Related papers: The Approach to Ergodicity in the Quantum Baker's …
We study the dynamics of a two-level quantum system interacting with an external electromagnetic field periodic and quasiperiodic in time. The quantum evolution is described exactly by the classical equations of motion of a gyromagnet in a…
We show that the ergodicity of an aperiodic automorphism of a Lebesgue space is equivalent to the continuity of a certain map on a metric Boolean algebra. A related characterization is also presented for periodic and totally ergodic…
We find a general formula for the distribution of time averaged observables for weakly non-ergodic systems. Such type of ergodicity breaking is known to describe certain systems which exhibit anomalous fluctuations, e.g. blinking quantum…
The random matrix ensembles (RME) of quantum statistical Hamiltonian operators, e.g. Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), are applied to following quantum statistical systems: nuclear…
The origin of non-classicality in physical systems and its connection to distinctly quantum features such as entanglement and coherence is a central question in quantum physics. This work analyses this question theoretically and…
We study the periodic properties of sequences of quantum channels sampled from an ergodic stochastic process satisfying a natural irreducibility condition. We relate these periodic properties to certain global spectral data defined by the…
It has been observed that an interesting class of non-Gaussian stationary processes is obtained when in the harmonics of a signal with random amplitudes and phases, frequencies can also vary randomly. In the resulting models, the…
Quantum mechanics is 'emergent' if a statistical treatment of large scale phenomena in a locally deterministic theory requires the use of quantum operators. These quantum operators may allow for symmetry transformations that are not present…
We investigate the transition from quantum to classical mechanics using a one-dimensional free particle model. In the classical analysis, we consider the initial positions and velocities of the particle drawn from Gaussian distributions.…
We develop a framework for simulating measure-preserving, ergodic dynamical systems on a quantum computer. Our approach provides a new operator-theoretic representation of classical dynamics by combining ergodic theory with quantum…
Consider $N\times N$ symmetric one-dimensional random band matrices with general distribution of the entries and band width $W \geq N^{3/4+\varepsilon}$ for any $\varepsilon>0$. In the bulk of the spectrum and in the large $N$ limit, we…
For a quantum walk on a graph, there exist many kinds of operators for the discrete-time evolution. We give a general relation between the characteristic polynomial of the evolution matrix of a quantum walk on edges and that of a kind of…
In this Chapter, we present some interesting properties of quantum walks on the line. We concentrate our attention in the emergence of invariance and provide some insights into the ultimate origin of the observed behavior. In the first part…
We look at two possible routes to classical behavior for the discrete quantum random walk on the line: decoherence in the quantum ``coin'' which drives the walk, or the use of higher-dimensional coins to dilute the effects of interference.…
The study of quantum resonances in the chaotic atom-optics kicked rotor system is of interest from two different perspectives. In quantum chaos, it marks out the regime of resonant quantum dynamics in which the atomic cloud displays…
It is shown how the programme of decoherence can be applied in the context of quantum field theory. To illustrate the role of gauge invariance, we first discuss the charge superselection rule in quantum electrodynamics in some detail. We…
We quantize graphs (networks) which consist of a finite number of bonds and vertices. We show that the spectral statistics of fully connected graphs is well reproduced by random matrix theory. We also define a classical phase space for the…
We investigate theoretically the emergence of classical statistical physics in a finite quantum system that is either totally isolated or otherwise subjected to a quantum measurement process. We show via a random matrix theory approach to…
General relation is derived which expresses the fidelity of quantum dynamics, measuring the stability of time evolution to small static variation in the hamiltonian, in terms of ergodicity of an observable generating the perturbation as…
The description of relativistic effects requires a preliminary definition of events localised in space-time while the clocks used for time definition and the fields used in synchronisation or localisation procedures are necessarily quantum…