Canonical averaging in the second order quantized Hamilton dynamics by extension of the coherent state thermodynamics of the harmonic oscillator

Abstract

A conceptually simple approximation to quantum mechanics, quantized Hamilton dynamics (QHD) includes zero-point energy, tunneling, dephasing, and other important quantum effects in a classical-like description. The hierarchy of coupled differential equations describing the time evolution of observables in QHD can be mapped in the second order onto a classical system with double the dimensionality of the original system. While QHD excels at dynamics with a single initial condition, the correct method for generating thermal initial conditions in QHD remains an open question. Using the coherent state representation of thermodynamics of the harmonic oscillator (HO) [Schnack, Europhys. Lett. 45, 647 (1999)], we develop canonical averaging for the second order QHD [Prezhdo, J. Chem. Phys. 117, 2995 (2002)]. The methodology is exact for the free particle and HO, and shows good agreement with quantum results for a variety of quartic potentials.

Communication: Quantum molecular dynamics simulation of liquid para-hydrogen by nuclear and electron wave packet approach

“…15 It is thus distinguished from most of the previous NWP approaches in which a potential surface was given in advance by a separate modeling and, in many cases, expanded quadratically around the moving NWP centers to perturbatively take into account the NQEs. 10,16,[18][19][20][21][22][23][24][25] Finally, we extend the above formulation for the 4e-4n system to a system composed of many-body hydrogen molecules. The extended Hamiltonian appearing in the EOM (4) for the N mol -body system is derived as 15 (4) with H ext (N mol ) where no empirical parameter to specify the intra-and inter-molecular interactions was introduced.…”

Investigations of α-helix↔β-sheet transition pathways in a miniprotein using the finite-temperature string method

“…15 It is thus distinguished from most of the previous NWP approaches in which a potential surface was given in advance by a separate modeling and, in many cases, expanded quadratically around the moving NWP centers to perturbatively take into account the NQEs. 10,16,[18][19][20][21][22][23][24][25] Finally, we extend the above formulation for the 4e-4n system to a system composed of many-body hydrogen molecules. The extended Hamiltonian appearing in the EOM (4) for the N mol -body system is derived as…”

“…The system dynamics can be described with the potential concept in this extended Hamiltonian. 16,17 In order to solve the EOM (4), we explicitly and nonperturbatively derive the potential expectation in Eq. (5) by the total wave function ψ(t).…”

“…Indeed, integration over all the NWP degrees of freedom to calculate average system energy in the Boltzmann distribution yields a surplus to the ZPE. 16 In the current NEWPMD simulations, the temperature is defined only by the kinetic temperature of WP center degrees of freedom assuming their canonical distribution even when embedded in a quantum WP simulation. 15 The assorted agreements of the self-diffusion coefficients and shear viscosities with the experiments demonstrate the validity of this definition since no microscopic adjusting parameter is introduced in the current NEWPMD.…”

Analytic dynamics of the Morse oscillator derived by semiclassical closures

“…Valuable approximations to the exact hierarchy can be obtained using the recently developed quantized Hamilton dynamics ͑QHD͒ methodology. 28,[32][33][34][35][36][37][38][39][40][41][42][43][44][45][46] QHD truncates the hierarchy by closures 47,48 and represents the higher-order expectations values of quantum-mechanical operators in terms of classical-like products of the lower-order expectation values. A number of semiclassical approximations can be obtained this way, depending on the decomposition level.…”