Damping of Bloch oscillations: Variational solutions of the Boltzmann equation beyond linear response

Abstract

Variational solutions of the Boltzmann equation usually rely on the concept of linear response. We extend the variational approach for tight-binding models at high entropies to a regime far beyond linear response. We analyze both weakly interacting fermions and incoherent bosons on a lattice. We consider a case where the particles are driven by a constant force, leading to the well-known Bloch oscillations, and we consider interactions that are weak enough not to overdamp these oscillations. This regime is computationally demanding and relevant for ultracold atoms in optical lattices. We derive a simple theory in terms of coupled dynamic equations for the particle density, energy density, current and heat current, allowing for analytic solutions. As an application, we identify damping coefficients for Bloch oscillations in the Hubbard model at weak interactions and compute them for a one-dimensional toy model. We also approximately solve the long-time dynamics of a weakly interacting, strongly Bloch-oscillating cloud of fermionic particles in a tilted lattice, leading to a subdiffusive scaling exponent.

arXiv commentPublished version, 13 pages, 7 figures

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Cited by in corpus (5)

• Ultrafast Dynamics of Strongly Correlated Fermions -- Nonequilibrium Green Functions and Selfenergy Approximations
• Two bosonic quantum walkers in one-dimensional optical lattices
• Many-body quantum dynamics of initially trapped systems due to a Stark potential --- thermalization vs. Bloch oscillations
• Revealing Hund's multiplets in Mott insulators under strong electric fields
• Undamped Bloch Oscillations in the $U\to \infty$ one-dimensional Hubbard model