Effective Hamiltonian theory: An approximation to the equilibrium state of open quantum systems

被引：0
作者：
Anto-Sztrikacs N. [1 ]
Min B. [1 ]
Brenes M. [1 ]
Segal D. [1 ,2 ]
机构：
[1] Department of Physics, Centre for Quantum Information and Quantum Control, University of Toronto, 60 Saint George St., Toronto, M5S 1A7, ON
[2] Department of Chemistry, University of Toronto, 80 Saint George St., Toronto, M5S 3H6, ON
来源：
Physical Review B | 2023年 / 108卷 / 11期
基金：
加拿大创新基金会; 加拿大自然科学与工程研究理事会;
关键词：
Polarons - Quantum optics;
D O I：
10.1103/PhysRevB.108.115437
中图分类号：
学科分类号：
摘要：
We extend and benchmark the recently developed Effective-Hamiltonian (EFFH) method [PRX Quantum 4, 020307 (2023)2691-339910.1103/PRXQuantum.4.020307] as an approximation to the equilibrium state ("mean-force Gibbs state") of a quantum system at strong coupling to a thermal bath. The EFFH method is an approximate framework. Through a combination of the reaction-coordinate mapping, a polaron transformation, and a controlled truncation, it imprints the system-bath coupling parameters into the system's Hamiltonian. First, we develop a variational EFFH technique. In this method, the system's parameters are renormalized by both the system-bath coupling parameters (as in the original EFFH approach) and bath temperature. Second, adopting the generalized spin-boson model, we benchmark the equilibrium state from the EFFH treatment against numerically exact simulations and demonstrate a good agreement for both polarization and coherences using the Brownian spectral function. Third, we contrast the (normal and variational) EFFH approach with the familiar (normal and variational) polaron treatment. We show that the two methods predict a similar structure for the equilibrium state, albeit the EFFH approach offers the advantage of simpler calculations and closed-form analytical results. Altogether, we argue that for temperatures comparable to the system's frequencies, the EFFH methodology provides a good approximation for the mean-force Gibbs state in the full range of system-bath coupling, from ultraweak to ultrastrong. © 2023 American Physical Society.
引用
收藏
相关论文
共 93 条
[1]  
Binder F., Correa L. A., Gogolin C., Anders J., Adesso G., Thermodynamics in the Quantum Regime: Fundamental Aspects and New Directions, (2018)
[2]  
Segal D., Nitzan A., Spin-Boson Thermal Rectifier, Phys. Rev. Lett, 94, (2005)
[3]  
Segal D., Heat flow in nonlinear molecular junctions: Master equation analysis, Phys. Rev. B, 73, (2006)
[4]  
Friedman H. M., Agarwalla B. K., Segal D., Quantum energy exchange and refrigeration: A full-counting statistics approach, New J. Phys, 20, (2018)
[5]  
He D., Thingna J., Cao J., Interfacial thermal transport with strong system-bath coupling: A phonon delocalization effect, Phys. Rev. B, 97, (2018)
[6]  
Wang C., Chen X.-M., Sun K.-W., Ren J., Heat amplification and negative differential thermal conductance in a strongly coupled nonequilibrium spin-boson system, Phys. Rev. A, 97, (2018)
[7]  
Strasberg P., Schaller G., Lambert N., Brandes T., Nonequilibrium thermodynamics in the strong coupling and non-Markovian regime based on a reaction coordinate mapping, New J. Phys, 18, (2016)
[8]  
Newman D., Mintert F., Nazir A., Performance of a quantum heat engine at strong reservoir coupling, Phys. Rev. E, 95, (2017)
[9]  
Perarnau-Llobet M., Wilming H., Riera A., Gallego R., Eisert J., Strong Coupling Corrections in Quantum Thermodynamics, Phys. Rev. Lett, 120, (2018)
[10]  
Mu A., Agarwalla B. K., Schaller G., Segal D., Qubit absorption refrigerator at strong coupling, New J. Phys, 19, (2017)
12345678910