Related papers: Classical versus Quantum Structure of the Scatteri…
The dynamics of states representing arbitrary N-level quantum systems, including dissipative systems, can be modelled exactly by the dynamics of classical coupled oscillators. There is a direct one-to-one correspondence between the quantum…
Recent developments in holographic gravity suggest that spacetime structure may be deeply related to quantum mechanics. In this work, from a different perspective, we demonstrate that wave-particle duality can be interpreted as the…
Given an arbitrary \(V \times V\) Hermitian matrix, considered as a finite discrete quantum Hamiltonian, we use methods from graph and ergodic theories to construct a \textit{quantum Poincar\'e map} at energy \(E\) and a corresponding…
We report on experiments that were performed with microwave waveguide systems and demonstrate that in the frequency range of a single transversal mode they may serve as a model for closed and open quantum graphs. These consist of bonds that…
We consider the statistics of time delay in a chaotic cavity having $M$ open channels, in the absence of time-reversal invariance. In the random matrix theory approach, we compute the average value of polynomial functions of the time delay…
The conductance of a waveguide containing finite number of periodically placed identical point-like impurities is investigated. It has been calculated as a function of both the impurity strength and the number of impurities using the…
We sketch the semiclassical core of a proof of the so-called Bohigas-Giannoni-Schmit conjecture: A dynamical system with full classical chaos has a quantum energy spectrum with universal fluctuations on the scale of the mean level spacing.…
We study classical and quantum dynamics of a particle in a circular billiard with a straight cut. This system can be integrable, nonintegrable with soft chaos, or nonintegrable with hard chaos, as we vary the size of the cut. We use a…
In this article we demonstrate the applications of classical and quantum machine learning in quantum transport and spintronics. With the help of a two-terminal device with magnetic impurity we show how machine learning algorithms can…
Classical transport equations with probabilistic initial conditions can be viewed as quantum systems. In a discrete version they are probabilistic automata. The time-local probabilistic information is encoded in a classical wave function.…
We extract the information of a quantum motion and decode it into a certain orbit via a single measurable quantity. Such that a quantum chaotic system can be reconstructed as a chaotic attractor. Two configurations for reconstructing this…
Motivated by a recent prediction to engineer the dispersion relation of a waveguide constructed from atomic components [arXiv:2104.08121], we explore the possibility to create directional transport in an open, collective quantum system. The…
We argue semiclassically, on the basis of Gutzwiller's periodic-orbit theory, that full classical chaos is paralleled by quantum energy spectra with universal spectral statistics, in agreement with random-matrix theory. For dynamics from…
The standard quantum mechanical harmonic oscillator has an exact, dual relationship with a completely classical system: a classical particle running along a circle. Duality here means that there is a one-to-one relation between all…
We describe both quantum particles and classical particles in terms of a classical statistical ensemble, characterized by a probability distribution in phase space. By use of a wave function in phase space both can be treated in the same…
We investigate electron transport through clean open quantum dots (quantum billiards). We present a semiclassical theory that allows to accurately reproduce quantum transport calculations. Quantitative agreement is reached for individual…
Quantum chaos is a major subject of interest in condensed matter theory, and has recently motivated new questions in the study of classical chaos. In particular, recent studies have uncovered interesting physics in the relationship between…
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…
We study the response of the quasi-energy levels in the context of quantized chaotic systems through the level velocity variance and relate them to classical diffusion coefficients using detailed semiclassical analysis. The systematic…
In classical stochastic theory, the joint probability distributions of a stochastic process obey by definition the Kolmogorov consistency conditions. Interpreting such a process as a sequence of physical measurements with probabilistic…