Instantons via breaking geometric symmetry in hyperbolic traps

摘要: Using geometrical and algebraic ideas, we study tunnel eigenvalue asymptotics bilocalization of eigenstates for certain class operators (quantum Hamiltonians) including the case Penning traps, well known in physical literature. For general hyperbolic traps with geometric asymmetry, resonance regimes which produce type algebras integrals motion. Such have polynomial (non-Lie) commutation relations creation-annihilation structure. Over this algebra, trap asymmetry (higher-order anharmonic terms near equilibrium) determines a pendulum-like Hamiltonian action-angle coordinates. The symmetry breaking term generates tunneling pseudoparticle (closed instanton). We instanton action corresponding spectral splitting.