From stochastic spin chains to quantum Kardar-Parisi-Zhang dynamics
- URL: http://arxiv.org/abs/2001.04278v1
- Date: Mon, 13 Jan 2020 14:30:36 GMT
- Title: From stochastic spin chains to quantum Kardar-Parisi-Zhang dynamics
- Authors: Tony Jin, Alexandre Krajenbrink and Denis Bernard
- Abstract summary: We introduce the asymmetric extension of the Quantum Symmetric Simple Exclusion Process.
We show that the time-integrated current of fermions defines a height field which exhibits a quantum non-linear dynamics.
- Score: 68.8204255655161
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We introduce the asymmetric extension of the Quantum Symmetric Simple
Exclusion Process which is a stochastic model of fermions on a lattice hopping
with random amplitudes. In this setting, we analytically show that the
time-integrated current of fermions defines a height field which exhibits a
quantum non-linear stochastic Kardar-Parisi-Zhang dynamics. Similarly to
classical simple exclusion processes, we further introduce the discrete
Cole-Hopf (or G\"artner) transform of the height field which satisfies a
quantum version of the Stochastic Heat Equation. Finally, we investigate the
limit of the height field theory in the continuum under the celebrated
Kardar-Parisi-Zhang scaling and the regime of almost-commuting quantum noise.
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