# Spectral Analysis of the Growth of Translational Superfluid Flow in a Bose Liquid

## TL;DR

This paper investigates the spectral properties of superfluid flow in a Bose liquid near the lambda transition, revealing how a statistical gap influences the growth of superfluidity and proposing a new interpretation of critical velocity.

## Contribution

It introduces a spectral analysis approach to understand superfluid flow growth, emphasizing the role of a Bose-statistics-induced gap and the size distribution of the coherent wave function.

## Key findings

- Spectral analysis shows a continuous change in fluidity spectrum above the lambda temperature.
- The emergence of a statistical gap suppresses transverse motion, facilitating superfluid growth.
- A new interpretation of the critical velocity based on spectral properties is proposed.

## Abstract

Spectral analysis of the translational superfluid flow of a Bose liquid is attempted. When cooling a dissipative flow of liquid helium 4 through a capillary at the lambda temperature,a superfluid flow abruptly appears at the lambda temperature. By a thought experiment in which the pressure difference between two ends of a capillary slowly oscillates, the spectrum of fluidity (the reciprocal of kinematic viscosity) just above the lambda temperature ($2.17 K<T<2.18 K$) is examined using a sum rule that incorporates the result of linear response theory and fluid mechanics. According to Feynman's picture on the many-body wave function of bosons, as the condensate grows in the flow, the transverse motion in the flow becomes suppressed by the emergence of a gap, originating from the Bose statistics, in the excitation spectrum. This statistical gap induces a continuous change in the fluidity spectrum just above the lambda temperature, which demonstrates the growth of a superfluid flow. For this mechanism, the size distribution of the coherent wave function plays an important role. As a byproduct, a new interpretation of the critical velocity is proposed.