# Exact Results for Tunneling Problems of Bogoliubov Excitations in the Critical Supercurrent State

## TL;DR

This paper provides an exact solution for Bogoliubov excitations in supercurrent states, demonstrating the absence of perfect transmission at low energies due to zero-energy density fluctuations.

## Contribution

It presents an exact zero-energy solution for Bogoliubov equations in critical supercurrent states with arbitrary barriers, revealing the mechanism behind transmission suppression.

## Key findings

- No perfect transmission of excitations at low energy.
- Zero-energy density fluctuations cause transmission disappearance.
- Explicit transmission coefficient expression provided.

## Abstract

We show the exact solution of Bogoliubov equations at zero-energy in the critical supercurrent state for arbitrary shape of potential barrier. With use of this solution, we prove the absence of perfect transmission of excitations in the low-energy limit by giving the explicit expression of transmission coefficient. The origin of disappearance of perfect transmission is the emergence of zero-energy density fluctuation near the potential barrier.