Effects of quantum pair creation and annihilation on a classical exclusion process: the transverse XY model with TASEP

We investigate how particle pair creation and annihilation, within the quantum transverse XY model, affects the non-equilibrium steady state (NESS) and Liouvillian gap of the stochastic totally asymmetric exclusion process. By utilising operator quantization we formulate a perturbative description o...

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Bibliographic Details
Published in:New journal of physics 2022-02, Vol.24 (2), p.23024
Main Authors: Kavanagh, K, Dooley, S, Slingerland, J K, Kells, G
Format: Article
Language:English
Subjects:
Anisotropy
ASEP
Lindblad
Liouvillian gap
Mathematical models
non-equilibrium steady state
Parameters
Phase transitions
Physics
XY model
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Summary:We investigate how particle pair creation and annihilation, within the quantum transverse XY model, affects the non-equilibrium steady state (NESS) and Liouvillian gap of the stochastic totally asymmetric exclusion process. By utilising operator quantization we formulate a perturbative description of the NESS. Furthermore, we estimate the Liouvillian gap by exploiting a Majorana canonical basis as the basis of super-operators. In this manner we show that the Liouvillian gap can remain finite in the thermodynamic limit provided the XY model anisotropy parameter remains non-zero. Additionally, we show that the character of the gap with respect to the anisotropy parameter differs depending on the phase of the XY model. The change of character corresponds to the quantum phase transition of the XY model.
ISSN:1367-2630
1367-2630
DOI:10.1088/1367-2630/ac4ee1