`Muhammad Ali effect' and incoherent destruction of Wannier-Stark localization in a stochastic field

Abstract

We calculate an exact expression for the probability propagator for a noisy electric field driven tight-binding lattice. The noise considered is a two-level jump process or a telegraph process (TP) which jumps randomly between two values $\pm \mu$. In the absence of a static field and in the limit of zero jump rate of the noisy field we find that the dynamics yield Bloch oscillations with frequency $\mu$, while with an additional static field $\epsilon$ we find oscillatory motion with a superposition of frequencies $(\epsilon \pm \mu )$. On the other hand, when the jump rate is `rapid', and in the absence of a static field, the stochastic field averages to zero if the two states of the TP are equally probable `a-priori'. In that case, we see a delocalization effect. The intimate relationship between the rapid relaxation case and the zero field case is a manifestation of what we call the `Muhammad Ali effect'. It is interesting to note that even for zero static field and rapid relaxation, Bloch oscillations ensue if there is a bias $\delta p$ in the probabilities of the two levels. Remarkably, the Wannier-Stark localization caused by an additional static field is destroyed if the latter is tuned to be exactly equal and opposite to the average stochastic field $\mu \delta p$. This is an example of \emph{incoherent} destruction of Wannier-Stark localization.

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• Stability of electric-field-driven MBL in an interacting long range hopping model
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• Controlling nonergodicity in quantum many-body systems by reinforcement learning
• Dephasing-assisted transport in a tight-binding chain with a linear potential
• Protecting coherence from the environment via Stark many-body localization in a Quantum-Dot Simulator
• Noise Induced Universal Diffusive Transport in Fermionic Chains
• Photonic Simulation of Localization Phenomena Using Boson Sampling
• Quantum transport under oscillatory drive with disordered amplitude