Reduced dynamics in quantum mechanics

John Harding

K. R. W. Jones

It is shown how a simple energy functional ansatz within Weinberg's theory of generalized quantum mechanics reduces the full functional dynamics to an effective classical dynamics governed by the equations of Hamilton.

Holger Friedrich Hofmann

Gen Kimura, Hiromichi Ohno, Milán Mosonyi

General property of the relation between the dynamics of reduced purity and correlations in quantum mechanical systems is investigated. We show that a non-zero time-derivative of the reduced purity of a system implies the existence of non-zero correlations with its environment for any unbounded Hamiltonian with finite variance. This shows the impact of local dynamical information on the correlations, as well as the role of correlations in the mechanism of purity change.

Shuang-Kai Yang, Wei-Min Zhang

Utilizing the general theory of open quantum systems to investigate the exact dynamical evolution of simple bilinear systems, we discover a mechanism of the dynamical genesis of quantum entanglement. We focus in detail on the exact quantum evolution dynamics of two photonic modes (or any two bosonic modes) coupled to each other through a linear interaction, as the simplest system of open quantum systems that we have investigated in the past two decades. Such a linear coupling alone fails to produce two-mode entanglement. We also start with an initially separable pure state of the two modes. By solving exactly the quantum equation of motion without relying on the probabilistic interpretation, we find that when the initial state of one mode is different from a coherent state (a minimum uncertainty wave packet with equal variance in the conjugate quadratures that corresponds to a well-defined classically "particle"), the causality in the time-evolution of each mode is internally violated. It also leads to the emergence of quantum entanglement between the two modes. The lack of causality is the nature of statistics. We discover that it is the internal violation of causality in the reduced (subsystem) dynamical evolution that results in the emergence of entanglement and statistic probability in quantum mechanics, even though the dynamical evolution of the whole system completely obeys the deterministic Schrödinger equation. This conclusion is valid for the quantum dynamics of more complicated composite systems. It may provide the fundamental mechanism of the dynamical genesis for both the entanglement and the statistical probability within the deterministic framework of quantum mechanics, which is the longest-standing problem that has not been fully understood since the birth of quantum mechanics.