On the superfluidity of classical liquid in nanotubes

TL;DR

This paper explores the superfluidity of classical liquids in nanotubes using ultra second quantization, deriving conditions under which superfluidity occurs based on particle interactions and nanotube radius.

Contribution

It introduces the application of ultra second quantization to analyze superfluidity in classical liquids confined in nanotubes, linking quantum concepts to classical fluid behavior.

Findings

Superfluidity occurs below a critical velocity related to Landau velocity.

Superfluidity depends on nanotube radius and particle interactions.

The model predicts conditions for superfluidity in classical liquids within nanotubes.

Abstract

In 2001, the author proposed the ultra second quantization method. The ultra second quantization of the Schr\"odinger equation, as well as its ordinary second quantization, is a representation of the N-particle Schr\"odinger equation, and this means that basically the ultra second quantization of the equation is the same as the original N-particle equation: they coincide in 3N-dimensional space. We consider a short action pairwise potential V(x_i -x_j). This means that as the number of particles tends to infinity, $N\to\infty$, interaction is possible for only a finite number of particles. Therefore, the potential depends on N in the following way: $V_N=V((x_i-x_j)N^{1/3})$. If V(y) is finite with support $\Omega_V$, then as $N\to\infty$ the support engulfs a finite number of particles, and this number does not depend on N. As a result, it turns out that the superfluidity occurs for velocities less than $\min(\lambda_{\text{crit}}, \frac{h}{2mR})$, where $\lambda_{\text{crit}}$ is the critical Landau velocity and R is the radius of the nanotube.