Quantum suppression of ratchet rectification in a Brownian system driven by a biharmonic force

Journal of Physical Chemistry B

Volumn 117, Issue 42, 2013, Pages 13132-13144

  Kato, Akihito ^a   Tanimura, Yoshitaka ^a,b  

^a KYOTO UNIVERSITY   (Japan)

^b UNIVERSITY OF AUGSBURG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

FOKKER PLANCK EQUATION; HAMILTONIANS; QUANTUM THEORY; TEMPERATURE;

COUPLING STRENGTHS; DISSIPATIVE DYNAMICS; FINITE TEMPERATURES; LOW TEMPERATURES; PERIODIC POTENTIALS; QUANTUM MECHANICAL EFFECTS; RATCHET POTENTIAL; WIGNER DISTRIBUTION;

EQUATIONS OF MOTION;

EID: 84886704375     PISSN: 15206106     EISSN: 15205207     Source Type: Journal    
DOI: 10.1021/jp403056h     Document Type: Article

References (95)

1. Smoluchowski, M. V. Experimentell Nachweisbare, der üblichen Thermodynamik Widersprechende Molekularphänomene Phys. Z. 1912, 13, 1069-1080
2. Feynman, R. P.; Leighton, R. B.; Sands, M. The Feynman Lectures on Physics; Addison Wesley: Reading, MA, 1966; Vol. 1, chapt. 46.
3. Hänggi, P.; Bartussek, R. In Nonlinear Physics of Complex Systems; Parisi, J.; Muller, S. C.,; Zimmermann, W., Eds.; Lecture Notes in Physics Vol. 476; Springer: Berlin, 1996; pp 294-308.
4. Jülicher, F.; Ajdari, A.; Prost, J. Modeling Molecular Motors Rev. Mod. Phys 1997, 69, 1269-1281
5. Astumian, R. D. Thermodynamics and Kinetics of a Brownian Motor Science 1997, 276, 917-922
6. Reimann, P. Brownian Motors: Noisy Transport far from Equilibrium Phys. Rep. 2002, 361, 57-265
7. Hänggi, P.; Marchesoni, F.; Nori, F. Brownian Motors Ann. Phys. (Leipzig, Ger.) 2005, 14, 51-70
8. Hänggi, P.; Marchesoni, F. Artificial Brownian Motors: Controlling Transport on the Nanoscale Rev. Mod. Phys 2009, 81, 387-442
9. Magnasco, M. O. Forced Thermal Ratchets Phys. Rev. Lett. 1993, 71, 1477-1481
10. Bartussek, R.; Hänggi, P.; Kissner, J. G. Periodically Rocked Thermal Ratchets Europhys. Lett. 1994, 28, 459-464
11. Schreier, M.; Reimann, P.; Hänggi, P.; Pollak, E. Giant Enhancement of Diffusion and Particle Selection in Rocked Periodic Potentials Europhys. Lett. 1998, 44, 416-422
12. Lehmann, J.; Kohler, S.; Hänggi, P.; Nitzan, A. Molecular Wires Acting as Coherent Quantum Ratchets Phys. Rev. Lett. 2002, 88, 228305
13. Scheidl, S.; Vinokur, V. M. Quantum Brownian Motion in Ratchet Potentials Phys. Rev. B. 2002, 65, 195305
14. Schneider, W.; Seeger, K. Harmonic Mixing of Microwaves by Warm Electrons in Germanium Appl. Phys. Lett. 1966, 8, 133-135
15. Wonneberger, W.; Breymayer, H.-J. Asymptotics of Harmonic Microwave Mixing in a Sinusoidal Potential Z. Phys. B 1981, 43, 329-334
16. Breymayer, H.-J.; Risken, H.; Vollmer, H. D.; Wonneberger, W. Harmonic Mixing in a Cosine Potential for Large Damping and Arbitrary Field Strengths Appl. Phys. B: Laser Opt. 1982, 28, 335-339
17. Breymayer, H.-J. Harmonic Mixing in a Cosine Potential for Arbitrary Damping Appl. Phys. A: Mater. Sci. Process. 1984, 33, 1-7
18. Marchesoni, F. Harmonic Mixing Signal: Doubly Dithered Ring Laser Gyroscope Phys. Lett A 1986, 119, 221-224
