Hermann Grabert

Quantum Brownian motion: The functional integral approach

Abstract The quantum mechanical dynamics of a particle coupled to a heat bath is treated by functional integral methods and a generalization of the Feynman-Vernon influence functional is derived. The extended theory describes the time evolution of nonfactorizing initial states and of equilibrium correlation functions. The theory is illuminated through exactly solvable models.

Theory of activated rate processes for arbitrary frequency dependent friction: Solution of the turnover problem

An analytical theory is formulated for the thermal (classical mechanical) rate of escape from a metastable state coupled to a dissipative thermal environment. The working expressions are given solely in terms of the quantities entering the generalized Langevin equation for the particle dynamics. The theory covers the whole range of damping strength and is applicable to an arbitrary memory friction. This solves what is commonly known as the Kramers turnover problem. The basic idea underlying the approach is the observation that the escape dynamics is governed by the unstable normal mode coordinate—and not the particle system coordinate. An application to the case of a particle moving in a piecewise harmonic potential with an exponentially decaying memory‐friction is presented. The comparison with the numerical simulation data of Straub, Borkovec, and Berne [J. Chem. Phys. 84, 1788 (1986)] exhibits good agreement between theory and simulation.

Quantum theory of the damped harmonic oscillator

A phenomenological stochastic modelling of the process of thermal and quantal fluctuations of a damped harmonic oscillator is presented. The divergence of the momentum dispersion associated with the Markovian limit is removed by a Drude regularization. The variances of position and momentum are evaluated in closed form at arbitrary temperature and for arbitrary damping. Properties of real and imaginary time correlation functions are discussed, and a spectral decomposition of the equilibrium density matrix is given.

Crossover from Fermi Liquid to Wigner Molecule Behavior in Quantum Dots

The crossover from weak to strong correlations in parabolic quantum dots at zero magnetic field is studied by numerically exact path-integral Monte Carlo simulations for up to eight electrons. By the use of a multilevel blocking algorithm, the simulations are carried out free of the fermion sign problem. We obtain a universal crossover governed only by the density parameter

Exact c-number representation of non-Markovian quantum dissipation.

{r}_{s}

Exact time evolution and master equations for the damped harmonic oscillator

. For

Strong Friction Limit in Quantum Mechanics: The Quantum Smoluchowski Equation

{r}_{s}g{r}_{c}

Friedel Oscillations for Interacting Fermions in One Dimension

, the data are consistent with a Wigner molecule description, while, for

Note on time evolution of non-Markov processes

{r}_{s}l{r}_{c}

IS THE DIRECT OBSERVATION OF ELECTRONIC COHERENCE IN ELECTRON TRANSFER REACTIONS POSSIBLE

, Fermi liquid behavior is recovered. The crossover value