Symmetrized Liouvillian Gap in Markovian Open Quantum Systems.

Markovian open quantum systems display complicated relaxation dynamics. The spectral gap of the Liouvillian characterizes the asymptotic decay rate towards the steady state, but it does not necessarily give a correct estimate of the relaxation time because the crossover time to the asymptotic regime may be too long. We here give a rigorous upper bound on the transient decay of auto-correlation functions in the steady state by introducing the symmetrized Liouvillian gap. The standard Liouvillian gap and the symmetrized one are identical in an equilibrium situation but differ from each other in the absence of the detailed balance condition. It is numerically shown that the symmetrized Liouvillian gap always give a correct upper bound on the decay of the auto-correlation function, but the standard Liouvillian gap does not.

[1]  A. Clerk,et al.  Anomalously large relaxation times in dissipative lattice models beyond the non-Hermitian skin effect , 2022, 2210.14212.

[2]  J. P. Garrahan,et al.  Inverse thermodynamic uncertainty relations: general upper bounds on the fluctuations of trajectory observables , 2022, 2210.04983.

[3]  Tatsuhiko N. Ikeda,et al.  Nonequilibrium steady states in the Floquet-Lindblad systems: van Vleck's high-frequency expansion approach , 2021, SciPost Physics Core.

[4]  F. Carollo,et al.  Exponentially Accelerated Approach to Stationarity in Markovian Open Quantum Systems through the Mpemba Effect. , 2021, Physical review letters.

[5]  Takashi Mori.  Metastability associated with many-body explosion of eigenmode expansion coefficients , 2021, Physical Review Research.

[6]  M. Znidaric,et al.  Fastest Local Entanglement Scrambler, Multistage Thermalization, and a Non-Hermitian Phantom , 2021, Physical Review X.

[7]  Raul Garcia-Patron,et al.  Limitations of optimization algorithms on noisy quantum devices , 2020, Nature Physics.

[8]  D. Deng,et al.  Solving the Liouvillian Gap with Artificial Neural Networks. , 2020, Physical review letters.

[9]  Patrick J. Coles,et al.  Noise-induced barren plateaus in variational quantum algorithms , 2020, Nature Communications.

[10]  Masahito Ueda,et al.  Liouvillian Skin Effect: Slowing Down of Relaxation Processes without Gap Closing. , 2020, Physical review letters.

[11]  Masahito Ueda,et al.  Exact Liouvillian Spectrum of a One-Dimensional Dissipative Hubbard Model. , 2020, Physical review letters.

[12]  Takashi Mori,et al.  Resolving Discrepancy between Liouvillian Gap and Relaxation Time in Boundary-Dissipated Quantum Many-Body Systems , 2020, 2006.10953.

[13]  E. Vernier,et al.  Mixing times and cutoffs in open quadratic fermionic systems , 2020, SciPost Physics.

[14]  Todd R. Gingrich,et al.  Thermodynamic uncertainty relations constrain non-equilibrium fluctuations , 2020, Nature Physics.

[15]  H. Katsura,et al.  Dissipative spin chain as a non-Hermitian Kitaev ladder , 2018, Physical Review B.

[16]  R. Kosloff,et al.  Shortcut to Equilibration of an Open Quantum System. , 2018, Physical review letters.

[17]  K. Funo,et al.  Speed limit for open quantum systems , 2018, New Journal of Physics.

[18]  Shuta Nakajima,et al.  Observation of the Mott insulator to superfluid crossover of a driven-dissipative Bose-Hubbard system , 2017, Science Advances.

[19]  C. Ciuti,et al.  Critical dynamical properties of a first-order dissipative phase transition , 2016, 1608.00717.

[20]  Changsuk Noh,et al.  Quantum simulations and many-body physics with light , 2016, Reports on progress in physics. Physical Society.

[21]  J. P. Garrahan,et al.  Towards a Theory of Metastability in Open Quantum Dynamics. , 2015, Physical review letters.

[22]  M. Znidaric.  Relaxation times of dissipative many-body quantum systems. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  Daniel A. Lidar,et al.  Quantum Speed Limits for Leakage and Decoherence. , 2015, Physical review letters.

[24]  C. Kollath,et al.  Two-time correlations probing the dynamics of dissipative many-body quantum systems: aging and fast relaxation. , 2014, Physical review letters.

[25]  Daniel A. Lidar,et al.  Review of Decoherence‐Free Subspaces, Noiseless Subsystems, and Dynamical Decoupling , 2012, 1208.5791.

[26]  K. Temme.  Lower bounds to the spectral gap of Davies generators , 2013, 1305.5591.

[27]  Zi Cai,et al.  Algebraic versus Exponential Decoherence in Dissipative Many-Particle Systems. , 2013, Physical review letters.

[28]  E. Lutz,et al.  Quantum speed limit for non-Markovian dynamics. , 2013, Physical review letters.

[29]  G. Barontini,et al.  Controlling the dynamics of an open many-body quantum system with localized dissipation. , 2012, Physical review letters.

[30]  M B Plenio,et al.  Quantum speed limits in open system dynamics. , 2012, Physical review letters.

[31]  J. Cirac,et al.  Dissipative phase transition in a central spin system , 2012, 1205.3341.

[32]  T. Monz,et al.  An open-system quantum simulator with trapped ions , 2011, Nature.

[33]  F. Verstraete,et al.  Quantum computation and quantum-state engineering driven by dissipation , 2009 .

[34]  Germany,et al.  Quantum states and phases in driven open quantum systems with cold atoms , 2008, 0803.1482.

[35]  I. Tamm,et al.  The Uncertainty Relation Between Energy and Time in Non-relativistic Quantum Mechanics , 1991 .

[36]  R. Alicki.  On the detailed balance condition for non-hamiltonian systems , 1976 .

[37]  G. Lindblad.  On the generators of quantum dynamical semigroups , 1976 .

[38]  E. Sudarshan,et al.  Completely Positive Dynamical Semigroups of N Level Systems , 1976 .