Instantons via breaking geometric symmetry in hyperbolic traps
In the model of Penning trap with a geometric asymmetry we study a resonance regime which produces a hyperbolic type algebra of integrals of motion. The algebra has qubic (non-Lie) commutation relations with creation-anihilation structure. The anharmonic part of the trap potential determines a top-like Hamiltonian over this algebra. The symmetry breaking term generates a tunnelling pseudoparticle (closed instanton). We study its action and corresponding spectral splitting.