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Resolving a Discrepancy between Liouvillian Gap and Relaxation Time in Boundary-Dissipated Quantum Many-Body Systems
Physical Review Letters ( IF 8.6 ) Pub Date : 2020-12-02 , DOI: 10.1103/physrevlett.125.230604
Takashi Mori , Tatsuhiko Shirai

The gap of the Liouvillian spectrum gives the asymptotic decay rate of a quantum dissipative system, and therefore its inverse has been identified as the slowest relaxation time. Contrary to this common belief, we show that the relaxation time due to diffusive transports in a boundary dissipated many-body quantum system is determined not by the gap or low-lying eigenvalues of the Liouvillian but by superexponentially large expansion coefficients for Liouvillian eigenvectors with nonsmall eigenvalues at an initial state. This finding resolves an apparent discrepancy reported in the literature between the inverse of the Liouvillian gap and the relaxation time in dissipative many-body quantum systems.

中文翻译:

解决边界耗散量子多体系统中Liouvillian间隙与弛豫时间之间的差异

Liouvillian谱的能隙给出了一个量子耗散系统的渐近衰减率,因此,其倒数被确定为最慢的弛豫时间。与此普遍的看法相反,我们表明,由边界耗散的多体量子系统中的扩散输运引起的弛豫时间,不是由Liouvillian的间隙或低本征值决定的,而是由非小Liouvillian特征向量的超指数大的膨胀系数决定的初始状态下的特征值。这一发现解决了文献中报道的Liouvillian间隙的逆与耗散多体量子系统中弛豫时间之间的明显差异。
更新日期:2020-12-02
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