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arXiv 1107.5010quant-phmath-phmath.MP
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压缩相干态的费米函数

On the Fermi Function of Squeezed Coherent States

Maurice A. de Gosson

摘要:

费米在1930年观察到,量子系统的状态可以用两种不同(但等价)的方式定义,即通过其波函数$Ψ$或通过与$Ψ$正则相关的相空间上的某个函数$g_F$。本文研究了$Ψ$为压缩相干态时的费米函数。我们将它与Wigner变换的$Ψ$,从而概括了以前的观察Benenti和Strini。我们证明了相空间椭球$g_{F}(x,p)\leq0$的辛容量是由$h/2$和$nh/2$(n为自由度)所限定的。

英文摘要:

Fermi observed in 1930 that the state of a quantum system may be defined in two different (but equivalent) ways, namely by its wavefunction $Ψ$ or by a certain function $g_F$ on phase space canonically associated with $Ψ$. In this Note we study we study Fermi's function when $Ψ$ is a squeezed coherent state. We relate it with the Wigner transform of $Ψ$, thus generalising a previous observation of Benenti and Strini. We show that the symplectic capacity of the phase space ellipsoid $g_{F}(x,p)\leq0$ is bounded by $h/2$ and $nh/2$ (n the number of degrees of freedom).

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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