Crossover between ballistic and diffusive transport: The quantum exclusion process

Journal of Statistical Mechanics: Theory and Experiment

Volumn 2011, Issue 6, 2011, Pages

  Eisler, Viktor ^a,b  

^a UNIVERSITY OF COPENHAGEN   (Denmark)

^b UNIVERSITY OF VIENNA   (Austria)

Author keywords

diffusion; quantum integrability (Bethe ansatz); quantum transport in one dimension; stochastic particle dynamics (theory)

Indexed keywords

EID: 79960229672     PISSN: None     EISSN: 17425468     Source Type: Journal    
DOI: 10.1088/1742-5468/2011/06/P06007     Document Type: Article

References (28)

1. Giamarchi T 2004 Quantum Physics in One Dimension (Oxford: Clarendon)
2. Castella H, Zotos X and Prelovsek P 1995 Integrability and ideal conductance at finite temperatures Phys. Rev. Lett. 74 972
3. Sirker J, Pereira R G and Affleck I 2009 Diffusion and ballistic transport in one-dimensional quantum systems Phys. Rev. Lett. 103 216602
4. Sirker J, Pereira R G and Affleck I 2011 Conservation laws, integrability and transport in one-dimensional quantum systems Phys. Rev. B 83 035115
5. For a review see: Heidrich-Meisner F, Honecker A and Brenig W 2007 Transport in quasi one-dimensional spin-1/2 systems Eur. Phys. J. Spec. Top. 151 135
6. Breuer H P and Petruccione F 2002 The Theory of Open Quantum Systems (Oxford: Oxford University Press)
7. Wichterich H, Henrich M J, Breuer H P, Gemmer J and Michel M 2007 Modeling heat transport through completely positive maps Phys. Rev. E 76 031115
8. Prosen T 2008 Third quantization: a general method to solve master equations for quadratic open Fermi systems New J. Phys. 10 043026
9. Karevski D and Platini T 2009 Quantum non-equilibrium steady states induced by repeated interactions Phys. Rev. Lett. 102 207207
10. Prosen T 2011 Open XXZ spin chain: nonequilibrium steady state and a strict bound on ballistic transport Phys. Rev. Lett. 106 217206
11. nidari M 2010 Exact solution for a diffusive nonequilibrium steady state of an open quantum chain J. Stat. Mech. L05002
12. nidari M 2010 Dephasing-induced diffusive transport in the anisotropic Heisenberg model New J. Phys. 12 043001
13. Temme K, Wolf M M and Verstraete F 2009 Stochastic exclusion processes versus coherent transport arXiv:0912.0858
14. Clark S R, Prior J, Hartmann M J, Jaksch D and Plenio M B 2009 Exact matrix product solutions in the Heisenberg picture of an open quantum spin chain New J. Phys. 12 025005
15. Prosen T and nidari M 2009 Matrix product simulations of non-equilibrium steady states of quantum spin chains J. Stat. Mech. P02035
16. Esposito M and Gaspard P 2005 Exactly solvable model of quantum diffusion J. Stat. Phys. 121 463
17. Esposito M and Gaspard P 2005 Emergence of diffusion in finite quantum systems Phys. Rev. B 71 214302
18. Mohseni M, Rebentrost P, Lloyd S and Aspuru-Guzik A 2008 Environment-assisted quantum walks in photosynthetic energy transfer J. Chem. Phys. 129 174106
19. Plenio M and Huelga S 2008 Dephasing assisted transport: quantum networks and biomolecules New J. Phys. 10 113019
20. Liggett T 1999 Stochastic Interacting Systems: Contact, Voter and Exclusion Processes (Berlin: Springer)
21. Lindblad G 1976 On the generators of quantum dynamical semigroups Commun. Math. Phys. 48 119
22. nidari M 2011 Solvable quantum nonequilibrium model exhibiting a phase transition and a matrix product representation Phys. Rev. E 83 011108
23. Schütz G M 1997 Exact solution of the master equation for the asymmetric exclusion process J. Stat. Phys. 88 427
24. Gradshteyn I S and Ryzhik I M 1980 Table of Integrals, Series, and Products (New York: Academic)
25. Tracy C and Widom H 2008 Integral formulas for the asymmetric simple exclusion process Commun. Math. Phys. 279 815
26. Derrida B and Gerschenfeld A 2009 Current fluctuations of the one-dimensional symmetric simple exclusion process with step initial condition J. Stat. Phys. 136 1
27. Antal T, Rcz Z, Rkos A and Schütz G M 1999 Transport in the xx chain at zero temperature: emergence of flat magnetization profiles Phys. Rev. E 59 4912
28. Antal T, Krapivsky P L and Rkos A 2008 Logarithmic current fluctuations in non-equilibrium quantum spin chains Phys. Rev. E 78 061115