TY - JOUR
T1 - Resolving a Discrepancy between Liouvillian Gap and Relaxation Time in Boundary-Dissipated Quantum Many-Body Systems
AU - Mori, Takashi
AU - Shirai, Tatsuhiko
N1 - Funding Information:
We would like to thank Hosho Katsura, Eric Vernier, and Marko Žnidarič for useful comments. This work was supported by the Japan Society for the Promotion of Science KAKENHI Grants No. 19K14622 and No. 18K13466. The numerical calculations have been done mainly on the supercomputer system at the Institute for Solid State Physics, University of Tokyo.
Publisher Copyright:
© 2020 American Physical Society.
PY - 2020/12/2
Y1 - 2020/12/2
N2 - 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.
AB - 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.
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U2 - 10.1103/PhysRevLett.125.230604
DO - 10.1103/PhysRevLett.125.230604
M3 - Article
C2 - 33337170
AN - SCOPUS:85097582373
SN - 0031-9007
VL - 125
JO - Physical Review Letters
JF - Physical Review Letters
IS - 23
M1 - 230604
ER -