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arXiv 1209.3153quant-ph
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自旋系统的无跃迁量子驱动

Transitionless quantum driving for spin systems

Kazutaka Takahashi

摘要:

我们将含时量子系统的无跃迁量子驱动方法应用于自旋系统。对于给定的哈密顿量,构造驱动哈密顿量,使得原系统的绝热态服从薛定谔方程。对于XY自旋链和Lipkin-Meshkov-Glick模型等几个典型系统,给出了驱动哈密顿量的显式构造。我们讨论了可能的有趣的情况下,当驱动哈密顿量变得与时间无关,当驱动哈密顿量是相当于原来的。对于多体系统,一个关键的问题发生在量子相变点,在该点,基态和第一激发态之间的能隙变为零。我们讨论了如何在目前的方法可以规避的缺陷。

英文摘要:

We apply the method of transitionless quantum driving for time-dependent quantum systems to spin systems. For a given Hamiltonian, the driving Hamiltonian is constructed so that the adiabatic states of the original system obey the Schroedinger equation. For several typical systems such as the XY spin chain and the Lipkin-Meshkov-Glick model, the driving Hamiltonian is constructed explicitly. We discuss possible interesting situations when the driving Hamiltonian becomes time independent and when the driving Hamiltonian is equivalent to the original one. For many-body systems, a crucial problem occurs at the quantum phase transition point where the energy gap between the ground and first excited states becomes zero. We discuss how the defect can be circumvented in the present method.

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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