Quantum evolution represented by Brownian motion.

We propose a stochastic Schrödinger equation in which the momentum is coupled to a white Gaussian noise. In the stochastic representation, the kinetic energy representing the self-interaction of momentum is reduced to a linear term of momentum. As such, the quantum evolution operator factorizes into two contributions due to the momentum and the potential, respectively.

A unified view of hierarchy approach and formula of differentiation.

The stochastic differential equation is a powerful tool for describing the dynamics of a dissipative system in which noise characterizes the influence of the environment. For the Ornstein-Uhlenbeck noise, both the formula of differentiation and the hierarchy approach provide efficient numerical simulations, with the stochastic differential equation transformed into a set of coupled, linear ordinary differential equations. We show that while these two deterministic schemes result in different sets of equations, they can be regarded as two representations of an underlying linear-dynamics.

Quantum Phase Transition in the Spin-Boson Model: A Multilayer Multiconfiguration Time-Dependent Hartree Study.

The multilayer improved relaxation is applied to study the delocalization-localization transition in the spin-boson model at zero temperature-a well-known example of quantum phase transition. Calculations of energy eigenstates are obtained by iteratively diagonalizing the matrix of the Boltzmann operator in the top layer representation, using a Lanczos/Arnoldi method while relaxing the single particle functions of all layers using the multilayer multiconfiguration time-dependent Hartree imaginary time propagation. Two properties are used to examine the quantum phase transition: the energy splitting for the lowest pair of eigenstates and the magnetic susceptibility.

A semiclassical initial-value representation for quantum propagator and boltzmann operator.

Starting from the position-momentum integral representation, we apply the correction operator method to the derivation of a uniform semiclassical approximation for the quantum propagator and then extend it to approximate the Boltzmann operator. In this approach, the involved classical dynamics is determined by the method itself instead of given beforehand. For the approximate Boltzmann operator, the corresponding classical dynamics is governed by a complex Hamiltonian, which can be described as a pair of real Hamiltonian systems.

Stationary state distribution and efficiency analysis of the Langevin equation via real or virtual dynamics.

Langevin dynamics has become a popular tool to simulate the Boltzmann equilibrium distribution. When the repartition of the Langevin equation involves the exact realization of the Ornstein-Uhlenbeck noise, in addition to the conventional density evolution, there exists another type of discrete evolution that may not correspond to a continuous, real dynamical counterpart. This virtual dynamics case is also able to produce the desired stationary distribution.

Theoretical Modeling of Plasmon-Enhanced Raman Images of a Single Molecule with Subnanometer Resolution.

Under local plasmonic excitation, Raman images of single molecules can now surprisingly reach subnanometer resolution. However, its physical origin has not been fully understood. Here we report a quantum-mechanical description of the interaction between a molecule and a highly confined plasmonic field.

Quantum Markovian master equation for scattering from surfaces.

We propose a semi-phenomenological Markovian Master equation for describing the quantum dynamics of atom-surface scattering. It embodies the Lindblad-like structure and can describe both damping and pumping of energy between the system and the bath. It preserves positivity and correctly accounts for the vanishing of the interaction of the particle with the surface when the particle is distant from the surface.

Dynamics of a two-level system coupled to a bath of spins.

The dynamics of a two-level system coupled to a spin bath is investigated via the numerically exact multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) theory. Consistent with the previous work on linear response approximation [N. Makri, J.

Derivation of exact master equation with stochastic description: dissipative harmonic oscillator.

A systematic procedure for deriving the master equation of a dissipative system is reported in the framework of stochastic description. For the Caldeira-Leggett model of the harmonic-oscillator bath, a detailed and elementary derivation of the bath-induced stochastic field is presented. The dynamics of the system is thereby fully described by a stochastic differential equation, and the desired master equation would be acquired with statistical averaging.

Frozen Gaussian series representation of the imaginary time propagator theory and numerical tests.

Thawed Gaussian wavepackets have been used in recent years to compute approximations to the thermal density matrix. From a numerical point of view, it is cheaper to employ frozen Gaussian wavepackets. In this paper, we provide the formalism for the computation of thermal densities using frozen Gaussian wavepackets.

Effects of initial correlations on the dynamics of dissipative systems.

The time correlation functions for a Gaussian wave-packet preparation of the dissipative harmonic oscillator evolving from three initial conditions for the heat bath are calculated and compared with each other for Ohmic heat baths. The three initial distributions for the bath are the factorized, partially factorized, and unfactorized distributions. Explicit analytical formulas are derived and then used to study the effect of the three initial distributions on the subsequent dynamics.

Solving the spin-boson model of strong dissipation with flexible random-deterministic scheme.

The zero-temperature dynamics of the spin-boson model with strong dissipation has been a challenging problem for more than 20 years. To solve this and quantum dynamics of dissipative systems at large, we recently proposed a mixed random-deterministic method. This scheme has been successfully used to simulate the time evolution of the spin-boson model at zero temperature for weak to moderate dissipation.

Stochastic fluctuations and chiral symmetry breaking: exact solution of Lente model.

The stochastic description for the autocatalytic process has been proposed by Lente (J. Phys. Chem.

Toward quantitative prediction of molecular fluorescence quantum efficiency: role of duschinsky rotation.

It is a highly desirable but difficult task to predict the molecular fluorescence quantum efficiency from first principles. The molecule in the excited state can undergo spontaneous radiation, conversion of electronic energy to nuclear motion, or chemical reaction. For relatively large molecules, it is impossible to obtain the full potential energy surfaces for the ground state and the excited states to study the excited-state dynamics.

Excited state radiationless decay process with Duschinsky rotation effect: formalism and implementation.

Duschinsky rotation effect is a simple and effective way to characterize the difference between the ground state and excited state potential energy surfaces. For complex molecules, harmonic oscillator model is still the practical way to describe the dynamics of excited states. Based on the first-order perturbation theory a la Fermi golden rule, the authors have applied the path integral of Gaussian type for the correlation function to derive an analytic formalism to calculate the internal conversion rate process with Duschinsky rotation effect being taken into account.

A new time evolving Gaussian series representation of the imaginary time propagator.

Frantsuzov and Mandelshtam [J. Chem. Phys.

Nonperturbative vibrational energy relaxation effects on vibrational line shapes.

A general formulation of nonperturbative quantum dynamics of solutes in a condensed phase is proposed to calculate linear and nonlinear vibrational line shapes. In the weak solute-solvent interaction limit, the temporal absorption profile can be approximately factorized into the population relaxation profile from the off-diagonal coupling and the pure-dephasing profile from the diagonal coupling. The strength of dissipation and the anharmonicity-induced dephasing rate are derived in Appendix A.

Decoupling quantum dissipation interaction via stochastic fields.

Based on the Hubbard-Stratonovich transformation, the dissipative interaction between the system of interest and the heat bath is decoupled and the separated system and bath thus evolve in common classical random fields. This manipulation allows us to establish a novel theoretical methodology by which the reduced density matrix is formulated as an ensemble average of its random realizations in the auxiliary white noise fields. Within the stochastic description, the interaction between the system and the bath is reflected in the mutually induced mean fields.