A derivation of centroid molecular dynamics and other approximate time evolution methods for path integral centroid variables

Several methods to approximately evolve path integral centroid variables in real time are presented in this paper, the first of which, the centroid molecular dynamics (CMD) method, is recast into the new formalism of the preceding paper and thereby derived. The approximations involved in the CMD method are thus fully characterized by mathematical derivations. Additional new approaches are also presented: centroid Hamiltonian dynamics (CHD), linearized quantum dynamics (LQD), and a perturbative correction of the LQD method (PT-LQD). The CHD method is shown to be a variation of the CMD method which conserves the approximate time dependent centroid Hamiltonian. The LQD method amounts to a linear approximation for the quantum Liouville equation, while the PT-LQD method includes a perturbative correction to the LQD method. All of these approaches are then tested for the equilibrium position correlation functions of three different one-dimensional nondissipative model systems, and it is shown that certain quant...

[1]  M. Klein,et al.  Centroid path integral molecular dynamics simulation of lithium para-hydrogen clusters , 1997 .

[2]  R. Kubo.  Statistical-Mechanical Theory of Irreversible Processes : I. General Theory and Simple Applications to Magnetic and Conduction Problems , 1957 .

[3]  Bruce J. Berne,et al.  An iterative scheme for the evaluation of discretized path integrals , 1983 .

[4]  J. Brickmann,et al.  Comparison of the numerical matrix multiplication and quantum Monte Carlo simulations: calculation of spatial delocalization parameters , 1997 .

[5]  K. Binder,et al.  The Monte Carlo Method in Condensed Matter Physics , 1992 .

[6]  Eric J. Heller,et al.  Frozen Gaussians: A very simple semiclassical approximation , 1981 .

[7]  Bruce J. Berne,et al.  On the Simulation of Quantum Systems: Path Integral Methods , 1986 .

[8]  C. DeWitt-Morette,et al.  Techniques and Applications of Path Integration , 1981 .

[9]  M. Suzuki,et al.  Decomposition formulas of exponential operators and Lie exponentials with some applications to quantum mechanics and statistical physics , 1985 .

[10]  Gregory A. Voth,et al.  Simple reversible molecular dynamics algorithms for Nosé-Hoover chain dynamics , 1997 .

[11]  H. Kleinert.  Path Integrals in Quantum Mechanics Statistics and Polymer Physics , 1990 .

[12]  Jianshu Cao,et al.  The formulation of quantum statistical mechanics based on the Feynman path centroid density. III. Phase space formalism and analysis of centroid molecular dynamics , 1994 .

[13]  M. Klein,et al.  Nosé-Hoover chains : the canonical ensemble via continuous dynamics , 1992 .

[14]  M. Ovchinnikov,et al.  Mixed-order semiclassical dynamics in coherent state representation: The connection between phonon sidebands and guest-host dynamics , 1998 .

[15]  R. Feynman,et al.  Quantum Mechanics and Path Integrals , 1965 .