Alireza Ataei: Spectral Selection in Quantum Systems via Dissipative Dynamics

Abstract: We study the Quantum Landau–Lifshitz–Gilbert (QLLG) equation as a nonlinear dissipative evolution equation for quantum many-body systems. Determining lowest-energy states of interacting quantum systems is computationally challenging because the dimension of the Hilbert space grows exponentially with system size, making direct spectral methods infeasible for large systems.

We show that QLLG dynamics generates monotone energy decay and drives generic initial states toward low-energy eigenspaces through nonlinear dissipation. For pure states, higher-energy components are exponentially suppressed, leading to convergence toward the ground-state sector. Under generic assumptions, the convergence time scales linearly with system size despite the exponential growth of the state space. We further extend the analysis to mixed states, where the dynamics induces an ordering of occupation probabilities according to energy. Numerical simulations for interacting spin systems illustrate efficient real-time ground-state selection and dissipative spectral filtering.