240 research outputs found
Universal wave functions structure in mixed systems
When a regular classical system is perturbed, non-linear resonances appear as
prescribed by the KAM and Poincar\`{e}-Birkhoff theorems. Manifestations of
this classical phenomena to the morphologies of quantum wave functions are
studied in this letter. We reveal a systematic formation of an universal
structure of localized wave functions in systems with mixed classical dynamics.
Unperturbed states that live around invariant tori are mixed when they collide
in an avoided crossing if their quantum numbers differ in a multiple to the
order of the classical resonance. At the avoided crossing eigenstates are
localized in the island chain or in the vicinity of the unstable periodic orbit
corresponding to the resonance. The difference of the quantum numbers
determines the excitation of the localized states which is reveled using the
zeros of the Husimi distribution.Comment: 6 pages, 4 figure
Loschmidt Echo and the Local Density of States
Loschmidt echo (LE) is a measure of reversibility and sensitivity to
perturbations of quantum evolutions. For weak perturbations its decay rate is
given by the width of the local density of states (LDOS). When the perturbation
is strong enough, it has been shown in chaotic systems that its decay is
dictated by the classical Lyapunov exponent. However, several recent studies
have shown an unexpected non-uniform decay rate as a function of the
perturbation strength instead of that Lyapunov decay. Here we study the
systematic behavior of this regime in perturbed cat maps. We show that some
perturbations produce coherent oscillations in the width of LDOS that imprint
clear signals of the perturbation in LE decay. We also show that if the
perturbation acts in a small region of phase space (local perturbation) the
effect is magnified and the decay is given by the width of the LDOS.Comment: 8 pages, 8 figure
Localized Structures Embedded in the Eigenfunctions of Chaotic Hamiltonian Systems
We study quantum localization phenomena in chaotic systems with a parameter.
The parametric motion of energy levels proceeds without crossing any other and
the defined avoided crossings quantify the interaction between states. We
propose the elimination of avoided crossings as the natural mechanism to
uncover localized structures. We describe an efficient method for the
elimination of avoided crossings in chaotic billiards and apply it to the
stadium billiard. We find many scars of short periodic orbits revealing the
skeleton on which quantum mechanics is built. Moreover, we have observed strong
interaction between similar localized structures.Comment: RevTeX, 3 pages, 6 figures, submitted to Phys. Rev. Let
Sensitivity to perturbations and quantum phase transitions
The local density of states or its Fourier transform, usually called fidelity
amplitude, are important measures of quantum irreversibility due to imperfect
evolution. In this Rapid Communication we study both quantities in a
paradigmatic many body system, the Dicke Hamiltonian, where a single-mode
bosonic field interacts with an ensemble of N two-level atoms. This model
exhibits a quantum phase transition in the thermodynamic limit, while for
finite instances the system undergoes a transition from quasi-integrability to
quantum chaotic. We show that the width of the local density of states clearly
points out the imprints of the transition from integrability to chaos but no
trace remains of the quantum phase transition. The connection with the decay of
the fidelity amplitude is also established.Comment: 5 pages, 4 figures, accepted for publication PRE rapid communicatio
Influence of phase space localization on the energy diffusion in a quantum chaotic billiard
The quantum dynamics of a chaotic billiard with moving boundary is considered
in this work. We found a shape parameter Hamiltonian expansion which enables us
to obtain the spectrum of the deformed billiard for deformations so large as
the characteristic wave length. Then, for a specified time dependent shape
variation, the quantum dynamics of a particle inside the billiard is integrated
directly. In particular, the dispersion of the energy is studied in the
Bunimovich stadium billiard with oscillating boundary. The results showed that
the distribution of energy spreads diffusively for the first oscillations of
the boundary ({ =2 D t). We studied the diffusion contant
as a function of the boundary velocity and found differences with theoretical
predictions based on random matrix theory. By extracting highly phase space
localized structures from the spectrum, previous differences were reduced
significantly. This fact provides the first numerical evidence of the influence
of phase space localization on the quantum diffusion of a chaotic system.Comment: 5 pages, 5 figure
Optimal control of many-body quantum dynamics: chaos and complexity
Achieving full control of the time-evolution of a many-body quantum system is
currently a major goal in physics. In this work we investigate the different
ways in which the controllability of a quantum system can be influenced by its
complexity, or even its chaotic properties. By using optimal control theory, we
are able to derive the control fields necessary to drive various physical
processes in a spin chain. Then, we study the spectral properties of such
fields and how they relate to different aspects of the system complexity. We
find that the spectral bandwidth of the fields is, quite generally, independent
of the system dimension. Conversely, the spectral complexity of such fields
does increase with the number of particles. Nevertheless, we find that the
regular o chaotic nature of the system does not affect signficantly its
controllability.Comment: 9 pages, 5 figure
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