arXiv math-ph/06030412006-03-15math-phmath.MP

倒谐振子奇异微扰的量子和经典保真度

Quantum and Classical Fidelity for Singular Perturbations of the Inverted and Harmonic Oscillator

M. Combescure, A. Combescure

备注：: To be published in Journal of Mathematical Analysis and Applications
发表信息：: Journal of Mathematical Analysis and Applications 326 (2006) 908-928
DOI：: 10.1016/j.jmaa.2006.03.044

摘要：

让我们考虑形式为\beq \label{0.1} H\_{g}^ε：= \frac{P^2}{2} + ε \frac{Q^2}{2} + \frac{g^2}{Q^2} \edq的哈密顿量的量子动力学与经典动力学，其中$ε= \pm 1$，$g$是实常数。我们将特别研究$H\_{g}^ε$和$H\_{0}^ε$之间的量子保真度，定义为\beq \label{0.2} F_{Q}^ε（t，g）：= < \exp（-itH_{0}^ε）<$，exp（-itH_{g}^ ε）<$> \edq对于相关算子域中的某个参考态$ψ$。我们还将提出一个经典保真度的定义，已经在文献中出现（\cite{becave1}，\cite{becave2}，\cite{ec}，\cite{prozni}，\cite{vepro}），并将其与量子保真度的行为进行比较，随着时间的推移，随着耦合常数$g$的变化。

英文摘要：

Let us consider the quantum/versus classical dynamics for Hamiltonians of the form \beq \label{0.1} H\_{g}^ε := \frac{P^2}{2}+ ε\frac{Q^2}{2}+ \frac{g^2}{Q^2} \edq where $ε= \pm 1$, $g$ is a real constant. We shall in particular study the Quantum Fidelity between $H\_{g}^ε$ and $H\_{0}^ε$ defined as \beq \label{0.2} F\_{Q}^ε(t,g):= < \exp(-it H\_{0}^ε)ψ, exp(-itH\_{g}^ ε)ψ> \edq for some reference state $ψ$ in the domain of the relevant operators. We shall also propose a definition of the Classical Fidelity, already present in the literature (\cite{becave1}, \cite{becave2}, \cite{ec}, \cite{prozni}, \cite{vepro}) and compare it with the behaviour of the Quantum Fidelity, as time evolves, and as the coupling constant $g$ is varied.

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摘要：

英文摘要：

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