Exact result for the polaron mass in a one-dimensional Bose gas

Abstract

We study the polaron quasiparticle in a one-dimensional Bose gas. In the integrable case described by the Yang-Gaudin model, we derive an exact result for the polaron mass. It is expressed in terms of the derivative with respect to the density of the ground-state energy per particle of the Bose gas without the polaron. This enables us to find high-order power series for the polaron mass in the regimes of weak and strong interaction.

Dispersion relation of a polaron in the Yang-Gaudin Bose gas

“…(33b) for C 1 is in full agreement with the general expression (35) after substituting m/m * evaluated in Ref. [22]. On the other hand, from Eq.…”

“…(38) in this case reduces to the form (19) with m/m * = 1 − 2 √ γ/3π and ν = 24/5π √ γ, in agrrement with Refs. [16,22]. On the other hand Eq.…”

“…Evaluation of the energy of the system in the excited state from Eq. ( 5) is more involved [22]. The final result in the thermodynamic limit can be expressed as E = N 0 +E(Q, η), where 0 is given by Eq.…”

“…( 19), ν is the dimensionless parameter that controls the quartic term and will be discussed later in the paper, while the quadratic term is controlled by m * , which denotes the mass of polaron excitation. It can be exactly expressed as [22]…”

“…Numerical studies of the polaron dispersion are performed for systems of a finite size [7,20] as well as in the thermodynamic limit [17]. On the other hand, explicit analytical results are obtained in the regimes of small momenta and in the limiting cases of interaction [16,18,21,22].…”