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Mathematical Physics Seminar

Cristian Giardina - Duality and boundary-driven non-equilibrium systems

Cristian Giardina

Location:  Webinar
Date & time: Wednesday, 16 September 2020 at 10:45AM - 11:45AM

Cristian Giardina – Modena and Reggio Emilia University

Wednesday, September 16, 10:45AM


“Duality and boundary-driven non-equilibrium systems.”

As a follow up of the August 27th seminar by Jorge Kurchan, we further argue that "duality of Markov processes" can be identified as a key tool in the analysis of non-equilibrium statistical mechanics systems. 

We do this by discussing examples in the class of boundary-driven processes, those possessing a Lie symmetry group, that can be analyzed via "duality technique". 

In such context, duality transforms the reservoirs to absorbing boundaries, thus reducing the computation of correlation functions to that of harmonic functions. A general by-product of duality, is the existence of a direct mapping (a conjugation) between the generator of the non-equilibrium process and the generator of the associated reversible equilibrium process.

In case the process is furthermore integrable, one can compute this conjugation explicitly.

The seminar will be self-contained and will present results from:

R. Frassek, C. Giardinà, J.Kurchan, 

[1] Non-compact quantum spin chains as integrable stochastic particle processes,  arXiv:1904.01048

[2] Duality and hidden equilibrium in transport models, arXiv:2004.12796

[3] Duality in quantum transport model, arXiv:2008.03476

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