A variational principle in Wigner phase-space with applications to statistical mechanics

Finite-Temperature Correlation Functions Obtained from Combined Real- and Imaginary-Time Propagation of Variational Thawed Gaussian Wavepackets

We apply the so-called variational Gaussian wavepacket approximation (VGA) for conducting both real- and imaginary-time dynamics to calculate thermal correlation functions. By considering strongly anharmonic systems, such as a quartic potential and a double-well potential at high and low temperatures, it is shown that this method is partially able to account for tunneling. This is contrary to other popular many-body methods, such as ring polymer molecular dynamics and the classical Wigner method, which fail in this respect. It is a historical peculiarity that no one has considered the VGA method for representing both the Boltzmann operator and the real-time propagation. This method should be well suited for molecular systems containing many atoms.

Feynman's clock, a new variational principle, and parallel-in-time quantum dynamics

We introduce a discrete-time variational principle inspired by the quantum clock originally proposed by Feynman and use it to write down quantum evolution as a ground-state eigenvalue problem. The construction allows one to apply ground-state quantum many-body theory to quantum dynamics, extending the reach of many highly developed tools from this fertile research area. Moreover, this formalism naturally leads to an algorithm to parallelize quantum simulation over time. We draw an explicit connection between previously known time-dependent variational principles and the time-embedded variational principle presented. Sample calculations are presented, applying the idea to a hydrogen molecule and the spin degrees of freedom of a model inorganic compound, demonstrating the parallel speedup of our method as well as its flexibility in applying ground-state methodologies. Finally, we take advantage of the unique perspective of this variational principle to examine the error of basis approximations in quantum dynamics.

The classical Wigner method with an effective quantum force: application to the collinear H + H2 reaction

To improve the classical Wigner (CW) model, we recently proposed the classical Wigner model with an effective quantum force (CWEQF). The results of the CWEQF model are more accurate than those of the CW model. Still the simplicity of the CW model is retained. The quantum force was obtained by defining a characteristic distance η(0) between two Feynman paths that enter the expression for the flux-flux correlation function. η(0) was considered independent of the position along the reaction path. The CWEQF leads to a lowering of the effective potential barrier. Here we develop the method to use position dependent η(0) values. The method is also generalized to two dimensions. Applications are carried out on one-dimensional model problems and the two-dimensional H + H(2) collinear reaction.