Dynamics and Transport Relaxation of a Large Acoustic Polaron in One Dimension.

V. Meden, J. Fricke, C. Wöhler +1 more

Rupert L. Frank, Benjamin Schlein

H.-B. Schüttler, Theodore D. Holstein

The transport dynamics of a large polaron has been studied in a one-dimensional system whose underlying vibrational spectrum is acoustic in character. Such a polaron moves as a heavy quasiparticle with transport relaxation time, $\ensuremath{\tau}$, determined mainly by collisions with thermally ambient phonons. Concrete results show that $\ensuremath{\tau}$ decreases monotonically with increasing temperature, in sharp contrast to the previously treated problem of a large polaron in a one-dimensional Einstein lattice.

Srijan Bhattacharyya, Thomas Sayer, Andrés Montoya−Castillo

Predicting the exact many-body quantum dynamics of polarons in materials with strong carrier-phonon interactions presents a fundamental challenge, often necessitating one to adopt approximations that sacrifice the ability to predict the transition from nonequilibrium relaxation to thermodynamic equilibrium. Here, we exploit a recent breakthrough that generalizes the concept of memory beyond its conventional temporal meaning to also encompass space. Specifically, we leverage our finding that the dynamics of observables in systems with local couplings satisfy Green's functions with kernels that are local in time and space. This enables us to employ the dynamics of small lattices over short times to predict the dynamics of thermodynamically large lattices over arbitrarily long timescales while circumventing the deleterious impacts of finite-size effects. We thus interrogate the exact nonequilibrium formation and migration of polarons in one- (1D) and two-dimensional (2D) systems, revealing that their motion approaches diffusive transport only asymptotically in time and system size. We also compare transport in 1D and 2D systems to investigate the effect of dimension in polaron migration physics, illustrating how energy variations can cause localization-a phenomenon observable via current microscopy experiments.

Eduardo C. Marino

S. Liu, Josef Sak

Abstract Starting with the Kubo formula, a transport equation for the acoustic polaron is derived. The collision integral in the transport equation contains not only irreducible vertex parts, but also “products” of them. These are products of irreducible verteces connected by non‐singular parts of Green's functions. They are important when one considers the second or higher order perturbations, as in the case of an acoustic polaron at very low temperatures.