skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: New mixed quantum/semiclassical propagation method

Abstract

The authors developed a new method for calculating the quantum evolution of multidimensional systems, for cases in which the system can be assumed to consist of a quantum subsystem and a bath subsystem of heavier atoms. The method combines two ideas: starting from a simple frozen Gaussian description of the bath subsystem, then calculate quantum corrections to the propagation of the quantum subsystem. This follows from recent work by one of them, showing how one can calculate corrections to approximate evolution schemes, even when the Hamiltonian that corresponds to these approximate schemes is unknown. Then, they take the limit in which the width of the frozen Gaussians approaches zero, which makes the corrections to the evolution of the quantum subsystem depend only on classical bath coordinates. The test calculations they present use low-dimensional systems, in which comparison to exact quantum dynamics is feasible.

Authors:
; ;  [1];  [2]
  1. Department of Biophysics, Albert Einstein College of Medicine, New York 10461 (United States)
  2. (United States)
Publication Date:
OSTI Identifier:
20991266
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Chemical Physics; Journal Volume: 126; Journal Issue: 18; Other Information: DOI: 10.1063/1.2731779; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; GAUSSIAN PROCESSES; HAMILTONIANS; QUANTUM MECHANICS; SCHROEDINGER EQUATION; SEMICLASSICAL APPROXIMATION

Citation Formats

Antoniou, Dimitri, Gelman, David, Schwartz, Steven D., and Department of Biophysics, Albert Einstein College of Medicine, Bronx, New York 10461 and Department of Biochemistry, Albert Einstein College of Medicine, Bronx, New York 10461. New mixed quantum/semiclassical propagation method. United States: N. p., 2007. Web. doi:10.1063/1.2731779.
Antoniou, Dimitri, Gelman, David, Schwartz, Steven D., & Department of Biophysics, Albert Einstein College of Medicine, Bronx, New York 10461 and Department of Biochemistry, Albert Einstein College of Medicine, Bronx, New York 10461. New mixed quantum/semiclassical propagation method. United States. doi:10.1063/1.2731779.
Antoniou, Dimitri, Gelman, David, Schwartz, Steven D., and Department of Biophysics, Albert Einstein College of Medicine, Bronx, New York 10461 and Department of Biochemistry, Albert Einstein College of Medicine, Bronx, New York 10461. Mon . "New mixed quantum/semiclassical propagation method". United States. doi:10.1063/1.2731779.
@article{osti_20991266,
title = {New mixed quantum/semiclassical propagation method},
author = {Antoniou, Dimitri and Gelman, David and Schwartz, Steven D. and Department of Biophysics, Albert Einstein College of Medicine, Bronx, New York 10461 and Department of Biochemistry, Albert Einstein College of Medicine, Bronx, New York 10461},
abstractNote = {The authors developed a new method for calculating the quantum evolution of multidimensional systems, for cases in which the system can be assumed to consist of a quantum subsystem and a bath subsystem of heavier atoms. The method combines two ideas: starting from a simple frozen Gaussian description of the bath subsystem, then calculate quantum corrections to the propagation of the quantum subsystem. This follows from recent work by one of them, showing how one can calculate corrections to approximate evolution schemes, even when the Hamiltonian that corresponds to these approximate schemes is unknown. Then, they take the limit in which the width of the frozen Gaussians approaches zero, which makes the corrections to the evolution of the quantum subsystem depend only on classical bath coordinates. The test calculations they present use low-dimensional systems, in which comparison to exact quantum dynamics is feasible.},
doi = {10.1063/1.2731779},
journal = {Journal of Chemical Physics},
number = 18,
volume = 126,
place = {United States},
year = {Mon May 14 00:00:00 EDT 2007},
month = {Mon May 14 00:00:00 EDT 2007}
}
  • We introduce a new semiclassical (SC) framework, the Mixed Quantum-Classical Initial Value Representation (MQC-IVR), that can be tuned to reproduce existing quantum-limit and classical-limit SC approximations to quantum real-time correlation functions. Applying a modified Filinov transformation to a quantum-limit SC formulation leads to the association of a Filinov parameter with each degree of freedom in the system; varying this parameter from zero to infinity controls the extent of quantization of the corresponding mode. The resulting MQC-IVR expression provides a consistent dynamic framework for mixed quantum-classical simulations and we demonstrate its numerical accuracy in the calculation of real-time correlation functions formore » a model 1D system and a model 2D system over the full range of quantum- to classical-limit behaviors.« less
  • A variational mixed quantum-semiclassical theory for the internal nuclear dynamics of a small molecule and the induced small-amplitude coherent motion of a low-temperature host medium is developed, tested, and used to simulate the temporal evolution of nonstationary states of the internal molecular and surrounding medium degrees of freedom. In this theory, termed the Fixed Vibrational Basis/Gaussian Bath (FVB/GB) method, the system is treated fully quantum mechanically while Gaussian wave packets are used for the bath degrees of freedom. An approximate time-dependent wave function of the entire model is obtained instead of just a reduced system density matrix, so the theorymore » enables the analysis of the entangled system and bath dynamics that ensues following initial displacement of the internal-molecular (system) coordinate from its equilibrium position. The norm- and energy-conserving properties of the propagation of our trial wave function are natural consequences of the Dirac-Frenkel-McLachlan variational principle. The variational approach also stabilizes the time evolution in comparison to the same ansatz propagated under a previously employed locally quadratic approximation to the bath potential and system-bath interaction terms in the bath-parameter equations of motion. Dynamics calculations are carried out for molecular iodine in a 2D krypton lattice that reveal both the time-course of vibrational decoherence and the details of host-atom motion accompanying energy dissipation and dephasing. This work sets the stage for the comprehensive simulation of ultrafast time-resolved optical experiments on small molecules in low-temperature solids.« less
  • A semiclassical method is proposed for the theoretical description of elastic light scattering by arbitrary semiconductor quantum dots under conditions of size quantization. This method involves retarded potentials and allows one to dispense with boundary conditions for electric and magnetic fields. Exact results for the Umov-Poynting vector at large distances from quantum dots in the case of monochromatic and pulsed irradiation and formulas for differential scattering cross sections are obtained.