Nonrelativistic Quantum Mechanics with Fundamental Environment

Ashot S Gevorkyan

doi:10.1007/s10701-010-9446-y

Abstract

Spontaneous transitions between bound states of an atomic system, “Lamb Shift” of energy levels and many other phenomena in real nonrelativistic quantum systems are connected within the influence of the quantum vacuum fluctuations (fundamental environment (FE)) which are impossible to consider in the limits of standard quantum-mechanical approaches. The joint system “quantum system (QS) + FE” is described in the framework of the stochastic differential equation (SDE) of Langevin-Schrödinger (L-Sch) type, and is defined on the extended space R 3 ⊗ R {ξ}, where R 3 and R {ξ} are the Euclidean and functional spaces, respectively. The density matrix for single QS in FE is defined. The entropy of QS entangled with FE is defined and investigated in detail. It is proved that as a result of interaction of QS with environment there arise structures of various topologies which are a new quantum property of the system.

Highlights

It is obvious that quantum mechanics enters in the 21st century into a principally new and important phase of its development which will cardinally change the currently used technical facilities in the areas of information and telecommunication technologies, exact measurements, medicine etc
3.8 Conclusion Any quantum system resulting from the fact that all beings are immersed into a physical vacuum is an open system [1,2,3]
It has been assumed that the evolution of a quantum system is such that it may be described by the Schrödinger equation on any small time interval, while the motion as a www.intechopen.com whole is described by a stochastic differential equation (SDE) for the wave function

Summary

Introduction

It is obvious that quantum mechanics enters in the 21st century into a principally new and important phase of its development which will cardinally change the currently used technical facilities in the areas of information and telecommunication technologies, exact measurements, medicine etc. The method of stochastic density matrix (SDM) is developed, which permits to construct all thermodynamic potentials of the quantum subsystem analytically, in the form of multiple integrals from the solution of a 2D second-order partial differential equation. Taking into account (3.5) and the well-known solution of autonomous quantum harmonic oscillator (3.6) (see [28]) for stochastic complex processes which describe the 1D QHO+FE closed system, we can write the following expression:

Results

Conclusion