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Non-Hermitian Fermi-Dirac Distribution in Persistent Current Transport.

Pei-Xin Shen^1,2, Zhide Lu², Jose L Lado³

¹International Research Centre MagTop, Institute of Physics, <a href="https://ror.org/01dr6c206">Polish Academy of Sciences</a>, Aleja Lotnikow 32/46, PL-02668 Warsaw, Poland.

Physical Review Letters

|September 6, 2024

Summary

Researchers developed a new theory for persistent currents in dissipative quantum systems using non-Hermitian Hamiltonians. This framework allows calculating currents from complex energy spectra, applicable to superconducting junctions and magnetic flux rings.

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Area of Science:

Condensed Matter Physics
Quantum Mechanics
Quantum Information Theory

Background:

Persistent currents are quantum phenomena where currents flow indefinitely without external energy input.
Existing theories often assume Hermitian Hamiltonians, limiting their applicability to dissipative systems.
Dissipation introduces unique behaviors in quantum systems, necessitating advanced theoretical frameworks.

Purpose of the Study:

To extend the theory of persistent currents to include dissipation using non-Hermitian quantum Hamiltonians.
To derive an analytical expression for persistent currents based on the complex energy spectrum.
To investigate the behavior of persistent currents in dissipative models, specifically superconducting junctions and magnetic rings.

Main Methods:

Utilized Green's function formalism to develop the theoretical framework.
Introduced a non-Hermitian Fermi-Dirac distribution.
Derived an analytical formula for persistent currents dependent on the complex spectrum.
Employed exact diagonalization for validation.
Extended the formalism to finite temperatures and interaction effects.

Main Results:

Developed a general formalism for computing quantum many-body observables in non-Hermitian systems.
Derived an analytical expression for persistent currents solely from the complex spectrum.
Showed that persistent currents in dissipative models (superconducting junctions, magnetic rings) do not exhibit anomalies at exceptional points.
Identified current susceptibility as the key indicator for exceptional points.

Conclusions:

The developed formalism provides a unified approach to study persistent currents in dissipative quantum systems.
The findings offer insights into the behavior of quantum systems described by non-Hermitian Hamiltonians.
The framework has potential for extension to non-equilibrium quantum phenomena.