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Entropy

Delocalization and Sensitivity of Quantum Wavepacket in Coherently Perturbed Kicked Anderson Model

Hiroaki S. Yamada

Published Mar 21, 2004• 0 citations
Publisher

Abstract

We consider quantum diffusion of the initially localized wavepacket in one-dimensional kicked disordered system with classical coherent perturbation. The wavepacket localizes in the unperturbed kicked Anderson model. However, the wavepacket get delocalized even by coupling with monochromatic perturbation. We call the state "dynamically delocalized state". It is numerically shown that the delocalized wavepacket spread obeying diffusion law, and the perturbation strength dependence of the diffusion rate is given. The sensitivity of the delocalized state is also shown by the time-reversal experiment after random change in phase of the wavepacket. Moreover, it is found that the diffusion strongly depend on the initial phase of the perturbation. We discuss a relation between the "classicalization" of the quantum wave packet and the time-dependence of the initial phase dependence. The complex structure of the initial phase dependence is related to the entropy production in the quantum system.

DOI
10.3390/e6010133

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We explore the onset of delocalization as a function of coupling strength for time-dependent wave packets started on specific phase-space structures in the quantum standard map. Coherent-state wave packets, initially placed on fixed points of the classical map, are propagated for a long time and the delocalization is quantitatively measured. In most cases the delocalization occurs rather abruptly as a function of the kicking strength. The relative quantum stability of various phase-space structures is determined.
We numerically investigate quantum dynamics in a one-dimensional double-well system emphasizing influence of a parametrically polychromatic perturbation on the dynamics. It is found that time dependence of transition probability for an initially localized wave packet between the wells shows two types of motion, coherent and incoherent motion, depending on the perturbation parameters. As the strength and/or the number of frequency components of the perturbation increase, coherent motion changes into incoherent one. The former is related to coherent tunneling of the wave packet due to coherence; the latter is related to a delocalized state caused by decoherence. In coherent motion, by virtue of coherence of the dynamics, the expectation value and the standard deviation of a dynamical variable such as the energy of the system show oscillatory time dependence around the initial values. On the contrary in incoherent motion, because of the decoherence, the time dependence fluctuates irregularly around a certain value after a rapid increase due to the resonance. We find that negativity of the Wigner function also show similar time dependence in each type of motion. We compare the classification of the quantum dynamics based on regularity of the time dependence with the one of corresponding classical dynamics based on the Lyapunov exponent. The classifications of the quantum and classical dynamics overlap well in the parameter space. Furthermore, we confirm decoherence of quantum dynamics in a kicked double-well system.
We study Anderson localization in a one-dimensional disordered system with long-range correlated hopping decaying as 1/ra1/r^{a}1/ra with complex hopping amplitudes that break time-reversal symmetry in a tunable fashion by varying their argument. We find analytically a corelation-induced algebraic localization that is robust to a finite strength of the time-reversal-symmetry-breaking parameter, beyond which all states delocalize. This establishes a localization--delocalization transition driven by the interplay between long-ranged correlated hopping and time-reversal symmetry breaking. In addition to obtaining the static localization phase diagram, we also investigate the dynamical phase diagram through the lens of wavepacket spreading. We find that the growth in time of the mean-squared displacement of a wavepacket, which is subdiffusive for the time-reversal symmetric case, becomes diffusive for any finite value of the time-reversal-symmetry-breaking parameter.
This work is a simple example of the quantum dynamics of a particle in a disordered system in one dimension.In particular, we illustrate numerically the phenomenon of Anderson localisation of a wave packet using a basic model constructed with small random rectangular potential barriers.Also, we study the dynamics of a quantum particle in a disordered potential formed by an harmonic oscillator perturbed by random rectangular barriers.To show the effects of disorder on the dynamics of the system, we compare the time evolution of the wave function of the unperturbed harmonic oscillator with the wave function of the disordered system.We do this by taking the scalar product between the unperturbed and perturbed wave functions at each timestep for different values of the perturbation parameters affecting the disordered wave packet.
We consider the evolution of an initially localized wave packet after a sudden change in the Hamiltonian, i.e.\ a quench. When both bound and scattering eigenstates exist in the post-quench Hamiltonian, one might expect partial delocalization of the wave packet to ensue. Here we show that if the quench consists of a sudden switching-off of short-range inter-particle interactions, then Tan's universal relations guarantee delocalization through the high-momentum tail of the momentum distribution. Furthermore, we consider the influence of the range of the interaction and show how a finite range alters the coupling to highly excited states. We illustrate our results using numerical simulations of externally trapped particles in one dimension. If the external potential is both disordered and correlated, then the interaction quench leads to transport via delocalized states, showing that localization in disordered systems is sensitive to non-adiabatic changes in the interactions between particles.