Quantum Systems with Variables in $${\mathbb Z}(d)$$

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.

Jan Jerzy Sławianowski

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

Horst R. Beyer

Apostol Vourdas

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.