Related papers: Quantum Repeated Interactions and the Chaos Game
We analyze the necessary physical conditions to model an open quantum system as a quantum game. By applying the formalism of Quantum Operations on a particular system, we use Kraus operators as quantum strategies. The physical…
An interaction system has a finite set of agents that interact pairwise, depending on the current state of the system. Symmetric decomposition of the matrix of interaction coefficients yields the representation of states by self-adjoint…
In this review the problem of statistical description of isolated quantum systems of interacting particles is discussed. Main attention is paid to a recently developed approach which is based on chaotic properties of compound states in the…
This paper gives an overview of recent results concerning the long time dynamics of repeated interaction quantum systems in a deterministic and random framework. We describe the non equilibrium steady states (NESS) such systems display and…
The intrinsic multivaluedness of interaction process, revealed in Part I of this series of papers, is interpreted as the origin of the true dynamical (in particular, quantum) chaos. The latter is causally deduced as unceasing series of…
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…
We propose the study of quantum games from the point of view of quantum information theory and statistical mechanics. Every game can be described by a density operator, the von Neumann entropy and the quantum replicator dynamics. There…
As a model of decohering environment, we show that quantum chaotic system behave equivalently as many-body system. An approximate formula for the time evolution of the reduced density matrix of a system interacting with a quantum chaotic…
The dynamics of a single microscopic or mesoscopic non quantum system interacting with a macroscopic environment is generally stochastic. In the same way, the reduced density operator of a single quantum system interacting with a…
We investigate minimal two-body Hamiltonians with random interactions that generate spectra resembling those of Gaussian random matrices, a phenomenon we term quadratic quantum chaos. Unlike integrable two-body fermionic systems, the…
We present a systematic investigation of the quantum games, constructed using a novel repeated game protocol, when played repeatedly ad infinitum. We focus on establishing that such repeated games -- by virtue of inherent quantum-mechanical…
There is a newly emerging understanding that in the chaotic domain of isolated finite interacting many particle systems smoothed densities define the statistical description of these systems and these densities follow from embedded…
The development of Quantum Chaos in finite interacting Fermi systems is considered. At sufficiently high excitation energy the direct two-particle interaction may mix into an eigen-state the exponentially large number of simple…
We address the dynamics of a bosonic system coupled to either a bosonic or a magnetic environment, and derive a set of sufficient conditions that allow one to describe the dynamics in terms of the effective interaction with a classical…
We derive stochastic master equations for a quantum system interacting with a Bose field prepared in a superposition of continuous-mode coherent states. To determine a conditional evolution of the quantum system we use a collision model…
We consider the dynamics of an arbitrary quantum system coupled to a large arbitrary and fully quantum mechanical environment through a random interaction. We establish analytically and check numerically the typicality of this dynamics, in…
An operatorial model of a system made by $N$ agents interacting each other with mechanisms that can be thought of as cooperative or competitive is presented. We associate to each agent an annihilation, creation and number fermionic…
The transition from arbitrary to chaotic fluctuation properties in quantum systems is studied in a random matrix model. It is assumed that the Hamiltonian can be written as the sum of an arbitrary and a chaos producing part. The Gaussian…
We study the dynamics of a "kicked" quantum system undergoing repeated measurements of momentum. A diffusive behavior is obtained for a large class of Hamiltonians, even when the dynamics of the classical counterpart is not chaotic. These…
We present novel approaches to the dynamics of an open quantum system coupled linearly to a non-Markovian fermionic or bosonic environment. In the first approach, we obtain a hierarchy of stochastic evolution equations of the diffusion…