Generating approximate Wigner distributions using Gaussian phase packets propagation in imaginary time.

Gerhard Wilhelm Bund, Salomon Sylvain Mizrahi, M. C. Tijero

The Gaussian wave-packet phase-space representation is used to show that the expansion in powers of \ensuremath{\Elzxh} of the quantum Liouville propagator leads, in the zeroth-order term, to results close to those obtained in the statistical quasiclassical method of Lee and Scully in the Weyl-Wigner picture. It is also verified that, propagating the Wigner distribution along the classical trajectories, the amount of error is less than that coming from propagating the Gaussian distribution along classical trajectories.

J. Banerji

The nonlinear evolution of certain quantum systems such as a Gaussian wave packet in an infinite potential well, can lead to fractional revivals of the initial wave packet. Analogously, a coherent state propagating through a Kerr medium can form the so-called Schrödinger cats and cat-like states. Recently, it was shown that a superposition of Schrödinger cats can give rise to sub-Planck structures in the Wigner distribution. The purpose of this review is to introduce and apply, in the above context, a phase space distribution ‘which differs but little from Wigner's and yet, had remained obscure for decades. This is the Kirkwood – Rihaczek (KR) distribution, which has aroused considerable interest in recent years. It is thus appropriate and timely to see how it compares with the Wigner distribution in analysing the above phenomena. Our detailed analysis shows that the KR distribution is just as adequate in explaining these phenomena as the Wigner distribution. Sub-Planck structures are obtained in the KR distribution as well, and despite important differences, the two phase space pictures are comparable.

R. Simon, E. C. G. Sudarshan, Narasimhaiengar Mukunda

Jens Aage Poulsen, Gunnar Nyman

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.

Helge Dietert, Johannes Keller, Stephanie Troppmann