Abstract The investigation of the Hamiltonian dynamical counterpart phase transitions, combined with Riemannian geometrization dynamics, has led to a preliminary formulation differential-topological theory transitions. In fact, in correspondence transition there are peculiar geometrical changes mechanical manifolds that found stem from their topology. These findings, together two theorems, have...

We review the effects of excited-state quantum phase transitions (ESQPTs) in interacting many-body systems with finite numbers collective degrees freedom. classify typical ESQPT signatures spectra energy eigenstates respect to underlying classical dynamics and outline a variety which they occur. describe thermodynamic dynamic consequences ESQPTs, like those microcanonical thermodynamics, quench...