Related papers: Analyzing symmetry breaking within a chaotic quant…
Complex quantum systems consisting of large numbers of strongly coupled states exhibit characteristic level repulsion, leading to a non-Poisson spacing distribution which can be described by Random Matrix Theory. Scattering resonances…
Assuming the validity of random matrices for describing the statistics of a closed chaotic quantum system, we study analytically some statistical properties of the S-matrix characterizing scattering in its open counterpart. In the first…
In this paper we develop a general framework for constructing and analysing coupled Markov chain Monte Carlo samplers, allowing for both (possibly degenerate) diffusion and piecewise deterministic Markov processes. For many performance…
We solve the problem of resonance statistics in systems with broken time-reversal invariance by deriving the joint probability density of all resonances in the framework of a random matrix approach and calculating explicitly all n-point…
Parameter space of a driven damped oscillator in a double well potential presents either a chaotic trajectory with sign oscillating amplitude or a non-chaotic trajectory with a fixed sign amplitude. A network of such delay coupled damped…
The photon statistics and bunching of a semiconductor laser with external optical feedback are investigated experimentally and theoretically. In a chaotic regime, the photon number distribution is measured and undergoes a transition from…
Chaotic systems, that have a small Lyapunov exponent, do not obey the common random matrix theory predictions within a wide "weak quantum chaos" regime. This leads to a novel prediction for the rate of heating for cold atoms in optical…
Failure probabilities for grid components are often estimated using parametric models which can capitalize on operational grid data. This work formulates a Bayesian hierarchical framework designed to integrate data and domain expertise to…
Incoherence in the controlled Hamiltonian is an important limitation on the precision of coherent control in quantum information processing. Incoherence can typically be modelled as a distribution of unitary processes arising from slowly…
Chimera states in coupled oscillator systems present both spatially coherent and incoherent domains. The number and size of these domains depend on many factors like the system parameters and initial conditions. Systematic investigations of…
Quantum mechanics requires that identical particles are treated as indistinguishable. This requirement leads to correlations in the fluctuating properties of a system. Theoretical predictions are made for an experiment on a multi-lead…
Employing both Bayesian statistics and the theory of nonlinear dynamics, we present a practically efficient method to extract a phase description of weakly coupled limit-cycle oscillators directly from time series observed in a rhythmic…
We consider quantum systems with a Hamiltonian containing a weak perturbation i.e. $\boldsymbol{H=H_0} + \boldsymbol{\lambda} \cdot \boldsymbol{\tilde{H}}$, $\boldsymbol{\lambda}= \{\lambda_1, \lambda_2,...\}$, $\boldsymbol{\tilde{H}}$ $=…
In this paper, we employ variational arguments to establish a connection between ensemble methods for Neural Networks and Bayesian inference. We consider an ensemble-based scheme where each model/particle corresponds to a perturbation of…
We study the reliability of phase oscillator networks in response to fluctuating inputs. Reliability means that an input elicits essentially identical responses upon repeated presentations, regardless of the network's initial condition. In…
We propose a Bayesian inference framework to estimate uncertainties in inverse scattering problems. Given the observed data, the forward model and their uncertainties, we find the posterior distribution over a finite parameter field…
The parametric bootstrap can be used for the efficient computation of Bayes posterior distributions. Importance sampling formulas take on an easy form relating to the deviance in exponential families and are particularly simple starting…
We study the signatures of a classical mixed phase space for open quantum systems. We find the scaling of the break time up to which quantum mechanics mimics the classical staying probability and derive the distribution of resonance widths.…
Analytical expressions for the width and conductance peak distributions of irregularly shaped quantum dots in the Coulomb blockade regime are presented in the limits of conserved and broken time-reversal symmetry. The results are obtained…
Before autonomous systems can be deployed in safety-critical applications, we must be able to understand and verify the safety of these systems. For cases where the risk or cost of real-world testing is prohibitive, we propose a…