Yoshitaka Tanimura

A test system is assumed to interact with a heat bath consisting of harmonic oscillators or an equivalent bath with a proper frequency spectrum producing a Gaussian-Markoffian random perturbation. The effect of reaction of the test system to the bath is considered in the high temperature approximation. Elimination of the bath using the influence functional method of Feynman and Vernon yields a continuous fraction expression for the reduced density matrix of the test system. The result affords a

Half century has past since the pioneering works of Anderson and Kubo on the stochastic theory of spectral line shape were published in J. Phys. Soc. Jpn. 9 (1954) 316 and 935, respectively. In this review, we give an overview and extension of the stochastic Liouville equation focusing on its theoretical background and applications to help further the development of their works. With the aid of path integral formalism, we derive the stochastic Liouville equation for density matrices of a system.

The nonlinear optical response of liquids subjected to a series of N femtosecond laser pulses is calculated using a multimode harmonic model for nuclear motions, with nonlinear coupling to the radiation field through the coordinate dependence of the electronic polarizability. Using electronically off-resonant optical fields, this multidimensional spectroscopy is shown to provide direct information regarding the homogeneous or the inhomogeneous nature of the spectral density obtained from optical

A method to determine the resolvent of a quantum system coupled to a harmonic-oscillator bath is derived by extending the continued-fraction theory of a Gaussian-Markovian bath that has been presented by Tanimura and Kubo [J. Phys. Soc. Jpn. 58, 101 (1989)]. The results are expressed in terms of continued fractions and apply to an oscillator bath with a general spectral density, corresponding to colored noise, at various temperatures. Exact values of the resolvent can be calculated for arbitrary

The quantum Fokker-Planck equation for a Gaussian-Markovian bath is deduced by applying a method proposed by Tanimura and Kubo [J. Phys. Soc. Jpn. 58, 101 (1989)]. The results are expressed in the form of simultaneous differential equations in terms of density operators and can treat strong system-bath interactions where the correlated effects of the noise play an important role. The classical Fokker-Planck equation for a Gaussian-Markovian noise is obtained by performing the Wigner transformati

Quantum coherence and its destruction (dephasing) by coupling to a dissipative environment plays an important role in time-resolved nonlinear optical response as well as nonadiabatic transitions and tunneling processes in condensed phases. Generating functions of density-matrix elements and multitime coordinate and momentum correlation functions related to these phenomena are calculated using a pathintegral approach by performing functional integration. The dissipative environment is assumed to

We consider a quantum mechanical system represented in phase space (referred to hereafter as "Wigner space"), coupled to a harmonic oscillator bath. We derive quantum hierarchal Fokker-Planck (QHFP) equations not only in real time but also in imaginary time, which represents an inverse temperature. This is an extension of a previous work, in which we studied a spin-boson system, to a Brownian system. It is shown that the QHFP in real time obtained from a correlated thermal equilibrium state of t

We discuss the interplay of various quantum effects on barrier crossing for a one-dimensional system with dissipation. This is based on a numerical study using a hierarchy of kinetic equations introduced by Tanimura and Kubo. The numerical work uses a grid in phase space for the Wigner distribution and deals with both the classical limit and the tunneling regimes.

The quantum Fokker–Planck equation of Caldeira and Leggett is generalized to a multistate system with anharmonic potentials and a coordinate dependent nonadiabatic coupling. A rigorous procedure for calculating the dynamics of nonadiabatic transitions in condensed phases and their monitoring by femtosecond pump–probe spectroscopy is developed using this equation. Model calculations for a harmonic system with various nonadiabatic coupling strengths and damping rates are presented. Nuclear wave pa

The optical Stark effect of a two-level system coupled to a Brownian oscillator (i.e. a harmonic mode which in turn is coupled to a heat bath) is studied using equations of motion for a reduced density matrix. These equations, derived using path integral techniques, can be used to study the combined effects of strong fields and dephasing processes at finite temperature, and interpolate continuously from the coherent to the overdamped limits where they reduce to the stochastic Gaussian-Markovian

Spectral line shapes in a condensed phase contain information from various dynamic processes that modulate the transition energy, such as microscopic dynamics, inter- and intramolecular couplings, and solvent dynamics. Because nonlinear response functions are sensitive to the complex dynamics of chemical processes, multidimensional vibrational spectroscopies can separate these processes. In multidimensional vibrational spectroscopy, the nonlinear response functions of a molecular dipole or polar

Two-time correlation functions of physical operators of a system interacting with a heat bath producing a Gaussian-Markoffian noise are treated with the use of Feynman-Vernon's influence functional formalism. The Laplace transforms of correlation functions are shown to be expressed in terms of continued fractions of relevant hyperoperators. The result is valid to all orders of the system-bath interaction. In the limitation of motional narrowing, it reduces to those obtained in conventional metho

Quantum coherence and its dephasing by coupling to a dissipative environment play an important role in time-resolved nonlinear optical response as well as nonadiabatic transitions in the condensed phase. We have discussed nonlinear optical processes on a multi-state one-dimensional system with Morse potential surfaces in a dissipative environment. This was based on a numerical study using the multi-state quantum Fokker–Planck equation for a colored Gaussian–Markovian noise bath, which was expres

The relaxation processes in a quantum system nonlinearly coupled to a harmonic Gaussian-Markovian heat bath are investigated by the quantum Fokker-Planck equation in the hierarchy form. This model describes frequency fluctuations in the quantum system with an arbitrary correlation time and thus bridges the gap between the Brownian oscillator model and the stochastic model by Anderson and Kubo. The effects of the finite correlation time and the system-bath coupling strength are studied for a harm

We have obtained Nth-order response functions for a two-level system described by displaced anharmonic potential surfaces coupled to a heat bath. The anharmonicity of the potentials has been taken into account as a perturbation of harmonic potentials. The heat-bath was assumed to be an ensemble of harmonic oscillators. Coupling between the two-level system and the bath was assumed to be bilinear. The calculations were done analytically using the Liouville-space generating functional, which had b