In recent years, Solid State Nuclear Magnetic Resonance (NMR) has given us the chance to observe surprising dynamical emergent phenomena [1]. This is possible because this technique addresses spins in the thermodynamic limit. We have addressed two phenomena: A) the polarization a spin dimmer, may have a Rabi oscillation that becomes an overdamped polarization transfer when the interaction with a spin environment becomes enough strong as compared with the Rabi frequency [2]. B) A dipolar scaled dynamics [2], which is seen as an apparent spin-diffusion through the study of Out of Time Order Correlations (OTOCs) associated with collective polarization. However, when the Hamiltonian strength is weak respect to uncontrollable residual interactions, Loschmidt Echo experiments reveals that dynamical transition from a reversible dynamics to an irreversible one whose time constant is fixed by the Hamiltonian itself, not by the residual interactions. This intrinsic irreversibility, shows that one should be careful in applying the Schrödinger Equation to many-body systems in the thermodynamic limit.
 

[1]- Attenuation of polarization echoes in NMR: A test for the emergence of Dynamical Irreversibility in Many-Body Quantum Systems. PR Levstein, G Usaj, HM Pastawski; J. Chem. Phys. 108, 2718-2724 (1998)
[2]- Environmentally induced quantum dynamical phase transition in the spin swapping operation. GA Álvarez, EP Danieli, PR Levstein, and HM Pastawski. J. Chem. Phys. 124, 1 (2006)
[3]-Emergent perturbation independent decay of the Loschmidt echo in a many-body system -Phys. Rev. Lett. (2020-in press) arXiv 1902.06628 CM Sánchez, AK Chattah, KX Wei, L Buljubasich, P Cappellaro, and HM Pastawski, https://docs.google.com/document/d/1rJAySKRmj_iNXi6djMd6vZ4Bb3dNpVWrc3OjIO6Rkw8/edit?usp=sharing
[4]-Loschmidt echo in many-spin systems: a quest for intrinsic decoherence and emergent irreversibility, PR Zangara and HM Pastawski. Phys. Scr. 92 033001(2017)