30 research outputs found
Beyond the First Recurrence in Scar Phenomena
The scarring effect of short unstable periodic orbits up to times of the
order of the first recurrence is well understood. Much less is known, however,
about what happens past this short-time limit. By considering the evolution of
a dynamically averaged wave packet, we show that the dynamics for longer times
is controlled by only a few related short periodic orbits and their interplay.Comment: 4 pages, 4 Postscript figures, submitted to Phys. Rev. Let
Signatures of homoclinic motion in quantum chaos
Homoclinic motion plays a key role in the organization of classical chaos in
Hamiltonian systems. In this Letter, we show that it also imprints a clear
signature in the corresponding quantum spectra. By numerically studying the
fluctuations of the widths of wavefunctions localized along periodic orbits we
reveal the existence of an oscillatory behavior, that is explained solely in
terms of the primary homoclinic motion. Furthermore, our results indicate that
it survives the semiclassical limit.Comment: 5 pages, 4 figure
Exact Coupling Coefficient Distribution in the Doorway Mechanism
In many--body and other systems, the physics situation often allows one to
interpret certain, distinct states by means of a simple picture. In this
interpretation, the distinct states are not eigenstates of the full
Hamiltonian. Hence, there is an interaction which makes the distinct states act
as doorways into background states which are modeled statistically. The crucial
quantities are the overlaps between the eigenstates of the full Hamiltonian and
the doorway states, that is, the coupling coefficients occuring in the
expansion of true eigenstates in the simple model basis. Recently, the
distribution of the maximum coupling coefficients was introduced as a new,
highly sensitive statistical observable. In the particularly important regime
of weak interactions, this distribution is very well approximated by the
fidelity distribution, defined as the distribution of the overlap between the
doorway states with interaction and without interaction. Using a random matrix
model, we calculate the latter distribution exactly for regular and chaotic
background states in the cases of preserved and fully broken time--reversal
invariance. We also perform numerical simulations and find excellent agreement
with our analytical results.Comment: 22 pages, 4 figure
Scarring by homoclinic and heteroclinic orbits
In addition to the well known scarring effect of periodic orbits, we show
here that homoclinic and heteroclinic orbits, which are cornerstones in the
theory of classical chaos, also scar eigenfunctions of classically chaotic
systems when associated closed circuits in phase space are properly quantized,
thus introducing strong quantum correlations. The corresponding quantization
rules are also established. This opens the door for developing computationally
tractable methods to calculate eigenstates of chaotic systems.Comment: 5 pages, 4 figure
Superscars in the LiNC=LiCN isomerization reaction
We demonstrate the existence of superscarring in the LiNC=LiCN isomerization
reaction described by a realistic potential interaction in the range of readily
attainable experimental energies. This phenomenon arises as the effect of two
periodic orbits appearing "out of the blue"in a saddle--node bifurcation taking
place in the dynamics of the system. Potential practical consequences of this
superlocalization in the corresponding wave functions are also considered.Comment: 6 pages, 5 figures. to appear in EP
Localization properties of groups of eigenstates in chaotic systems
In this paper we study in detail the localized wave functions defined in
Phys. Rev. Lett. {\bf 76}, 1613 (1994), in connection with the scarring effect
of unstable periodic orbits in highly chaotic Hamiltonian system. These
functions appear highly localized not only along periodic orbits but also on
the associated manifolds. Moreover, they show in phase space the hyperbolic
structure in the vicinity of the orbit, something which translates in
configuration space into the structure induced by the corresponding self--focal
points. On the other hand, the quantum dynamics of these functions are also
studied. Our results indicate that the probability density first evolves along
the unstable manifold emanating from the periodic orbit, and localizes
temporarily afterwards on only a few, short related periodic orbits. We believe
that this type of studies can provide some keys to disentangle the complexity
associated to the quantum mechanics of these kind of systems, which permits the
construction of a simple explanation in terms of the dynamics of a few
classical structures.Comment: 9 pages, 8 Postscript figures (low resolution). For high resolution
versions of figs http://www.tandar.cnea.gov.ar/~wisniack/ To appear in Phys.
Rev.
Classical invariants and the quantization of chaotic systems
Long periodic orbits constitute a serious drawback in Gutzwiller's theory of
chaotic systems, and then it would be desirable that other classical
invariants, not suffering from the same problem, could be used in the
quantization of such systems. In this respect, we demonstrate how a suitable
dynamical analysis of chaotic quantum spectra unveils the fundamental role
played by classical invariant areas related to the stable and unstable
manifolds of short periodic orbits.Comment: 4 pages, 3 postscript figure
Deformations and dilations of chaotic billiards, dissipation rate, and quasi-orthogonality of the boundary wavefunctions
We consider chaotic billiards in d dimensions, and study the matrix elements
M_{nm} corresponding to general deformations of the boundary. We analyze the
dependence of |M_{nm}|^2 on \omega = (E_n-E_m)/\hbar using semiclassical
considerations. This relates to an estimate of the energy dissipation rate when
the deformation is periodic at frequency \omega. We show that for dilations and
translations of the boundary, |M_{nm}|^2 vanishes like \omega^4 as \omega -> 0,
for rotations like \omega^2, whereas for generic deformations it goes to a
constant. Such special cases lead to quasi-orthogonality of the eigenstates on
the boundary.Comment: 4 pages, 3 figure
Characterization of Landau-Zener Transitions in Systems with Complex Spectra
This paper is concerned with the study of one-body dissipation effects in
idealized models resembling a nucleus. In particular, we study the quantum
mechanics of a free particle that collides elastically with the slowly moving
walls of a Bunimovich stadium billiard. Our results are twofold. First, we
develop a method to solve in a simple way the quantum mechanical evolution of
planar billiards with moving walls. The formalism is based on the {\it scaling
method} \cite{ver} which enables the resolution of the problem in terms of
quantities defined over the boundary of the billiard. The second result is
related to the quantum aspects of dissipation in systems with complex spectra.
We conclude that in a slowly varying evolution the energy is transferred from
the boundary to the particle through LandauZener transitions.Comment: 24 pages (including 7 postcript figures), Revtex. Submitted to PR
Computationally efficient method to construct scar functions
Phys. Rev. E 85, 026214-026219 (2012) Desarrollo de un nuevo y eficiente método para la construcción de funciones de scar a lo largo de las órtbitas periódicas inestables de sistemas clásicamente caótico