Quantum mechanics of non-conservative systems

Kunio Yasue

Yue Su

The energy Conservation for a non relativistic quantum mechanics system is derived and discussed

Andreas Hofmann

Seiji Sakocia, Minoru Omote, S. Kamefuchi

By constructing a quantum conserved quantity even for a system with timedependent Hamiltonian, we develop the quantum version of Hamilton-Jacobi theory, that is applicable for non-conserved systems as well as conserved ones. A novel viewpoint, Hamilton-Jacobi picture, of the quantum mechanics will be introduced.

Kui Cao, Su-Peng Kou

We present a systematic study of statistical mechanics for non-Hermitian quantum systems. Our work reveals that the stability of a non-Hermitian system necessitates the existence of a single path-dependent conserved quantity, which, in conjunction with the system's Hamiltonian, dictates the equilibrium state. By elucidating the relationship between the Hamiltonian and the supported conserved quantity, we propose criteria for discerning equilibrium states with finite relaxation times. Although our findings indicate that only non-Hermitian systems with real energy spectrum precisely possess such conserved quantities, we also demonstrate that an effective conserved quantity can manifest in certain systems with complex energy spectra. The effective conserved quantity, alongside the effective transitions within their associated subspace, collectively determines the system's equilibrium state. Our results provide valuable insights into non-Hermitian systems across more realistic contexts and hold potential for applications in a diverse range of physical systems.

Akakii Melikidze