Exact dynamics of driven Brownian oscillators.

Exact quantum master equation for a driven Brownian oscillator system is constructed via a Wigner phase-space Gaussian wave packet approach. The interplay between external field and dissipation leads to this system an effective field correction that enhances the polarization. This cooperative property is resulted from an effective bath response to the external field applied on the system. It is important in the low-frequency driving and intermediate bath memory region. We demonstrate this non-Markovian effect on the linear response and nonlinear dynamics and analyze the results together with analytical asymptotic expressions.

[1]  Yijing Yan,et al.  Dynamic Coulomb blockade in single-lead quantum dots , 2008, 0807.4282.

[2]  A. Ishizaki,et al.  Nonperturbative non-Markovian quantum master equation: Validity and limitation to calculate nonlinear response functions , 2008 .

[3]  J. Shao,et al.  Solving the spin-boson model of strong dissipation with flexible random-deterministic scheme. , 2008, The Journal of chemical physics.

[4]  Yijing Yan,et al.  Exact dynamics of dissipative electronic systems and quantum transport: Hierarchical equations of motion approach. , 2007, The Journal of chemical physics.

[5]  T. Yu,et al.  Exact master equation and quantum decoherence of two coupled harmonic oscillators in a general environment. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  R. Xu,et al.  Dynamics of quantum dissipation systems interacting with bosonic canonical bath: hierarchical equations of motion approach. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  Y. Tanimura.  Stochastic Liouville, Langevin, Fokker–Planck, and Master Equation Approaches to Quantum Dissipative Systems , 2006 .

[8]  A. Nitzan.  Chemical Dynamics in Condensed Phases , 2006 .

[9]  H. Grabert.  Can quantum Brownian motion be Markovian , 2006 .

[10]  A. Ishizaki,et al.  Quantum Dynamics of System Strongly Coupled to Low-Temperature Colored Noise Bath: Reduced Hierarchy Equations Approach , 2005 .

[11]  P. Cui,et al.  Correlation and response functions with non-Markovian dissipation: a reduced Liouville-space theory. , 2005, The Journal of chemical physics.

[12]  J. Ankerhold,et al.  Quantum Brownian motion with large friction. , 2004, Chaos.

[13]  P. Hänggi,et al.  Fundamental aspects of quantum Brownian motion. , 2004, Chaos.

[14]  Yun-An Yan,et al.  Hierarchical approach based on stochastic decoupling to dissipative systems , 2004 .

[15]  P. Cui,et al.  Exact quantum master equation via the calculus on path integrals. , 2004, The Journal of chemical physics.

[16]  Herschel Rabitz,et al.  Optimal control of quantum non-Markovian dissipation: reduced Liouville-space theory. , 2004, The Journal of chemical physics.

[17]  T. Yu,et al.  Convolutionless Non-Markovian master equations and quantum trajectories: Brownian motion , 2003, quant-ph/0312103.

[18]  G. W. Ford,et al.  Exact solution of the Hu-Paz-Zhang master equation , 2001, quant-ph/0301053.

[19]  W. Zurek.  Decoherence, einselection, and the quantum origins of the classical , 2001, quant-ph/0105127.

[20]  Yijing Yan.  Quantum Fokker-Planck theory in a non-Gaussian-Markovian medium , 1998 .

[21]  P. Hänggi,et al.  Driven quantum tunneling , 1998 .

[22]  P. Hānggi,et al.  Floquet-Markovian description of the parametrically driven, dissipative harmonic quantum oscillator , 1998, quant-ph/9809088.

[23]  P. Hänggi,et al.  Quantum Transport and Dissipation , 1998 .

[24]  Jianshu Cao,et al.  A phase-space study of Bloch–Redfield theory , 1997 .

[25]  H. Grabert,et al.  Exact time evolution and master equations for the damped harmonic oscillator , 1996, physics/9610001.

[26]  Halliwell,et al.  Alternative derivation of the Hu-Paz-Zhang master equation of quantum Brownian motion. , 1996, Physical review. D, Particles and fields.

[27]  Christine Zerbe,et al.  Brownian parametric quantum oscillator with dissipation. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[28]  S. Mukamel.  Principles of Nonlinear Optical Spectroscopy , 1995 .

[29]  P. Hänggi,et al.  Driven tunnelling with dissipation , 1993 .

[30]  U. Weiss.  Quantum Dissipative Systems , 1993 .

[31]  Paz,et al.  Quantum Brownian motion in a general environment: Exact master equation with nonlocal dissipation and colored noise. , 1992, Physical review. D, Particles and fields.

[32]  Graham,et al.  Dynamical localization in the microwave interaction of Rydberg atoms: The influence of noise. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[33]  Zurek,et al.  Reduction of a wave packet in quantum Brownian motion. , 1989, Physical review. D, Particles and fields.

[34]  S. Mukamel,et al.  Electronic dephasing, vibrational relaxation, and solvent friction in molecular nonlinear optical line shapes , 1988 .

[35]  Gert-Ludwig Ingold,et al.  Quantum Brownian motion: The functional integral approach , 1988 .

[36]  Reibold,et al.  Strong damping and low-temperature anomalies for the harmonic oscillator. , 1985, Physical review. A, General physics.

[37]  G. Agarwal.  Brownian Motion of a Quantum Oscillator , 1971 .

[38]  G. S. Agarwal,et al.  Master Equations in Phase-Space Formulation of Quantum Optics , 1969 .

[39]  R. Feynman,et al.  The Theory of a general quantum system interacting with a linear dissipative system , 1963 .

[40]  YiJing Yan,et al.  Quantum mechanics of dissipative systems. , 2005, Annual review of physical chemistry.

[41]  Claus Klingshirn,et al.  Semiconductor Optics , 1995 .