Related papers: Complex trajectories in chaotic dynamical tunnelin…

We discover that quantum dynamical tunneling, occurring between phase space regions in a classically forbidden way, can break conserved quantities in pseudointegrable systems. We rigorously prove that a conserved quantity in a class of…

The quasipotential is a natural generalization of the concept of energy functions to non-equilibrium systems. In the analysis of rare events in stochastic dynamics, it plays a central role in characterizing the statistics of transition…

We derive semiclassical expressions for spectra, weighted by matrix elements of a Gaussian observable, relevant to a range of molecular and mesoscopic systems. We apply the formalism to the particular example of the resonant tunneling diode…

Trajectories in the space of the unitarily inequivalent representations of the canonical commutation relations are shown to be classical trajectories. Under convenient conditions, they may exhibit properties typical of chaotic behavior in…

Iterative trajectory optimization techniques for non-linear dynamical systems are among the most powerful and sample-efficient methods of model-based reinforcement learning and approximate optimal control. By leveraging time-variant local…

A detailed discussion of semiclassical trace formulae is presented and it is demonstrated how a regularized trace formula can be derived while dealing only with finite and convergent expressions. Furthermore, several applications of trace…

We propose a sampling-based trajectory optimization methodology for constrained problems. We extend recent works on stochastic search to deal with box control constraints,as well as nonlinear state constraints for discrete dynamical…

We present a semiclassical theory of current correlations in multiterminal chaotic dot-superconductor junctions, valid in the absence of the proximity effect in the dot. For a dominating coupling of the dot to the normal terminals and a…

We present an inverse method to construct large classes of chaotic invariant sets together with their exact statistics. The associated dynamical systems are characterized by a probability distribution and a two-form. While our emphasis is…

We develop a quantitative semiclassical theory for the resosnant tunneling through a quantum well in a tilted magnetic field. It is shown, that in the leading semiclassical approximation the tunneling current depends only on periodic orbits…

In generic Hamiltonian systems that are neither completely integrable nor fully chaotic, phase space consists of a mixture of regular and chaotic components. In classical dynamics, transitions between different invariant sets in phase space…

We address frequency-dependent quantum transport through mesoscopic conductors in the semiclassical limit. By generalizing the trajectory-based semiclassical theory of dc quantum transport to the ac case, we derive the average screened…

Tensor networks represent the state-of-the-art in computational methods across many disciplines, including the classical simulation of quantum many-body systems and quantum circuits. Several applications of current interest give rise to…

We study quantum-mechanical tunneling between symmetry-related pairs of regular phase space regions that are separated by a chaotic layer. We consider the annular billiard, and use scattering theory to relate the splitting of…

This paper examines the complex trajectories of a classical particle in the potential V(x)=-cos(x). Almost all the trajectories describe a particle that hops from one well to another in an erratic fashion. However, it is shown analytically…

Chaotic tunneling in a driven double-well system is investigated in absence as well as in the presence of dissipation. As the constitutive mechanism of chaos-assisted tunneling, we focus on the dynamics in the vicinity of three-level…

We develop a quantum-classical hybrid algorithm for function optimization that is particularly useful in the training of neural networks since it makes use of particular aspects of high-dimensional energy landscapes. Due to a recent…

Classically integrable approximants are here constructed for a family of predominantly chaotic periodic systems by means of the Baker-Hausdorff-Campbell formula. We compare the evolving wave density for the corresponding exact quantum…

We develop a quantitative semiclassical formula for the resonant tunneling current through a quantum well in a tilted magnetic field. It is shown that the current depends only on periodic orbits within the quantum well. The theory explains…

In stochastic systems, numerically sampling the relevant trajectories for the estimation of the large deviation statistics of time-extensive observables requires overcoming their exponential (in space and time) scarcity. The optimal way to…