An attractor dynamics in a non-Hermitian two-level system

TL;DR

This paper introduces an exactly solvable attractor dynamics in a two-level non-Hermitian system, enabling evolution to a coalescence state that is insensitive to initial conditions, contrasting with chaotic attractors.

Contribution

It presents the first exact solution for attractor dynamics in a non-Hermitian two-level system, demonstrating controlled evolution to a coalescence state.

Findings

Achieved exact attractor solutions in a non-Hermitian two-level system

Demonstrated insensitivity to initial conditions in attractor behavior

Showed attractor-like behavior persists in adiabatic processes

Abstract

Exceptional point in non-Hermitian system possesses fascinating properties. We present an exactly solvable attractor dynamics for the first time from a two-level time dependent non-Hermitian Hamiltonian. It allows a way to evolve to the coalescence state from a pure or mixed initial state through varying the imaginary parameter along a specific diabatic passage. Contrast to a chaotic attractor that is ultrasensitive to the initial condition, the designed attractor is insensitive to the initial conditions. The attractor-like behavior still exists for several adiabatic processes.