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SUMMARY:David J. Luitz (Max Planck Institute for the Physics of Complex Sy
 stems\, Dresden)
DTSTART:20210412T160000Z
DTEND:20210412T170000Z
DTSTAMP:20260423T024701Z
UID:QM3/36
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/QM3/36/">Hie
 rarchy of Relaxation Timescales in Local Random Liouvillians</a>\nby David
  J. Luitz (Max Planck Institute for the Physics of Complex Systems\, Dresd
 en) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAbstract\nTo
  characterize the generic behavior of open quantum many-body systems\, we 
 consider random\, purely dissipative Liouvillians with a notion of localit
 y. We find that the positivity of the map implies a sharp separation of th
 e relaxation timescales according to the locality of observables. Specific
 ally\, we analyze a spin-$1/2$ system of size $\\ell$ with up to n-body L
 indblad operators\, which are n local in the complexity-theory sense. With
 out locality ($n=l$)\, the complex Liouvillian spectrum densely covers a 
 “lemon”-shaped support\, in agreement with recent findings [S. Denisov
  et al.\, Phys. Rev. Lett. 123\, 140403 (2019)\, L. Sa et al.\, JPA 53\, 3
 05303].\nHowever\, for local Liouvillians ($n < l$)\, we find that the spe
 ctrum is composed of several dense clusters with random matrix spacing sta
 tistics\, each featuring a lemon-shaped support wherein all eigenvectors c
 orrespond to $n$-body decay modes. This implies a hierarchy of relaxation 
 timescales of n-body observables\, which we verify to be robust in the the
 rmodynamic limit. Our findings for n locality generalize immediately to th
 e case of spatial locality\, introducing further splitting of timescales d
 ue to the additional structure. \n\nTo test our theoretical prediction\, 
 we perform experiments on the IBM quantum computing platform\, designing d
 ifferent "waiting circuits" to inject two body dissipative interactions by
  two qubit entangling gates. We find excellent agreement with our theory a
 nd observe the predicted hierarchy of timescales.\n\n\n\n\n\n[1] K. Wang\,
  F. Piazza\, D. J. Luitz ” Hierarchy of relaxation timescales in local r
 andom Liouvillians “ Phys. Rev. Lett. 124\, 100604 (2020)\n\n[2] O. E. S
 ommer\, F. Piazza\, and D. J. Luitz “Many-body Hierarchy of Dissipative 
 Timescales in a Quantum Computer” arXiv:2011.08853\n
LOCATION:https://researchseminars.org/talk/QM3/36/
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