Energies and collapse times of symmetric and symmetry-breaking states of finite systems with a U(1) symmetry.
Energies and collapse times of symmetric and symmetry-breaking states of finite systems with a U(1) symmetry.
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具有 U(1) 对称性的有限系统的对称和对称破缺状态的能量和塌缩时间。
DOI：
10.1103/physreve.64.056121
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发表时间：
2001
期刊：
影响因子：
--
通讯作者：
T. Miyadera
中科院分区：
文献类型：
--
作者：
A. Shimizu;T. Miyadera
我们研究体积为V的量子系统，当V很大但有限时，它将在V->无穷大的极限中表现出U（1）对称性的破缺。我们估计了“对称基态”（SGS）和“纯相真空”（PPV）之间的能量差，前者是不破坏对称性的最低能量状态，后者在V->无穷大时接近破缺真空。在对SGS能量的一些自然假设下，证明了PPV总是具有比SGS更高的能量，并导出了多余能量的下界。我们认为，下界是O（V0），这变得比低激发态的激发能大得多的大V。我们还讨论了相互作用的许多玻色子的PPV的崩溃时间。结果表明，波函数崩溃在微观时间尺度，因为PPV不是能量本征态。然而，我们表明，PPV的期望值的任何观察，这是一个有限的玻色子算子及其衍生物的多项式，不崩溃的宏观时间尺度。从这个意义上说，PPV的塌陷时间在宏观上很长。
We study quantum systems of volume V, which will exhibit the breaking of a U(1) symmetry in the limit of V-->infinity, when V is large but finite. We estimate the energy difference between the "symmetric ground state" (SGS), which is the lowest-energy state that does not break the symmetry, and a "pure phase vacuum" (PPV), which approaches a symmetry-breaking vacuum as V-->infinity. Under some natural postulates on the energy of the SGS, it is shown that PPVs always have a higher energy than the SGS, and we derive a lower bound of the excess energy. We argue that the lower bound is O(V0), which becomes much larger than the excitation energies of low-lying excited states for a large V. We also discuss the collapse time of PPVs for interacting many bosons. It is shown that the wave function collapses in a microscopic time scale, because PPVs are not energy eigenstates. We show, however, that for PPVs the expectation value of any observable, which is a finite polynomial of boson operators and their derivatives, does not collapse for a macroscopic time scale. In this sense, the collapse time of PPVs is macroscopically long.