongly mix.
We show that warped higgsless models of electro-weak symmetry breaking are
explicit and tractable realizations of this limiting case.
The relation between the naive radion profile often adopted in the study of
holographic realizations of the light dilaton scenario and the actual dynamical
dilaton field is clarified in the Appendix.Comment: 21 page
The lattice Schwarzian KdV equation and its symmetries
In this paper we present a set of results on the symmetries of the lattice
Schwarzian Korteweg-de Vries (lSKdV) equation. We construct the Lie point
symmetries and, using its associated spectral problem, an infinite sequence of
generalized symmetries and master symmetries. We finally show that we can use
master symmetries of the lSKdV equation to construct non-autonomous
non-integrable generalized symmetries.Comment: 11 pages, no figures. Submitted to Jour. Phys. A, Special Issue SIDE
VI
Geon black holes and quantum field theory
Black hole spacetimes that are topological geons in the sense of Sorkin can
be constructed by taking a quotient of a stationary black hole that has a
bifurcate Killing horizon. We discuss the geometric properties of these geon
black holes and the Hawking-Unruh effect on them. We in particular show how
correlations in the Hawking-Unruh effect reveal to an exterior observer
features of the geometry that are classically confined to the regions behind
the horizons.Comment: 11 pages. Talk given at the First Mediterranean Conference on
Classical and Quantum Gravity, Kolymbari (Crete, Greece), September 2009.
Dedicated to Rafael Sorkin. v2: typesetting bug fixe
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