Related papers: Open quantum systems and Random Matrix Theory
A new model of quantum random walks is introduced, on lattices as well as on finite graphs. These quantum random walks take into account the behavior of open quantum systems. They are the exact quantum analogues of classical Markov chains.…
This contribution describes a statistical model for decaying quantum systems (e.g. photo-dissociation or -ionization). It takes the interference between direct and indirect decay processes explicitely into account. The resulting expressions…
We investigate the spread complexity of a generic two-level subsystem of a larger system to analyze the influence of energy level statistics, comparing chaotic and integrable systems. Initially focusing on the nearest-neighbor level…
We use the fact that some linear Hamiltonian systems can be considered as ``finite level'' quantum systems, and the description of quantum mechanics in terms of probabilities, to associate probability distributions with this particular…
We investigate the transition to quantum chaos, induced by static imperfections, for an operating quantum computer that simulates efficiently a dynamical quantum system, the sawtooth map. For the different dynamical regimes of the map, we…
We study the problem of the basis of an open quantum system, under a quantum chaotic environment, which is preferred in view of its stationary reduced density matrix (RDM), that is, the basis in which the stationary RDM is diagonal. It is…
We review the ideas of how random matrix theory has to be properly applied to quantum physics; particularly we focus on how the spectrum has to be properly prepared and the random matrix correctly identified before the random matrix and the…
In this work, we develop a mathematical framework to model a quantum system whose Hamiltonian may depend on the state of changing environment, that evolves according to a Markovian process. When the environment changes its state, the…
Open quantum systems interact with their environment and their dynamical behaviour depends strongly both on the spectral properties of the environment and the structure of the interaction between the physical system and the environment. We…
Except for the universe, all quantum systems are open, and according to quantum state diffusion theory, many systems localize to wave packets in the neighborhood of phase space points. This is due to decoherence from the interaction with…
Chaotic Hamiltonians are known to follow Random Matrix Theory (RMT) ensembles in the apparent randomness of their spectra and wavefunction statistics. Deviations form RMT also do occur, however, due to system-specific properties, or as…
Based on the general form of the master equation for open quantum systems the tunneling is considered. Using the path integral technique a simple closed form expression for the tunneling rate through a parabolic barrier is obtained. The…
We study the dynamics of a simple model for quantum decay, where a single state is coupled to a set of discrete states, the pseudo continuum, each coupled to a real continuum of states. We find that for constant matrix elements between the…
Random-matrix theory is applied to transition-rate matrices in the Pauli master equation. We study the distribution and correlations of eigenvalues, which govern the dynamics of complex stochastic systems. Both the cases of identical and of…
The purpose of this review article is to present some of the latest developments using random techniques, and in particular, random matrix techniques in quantum information theory. Our review is a blend of a rather exhaustive review,…
The statistical properties of spectra of quantum systems within the framework of random matrix theory is widely used in many areas of physics. These properties are affected, if two or more sets of spectra are superposed, resulting from the…
We study the effect of electron tunneling on the level statistics of quantum dots. While the coupling between individual levels and the electron reservoir leads predominantly to the expected level broadening, the indirect coupling of…
A multi-branch quantum circuit is considered from the viewpoint of coherent electron or wave transport. Starting with the closed system, we give analytical conditions for the appearance of two isolated localized states out of the energy…
Analyzing the dynamics of open quantum systems has a long history in mathematics and physics. Depending on the system at hand, basic physical phenomena that one would like to explain are, for example, convergence to equilibrium, the…
Open quantum systems exhibiting initial system-environment correlations are notoriously difficult to simulate. We point out that given a sufficiently long sample of the exact short-time evolution of the open system dynamics, one may employ…