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A small quantum system is studied which is a superposition of states localized in different positions in a static gravitational field. The time evolution of the correlation between different positions is investigated, and it is seen that…

A generalized formal framework for decoherence, that can be used both in open and closed quantum systems, is sketched. In this context, the relationship between the decoherence of a closed system and the decoherence of its subsystems is…

Quantum mechanics describes the unitary time evolution of isolated systems. In reality, every quantum system interacts with its environment, leading to an irreversible loss of the phase relation. Path integral based methods provide a…

It is argued that the dynamics of an isolated system, due to the concrete procedure by which it is separated from the environment, has a non-Hamiltonian contribution. By a unified quantum field theoretical treatment of typical subdynamics,…

We investigate the meaning of gravity-induced decoherence in quantum theory, known as `intrinsic' or `fundamental' decoherence in the literature. We explore a range of issues relevant to this problem, including the meaning of modified…

The use of a relational time in quantum mechanics is a framework in which one promotes to quantum operators all variables in a system, and later chooses one of the variables to operate like a ``clock''. Conditional probabilities are…

A simplified Heisenberg spin model is studied in order to examine the idea of decoherence in closed quantum systems. For this purpose, we present a quantifiable definition to quantum coherence $\Xi$, and discuss in some detail a general…

In the framework of the Lindblad theory for open quantum systems, we determine the degree of quantum decoherence of a harmonic oscillator interacting with a thermal bath. It is found that the system manifests a quantum decoherence which is…

We study decoherence in a simple quantum mechanical model using two approaches. Firstly, we follow the conventional approach to decoherence where one is interested in solving the reduced density matrix from the perturbative master equation.…

With a choice of boundary conditions for solutions of the Schr\"odinger equation, state vectors and density operators even for closed systems evolve asymmetrically in time. For open systems, standard quantum mechanics consequently predicts…

A question of the time the system spends in the specified state, when the final state of the system is given, is raised. The model of weak measurements is used to obtain the expression for the time. The conditions for determination of such…

Experiments with trapped atomic gases have opened novel possibilities for studying the evolution of nonequilibrium finite quantum systems, which revived the necessity of reconsidering and developing the theory of such processes. This review…

This paper studies the energy decoherence of an interacting quantum system. It first reviews the experiments that motivated the postulates of quantum mechanics. It then discusses a decoherence that occurs dynamically in a closed system.…

A pedagogical introduction is given to the quantum mechanics of closed systems, most generally the universe as a whole. Quantum mechanics aims at predicting the probabilities of alternative coarse-grained time histories of a closed system.…

Unitarity is a pillar of quantum theory. Nevertheless, it is also a source of several of its conceptual problems. We note that in a world where measurements are relational, as is the case in gravitation, quantum mechanics exhibits a…

A recently introduced discrete formalism allows to solve the problem of time in quantum gravity in a relational manner. Quantum mechanics formulated with a relational time is not exactly unitary and implies a fundamental mechanism for…

We study the intrinsic, disorder-induced decoherence of an isolated quantum system under its own dynamics. Specifically, we investigate the characteristic time scale (i.e., the decoherence time) associated with an interacting many-body…

This work proposes a series of quantum experiments that can, at least in principle, allow for examining microscopic mechanisms associated with decoherence. These experiments can be interpreted as a quantum-mechanical version of…

We show that the physical mechanism for the equilibration of closed quantum systems is dephasing, and identify the energy scales that determine the equilibration timescale of a given observable. For realistic physical systems (e.g those…

Mathematical models of quantum computers such as a multidimensional quantum Turing machine and quantum circuits are described and its relations with lattice spin models are discussed. One of the main open problems one has to solve if one…