Abstract
In this review we give a comprehensive account on the dissipaton equation of motion (DEOM) approach to quantum mechanics of open systems. This approach provides a statistical quasi-particle (dissipaton) picture for the environment, as it participates in the correlated system-and-bath dynamics. The underlying dissipaton algebra is de facto established via a close comparison with the celebrated hierarchical equations of motion formalism that is rooted at the Feynman-Vernon influence functional path integral formalism. As a quasi-particle generalization, DEOM identifies unambiguously the physical meanings of all involving dynamical variables as many-dissipaton configurations. It addresses the dynamics of not only systems but also hybridizing bath degrees of freedom. We demonstrate these features of DEOM via its real-time evaluation of the Fano interference of an analytically solvable model system, with the highlight that the statistical quasi-particle picture is ubiquitous, implied even in those commonly used quantum master equations.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Weiss U. Quantum Dissipative Systems. Series in Modern Condensed Matter Physics, Vol. 13. Singapore: World Scientific, 2008, 3rd ed.
Kleinert H. Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets. Singapore: World Scientific, 5th edition, 2009.
Feynman RP, Vernon, Jr. FL. The theory of a general quantum system interacting with a linear dissipative system. Ann Phys, 1963, 24: 118–173
Yan YJ, Shuang F, Xu RX, Cheng JX, Li XQ, Yang C, Zhang HY. Unified approach to the Bloch-Redfield theory and quantum Fokker-Planck equations. J Chem Phys, 2000, 113: 2068–2078
Yan YJ, Xu RX. Quantum mechanics of dissipative systems. Annu Rev Phys Chem, 2005, 56: 187–219
Tanimura Y. Nonperturbative expansion method for a quantum system coupled to a harmonic-oscillator bath. Phys Rev A, 1990, 41: 6676–6687
Tanimura Y. Stochastic Liouville, Langevin, Fokker-Planck, and master equation approaches to quantum dissipative systems. J Phys Soc Jpn, 2006, 75: 082001
Xu RX, Cui P, Li XQ, Mo Y, Yan YJ. Exact quantum master equation via the calculus on path integrals. J Chem Phys, 2005, 122: 041103
Xu RX, Yan YJ. Dynamics of quantum dissipation systems interacting with bosonic canonical bath: Hierarchical equations of motion approach, Phys Rev E, 2007, 75: 031107
Ding JJ, Xu RX, Yan YJ. Optimizing hierarchical equations of motion for quantum dissipation and quantifying quantum bath effects on quantum transfer mechanisms. J Chem Phys, 2012, 136: 224103
Jin JS, Zheng X, Yan YJ. Exact dynamics of dissipative electronic systems and quantum transport: Hierarchical equations of motion approach. J Chem Phys, 2008, 128: 234703
Shi Q, Chen LP, Nan GJ, Xu RX, Yan YJ. Electron transfer dynamics: Zusman equation versus exact theory. J Chem Phys, 2009, 130: 164518
Zhu KB, Xu RX, Zhang HY, Hu J, Yan YJ. Hierarchical dynamics of correlated system-environment coherence and optical spectroscopy. J Phys Chem B, 2011, 115: 5678–5684
Shao JS. Decoupling quantum dissipation interaction via stochastic fields. J Chem Phys, 2004, 120: 5053–5056
Yan YA, Yang F, Liu Y, Shao JS. Hierarchical approach based on stochastic decoupling to dissipative systems. Chem Phys Lett, 2004, 395: 216–221
Yan YJ. Theory of open quantum systems with bath of electrons and phonons and spins: Many-dissipaton density matrixes approach. J Chem Phys, 2014, 140: 054105
Zhang HD, Xu RX, Zheng X, Yan YJ. Nonperturbative spin C boson and spin C spin dynamics and nonlinear Fano interferences: a unified dissipaton theory based study. J Chem Phys, 2015, 142: 024112
Fano U. Effects of configuration interaction on intensities and phase shifts. Phys Rev, 1961, 124: 1866–1878
Zhang Y, Tang TT, Girit C, Hao Z, Martin MC, Zettl A, Crommie MF, Shen YR, Wang F. Direct observation of a widely tunable bandgap in bilayer graphene. Nature, 2009, 459: 820–823
Tang TT, Zhang Y, Park CH, Geng B, Girit C, Hao Z, Martin MC, Zettl A, Crommie MF, Louie SG, Shen YR, Wang F. A tunable phononexciton Fano system in bilayer graphene. Nature Nanotech, 2010, 5: 32–36
Clerk AA, Devoret MH, Girvin SM, Marquardt F, Schoelkopf RJ. Introduction to quantum noise, measurement, and amplification. Rev Mod Phys, 2010, 82: 1155–1208
Jin JS, Wang SK, Zheng X, Yan YJ. Current noise spectra and mechanisms with dissipaton equation of motion theory. J Chem Phys, 2015, 142: 234108
Yang H, Luo G, Karnchanaphanurach P, Louie TM, Rech I, Cova S, Xun L, Xie XLS. Protein conformational dynamics probed by singlemolecule electron transfer. Science, 2003, 302: 262–266
Min W, Luo G, Cherayil BJ, Kou SC, Xie XLS. Observation of a power-Law memory kernel for fluctuations within a single protein molecule. Phys Rev Lett, 2005, 94: 198302
Ishizaki A, Tanimura Y. Quantum dynamics of system strongly coupled to low temperature colored noise bath: Reduced hierarchy equations approach. J Phys Soc Jpn, 2005, 74: 3131–3134
Xu RX, Tian BL, Xu J, Shi Q, Yan YJ. Hierarchical quantum master equation with semiclassical Drude dissipation. J Chem Phys, 2009, 131: 214111
Tian BL, Ding JJ, Xu RX, Yan YJ. Bi-exponential theory of Drude dissipation via hierarchical quantum master equation. J Chem Phys, 2010, 133: 114112
Ding JJ, Xu J, Hu J, Xu RX, Yan YJ. Optimized hierarchical equations of motion for Drude dissipation with applications to linear and nonlinear optical responses. J Chem Phys, 2011, 135: 164107
Hu J, Xu RX, Yan YJ. Padé spectrum decomposition of Fermi function and Bose function. J Chem Phys, 2010, 133: 101106
Hu J, Luo M, Jiang F, Xu RX, Yan YJ. Padé spectrum decompositions of quantum distribution functions and optimal hierarchial equations of motion construction for quantum open systems. J Chem Phys, 2011, 134: 244106
Miroshnichenko AE, Flach S, Kivshar YS. Fano resonances in nanoscale structures. Rev Mod Phys, 2010, 82: 2257–2298
Mukamel S. The Principles of Nonlinear Optical Spectroscopy. New York: Oxford University Press, 1995.
Yan YJ, Mukamel S. Electronic dephasing, vibrational relaxation, and solvent friction in molecular nonlinear optical lineshapes. J Chem Phys, 1988, 89: 5160–5176
Author information
Authors and Affiliations
Corresponding authors
Additional information
Dedicated to Professor Lemin Li on the occasion of his 80th birthday.
Rights and permissions
About this article
Cite this article
Xu, RX., Zhang, HD., Zheng, X. et al. Dissipaton equation of motion for system-and-bath interference dynamics. Sci. China Chem. 58, 1816–1824 (2015). https://doi.org/10.1007/s11426-015-5499-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11426-015-5499-2