Soliton solutions in polaron theory

B. Pietrass

Abdelâali Boudjemâa

N. H. Christ, T. D. Lee

Nikolay Yegovtsev, Taha Alper Yogurt, Matthew T. Eiles +1 more

We present a unified description of attractive and repulsive polarons, formed in a one-dimensional Bose gas hosting an impurity particle, by obtaining all ground- and excited-state solutions to the Gross-Pitaevskii equation. Modeling the impurity with an attractive square-well potential, we characterize the excited-state energy branches as a function of interaction strength. As the impurity-bath coupling increases, the excited states change from distinct soliton configurations to hybridized soliton-polaron states, eventually crossing over from repulsive to attractive polarons at unitarity. We identify a universal regime near this crossover where the polaron properties are accurately characterized by the zero-energy scattering length.

Nikolay N. Bogolubov, Nikolay N. Bogolubov

Vladislav Čápek

For an electron interacting with harmonic dispersive phonons in a periodic lattice, the possibility of wave (soliton)-like solutions of the generalised master equations (GME) for the electron site occupation probabilities is investigated. For the current form of the small-polaron Hamiltonian, the long-time asymptotics of the memory functions (kernels of the GME) in the small-polaron basis are discussed to all orders in the electron hopping integrals.Using this result, one obtains (for the initially localised electron) the t 2 -behaviour of the mean-square electron displacement at zero temperature. This corresponds to existing soliton solutions of the Schrodinger equation. At non-zero temperatures, the wave solution is damped.