Semiquantal and Semiclassical Dynamics of Gaussian Wave Packets.

Konrad Singer, William Richard Smith

Andrey Pereverzev, Eric R. Bittner

P. A. Horváthy, L. Martina

Wei-Min Zhang, D.H. Feng

The spreading of a wave packet in various nonlinear external potentials with dissipation is studied. The dynamical description of this spreading is given by the use of the squeezed states and the semiquantal approach. We show that the position uncertainty of a Gaussian wave packet is dictated by quantum correlation and the behavior of its evolution can be vividly displayed. For various external potentials with dissipation, we find that the spreading of the wave packet is inevitably suppressed.

Robert G. Littlejohn

Rahul Sharma, Amartya Bose

Time-slicing has emerged as a strategy for incorporating semiclassical propagation into real-time path integral formulation and recovering full quantum dynamics. A central step is the decomposition of a time-evolved wave function into a superposition of Gaussian wave packets (GWPs). Here we introduce a quadrature-free variational framework for GWP decomposition, reformulating it as an optimization problem in which the GWP parameters are chosen to maximize the overlap with the time-evolving wave function. An autoencoderdecoder neural network is used for this optimization, with the representation being adaptively reoptimized during propagation. Each wave packet in this decomposition represents a localized patch of the underlying semiclassical manifold, while retaining full correlations between all degrees of freedom. This variational adaptive Gaussian decomposition (VAGD) approach yields a compact Gaussian expansion, providing a scalable route to time-sliced semiclassical quantum dynamics. While general, applying VAGD to facilitate time-slicing of thawed Gaussian dynamics allows a route to improving the semiclassical treatment to the full quantum mechanical result in a systematic manner.