Two-particle quantum correlations in stochastically-coupled networks

Abstract

Quantum walks in dynamically-disordered networks have become an invaluable tool for understanding the physics of open quantum systems. Although much work has been carried out considering networks affected by diagonal disorder, it is of fundamental importance to study the effects of fluctuating couplings. This is particularly relevant in materials science models, where the interaction forces may change depending on the species of the atoms being linked. In this work, we make use of stochastic calculus to derive a master equation for the dynamics of one and two non-interacting correlated particles in tight-binding networks affected by off-diagonal dynamical disorder. We show that the presence of noise in the couplings of a quantum network creates a pure-dephasing-like process that destroys all coherences in the single-particle Hilbert subspace. Moreover, we show that when two or more correlated particles propagate in the network, coherences accounting for particle indistinguishability are robust against the impact of off-diagonal noise, thus showing that it is possible, in principle, to find specific conditions for which many indistinguishable particles can traverse stochastically-coupled networks without losing their ability to interfere.

Universal equilibration dynamics of the Sachdev-Ye-Kitaev model

“…The Novikov-Furutsu theorem has been used extensively in the literature for the study of systems with noise of short correlation time [91][92][93], and equations equivalent to those derived in Sec. IV have been obtained to second order in perturbative noise strength [94-96, 128, 129].…”

“…That property enables us to tap into the vast literature employing the Novikov-Furutsu theorem in the context of noise with finite correlation time (see, e.g., Refs. [91,[94][95][96]).…”

“…Here, we present an alternative, mathematically elegant route to Gaussian disorder averaging based on the Novikov-Furutsu theorem. In earlier works, this theorem has been applied in the context of averaging noise with finite correlation times in, for instance, quantum walks subjected to pure dephasing noise [91,92], stochastic Schrödinger equations [93], or proposals for simulating dissipation via noisy unitary dynamics [94][95][96][97]. We exploit that framework by formally promoting the quenched disorder to noise with infinite correlation time, permitting a fruitful application to a generic system with Gaussian disorder.…”

Quantum transport in non-Markovian dynamically-disordered photonic lattices

“…Looking forward, and following the ideas of Refs. [35,58], it would be interesting to go beyond the single excitation regime and derive the corresponding master equation of, for example, two correlated particles propagating over these stochastic networks affected by non-Markovian noise. The time derivative of the density matrix σ nm (t) ≡ ψ n ψ * m is given as…”