Related papers: Dynamical Tunneling in Many-Dimensional Chaotic Sy…
This article summarizes the recent work on the influence of dynamical tunneling on the control of quantum systems. Specifically, two examples are discussed. In the first, it is shown that the bichromatic control of tunneling in a driven…
We uncover a dynamical entanglement transition in a monitored quantum system that is heralded by a local order parameter. Classically, chaotic systems can be stochastically controlled onto unstable periodic orbits and exhibit controlled and…
We theoretically explore a dynamical generalization of the Aubry-Andr\'e model in two dimensions formed by superimposing two square-lattice potentials. Motivated by the rich physics emerging at different twist angles between the two…
This work establishes a firm relationship between classical nonlinear resonances and the phenomenon of dynamical tunneling. It is shown that the classical phase space with its hierarchy of resonance islands completely characterizes…
We discuss the statistics of tunnelling rates in the presence of chaotic classical dynamics. This applies to resonance widths in chaotic metastable wells and to tunnelling splittings in chaotic symmetric double wells. The theory is based on…
For generic Hamiltonian systems we derive predictions for dynamical tunneling from regular to chaotic phase-space regions. In contrast to previous approaches, we account for the resonance-assisted enhancement of regular-to-chaotic tunneling…
We compute the dispersion laws of chaotic periodic systems using the semiclassical periodic orbit theory to approximate the trace of the powers of the evolution operator. Aside from the usual real trajectories, we also include complex…
We study the effect of many-body quantum interference on the dynamics of coupled periodically kicked systems whose classical dynamics is chaotic and shows an unbounded energy increase. We specifically focus on a $N$ coupled kicked rotors…
We present an extension of the chaos-assisted tunneling mechanism to spatially periodic lattice systems. We demonstrate that driving such lattice systems in an intermediate regime of modulation maps them onto tight-binding Hamiltonians with…
We study the interplay between coherent transport by tunneling and diffusive transport through classically chaotic phase-space regions, as it is reflected in the Floquet spectrum of the periodically driven quartic double well. The tunnel…
We derive a trace formula for the splitting-weighted density of states suitable for chaotic potentials with isolated symmetric wells. This formula is based on complex orbits which tunnel through classically forbidden barriers. The theory is…
In the presence of a complex classical dynamics associated with a mixed phase space, a quantum wave function can tunnel between two stable islands through the chaotic sea, an effect that has no classical counterpart. This phenomenon,…
High-dimensional dynamical systems projected onto a reduced-order model cease to be deterministic and are best described by probability distributions in state space. Their equations of motion map onto an evolution operator with a…
We show that quantum wavepackets exhibit a sharp macroscopic peak as they spread in the vicinity of the critical point of the Anderson transition. The peak gives a direct access to the mutifractal properties of the wavefunctions and…
A basic result about the dynamics of spinless quantum systems is that the Maryland model exhibits dynamical localization in any dimension. Here we implement mathematical spectral theory and numerical experiments to show that this result…
We use an effective Hamiltonian to characterize particle dynamics and find escape rates in a periodically kicked Hamiltonian. We study a model of particles in storage rings that is described by a chaotic symplectic map. Ignoring the…
Recent theoretical investigations have revealed unconventional transport mechanisms within high Brilliouin zones of two-dimensional superlattices. Electrons can navigate along channels we call superwires, gently guided without brute force…
Chaotic instanton approach is used to describe dynamical tunneling in kicked double well system. Effective Hamiltonian for the kicked system is obtained using matrix expansion formula for operator exponent and exploited to construct an…
Contrary to a driven classical system that exhibits chaos phenomena and diffusive energy growth, a driven quantum system can exhibit dynamical localization that features energy saturation. However, the evolution of the dynamically localized…
Dynamical tunnelling between symmetry-related stable modes is studied in the periodically driven pendulum. We present strong evidence that the tunnelling process is governed by nonlinear resonances that manifest within the regular…