Related papers: Dynamical typicality of quantum expectation values
Schroedinger equation on a Hilbert space ${\cal H}$, represents a linear Hamiltonian dynamical system on the space of quantum pure states, the projective Hilbert space $P {\cal H}$. Separable states of a bipartite quantum system form a…
The question of controllability is investigated for a quantum control system in which the Hamiltonian operator components carry explicit time dependence which is not under the control of an external agent. We consider the general situation…
Newtonian and Schrodinger dynamics can be formulated in a physically meaningful way within the same Hilbert space framework. This fact was recently used to discover an unexpected relation between classical and quantum motions that goes…
During a continuous measurement, quantum systems can be described by a stochastic Schr\"odinger equation which, in the appropriate limit, reproduces the von Neumann wave-function collapse. The average behavior on the ensemble of all…
An adapted representation of quantum mechanics sheds new light on the relationship between quantum states and classical states. In this approach the space of quantum states splits into a product of the state space of classical mechanics and…
We propose a generalization of Heisenberg picture quantum mechanics in which a Lagrangian and Hamiltonian dynamics is formulated directly for dynamical systems on a manifold with non--commuting coordinates, which act as operators on an…
The dynamics of finite dimension open quantum systems is studied with the help of the simplest possible form of projection operators, namely the ones which project only onto one dimensional subspaces. The simplicity of the action of the…
We investigate consequences of allowing the Hilbert space of a quantum system to have a time-dependent metric. For a given possibly nonstationary quantum system, we show that the requirement of having a unitary Schreodinger time-evolution…
Using a simple geometrical construction based upon the linear action of the Heisenberg--Weyl group we deduce a new nonlinear Schr\"{o}dinger equation that provides an exact dynamic and energetic model of any classical system whatsoever, be…
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…
The report presents an exhaustive review of the recent attempt to overcome the difficulties that standard quantum mechanics meets in accounting for the measurement (or macro-objectification) problem, an attempt based on the consideration of…
The semiclassically scaled time-dependent multi-particle Schr\"odinger equation describes, inter alia, quantum dynamics of nuclei in a molecule. It poses the combined computational challenges of high oscillations and high dimensions. This…
Time-dependent Schroedinger equation represents the basis of any quantum-theoretical approach. The question concerning its proper content in comparison to the classical physics has not been, however, fully answered until now. It will be…
We provide a detailed comparison between the dynamics of high-temperature spatiotemporal correlation functions in quantum and classical spin models. In the quantum case, our large-scale numerics are based on the concept of quantum…
We address the issue of when generalized quantum dynamics, which is a classical symplectic dynamics for noncommuting operator phase space variables based on a graded total trace Hamiltonian ${\bf H}$, reduces to Heisenberg picture complex…
Loosely speaking, the concept of quantum typicality refers to the fact that a single pure state can imitate the full statistical ensemble. This fact has given rise to a rather simple but remarkably useful numerical approach to simulate the…
In this paper we propose the idea that there is a corresponding relation between quantum states and points of the complex projective space, given that the number of dimensions of the Hilbert space is finite. We check this idea through…
Many processes in nature seem to be entirely controlled by transition rates and the corresponding statistical dynamics. Some of them are in essence quantum, like the decay of excited states, the tunneling through barriers or the decay of…
In this article we derive a useful expectation identity using the language of quantum statistical mechanics, where density matrices represent the state of knowledge about the system. This identity allows to establish relations between…
It is shown that Schroedinger's equation may be derived from three postulates. The first is a kind of statistical metamorphosis of classical mechanics, a set of two relations which are obtained from the canonical equations of particle…