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Exact Dirac-Bogoliubov-de Gennes Dynamics for Inhomogeneous Quantum Liquids

¹Institute for Theoretical Physics, ETH Zurich, Wolfgang-Pauli-Strasse 27, 8093 Zürich, Switzerland.

Physical Review Letters

|September 22, 2023

Summary

This study analyzes inhomogeneous quantum many-body systems using Tomonaga-Luttinger-liquid theory. Researchers derived exact solutions for quantum Hall edges, revealing universal behaviors in dynamics and Andreev reflections.

Area of Science:

Condensed Matter Physics
Quantum Field Theory

Background:

Tomonaga-Luttinger-liquid theory describes 1+1-dimensional quantum many-body systems.
Such systems are relevant for ultracold atoms and quantum Hall edges.
Inhomogeneous parameters introduce spatial variations in system properties.

Purpose of the Study:

To investigate the dynamics of inhomogeneous 1+1D quantum many-body systems.
To apply Tomonaga-Luttinger-liquid theory to quantum Hall edges with inhomogeneous interactions.
To analytically solve the governing equations and obtain Green's functions and scattering matrices.

Main Methods:

Utilizing Tomonaga-Luttinger-liquid theory for inhomogeneous systems.
Mapping the problem to inhomogeneous Dirac-Bogoliubov-de Gennes equations.
Employing a Magnus expansion for analytical solutions.

Main Results:

Exact Green's functions and scattering matrices were obtained.
The dynamics were shown to be governed by coupled continuity equations.
Universal late-time evolution and Andreev reflections were revealed.

Conclusions:

The study provides analytical solutions for complex quantum systems.
Results offer insights into the behavior of quantum Hall edges under inhomogeneous conditions.
The findings highlight universal dependencies in stationary and non-equilibrium states.

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