19. Goychuk, I.; Hänggi, P. Quantum Rectifiers from Harmonic Mixing Europhys. Lett. 1998, 43, 503-509
20. Linke, H.; Sheng, W.; Löfgren, A.; Hongqi, Xu.; Omling, P.; Lindelof, P. E. A Quantum Dot Ratchet: Experiment and Theory Europhys. Lett. 1998, 44, 341-347
21. Linke, H.; Humphrey, T. E.; Löfgren, A.; Sushkov, A. O.; Newbury, R.; Taylor, R. P.; Omling, P. Experimental Tunneling Ratchets Science 1999, 286, 2314-2317
22. Linke, H. Ratchets and Brownian Motors: Basics, Experiments and Applications Appl, Phys. 2002, 75, 167-167
23. Majer, J. B.; Peguiron, J.; Grifoni, M.; Tusveld, M.; Mooij, J. E. Quantum Ratchet Effect for Vortices Phys. Rev. Lett. 2003, 90, 056802
24. Villegas, J. E.; Savel'ev, S.; Nori, F.; Gonzalez, E. M.; Anguita, J. V.; Garcia, R.; Vicent, J. L. A Superconducting Reversible Rectifier that Controls the Motion of Magnetic Flux Quanta Science 2003, 302, 1188-1191
25. Ustinov, A. V.; Coqui, C.; Kemp, A.; Zolotaryuk, Y.; Salerno, M. Ratchetlike Dynamics of Fluxons in Annular Josephson Junctions Driven by Biharmonic Microwave Fields Phys. Rev. Lett. 2004, 93, 087001
26. Shiavoni, M.; S-Palencia, L.; Renzoni, F.; Grynberg, G. Phase Control of Directed Diffusion in a Symmetric Optical Lattice Phys. Rev. Lett. 2003, 90, 094101
27. Gommers, R.; Bergamini, S.; Renzoni, F. Dissipation-Induced Symmetry Breaking in a Driven Optical Lattice Phys. Rev. Lett. 2005, 95, 073003
28. Salger, T.; Kling, S.; Hecking, T.; Geckeler, C.; Morales-Molina, L.; Weitz, M. Directed Transport of Atoms in a Hamiltonian Quantum Ratchet Science 2009, 326, 1241-1243
29. Astumian, R. D.; Derenyi, I. Fluctuation Driven Transport and Models of Molecular Motors and Pumps Eur. Biophys 1998, 27, 474-489
30. Nishiyama, M.; Higuchi, H.; Ishii, Y.; Taniguchi, Y.; Yanagida, T. Single Molecule Processes on the Stepwise Movement of ATP-Driven Molecular Motors BioSystems 2003, 71, 145-156
31. Kolomeisky, A. B.; Fisher, M. E. Molecular Motors; A Theorist's Perspective Annu. Rev. Phys. Chem. 2007, 58, 675-695
32. Flach, S.; Yevtushenko, O.; Zolotaryuk, Y. Directed Current Due to Broken Time-Space Symmetry Phys. Rev. Lett. 2000, 84, 2358-2361
33. Yevtushenko, O.; Flach, S.; Zolotaryuk, Y.; Ovchinnikov, A. A. Rectification of Current in AC-Driven Nonlinear Systems and Symmetry Properties of the Boltzmann Equation Europhys. Lett. 2001, 54, 141-147
34. Denisov, S.; Flach, S.; Ovchinnikov, A. A.; Yevtushenko, O.; Zolotaryuk, Y. Broken Space-Time Symmetries and Mechanisms of Rectification of AC Fields by Nonlinear (non)Adiabatic Response Phys. Rev. E 2002, 66, 041104
35. Reimann, P. Supersymmetric Ratchets Phys. Rev. Lett. 2001, 86, 4992-4995
36. Quintero, N. R.; Cuesta, J. A.; A-Nodarse, R. Symmetries Shape the Current in Ratchets Induced by a Biharmonic Driving Force Phys. Rev. E 2010, 81, 030102
37. Reimann, P.; Grifoni, M.; Hänggi, P. Quantum Ratchets Phys. Rev. Lett. 1997, 79, 10-13
38. Reimann, P.; Hänggi, P. Quantum Features of Brownian Motors and Stochastic Resonance Chaos. 1998, 8, 629-642
