arXiv subjects

G. Hur

Publications and source records attributed to G. Hur.

4 recordsLinked to original sources

arXiv2008

Quantum Localization in Open Chaotic Systems

We study a quasi-Floquet state of a $δ$-kicked rotor with absorbing boundaries focusing on the nature of the dynamical localization in open quantum systems. The localization lengths $ξ$ of lossy quasi-Floquet states located near the absorbing boundaries decrease as they approach the boundary while the corresponding decay rates $Γ$ are dramatically enhanced. We find the relation $ξ\sim Γ^{-1/2}$ and explain it based upon the finite time diffusion, which can also be applied to a random unitary operator model. We conjecture that this idea is valid for the system exhibiting both the diffusion in classical dynamics and the exponential localization in quantum mechanics.

quant-ph↗

arXiv2005

$2δ$-Kicked Quantum Rotors: Localization and `Critical' Statistics

The quantum dynamics of atoms subjected to pairs of closely-spaced $δ$-kicks from optical potentials are shown to be quite different from the well-known paradigm of quantum chaos, the singly-$δ$-kicked system. We find the unitary matrix has a new oscillating band structure corresponding to a cellular structure of phase-space and observe a spectral signature of a localization-delocalization transition from one cell to several. We find that the eigenstates have localization lengths which scale with a fractional power $L \sim \hbar^{-.75}$ and obtain a regime of near-linear spectral variances which approximate the `critical statistics' relation $Σ_2(L) \simeq χL \approx {1/2}(1-ν) L$, where $ν\approx 0.75$ is related to the fractal classical phase-space structure. The origin of the $ν\approx 0.75$ exponent is analyzed.

physics.atom-ph↗

arXiv2004

Chaotic quantum ratchets and filters with cold atoms in optical lattices: properties of Floquet states

Recently, cesium atoms in optical lattices subjected to cycles of unequally-spaced pulses have been found to show interesting behavior: they represent the first experimental demonstration of a Hamiltonian ratchet mechanism, and they show strong variability of the Dynamical Localization lengths as a function of initial momentum. The behavior differs qualitatively from corresponding atomic systems pulsed with equal periods, which are a textbook implementation of a well-studied quantum chaos paradigm, the quantum delta-kicked particle (delta-QKP). We investigate here the properties of the corresponding eigenstates (Floquet states) in the parameter regime of the new experiments and compare them with those of the eigenstates of the delta-QKP at similar kicking strengths. We show that, with the properties of the Floquet states, we can shed light on the form of the observed ratchet current as well as variations in the Dynamical Localization length.

physics.atom-ph↗

arXiv2004

Atoms in double-delta-kicked periodic potentials: chaos with long-range correlations

We report an experimental and theoretical study of the dynamics of cold atoms subjected to closely-spaced pairs of pulses in an optical lattice. The experiments show the interplay between fully coherent quantum dynamics and a novel momentum-diffusion regime: for all previously-studied delta-kicked systems, chaotic classical dynamics shows diffusion with short-time (2 or 3-kick) correlations; here, chaotic diffusion combines with new types of long-ranged 'global' correlations, between all kick-pairs, which control transport through trapping regions in phase-space. Analytical formulae are presented and, with quantum localization, are used to analyse the experiments.

physics.atom-ph↗