Dynamics of noisy quantum systems in the Heisenberg picture: application to the stability of fractional charge

Abstract

Based on the Heisenberg-picture analog of the master equation, we develop a method for computing the exact time dependence of noise-averaged observables for general noninteracting fermionic systems with noisy fluctuations. Upon noise averaging, these fluctuations generate effective interactions, limiting analytical approaches. While the short-time dynamics can be studied with Langevin-type numerical simulations, the long-time limit is not amenable to such simulations. Our results provide access to this long-time limit. As a simple example, we examine the fate of the fractional charge in cold-atom emulations of polyacetylene after stochastic driving. We find that in a quantum quench to a fluctuating hopping Hamiltonian, the fractional charge remains robust for hopping between different sublattices, while it becomes unstable in the presence of noisy hopping on the same sublattice.

7 pages, 3 figures (to appear in PRA)

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• Anti-Kibble-Zurek behavior of a noisy transverse-field XY chain and its quantum simulation with two-level systems
• Optimal diabatic dynamics of Majorana-based quantum gates
• Optimal noise-canceling shortcuts to adiabaticity: application to noisy Majorana-based gates
• Exact dynamics of quantum dissipative $XX$ models: Wannier-Stark localization in the fragmented operator space
• Duality between open systems and closed bilayer systems: Thermofield double states as quantum many-body scars
• Engineering quasi-steady-state correlations in uncorrelated thermal states using stochastic driving