Search results for "quantum chaos"

Reversible and irreversible dynamics of a qubit interacting with a small environment

2006

We analyze the dynamics of a system qubit interacting by means a sequence of pairwise collisions with an environment consisting of just two qubits. We show that the density operator of the qubits approaches a common time averaged equilibrium state, characterized by large fluctuations, only for a random sequence of collisions. For a regular sequence of collisions the qubitstates of the system and of the reservoir undergo instantaneous periodic oscillations and do not relax to a common state. Furthermore we show that pure bipartite entanglement is developed only when at least two qubits are initially in the same purestate while otherwise also genuine multipartite entanglement builds up.

Overview on the phenomenon of two-qubit entanglement revivals in classical environments

2017

The occurrence of revivals of quantum entanglement between separated open quantum systems has been shown not only for dissipative non-Markovian quantum environments but also for classical environments in absence of back-action. While the phenomenon is well understood in the first case, the possibility to retrieve entanglement when the composite quantum system is subject to local classical noise has generated a debate regarding its interpretation. This dynamical property of open quantum systems assumes an important role in quantum information theory from both fundamental and practical perspectives. Hybrid quantum-classical systems are in fact promising candidates to investigate the interplay…

Rotating electrons in quantum dots: Classical limit

2007

We solve the problem of a few electrons in a two-dimensional harmonic confinement using a quantum mechanical exact diagonalization technique, on the one hand, and classical mechanics, on the other. The quantitative agreement between the results of these two calculations suggests that, at low filling factors, all the low energy excitations of a quantum Hall liquid are classical vibrations of localized electrons. The Coriolis force plays a dominant role in determining the classical vibration frequencies.

Solitons ofq-deformed quantum lattices and the quantum soliton

2001

We use the classical N-soliton solution of a q-deformed lattice, the Maxwell-Bloch (MB) lattice, which we reported recently (Rybin A V, Varzugin G G, Timonen J and Bullough R K Year 2001 J. Phys. A: Math. Gen. 34 157) in order, ultimately, to fully comprehend the `quantum soliton'. This object may be the source of a new information technology (Abram I 1999 Quantum solitons Phys. World 21-4). We suggested in Rybin et al 2001 that a natural quantum mechanical matrix element of the q-deformed quantum MB lattice becomes in a suitable limit the classical 1-soliton solution of the classical q-deformed MB lattice explicitly derived by a variant of the Darboux-Backlund method. The classical q-defor…

Erratum to: Classical and Quantum Dynamics: From Classical Paths to Path Integrals

2017

Nonlinearity and Disorder in the Statistical Mechanics of Integrable Systems

1992

Attention is drawn to a theory of the statistical mechanics (SM) of the integrable models in 1+1 dimension — a theory of ‘soliton statistical mechanics’ classical and quantum [1–17]. This SM provides a generic example of integrable nonlinearity interacting with disorder. In the generic classical examples, such as the classical SM of the sine-Gordon model, phonons provide disorder in which sit coherent structures — the kink-like solitons. But these solitons are dressed by the disorder, in equilibrium, while the breather-like solitons break up to form the disordered structures which are the phonons in thermal equilibrium. On the other hand quantum solitons, dressed by both the vacuum and fini…

Intrinsic quantum chaos and spectral fluctuations within the protactinium atom

2018

Soliton Statistical Mechanics: Statistical Mechanics of the Quantum and Classical Integrable Models

1988

It is shown how the Bethe Ansatz (BA) analysis for the quantum statistical mechanics of the Nonlinear Schrodinger Model generalises to the other quantum integrable models and to the classical statistical mechanics of the classical integrable models. The bose-fermi equivalence of these models plays a fundamental role even at classical level. Two methods for calculating the quantum or classical free energies are developed: one generalises the BA method the other uses functional integral methods. The familiar classical action-angle variables of the integrable models developed for the real line R are used throughout, but the crucial importance of periodic boundary conditions is recognized and t…

Unveiling two-dimensional discrete quantum walks dynamics via dispersion relations

2011

The discrete, or coined, quantum walk (QW) [1] is a process originally introduced as the quantum counterpart of the classical random walk (RW). In both cases there is a walker and a coin: at every time step the coin is tossed and the walker moves depending on the toss output. Unlike the RW, in the QW the walker and coin are quantum in nature what allows the coherent superpositions right/left and head/tail happen. This feature endows the QW with outstanding properties, such as making the standard deviation of the position of an initially localized walker grow linearly with time t, unlike the RW in which this growth goes as t1/2. This has strong consequences in algorithmics and is one of the …

Spectral analysis and quantum chaos in two-dimensional nanostructures

2015

This thesis describes a study into the eigenvalues and eigenstates of twodimensional (2D) quantum systems. The research is summarized in four scientific publications by the author. The underlying motivation for this work is the grand question of quantum chaos: how does chaos, as known in classical mechanics, manifest in quantum mechanics? The search and analysis of these quantum fingerprints of chaos requires efficient numerical tools and methods, the development of which is given a special emphasis in this thesis. The first publication in this thesis concerns the eigenspectrum analysis of a nanoscale device. It is shown that a measured addition energy spectrum can be explained by a simple …