# Graphene lattice-layer entanglement under non-Markovian phase noise. (arXiv:1801.00755v1 [cond-mat.mes-hall])

The evolution of single particle excitations of bilayer graphene under

effects of non-Markovian noise is described with focus on the decoherence

process of lattice-layer (LL) maximally entangled states. Once that the

noiseless dynamics of an arbitrary initial state is identified by the

correspondence between the tight-binding Hamiltonian for the AB-stacked bilayer

graphene and the Dirac equation -- which includes pseudovector- and tensor-like

field interactions -- the noisy environment is described as random fluctuations

on bias voltage and mass terms. The inclusion of noisy dynamics reproduces the

Ornstein-Uhlenbeck processes: a non-Markovian noise model with a well-defined

Markovian limit. Considering that an initial amount of entanglement shall be

dissipated by the noise, two profiles of dissipation are identified. On one

hand, for eigenstates of the noiseless Hamiltonian, deaths and revivals of

entanglement are identified along the oscillation pattern for long interaction

periods. On the other hand, for departing LL Werner and Cat states, the

entanglement is suppressed although, for both cases, some identified memory

effects compete with the pure noise-induced decoherence in order to preserve

the the overall profile of a given initial state.