86 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
Universal Response of Quantum Systems with Chaotic Dynamics
The prediction of the response of a closed system to external perturbations
is one of the central problems in quantum mechanics, and in this respect, the
local density of states (LDOS) provides an in- depth description of such a
response. The LDOS is the distribution of the overlaps squared connecting the
set of eigenfunctions with the perturbed one. Here, we show that in the case of
closed systems with classically chaotic dynamics, the LDOS is a Breit-Wigner
distribution under very general perturbations of arbitrary high intensity.
Consequently, we derive a semiclassical expression for the width of the LDOS
which is shown to be very accurate for paradigmatic systems of quantum chaos.
This Letter demonstrates the universal response of quantum systems with
classically chaotic dynamics.Comment: 4 pages, 3 figure
Scarring in open quantum systems
We study scarring phenomena in open quantum systems. We show numerical
evidence that individual resonance eigenstates of an open quantum system
present localization around unstable short periodic orbits in a similar way as
their closed counterparts. The structure of eigenfunctions around these
classical objects is not destroyed by the opening. This is exposed in a
paradigmatic system of quantum chaos, the cat map.Comment: 4 pages, 4 figure
Comment on "modified quantum-speed-limit bounds for open quantum dynamics in quantum channels"
In a recent paper [Phys. Rev. A 95, 052118 (2017)2469-992610.1103/PhysRevA.95.052118], the authors claim that our criticism, in Phys. Rev. A 94, 052125 (2016)2469-992610.1103/PhysRevA.94.052125, to some quantum speed limit bounds for open quantum dynamics that appeared recently in literature are invalid. According to the authors, the problem with our analysis would be generated by an artifact of the finite-precision numerical calculations. We analytically show here that it is not possible to have any inconsistency associated with the numerical precision of calculations. Therefore, our criticism of the quantum speed limit bounds continues to be valid.Fil: Mirkin, Nicolás. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de FĂsica; ArgentinaFil: Toscano, Fabricio. Centro Brasileiro de Pesquisas FĂsicas; BrasilFil: Wisniacki, Diego Ariel. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de FĂsica; Argentin
Quantum non-Markovian behavior at the chaos border
In this work we study the non-Markovian behaviour of a qubit coupled to an
environment in which the corresponding classical dynamics change from
integrable to chaotic. We show that in the transition region, where the
dynamics has both regular islands and chaotic areas, the average non-Markovian
behaviour is enhanced to values even larger than in the regular regime. This
effect can be related to the non-Markovian behaviour as a function of the the
initial state of the environment, where maxima are attained at the regions
dividing separate areas in classical phase space, particularly at the borders
between chaotic and regular regions. Moreover, we show that the fluctuations of
the fidelity of the environment -- which determine the non-Markovianity measure
-- give a precise image of the classical phase portrait.Comment: 23 pages, 9 figures (JPA style). Closest to published versio
- …