Degenerated Liouvillians and steady-state reduced density matrices

被引:16
作者
Thingna, Juzar [1 ,2 ]
Manzano, Daniel [3 ,4 ]
机构
[1] Inst Basic Sci IBS, Ctr Theoret Phys Complex Syst, Daejeon 34126, South Korea
[2] Univ Sci & Technol, Basic Sci Program, Daejeon 34113, South Korea
[3] Univ Granada, Dept Electromagnetismo & Fis Mat, Granada 18071, Spain
[4] Univ Granada, Inst Carlos I Fis Teor & Computac, Granada 18071, Spain
关键词
GENERATORS;
D O I
10.1063/5.0045308
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Symmetries in an open quantum system lead to degenerated Liouvillians that physically imply the existence of multiple steady states. In such cases, obtaining the initial condition independent steady states is highly nontrivial since any linear combination of the true asymptotic states, which may not necessarily be a density matrix, is also a valid asymptote for the Liouvillian. Thus, in this work, we consider different approaches to obtain the true steady states of a degenerated Liouvillian. In the ideal scenario, when the open system symmetry operators are known, we show how these can be used to obtain the invariant subspaces of the Liouvillian and hence the steady states. We then discuss two other approaches that do not require any knowledge of the symmetry operators. These could be powerful numerical tools to deal with quantum many-body complex open systems. The first approach that is based on Gram-Schmidt orthonormalization of density matrices allows us to obtain all the steady states, whereas the second one based on large deviations allows us to obtain the non-degenerated maximum and minimum current carrying states. We discuss the symmetry-decomposition and the orthonormalization methods with the help of an open para-benzene ring and examine interesting scenarios such as the dynamical restoration of Hamiltonian symmetries in the long-time limit and apply the method to study the eigenspacing statistics of the nonequilibrium steady state. Published under an exclusive license by AIP Publishing.
引用
收藏
页数:11
相关论文
共 42 条
  • [1] Symmetries and conserved quantities in Lindblad master equations
    Albert, Victor V.
    Jiang, Liang
    [J]. PHYSICAL REVIEW A, 2014, 89 (02):
  • [2] Heat transport through lattices of quantum harmonic oscillators in arbitrary dimensions
    Asadian, A.
    Manzano, D.
    Tiersch, M.
    Briegel, H. J.
    [J]. PHYSICAL REVIEW E, 2013, 87 (01):
  • [3] Distribution of the Ratio of Consecutive Level Spacings in Random Matrix Ensembles
    Atas, Y. Y.
    Bogomolny, E.
    Giraud, O.
    Roux, G.
    [J]. PHYSICAL REVIEW LETTERS, 2013, 110 (08)
  • [4] LEVEL CLUSTERING IN REGULAR SPECTRUM
    BERRY, MV
    TABOR, M
    [J]. PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1977, 356 (1686): : 375 - 394
  • [5] QUANTIZING A CLASSICALLY ERGODIC SYSTEM - SINAI BILLIARD AND THE KKR METHOD
    BERRY, MV
    [J]. ANNALS OF PHYSICS, 1981, 131 (01) : 163 - 216
  • [6] Breuer H P., 2007, The Theory of Open Quantum Systems
  • [7] A note on symmetry reductions of the Lindblad equation: transport in constrained open spin chains
    Buca, Berislav
    Prosen, Tomaz
    [J]. NEW JOURNAL OF PHYSICS, 2012, 14
  • [8] Random Lindblad dynamics
    Can, Tankut
    [J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2019, 52 (48)
  • [9] Reconciliation of quantum local master equations with thermodynamics
    De Chiara, Gabriele
    Landi, Gabriel
    Hewgill, Adam
    Reid, Brendan
    Ferraro, Alessandro
    Roncaglia, Augusto J.
    Antezza, Mauro
    [J]. NEW JOURNAL OF PHYSICS, 2018, 20
  • [10] Universal Spectra of Random Lindblad Operators
    Denisov, Sergey
    Laptyeva, Tetyana
    Tarnowski, Wojciech
    Chruscinski, Dariusz
    Zyczkowski, Karol
    [J]. PHYSICAL REVIEW LETTERS, 2019, 123 (14)