论文标题
在非赫米特谐波振荡器中的量子相变
Quantum phase transitions in nonhermitian harmonic oscillator
论文作者
论文摘要
石材定理要求在物理希尔伯特空间中$ {\ cal h} $稳定量子系统的时间进化是统一的，并且仅当相应的汉密尔顿$ h $是自我伴侣时。有时，可以在明显的非物理Hilbert Space $ {\ cal K} $中构建的更简单的进化图，其中$ h $是nonhermitian，但$ {\ cal pt} - $ symmetric。不幸的是，在应用程序中，很少有人成功地规避关键的技术障碍，这在于必要的重建物理希尔伯特空间$ {\ cal H} $。对于$ {\ cal pt} - 加标谐波振荡器的$对称版本，我们表明，在不避免的级别交叉点的动态状态下，这种重建为$ {\ cal H} $变得可行，并且可以通过非数字手段获得。 $ {\ cal H} $重建的一般形式使人们能够将每个特殊的不可避免的跨点构成可作为真正，现象学上最具吸引力的量子 - 相变的瞬间。
The Stone theorem requires that in a physical Hilbert space ${\cal H}$ the time-evolution of a stable quantum system is unitary if and only if the corresponding Hamiltonian $H$ is self-adjoint. Sometimes, a simpler picture of the evolution may be constructed in a manifestly unphysical Hilbert space ${\cal K}$ in which $H$ is nonhermitian but ${\cal PT}-$symmetric. In applications, unfortunately, one only rarely succeeds in circumventing the key technical obstacle which lies in the necessary reconstruction of the physical Hilbert space ${\cal H}$. For a ${\cal PT}-$symmetric version of the spiked harmonic oscillator we show that in the dynamical regime of the unavoided level crossings such a reconstruction of ${\cal H}$ becomes feasible and, moreover, obtainable by non-numerical means. The general form of such a reconstruction of ${\cal H}$ enables one to render every exceptional unavoided-crossing point tractable as a genuine, phenomenologically most appealing quantum-phase-transition instant.
