A perturbation solution of the equation of motion for the density matrix

Hiroshi Nakatsuji

Toshio Tsuzuki

Quantum statistical mechanics of spin systems is formulated by the use of the representation of atomic coherent state of spin, which is specified by a complex number. After introducing a newly defined distribution function of spin, the Bloch equation for the equilibrium density matrix, the von Neumann equation for the nonequilibrium density matrix and the Heisenberg equation of motion are converted into partial differential equations of the type of separating variables respectively. Formal solutions of them are presented. Any operator which is composed of spins can be converted uniquely into a differential operator. Thus we succeed in formulating equilibrium and nonequilibrium quantum statistical mechanics in the complex variable space, which differs from the previous one in the diagonal representation of density matrix. We further introduce the interaction representation for the perturbational expansion. The linear response formula is written down in the present representation.

Г. А. Варданян, G S Mkrtchyan

Mitchel Weissbluth

M. Nisoli

Basic concepts of quantum mechanics: Schroedinger equation; Dirac notation; the energy representation; expectation value; Hermite operators; coherent superposition of states and motion in the quantum world; perturbation Hamiltonian. Time-dependent perturbation theory: harmonic perturbation. Transition rate: Fermi’s golden rule. The density matrix; pure and mixed states. Temporal dependence of the density operator: von Neuman equation. Randomizing Hamiltonian. Longitudinal and transverse relaxation times. Density matrix and entropy.

C. J. Tymczak