Modelling the ultra-strongly coupled spin-boson model with unphysical modes
Artikel i vetenskaplig tidskrift, 2019

A quantum system weakly coupled to a zero-temperature environment will relax, via spontaneous emission, to its ground-state. However, when the coupling to the environment is ultra-strong the ground-state is expected to become dressed with virtual excitations. This regime is difficult to capture with some traditional methods because of the explosion in the number of Matsubara frequencies, i.e., exponential terms in the free-bath correlation function. To access this regime we generalize both the hierarchical equations of motion and pseudomode methods, taking into account this explosion using only a biexponential fitting function. We compare these methods to the reaction coordinate mapping, which helps show how these sometimes neglected Matsubara terms are important to regulate detailed balance and prevent the unphysical emission of virtual excitations. For the pseudomode method, we present a general proof of validity for the use of superficially unphysical Matsubara-modes, which mirror the mathematical essence of the Matsubara frequencies.


Neill Lambert


Shahnawaz Ahmed

Chalmers, Mikroteknologi och nanovetenskap (MC2), Tillämpad kvantfysik


Mauro Cirio

China Academy of Engineering Physics

Franco Nori

University of Michigan


Nature Communications

2041-1723 (ISSN)

Vol. 10 1 3721


Atom- och molekylfysik och optik

Annan fysik

Teoretisk kemi



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