Related papers: "Weak Quantum Chaos" and its resistor network mode…
Weakly pumped systems with approximate conservation laws can be efficiently described by a generalized Gibbs ensemble if the steady state of the system is unique. However, such a description can fail if there are multiple steady state…
The present work address the problem of energy shaping for stochastic port-Hamiltonian system. Energy shaping is a powerful technique that allows to systematically find feedback law to shape the Hamiltonian of a controlled system so that,…
We show that weakly reversible mass-action systems can have a continuum of positive steady states, coming from the zeroes of a multivariate polynomial. Moreover, the same is true of systems whose underlying reaction network is reversible…
Bayesian inference is applied to the level fluctuations of two coupled microwave billiards in order to extract the coupling strength. The coupled resonators provide a model of a chaotic quantum system containing two coupled symmetry classes…
We investigate the random matrix configurations for two or three interacting electrons in one-dimensional disordered systems. In a suitable non-interacting localized electron basis we obtain a sparse random matrix with very long tails which…
Random matrix spectral correlations is a defining feature of quantum chaos. Here, we study such correlations in a minimal model of chaotic many-body quantum dynamics where interactions are confined to the system's boundary, dubbed…
We study the ensemble-averaged conductance as a function of applied magnetic field for ballistic electron transport across few-channel microstructures constructed in the shape of classically chaotic billiards. We analyse the results of…
The spectral properties of interacting strongly chaotic systems are investigated for growing interaction strength. A very sensitive transition from Poisson statistics to that of random matrix theory is found. We introduce a new random…
The hierarchical cold dark matter (CDM) model for structure formation is a well defined and testable model. Direct detection is the best technique for confirming the model yet predictions for the energy and density distribution of particles…
The barrier billiard is the simplest example of pseudo-integrable models with interesting and intricate classical and quantum properties. Using the Wiener-Hopf method it is demonstrated that quantum mechanics of a rectangular billiard with…
The transitory and stationary behavior of a quantum chaotic ratchet consisting of a biharmonic potential under the effect of different drivings in contact with a thermal environment is studied. For weak forcing and finite $\hbar$, we…
We investigate the coherence properties of thermal atoms confined in optical dipole traps where the underlying classical dynamics is chaotic. A perturbative expression derived for the coherence of the echo scheme of [Andersen et. al., Phys.…
We present experimental results on the eigenfrequency statistics of a superconducting, chaotic microwave billiard containing a rotatable obstacle. Deviations of the spectral fluctuations from predictions based on Gaussian orthogonal…
One of the major breakthroughs in science of the last (20th) century was building a bridge between the worlds of stochastic (random) systems and deterministic (dynamical) systems. It was started by the celebrated 1958 paper by…
This is an expository paper on Lyapunov stability of equilibria of autonomous Hamiltonian systems. Our aim is to clarify the concept of weak instability, namely instability without non-constant motions which have the equilibrium as limit…
We consider a one-dimensional lattice model with the nearest-neighbor interaction $V_1$ and the next-nearest neighbor interaction $V_2$ with filling factor 1/2 at zero temperature. The particles are assumed to be spinless fermions or…
A resistor-network picture of transitions is appropriate for the study of energy absorption by weakly chaotic or weakly interacting driven systems. Such "sparse" systems reach a novel non-equilibrium steady state (NESS) once coupled to a…
We present numerical and experimental results for the development of islands of stability in atom-optics billiards with soft walls. As the walls are soften, stable regions appear near singular periodic trajectories in converging (focusing)…
A quantum integrable system slightly perturbed away from integrability is typically expected to thermalize on timescales of order $\tau\sim \lambda^{-2}$, where $\lambda$ is the perturbation strength. We here study classes of perturbations…
We consider the radially vibrating spherical quantum billiard as a representative example of vibrating quantum billiards. We derive necessary conditions for quantum chaos in $d$-term superposition states. These conditions are symmetry…