Related papers: Generalized Gaussian wave packet dynamics: Integra…
We analyze the semiclassical evolution of Gaussian wavepackets in chaotic systems. We prove that after some short time a Gaussian wavepacket becomes a primitive WKB state. From then on, the state can be propagated using the standard TDWKB…
Gaussian wavepackets are a popular tool for semiclassical analyses of classically chaotic systems. We demonstrate that they are extremely powerful in the semiquantal analysis of such systems, too, where their dynamics can be recast in an…
Semiclassical methods are extremely important in the subjects of wave packet and coherent state dynamics. Unfortunately, these essentially saddle point approximations are considered nearly impossible to carry out in detail for systems with…
Simulation and analysis of multidimensional dynamics of a quantum non-Hmeritian system is a challenging problem. Gaussian wavepacket dynamics has proven to be an intuitive semiclassical approach to approximately solving the dynamics of…
One-dimensional integrable and quasi-integrable systems display, on macroscopic scales, a universal form of transport known as Generalized Hydrodynamics (GHD). In its standard Euler-scale formulation, GHD mirrors the equations of a…
The paper gives a symplectic-geometric account of semiclassical Gaussian wave packet dynamics. We employ geometric techniques to "strip away" the symplectic structure behind the time-dependent Schr\"odinger equation and incorporate it into…
The dynamics of quantum systems can be approximated by the time propagation of Gaussian wave packets. Applying a time dependent variational principle, the time evolution of the parameters of the coupled Gaussian wave packets can be…
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…
We consider a semiclassical approximation for the time evolution of an originally gaussian wave packet in terms of complex trajectories. We also derive additional approximations replacing the complex trajectories by real ones. These yield…
Gaussian wave packets (GWPs) are well suited as basis functions to describe the time evolution of arbitrary wave functions in systems with nonsingular smooth potentials. They are less so in atomic systems on account of the singular behavior…
Path integral derivations are presented for two recently developed complex trajectory techniques for the propagation of wave packets, Complex WKB and BOMCA. Complex WKB is derived using a standard saddle point approximation of the path…
It is well known that the Gaussian wave packet dynamics can be written in terms of Hamilton equations in the extended phase space that is twice as large as in the corresponding classical system. We construct several generalizations of this…
In this article, we develop and analyse a new spectral method to solve the semi-classical Schr\"odinger equation based on the Gaussian wave-packet transform (GWPT) and Hagedorn's semi-classical wave-packets (HWP). The GWPT equivalently…
We assessed three schemes for propagating a variable-width (thawed) Gaussian wave packet moving under the influence of Morse or double-well potentials with parameters that are chemically representative. The most rigorous scheme is based on…
We generalize our earlier work on the symplectic/Hamiltonian formulation of the dynamics of the Gaussian wave packet to non-Gaussian semiclassical wave packets. We find the symplectic forms and asymptotic expansions of the Hamiltonians…
We study smooth, caustic-free, chaotic semiclassical dynamics on two-dimensional phase space and find that the dynamics can be approached by an iterative procedure which constructs an approximation to the exact long-time semiclassical…
This article introduces the notion of Generalized Poisson-Kac (GPK) processes which generalize the class of "telegrapher's noise dynamics" introduced by Marc Kac in 1974, usingPoissonian stochastic perturbations. In GPK processes the…
We examine an extension to the theory of Gaussian wave packet dynamics in a one-dimensional potential by means of a sequence of time dependent displacement and squeezing transformations. Exact expressions for the quantum dynamics are found,…
In this article we present an exact and unified description of wave-packet dynamics in various 2D systems in presence of a transverse magnetic field. We consider an initial minimum-uncertainty Gaussian wave-packet, and find that its long…
Rich and complex time-series data, such as those generated from engineering systems, financial markets, videos or neural recordings, are now a common feature of modern data analysis. Explaining the phenomena underlying these diverse data…