Symplectic Coarse-Grained Classical and Semi-Classical Evolution of Subsystems: New Theoretical Aspects
arXiv:2002.06641
Abstract
We study the classical and semiclassical time evolutions of subsystems of a Hamiltonian system; this is done using a generalization of Heller's thawed Gaussian approximation introduced by Littlejohn. The key tool in our study is an extension of Gromov's "principle of the symplectic camel" obtained in collaboration with N. Dias and J. Prata. This extension says that the orthogonal projection of a symplectic phase space ball on a phase space with a smaller dimension also contains a symplectic ball with the same radius. In the quantum case, the radii of these symplectic balls are taken equal to sqrt(h_bar) and represent ellipsoids of minimum uncertainty, which we have called "quantum blobs" in previous work.
arXiv commentRevised versio. To appwear in J.Math.Phys
References in corpus (8)
- The Real Symplectic Groups in Quantum Mechanics and Optics
- Computing quantum dynamics in the semiclassical regime
- On-the-fly ab initio semiclassical dynamics: Identifying degrees of freedom essential for emission spectra of oligothiophenes
- Quantum Harmonic Analysis of the Density Matrix
- Time irreversibility from symplectic non-squeezing
- Irreversibility from staircases in symplectic embeddings
- A contact camel theorem
- Localization of quantum wave packets