Analytic Representations for Quantum Systems on a Circle with Magnetic Flux

Artyom M. Grigoryan, Sos S. Agaian

Muna Tabuni

Pavlos Evangelides

We develop an analytic framework for quantum systems 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 relevant 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 observables such as persistent currents and phase shifts.Future 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.

裕也 檀, Yuya Dan

Pavlos Evangelides

Quantum systems in a d-dimensional Hilbert space are considered, where \nthe phase spase is Z(d) x Z(d). An analytic representation in a cell S in the \ncomplex plane using Theta functions, is defined. The analytic functions have \nexactly d zeros in a cell S. The reproducing kernel plays a central role in \nthis formalism. Wigner and Weyl functions are also studied. \nQuantum systems with positions in a circle S and momenta in Z are also \nstudied. An analytic representation in a strip A in the complex plane is also \ndefined. Coherent states on a circle are studied. The reproducing kernel is \ngiven. Wigner and Weyl functions are considered.

Pavlos Evangelides, Chao Lei, Apostol Vourdas

An analytic representation with Theta functions on a torus, for systems with variables in Z(d), is considered. Another analytic representation with Theta functions on a strip, for systems with positions in a circle S and momenta in Z, is also considered. The reproducing kernel formalism for these two systems is studied. Wigner and Weyl functions in this language, are also studied