39. Goychuk, I.; Grifoni, M.; Hänggi, P. Nonadiabatic Quantum Brownian Rectifiers Phys. Rev. Lett. 1998, 81, 649-652
40. Goychuk, I.; Grifoni, M.; Hänggi, P. Nonadiabatic Quantum Brownian Rectifiers (Erratum) Phys. Rev. Lett. 1998, 81, 2837
41. Grifoni, M.; Ferreira, M. S.; Peguiron, J.; Majer, J. B. Quantum Ratchets with Few Bands below the Barrrier Phys. Rev. Lett. 2002, 89, 146801
42. Garcia-Palacios, J. L.; Zueco, D. The Caldeira-Leggett Quantum Master Equation in Wigner Phase Space: Continued-Fraction Solution and Application to Brownian Motion in Periodic Potentials J. Phys. A: Math. Gen. 2004, 37, 10735-10770
43. Maier, S. A.; Ankerhold, J. Low-Temperature Quantum Fluctuations in Overdamped Ratchets Phys. Rev. E 2010, 82, 021104
44. Zhan, F.; Denisov, S.; Ponomarev, A.; Hänggi, P. Quantum Ratchet Transport with Minimal Dispersion Rate Phys. Rev. A 2011, 84, 043617
45. Denisov, S.; Morales-Molina, L.; Flach, S.; Hänggi, P. Periodically Driven Quantum Ratchets: Symmetries and Resonances Phys. Rev. A 2007, 75, 063424
46. Denisov, S.; Kohler, S.; Hänggi, P. Underdamped Quantum Ratchets Europhys. Lett. 2009, 85, 40003
47. Rohling, N.; Grossmann, F. Optimization of Electron Pumping by Harmonic Mixing Phys. Rev. B 2011, 83, 205310
48. Denisov, S.; Hänggi, P.; Mateos, J. L. AC-Driven Brownian Motors: A Fokker-Planck Treatment Am. J. Phys. 2009, 77, 602-606
49. Machura, L.; Luczka, J. Transport Driven by Biharmonic Forces: Impact of Correlated Thermal Noise Phys. Rev. E 2010, 82, 031133
50. Kohler, S.; Dittrich, T.; Hänggi, P. Floquet-Markovian Description of Parametrically Driven, Dissipative Harmonic Quantum Oscillator Phys. Rev. E 1997, 85, 300-313
51. Caldeira, A. O.; Leggett, A. J. Path Integral Approach to Quantum Brownian Motion Physica A 1983, 121, 587-616
52. Chang, L.-D.; Waxman, D. Quantum Fokker-Planck Equation J. Phys. C 1985, 18, 5873-5879
53. Coffey, W. T.; Kalmykov, Yu. P.; Titov, S. V.; Mulligan, B. P. Semiclassical Master Equation in Wigners Phase Space Applied to Brownian Motion in a Periodic Potential Phys. Rev. E 2007, 75, 041117
54. Coffey, W. T.; Kalmykov, Yu. P.; Titov, S. V.; Mulligan, B. P. Wigner Function Approach to the Quantum Brownian Motion of a Particle in a Potential Phys. Chem. Chem. Phys. 2007, 9, 3361-3382
55. Shit, A.; Chattopadhyay, S.; Chaudhuri, J. R. Towards an Understanding of Escape Rate and State Dependent Diffusion for a Quantum Dissipative System Chem. Phys. 2011, 386, 56-72
56. Tanimura, Y. Stochastic Liouville, Langevin, Fokker-Planck, and Master Equation Approaches to Quantum Dissipative Systems J. Phys. Soc. Jpn. 2006, 75, 082001
57. Tanimura, Y.; Wolynes, P. G. Quantum and Classical Fokker-Planck Equations for a Gaussian-Markovian Noise Bath Phys. Rev. A 1991, 43, 4131-4142
58. Tanimura, Y.; Wolynes, P. G. The Interplay of Tunneling, Resonance, and Dissipation in Quantum Barrier Crossing: A Numerical Study J. Chem. Phys. 1992, 96, 8485-8496
59. Tanimura, Y.; Steffen, T. Two Dimensional Spectroscopy for Harmonic Vibrational Modes with Nonlinear System-Bath Interactions: II. Gaussian-Markovian Case J. Phys. Soc. Jpn. 2000, 69, 4095-4106
