Comment on ``Nonlinear band structure in Bose-Einstein condensates: Nonlinear Sch\"odinger equation with a Kronig Penney potential"

TL;DR

This paper reexamines the band structure of Bose-Einstein condensates in a Kronig-Penney potential, revealing that the effective mass can be negative even with swallow-tail loops, challenging previous interpretations related to superfluidity.

Contribution

It provides a detailed calculation showing the effective mass can be negative with swallow-tails, offering a new perspective on their physical significance.

Findings

Effective mass can be negative with swallow-tails.

Challenging previous assumptions about positive effective mass.

Implications for understanding superfluidity in condensates.

Abstract

In their recent paper [Phys. Rev. A 71, 033622], B. T. Seaman et al. studied Bloch states of the condensate wave function in a Kronig-Penney potential and calculated the band structure. They argued that the effective mass is always positive when a swallow-tail energy loop is present in the band structure. In this comment, we reexamine their argument by actually calculating the effective mass. It is found that there exists a region where the effective mass is negative even when a swallow-tail is present. Based on this fact, we discuss the interpretation of swallow-tails in terms of superfluidity.