Related papers: Localization of resonance eigenfunctions on quantu…

We study families of open chaotic maps that classically share the same asymptotic properties -- forward and backwards trapped sets, repeller dimensions, escape rate -- but differ in their short time behavior. When these maps are quantized…

We study the resonance eigenstates of a particular quantization of the open baker map. For any admissible value of Planck's constant, the corresponding quantum map is a subunitary matrix, and the nonzero component of its spectrum is…

We study the quantum mechanics of a generalized version of the baker's map. We show that the Ruelle resonances (which govern the approach to ergodicity of classical distributions on phase space) also appear in the quantum correlation…

We study the spectrum of quantized open maps, as a model for the resonance spectrum of quantum scattering systems. We are particularly interested in open maps admitting a fractal repeller. Using the ``open baker's map'' as an example, we…

There has been a very recent surge in the interest on the localization properties of resonances associated to partially open (scattering) systems, which are of great relevance when studying resonant cavities such as those used in…

A new type of localization - localization over the quantum resonance cells - in an intrinsically degenerate system is explored by using the quasienergy eigenstates.

We apply a recently developed semiclassical theory of short periodic orbits to the continuously open quantum tribaker map. In this paradigmatic system the trajectories are partially bounced back according to continuous reflectivity…

We develop the technique to prove localization through the analysis of eigenfunctions in presence of both exponential frequency resonances and exponential phase barriers (anti-resonances) and use it to prove localization for the Maryland…

We study relevant features of the spectrum of the quantum open baker map. The opening consists of a cut along the momentum $p$ direction of the 2-torus phase space, modelling an open chaotic cavity. We study briefly the classical forward…

Robustly manipulating waves on subwavelength scales can be achieved by, firstly, designing a structure with a subwavelength band gap and, secondly, introducing a defect so that eigenfrequencies fall within the band gap. Such frequencies are…

Insertion of disorder in thermal interacting quantum systems decreases the amount of level repulsion and can turn them into many body localized phases. In this paper we use the many body picture to perturbatively study the effect of level…

Modern experiments in resonators are moving to ever more extreme quantum regimes, posing major challenges to established theoretical approaches, such as so-called few-mode models. While these models have driven major insights for…

The multiple scattering model of a quantum particle in a random Lorentz gas consisting of fixed point scatterers is considered in arbitrary dimension. An efficient method is developed to numerically compute the map of the density of…

The classical Bernoulli and baker maps are two simple models of deterministic chaos. On the level of ensembles, it has been shown that the time evolution operator for these maps admits generalized spectral representations in terms of…

We quantise and study several versions of finite multibaker maps. Classically these are exactly solvable K-systems with known exponential decay to global equilibrium. This is an attempt to construct simple models of relaxation in quantum…

The quantum baker's map is the quantization of a simple classically chaotic system, and has many generic features that have been studied over the last few years. While there exists a semiclassical theory of this map, a more rigorous study…

Resonances of the (Frobenius-Perron) evolution operator P for phase-space densities have recently attracted considerable attention, in the context of interrelations between classical and quantum dynamics. We determine these resonances as…

We extend the semiclassical theory of short periodic orbits [Phys. Rev. E {\bf 80}, 035202(R) (2009)] to partially open quantum maps. They correspond to classical maps where the trajectories are partially bounced back due to a finite…

The quantum mechanical equivalent of parametric resonance is studied. A simple model of a periodically kicked harmonic oscillator is introduced which can be solved exactly. Classically stable and unstable regions in parameter space are…

In the state-vector space for relativistic quantum fields a new set of basis vectors are introduced, which are taken to be eigenstates of the field operators themselves. The corresponding eigenvalues are then interpreted as representing…