Related papers: Asymptotic Evolution of Random Unitary Operations
Instabilities of equilibrium quantum mechanics are common and well-understood. They are manifested for example in phase transitions, where a quantum system becomes so sensitive to perturbations that a symmetry can be spontaneously broken.…
Random operators constitute fundamental building blocks of models of complex systems yet are far from fully understood. Here, we explain an asymmetry emerging upon repeating identical isotropic (uniformly random) operations. Specifically,…
The understanding of symmetry operations has brought enormous advancements in physics, ranging from elementary particle to condensed matter systems. In quantum mechanics, symmetry operations are described by either unitary or antiunitary…
We consider a bipartite quantum object, composed of a quantum system and a quantum actuator which is periodically reset. We show that the reduced dynamics of the system approaches unitarity as the reset frequency of the actuator is…
We study the entanglement dynamics of discrete time quantum walks acting on bounded finite sized graphs. We demonstrate that, depending on system parameters, the dynamics may be monotonic, oscillatory but highly regular, or quasi-periodic.…
We investigate the evolution of a single qubit subject to a continuous unitary dynamics and an additional interrupting influence which occurs periodically. One may imagine a dynamically evolving closed quantum system which becomes open at…
We study the dynamics of a quantum system in which an intermediate property $m$ is measured in between initial and final measurements of two different non-commuting properties $a$ and $b$. Since this intermediate measurement must involve an…
The evolution of a quantum system interacting with an environment can be described as a unitary process acting on both the system and the environment. In this framework, the system's evolution can be predicted by tracing out the…
Among the discrete evolution equations describing a quantum system $\rH_S$ undergoing repeated quantum interactions with a chain of exterior systems, we study and characterize those which are directed by classical random variables in…
We compare two approaches to non-Markovian quantum evolution: one based on the concept of divisible maps and the other one based on distinguishability of quantum states. The former concept is fully characterized in terms of local generator…
A new approach to quantum walks is presented. Considering a quantum system undergoing some unitary discrete-time evolution in a directed graph G, we think of the vertices of G as sites that are occupied by the quantum system, whose internal…
Systems evolving under the influence of competing two-body and three-body interactions, are of particular interest in exploring the stability of equilibrium states of strongly interacting many-body system. We present a solvable model based…
We consider $d$-dimensional quantum systems which for positive times evolve with a time-independent Hamiltonian in a nonequilibrium state that we keep generic in order to account for arbitrary evolution at negative times. We show how the…
A finite-dimensional pseudo-unitary framework is set up for describing the dynamics of free elementary particles in a purely relativistic quantum mechanical way. States of any individual particles or antiparticles are defined as suitably…
We study the asymptotic position distribution of general quantum walks on a lattice, including walks with a random coin, which is chosen from step to step by a general Markov chain. In the unitary (i.e., non-random) case, we allow any…
The dynamics of a quantum system, undergoing unitary evolution and continuous monitoring, can be described in term of quantum trajectories. Although the averaged state fully characterises expectation values, the entire ensamble of…
The coin-position entanglement generated by the evolution operator of a discrete--time quantum walk converges, in the long time limit, to a well defined value which depends on the initial state. We also discuss the asymptotic bi-partite…
We study the asymptotic behavior of the trajectory of a nonautonomous evolution equation governed by a quasi-nonexpansive operator in Hilbert spaces. We prove the weak convergence of the trajectory to a fixed point of the operator by…
We develop a rigorous formalism for the description of the evolution of observables of quantum systems of particles in the mean-field scaling limit. The corresponding asymptotics of a solution of the initial-value problem of the dual…
The random matrix ensembles are applied to the quantum statistical two-dimensional systems of electrons. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The…