Mori Takashi, Shirai Tatsuhiko
RIKEN Center for Emergent Matter Science (CEMS), Wako 351-0198, Japan.
Department of Computer Science and Communications Engineering, Waseda University, Tokyo 169-8555, Japan.
Phys Rev Lett. 2020 Dec 4;125(23):230604. doi: 10.1103/PhysRevLett.125.230604.
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.
刘维尔谱的间隙给出了量子耗散系统的渐近衰减率，因此其倒数被认为是最慢的弛豫时间。与这种普遍看法相反，我们表明，在边界耗散多体量子系统中，由于扩散输运导致的弛豫时间不是由刘维尔算符的间隙或低阶本征值决定的，而是由初始状态下具有非小本征值的刘维尔本征向量的超指数大展开系数决定的。这一发现解决了文献中报道的关于刘维尔间隙倒数与耗散多体量子系统弛豫时间之间的明显差异。
