Nonlinear thermodynamic quantum master equation: Properties and examples

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 82, Issue 5, 2010, Pages

  Öttinger, Hans Christian ^a  

^a ETH ZURICH   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

CANONICAL EQUILIBRIUM; COUPLED EVOLUTION; DAMPED HARMONIC OSCILLATOR; DENSITY MATRIX; EIGENSTATES; EIGENVALUES; HEISENBERG; MARKOVIAN; NON-LINEARITY; NONLINEAR CONTRIBUTIONS; NONLINEAR THERMODYNAMICS; QUANTUM MASTER EQUATIONS; QUANTUM SYSTEM; SOLUTION STRATEGY; TWO-LEVEL SYSTEM;

CONTROL NONLINEARITIES; EIGENVALUES AND EIGENFUNCTIONS; OSCILLATORS (ELECTRONIC); QUANTUM ELECTRONICS; QUANTUM OPTICS; THERMODYNAMICS;

NONLINEAR EQUATIONS;

EID: 78650978865     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.82.052119     Document Type: Article

References (41)

1. H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, England, 2002).
2. U. Weiss, Quantum Dissipative Systems, 3rd ed. Series in Modern Condensed Matter Physics, Vol. 13 (World Scientific, Singapore, 2008).
3. G. Lindblad, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF01608499 48, 119 (1976).
4. H. Grabert, Z. Phys. B ZPCMDN 0722-3277 10.1007/BF01314753 49, 161 (1982).
5. H. Grabert and P. Talkner, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.50.1335 50, 1335 (1983).
6. P. Talkner, Ann. Phys. (NY) APNYA6 0003-4916 10.1016/0003-4916(86)90207-1 167, 390 (1986).
7. H. Grabert, Chem. Phys. CMPHC2 0301-0104 10.1016/j.chemphys.2005.08.012 322, 160 (2006).
8. R. Karrlein and H. Grabert, Phys. Rev. E CMPHC2 1539-3755 10.1103/PhysRevE.55.153 55, 153 (1997).
9. H. C. Öttinger, e-print arXiv: 1002.2938.
10. M. Grmela and H. C. Öttinger, Phys. Rev. E CMPHC2 1539-3755 10.1103/PhysRevE.56.6620 56, 6620 (1997).
11. H. C. Öttinger and M. Grmela, Phys. Rev. E CMPHC2 1539-3755 10.1103/PhysRevE.56.6633 56, 6633 (1997).
12. H. C. Öttinger, Beyond Equilibrium Thermodynamics (Wiley, Hoboken, NJ, 2005).
13. P. A. M. Dirac, The Principles of Quantum Mechanics, 4th ed. International Series of Monographs on Physics, Vol. 27 (Oxford University Press, Oxford, England, 1981).
14. R. Kapral, Annu. Rev. Phys. Chem. ARPLAP 0066-426X 10.1146/annurev. physchem.57.032905.104702 57, 129 (2006).
15. R. Grunwald and R. Kapral, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.2567164 126, 114109 (2007).
16. J. P. Rank and R. Kapral, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.3310811 132, 074106 (2010).
17. P. Hänggi and G.-L. Ingold, Chaos CHAOEH 1054-1500 10.1063/1.1853631 15, 026105 (2005).
18. R. P. Feynman and F. L. Vernon, Ann. Phys. (NY) APNYA6 0003-4916 10.1016/0003-4916(63)90068-X 24, 118 (1963).
19. H. Grabert, P. Schramm, and G.-L. Ingold, Phys. Rep. PRPLCM 0370-1573 10.1016/0370-1573(88)90023-3 168, 115 (1988).
20. R. Kubo, M. Toda, and N. Hashitsume, Nonequilibrium Statistical Mechanics, 2nd ed. Vol. II of Series Statistical Physics (Springer, Berlin, 1991).
21. H. Grabert, Projection Operator Techniques in Nonequilibrium Statistical Mechanics (Springer, Berlin, 1982).
22. A. N. Beris and B. J. Edwards, The Thermodynamics of Flowing Systems (Oxford University Press, New York, 1994).
23. J. E. Marsden, Lectures on Mechanics (Cambridge University Press, Cambridge, England, 1992).
24. J. E. Marsden and T. S. Ratiu, Introduction to Mechanics and Symmetry, 2nd ed. Texts in Applied Mathematics, Vol. 17 (Springer, New York, 1999).
25. B. J. Edwards and H. C. Öttinger, Phys. Rev. E PRPLCM 1539-3755 10.1103/PhysRevE.56.4097 56, 4097 (1997).
26. H. C. Öttinger, Phys. Rev. E PRPLCM 1539-3755 10.1103/PhysRevE.73. 036126 73, 036126 (2006).
27. A. N. Beris and H. C. Öttinger, J. Non-Newtonian Fluid Mech. JNFMDI 0377-0257 10.1016/j.jnnfm.2007.10.017 152, 2 (2008).
28. H. C. Öttinger, J. Non-Newtonian Fluid Mech. JNFMDI 0377-0257 10.1016/j.jnnfm.2007.08.001 152, 66 (2008).
29. H. C. Öttinger, D. Bedeaux, and D. C. Venerus, Phys. Rev. E JNFMDI 1539-3755 10.1103/PhysRevE.80.021606 80, 021606 (2009).
30. L. M. C. Sagis, Adv. Colloid Interface Sci. ACISB9 0001-8686 10.1016/j.cis.2009.12.003 153, 58 (2010).
31. E. L. Hahn, Concepts Magn. Reson. ACISB9 1043-7347 10.1002/(SICI)1099- 0534(1997)9:2<69::AID-CMR2>3.0.CO;2-K 9, 69 (1997).
32. F. Bloch, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.70.460 70, 460 (1946).
33. S. Bougouffa and S. Al-Awfi, J. Mod. Opt. JMOPEW 0950-0340 10.1080/09500340701485522 55, 473 (2008).
34. R. K. Wangsness and F. Bloch, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.89.728 89, 728 (1953).
35. M. Czachor and M. Kuna, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.58.128 58, 128 (1998).
36. J. Dalibard, Y. Castin, and K. Mølmer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.68.580 68, 580 (1992).
37. R. Dum, P. Zoller, and H. Ritsch, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.45.4879 45, 4879 (1992).
38. H.-P. Breuer and F. Petruccione, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.74.3788 74, 3788 (1995).
39. H.-P. Breuer and F. Petruccione, Phys. Rev. E PRLTAO 1539-3755 10.1103/PhysRevE.52.428 52, 428 (1995).
40. H. C. Öttinger, e-print arXiv: 1005.1190.
41. H. C. Öttinger, e-print arXiv: 1008.1867.