We have included nonadiabatic effects in the calculation of the dynamical evolution of a system where a quantum particle in a double well is coupled to a classical oscillator. By performing an exponential resummation of the evolution operator we have included ‘‘polarization’’ effects (similar to the self-energy corrections for an electron that moves in a polarizable medium) which lead to a renormalization of the energy of the quantum particle.
We have included nonadiabatic effects in the calculation of the dynamical evolution of a system where a quantum particle in a double well is coupled to a classical oscillator. By performing an exponential resummation of the evolution operator we have included ‘‘polarization’’ effects (similar to the self-energy corrections for an electron that moves in a polarizable medium) which lead to a renormalization of the energy of the quantum particle.
This paper presents a new approach to operator resummation corrections to adiabatic evolution operators. It is shown that an infinite order correction produces an operator that is equivalent to a propagator in the interaction representation. For a problem in which the adiabatic approximation assumes that certain degrees of freedom are held fixed, the interaction representation correction is just the interaction propagator of the coupling for these degrees of freedom. This formulation allows simple physical interpretation and simple mathematical evaluation of the full correction. No power series or cumulant methods are needed. Application to double well splitting when coupled to a bath oscillator shows the approach to be highly accurate.
The simulation of the dynamics of quantum systems is very difficult, due to the fact that, in general, it cannot be calculated exactly for interacting many-body systems. Brute force simulations of quantum dynamics are simply not feasible, and approximations need to be made. In many instances a quantum system can be approximated as a quantum-classical system, where only a subsystem of interest is treated quantum mechanically, and the rest is considered as a classical bath. When energy is free to be exchanged between the subsystem and its environment, the dynamics that occur is said to be nonadiabatic. This type of dynamics is challenging to calculate on a computer, as it can lead to large statistical errors at long times. Hence, there is a need for improved algorithms for nonadiabatic dynamics. In this thesis, a recently introduced nonadiabatic sampling scheme [A. Sergi and F. Petruccione, Phys. Rev. E 81, 032101 (2010)] is used to calculate the long-time dynamics of a model system comprising a quantum spin coupled to a bath of harmonic oscillators. Also, various technical aspects of the algorithm are investigated.
The adiabatic approximation is set up to estimate variationally the energy of a quantum particle interacting with a quantum harmonic oscillator. This example is seen as a prototype for a wide range of problems, including molecular clusters, free or in condensed matter. A heirarchy of approximations is introduced, labelled simplified adiabatic, average field, and classical field. The quasiadiabatic limit is then introduced, in which the oscillator takes account, as much as possible, of the instantaneous particle position, and an interpolation procedure between the average field adiabatic and quasiadiabatic limits is derived. Questions of implementation are discussed. In particular, an approximation is introduced, in which the quasiadiabatic generalization of the average field case is found to be energetically favored, and which reduces to a problem similar to the static-field case, for which many-electron computational methods are well developed. Now, however, oscillator zero-point effects are incorporated in a renormalized oscillator self-energy and a modified effective particle-oscillator interaction.
Our aim in this paper is to study classical dynamics in two-level molecular systems. We first derive, through the Wigner phase-space transform, a classical limit that reduces unfortunately to the adiabatic approximation. This lead us to develop a one-center quantal approximation whose variables can be interpreted in a fully classical Hamiltonian scheme. As a prominent feature, this Hamiltonian couples polarization and spatial motion. We apply it successfully to the Rosenthal-St\"uckelberg oscillations. We analyze one-dimensional diffusion similar to a molecular reaction, it appears to exhibit chaotic behavior.
An approach to nonadiabatic dynamics of atoms in molecular and condensed matter systems under general nonequilibrium conditions is proposed. In this method interaction between nuclei and electrons is considered explicitly up to the second order in atomic displacements defined with respect to the mean atomic trajectory, enabling one to consider movement of atoms beyond their simple vibrations. Both electrons and nuclei are treated fully quantum-mechanically using a combination of path integrals applied to nuclei and nonequilibrium Green's functions to electrons. Our method is partitionless: initially, the entire system is coupled and assumed to be at thermal equilibrium. Then, the exact application of the Hubbard-Stratonovich transformation in mixed real and imaginary times enables us to obtain, without doing any additional approximations, an exact expression for the reduced density matrix for nuclei and hence an effective quantum Liouville equation for them, both containing Gaussian noises. It is shown that the time evolution of the expectation values for atomic positions is described by an infinite hierarchy of stochastic differential equations for atomic positions and momenta and their various fluctuations. The actual dynamics is obtained by sampling all stochastic trajectories. It is expected that applications of the method may include photoinduced chemical reactions (e.g., dissociation), electromigration, and atomic manipulation in scanning tunneling microscopy, to name just a few.
The polarizable embedding (PE) approach is a flexible embedding model where a preselected region out of a larger system is described quantum mechanically, while the interaction with the surrounding environment is modeled through an effective operator. This effective operator represents the environment by atom-centered multipoles and polarizabilities derived from quantum mechanical calculations on (fragments of) the environment. Thereby, the polarization of the environment is explicitly accounted for. Here, we present the coupling of the PE approach with the density matrix renormalization group (DMRG). This PE-DMRG method is particularly suitable for embedded subsystems that feature a dense manifold of frontier orbitals which requires large active spaces. Recovering such static electron-correlation effects in multiconfigurational electronic structure problems, while accounting for both electrostatics and polarization of a surrounding environment, allows us to describe strongly correlated electronic structures in complex molecular environments. We investigate various embedding potentials for the well-studied first excited state of water with active spaces that correspond to a full configuration-interaction treatment. Moreover, we study the environment effect on the first excited state of a retinylidene Schiff base within a channelrhodopsin protein. For this system, we also investigate the effect of dynamical correlation included through short-range density functional theory.