60. Kato, T.; Tanimura, Y. Vibrational Spectroscopy of a Harmonic Oscillator System Nonlinearly Coupled to a Heat Bath J. Chem. Phys. 2002, 117, 6221-6234
61. Sakurai, A.; Tanimura, Y. Does â., Play a Role in Multidimensional Spectroscopy? Reduced Hierarchy Equations of Motion Approach to Molecular Vibrations J. Phys. Chem. A 2011, 115, 4009-4022
62. Sakurai, A.; Tanimura, Y. An Approach to Quantum Transport Based on Reduced Hierarchy Equations of Motion: Application to a Resonant Tunneling Diode J. Phys. Soc. Jpn. 2013, 82, 033707
63. Sakurai, A.; Tanimura, Y. Self-Excited Current Oscillations in a Resonant Tunneling Diode Described by a Model Based on the Caldeira-Leggett Hamiltonian. 2013, arXiv:1304.5596. arXiv.org e-Print archive. http://arxiv.org/abs/1304. 5596 (accessed April 20, 2013).
64. Tanimura, Y.; Kubo, R. Time Evolution of a Quantum System in Contact with a Nearly Gaussian-Markoffian Noise Bath J. Phys. Soc. Jpn. 1989, 58, 101-114
65. Ishizaki, A.; Fleming, G. R. Theoretical Examination of Quantum Coherence in a Photosynthetic System at Physiological Temperature Proc. Natl. Acad. Sci. U.S.A. 2009, 106, 17255-17260
66. Chen, L.; Zheng, R.; Jing, Y.; Shi, Q. Simulation of the Two-Dimensional Electronic Spectra of the Fenna-Matthews-Olson Complex using the Hierarchical Equations of Motion Method J. Phys. Chem. 2011, 134, 194508
67. Kreisbeck, C.; Kramer, T. Long-Lived Electronic Coherence in Dissipative Exciton Dynamics of Light-Harvesting Complexes J. Phys. Chem. Lett. 2012, 3, 2828-2833
68. Strümpfer, J.; Schulten, K. Excited State Dynamics in Photosynthetic Reaction Center and Light Harvesting Complex 1 J. Chem. Phys. 2012, 137, 065101
69. Dijkstra, A. G.; Tanimura, Y. Correlated Fluctuations in the Exciton Dynamics and Spectroscopy of DNA New J. Phys. 2010, 12, 055005
70. Xu, R.-X.; Chen, Y.; Cui, P.; Ke, H. W.; Yan, Y.-J. The Quantum Solvation, Adiabatic versus Nonadiabatic, and Markovian versus Non-Markovian Nature of Electron-Transfer Rate Processes J. Phys. Chem. A 2007, 111, 9618-9626
71. Tanaka, M.; Tanimura, Y. Quantum Dissipative Dynamics of Electron Transfer Reaction System: Nonperturbative Hierarchy Equation Approach J. Phys. Soc. Jpn. 2009, 78, 073802
72. Tanaka, M.; Tanimura, Y. Multistate Electron Transfer Dynamics in the Condensed Phase: Exact Calculations from the Reduced Hierarchy Equations of Motion Approach J. Chem. Phys. 2010, 132, 214502
73. Tanimura, Y. Reduced Hierarchy Equations of Motion Approach with Drude Plus Brownian Spectral Distribution: Probing Electron Transfer Processes by Means of Two-Dimensional Correlation Spectroscopy J. Chem. Phys. 2012, 137, 22A550
74. Dijkstra, A. G.; Tanimura, Y. Non-Markovian Entanglement Dynamics in the Presence of System-Bath Coherence Phys. Rev. Lett. 2010, 104, 250401
75. Yin, X.; Ma, J.; Wang, X.; Nori, F. Spin Squeezing under non-Markovian Channels by the Hierarchy Equation Method Phys. Rev. A 2012, 86, 012308
