Long time semiclassical approximation of quantum flows: a proof of the Ehrenfest time
| dc.creator | Bambusi, Dario | |
| dc.creator | Graffi, Sandro | |
| dc.creator | Paul, Thierry | |
| dc.date | 1998-05-19 | |
| dc.date.accessioned | 2026-07-07T04:32:24Z | |
| dc.date.available | 2026-07-07T04:32:24Z | |
| dc.description | Let ${\cal H}(x,ξ)$ be a holomorphic Hamiltonian of quadratic growth on $ R^{2n}$, $b$ a holomorphic exponentially localized observable, $H$, $B$ the corresponding operators on $L^2(R^n)$ generated by Weyl quantization, and $U(t)=\exp{iHt/\hbar}$. It is proved that the $L^2$ norm of the difference between the Heisenberg observable $B_t=U(t)BU(-t)$ and its semiclassical approximation of order ${N-1}$ is majorized by $K N^{(6n+1)N}(-\hbar ln\hbar)^N$ for $t\in [0,T_N(\hbar)]$ where $T_N(\hbar)=-{2 ln\hbar\over {N-1}}$. Choosing a suitable $N(\hbar)$ the error is majorized by $C\hbar^{ln|ln\hbar|}$, $0\leq t\leq |ln\hbar|/ln|ln\hbar|$. (Here $K,C$ are constants independent of $N,\hbar$). | |
| dc.description | 14 pages, plain Tex | |
| dc.identifier | https://arxiv.org/abs/math-ph/9805018 | |
| dc.identifier | http://arxiv.org/abs/math-ph/9805018 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/58176 | |
| dc.subject | Mathematical Physics | |
| dc.title | Long time semiclassical approximation of quantum flows: a proof of the Ehrenfest time | |
| dc.type | text |