Quantum mechanics of damped systems

TL;DR

This paper explores the quantum behavior of damped systems, revealing that their quantization results in a Hamiltonian with complex eigenvalues linked to resonant states, which explain irreversible quantum dynamics.

Contribution

It introduces a self-adjoint Hamiltonian for damped systems with complex eigenvalues, connecting resonant states to irreversible quantum processes.

Findings

Complex eigenvalues correspond to resonant states.

Resonant states explain irreversibility in quantum damping.

Hamiltonian remains self-adjoint despite damping effects.

Abstract

We show that the quantization of a simple damped system leads to a self-adjoint Hamiltonian with a family of complex generalized eigenvalues. It turns out that they correspond to the poles of energy eigenvectors when continued to the complex energy plane. Therefore, the corresponding generalized eigenvectors may be interpreted as resonant states. We show that resonant states are responsible for the irreversible quantum dynamics of our simple model.