76. Frensley, W. R. Boundary Conditions for Open Quantum Systems Driven far from Equilibrium Rev. Mod. Phys. 1990, 62, 745-791
77. Caldeira, A. O.; Leggett, A. J. Quantum Tunneling in a Dissipative System Ann. Phys. 1983, 149, 374-456
78. Grabert, H.; Schramm, P.; Ingold, G. L. Quantum Brownian Motion: The Functional Integral Approach Phys. Rep. 1988, 168, 115-207
79. Kubo, R.; Toda, M.; Hashitsume, N. Statistical Physics; Springer-Verlag: Berlin, 1985; Vol. 2.
80. Tanimura, Y. Nonperturbative Expansion Method for a Quantum System Coupled to a Harmonic-Oscillator Bath Phys. Rev. A 1990, 41, 6676-6687
81. Ishizaki, A.; Tanimura, Y. Quantum Dynamics of a System Strongly Coupled to a Low Temperature Colored Noise Bath: Reduced Hierarchy Equations Approach J. Phys. Soc. Jpn. 2005, 74, 3131-3134
82. Carmichael, H. J. Statistical Methods in Quantum Optics 1; Springer: Berlin, 1999.
83. Hänggi, P.; Grabert, H.; Ingold, G. L.; Weiss, U. Quantum Theory of Activated Events in Presence of Long-Time Memory Phys. Rev. Lett. 1985, 55, 761-764
84. Hillery, M.; O'Connell, R. F.; Scully, M. O.; Wigner, E. P. Distribution Functions in Physics: Fundamentals Phys. Rep. 1984, 106, 121-167
85. Griff, U.; Grabert, H.; Hänggi, P.; Riseborough, P. S. Possibility of Quantum Effects Reducing the Rate of Escape from a Metastable Well Phys. Rev. B 1989, 40, 7295-7297
86. Shushin, A. I.; Pollak, E. Quantum and Classical Aspects of Activated Surface Diffusion J. Chem. Phys. 2003, 119, 10941-10952
87. Shi, Q.; Chen, L. P.; Nan, G. J.; Xu, R. X.; Yan, Y.-J. Efficient Hierarchical Liouville Space Propagator to Quantum Dissipative Dynamics J. Phys. Chem. 2009, 130, 084105
88. Hu, J.; Xu, R. X.; Yan, Y.-J. Communication: Padé Spectrum Decomposition of Fermi Function and Bose Function J. Chem. Phys. 2010, 133, 101106
89. Tian, B. L.; Ding, J. J.; Xu, R. X.; Yan, Y.-J. Biexponential Theory of Drude Dissipation via Hierarchical Quantum Master Equation J. Chem. Phys. 2010, 133, 114112
90. Zhu, J.; Kais, S.; Rebentros, P.; Aspuru-Guzik, A. Modified Scaled Hierarchical Equation of Motion Approach for the Study of Quantum Coherence in Photosynthetic Complex J. Phys. Chem. B 2011, 115, 1531-1537
91. Kreisbeck, C.; Kramer, T.; Rodriguez, M.; Hein, B. High-Performance Solution of Hierarchical Equations of Motion for Studying Energy Transfer in Light-Harvesting Complexes J. Chem. Theory Comput. 2011, 7, 2166-2174
92. Strümpfer, J.; Schulten, K. Open Quantum Dynamics Calculations with the Hierarchy Equations of Motion on Parallel Computers J. Chem. Theory Comput. 2012, 8, 2808-2816
93. Meyer, H.-D.; Manthe, U.; Cederbaum, L. S. The Multi-Configurational Time-Dependent Hartree Approach Chem. Phys. Lett. 1990, 165, 73-78
94. Wang, H.; Thoss, M. Multilayer Formulation of the Multiconfiguration Time-Dependent Hartree Theory J. Chem. Phys. 2003, 119, 1580111
95. Burghardt, I.; Worth, G. A. Multimode Quantum Dynamics using Gaussian Wavepackets: The Gaussian-Based Multiconfiguration Time-Dependent Hartree (G-MCTDH) Method Applied to the Absorption Spectrum of Pyrazine J. Chem. Phys. 2008, 129, 174104