A New Expansion of the Heisenberg Equation of Motion with Projection Operator

Abstract

We derive a new expansion of the Heisenberg equation of motion based on the projection operator method proposed by Shibata, Hashitsume and Shingū. In their projection operator method, a certain restriction is imposed on the initial state. As a result, one cannot prepare arbitrary initial states, for example a coherent state, to calculate the time development of quantum systems. In this paper, we generalize the projection operator method by relaxing this restriction. We explain our method in the case of a Hamiltonian both with and without explicit time dependence. Furthermore, we apply it to an exactly solvable model called the damped harmonic oscillator model and confirm the validity of our method.

arXiv comment16 pages, revtex, no figures, To appear in Prog.Theor.Phys

Cited by in corpus (10)

• Mori-Zwanzig projection operator formalism for systems with time-dependent Hamiltonians
• Projection operators in statistical mechanics: a pedagogical approach
• Transport Coefficients of Non-Newtonian Fluid and Causal Dissipative Hydrodynamics
• Bulk Viscosity and Relaxation Time of Causal Dissipative Relativistic Fluid Dynamics
• Microscopic formula for transport coefficients of causal hydrodynamics
• Microscopic Derivation of Causal Diffusion Equation using Projection Operator Method
• Enhancement of Critical Slowing Down in Chiral Phase Transition -- Langevin Dynamics Approach --
• Mori-Zwanzig formalism for general relativity: a new approach to the averaging problem
• Shear viscosity, Bulk viscosity and Relaxation Times of Causal Dissipative Relativistic Fluid-Dynamics at Finite Temperature and Chemical Potential
• Phenomenological approach to the critical dynamics of the QCD phase transition revisited