Irreversible and Nonlinear Dynamics of Open Systems

H. D. Doebner, V. K. Dobrev, P. Nattermann

Xiao‐Feng Qian, Joseph H. Eberly

We report an approach to quantum open system dynamics that leads to novel nonlinear constant relations governing information flow among the participants. Our treatment is for mixed state systems entangled in a pure state fashion with an unspecified party that was involved in preparing the system for an experimental test, but no longer interacts after $t=0$. Evolution due to subsequent interaction with another party is treated as an amplitude flow channel and uses Schmidt-type bipartite decomposition of the evolving state. We illustrate this with three examples, including both reversible and irreversible information flows, and give formulas for the new nonlinear constraints in each case.

Olivier Martin

Durhan Yazir

We introduce a class of nonlinear, state-dependent Lindblad operators that model irreversible annihilation processes in open quantum systems. Termed the "Terminator Operator," this mechanism activates only when an instability functional \mathcal{I}[\rho] = \Tr(\rho \mathbf{L}_\perp) exceeds a critical threshold. Unlike standard amplitude damping, the decay rate \gamma_T(\mathcal{I}) depends on the degree of instability, leading to nonlinear quantum dynamics and an absorbing phase transition. The threshold emerges naturally from a rate equation for \mathcal{I}, which includes growth, nonlinear saturation, and removal terms. We analyze a two-level system and show that the model predicts non-exponential decay, critical slowing down, and hysteresis—signatures distinct from conventional dissipative channels. An effective non-Hermitian Hamiltonian captures the short-time dynamics, while the full Lindblad treatment reveals a bifurcation separating stable and unstable regimes. The framework unifies concepts from quantum Zeno effect, dissipative phase transitions, and feedback control. Potential applications range from quantum error correction (active termination of uncorrectable errors) to modelling catastrophic events in driven quantum systems.

L. A. Lugiato

Heinz Dietrich Doebner, V. K. Dobrev, P. Nattermann

Intrinsically irreversible representations of unstable quantum systems, I. Antoniou quantum mechanical arrows of time, A. Bohm isotropic harmonic oscillator on the quantum euclidean space, G. Fiore relevant and irrelevant nonlinear schrodinger equation, N. Gisin diffeomorphism groups and nonlinear quantum mechanics, G.A. Goldin from Hamiltonian mechanics to nonlinear Schrodinger equations, J.-D. Hennig nonlinear Schrodinger dynamics and nonlinear observables, W. Lucke nonlinear gauge transformations and the Doebner-Goldin equation, P. Nattermann chaos and the limit of classical and quantum mechanics, T. Petrosky why irreversibility? the formulation of classical and quantum mechanics for unstable dynamical systems, I. Prigogine harmonic oscillators on quantum space, S. Watamura. (Part Contents).