21,630 research outputs found
Resonances, Unstable Systems and Irreversibility: Matter Meets Mind
The fundamental time-reversal invariance of dynamical systems can be broken
in various ways. One way is based on the presence of resonances and their
interactions giving rise to unstable dynamical systems, leading to well-defined
time arrows. Associated with these time arrows are semigroups bearing time
orientations. Usually, when time symmetry is broken, two time-oriented
semigroups result, one directed toward the future and one directed toward the
past. If time-reversed states and evolutions are excluded due to resonances,
then the status of these states and their associated backwards-in-time oriented
semigroups is open to question. One possible role for these latter states and
semigroups is as an abstract representation of mental systems as opposed to
material systems. The beginnings of this interpretation will be sketched.Comment: 9 pages. Presented at the CFIF Workshop on TimeAsymmetric Quantum
Theory: The Theory of Resonances, 23-26 July 2003, Instituto Superior
Tecnico, Lisbon, Portugal; and at the Quantum Structures Association Meeting,
7-22 July 2004, University of Denver. Accepted for publication in the
Internation Journal of Theoretical Physic
Competing interactions of spin and lattice in the Kondo lattice model
The magnetic properties of a system of coexisting localized spins and
conduction electrons are investigated within an extended version of the one
dimensional Kondo lattice model in which effects stemming from the
electron-lattice and on-site Coulomb interactions are explicitly included.
After bosonizing the conduction electrons, is it observed that intrinsic
inhomogeneities with the statistical scaling properties of a Griffiths phase
appear, and determine the spin structure of the localized impurities. The
appearance of the inhomogeneities is enhanced by appropriate phonons and acts
destructively on the spin ordering. The inhomogeneities appear on well defined
length scales, can be compared to the formation of intrinsic mesoscopic
metastable patterns which are found in two-fluid systems.Comment: 9 pages, to appear in Jour. Superconductivit
Linearized solutions of the Einstein equations within a Bondi-Sachs framework, and implications for boundary conditions in numerical simulations
We linearize the Einstein equations when the metric is Bondi-Sachs, when the
background is Schwarzschild or Minkowski, and when there is a matter source in
the form of a thin shell whose density varies with time and angular position.
By performing an eigenfunction decomposition, we reduce the problem to a system
of linear ordinary differential equations which we are able to solve. The
solutions are relevant to the characteristic formulation of numerical
relativity: (a) as exact solutions against which computations of gravitational
radiation can be compared; and (b) in formulating boundary conditions on the
Schwarzschild horizon.Comment: Revised following referee comment
A discrete nonlinear model with substrate feedback
We consider a prototypical model in which a nonlinear field (continuum or
discrete) evolves on a flexible substrate which feeds back to the evolution of
the main field. We identify the underlying physics and potential applications
of such a model and examine its simplest one-dimensional Hamiltonian form,
which turns out to be a modified Frenkel-Kontorova model coupled to an extra
linear equation. We find static kink solutions and study their stability, and
then examine moving kinks (the continuum limit of the model is studied too). We
observe how the substrate effectively renormalizes properties of the kinks. In
particular, a nontrivial finding is that branches of stable and unstable kink
solutions may be extended beyond a critical point at which an effective
intersite coupling vanishes; passing this critical point does not destabilize
the kink. Kink-antikink collisions are also studied, demonstrating alternation
between merger and transmission cases.Comment: a revtex text file and 6 ps files with figures. Physical Review E, in
pres
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