One-Dimensional Exactly Solvable Model of Polaron

TL;DR

This paper introduces a one-dimensional exactly solvable model for polarons, providing explicit calculations of spectral bands, states, and effective mass, with potential applications to quantum wire phonon dynamics.

Contribution

It presents a novel exactly solvable 1D polaron model using Jacobi matrices, with explicit spectral and effective mass calculations.

Findings

Explicit spectral band calculations for polarons and scattering states

Derived formula for polaron effective mass

Suggested model parameters fitting and connection to quantum wires

Abstract

Using for unperturbed electron and phonon Hamiltonians a representation by the Jacobi matrices a one-dimensional model of the electron-phonon interaction is constructed. In frame of the model the polaron and scattering spectral bands are calculated explicitly as well as the corresponding states. An explicit formula for the polaron effective mass is derived and the fit of model parameters is suggested. A connection of the model with the description of phonon degrees of freedom for quantum wires is discussed.