Theta Function Framework for Quantum Systems with Magnetic Flux

We develop an analytic framework for quantum sys- tems defined on a circle threaded by magnetic flux, generalizing the Bargmann representation via Theta functions. By introducing flux-dependent coherent states and displacement operators, we construct entire analytic wavefunctions and derive a reproducing kernel with quasi-periodic boundary conditions. This approach captures topological effects such as the Aharonov–Bohm phase and provides tools rele- vant for mesoscopic rings and topological quantum computation. Compared to flux-free analytic approaches, the present framework directly encodes quasi-periodic boundary conditions, making it suitable for simulating observ- ables such as persistent currents and phase shifts. Fu- ture work includes numerical implementations of the Theta function framework for flux qubits, extensions to multi-particle systems, and exploration of connections to non-Abelian topological phases.