|
Since the early days of magnetic resonance the narrowing of certain spectral lines and the collapse of some pairs of them turned out a challenging problem [1]. Taken in their extreme case, simple perturbation theories allowed to estimate the magnitude of the exchange interaction (for exchange narrowing) or characterictic fluctuation times (motional narrowing) but failed to describe the whole phenomenom. A simple way to rationalize an expresion lead to P. W. Anderson to consider imaginary probalities in a Markov matrix [2]. Nowadays we know that relaxation and decoherence induced by the interaction with the infinite degrees of an environment can be described by a non-Hermitian term in the Hamiltonian and thus provides a better justification for Anderson's "leaking" probabilities [2]. Here, we review our own approach to this problem, which started with the experimental observation of a dynamical phase transition in a SWAP gate in NMR [3,4]. The same kind of phenomena appear in electron paramagnetic resonance experiments which have been interpreted under the new perspective as environmentally induced dynamical phase transitions [5]. [1 ]Exchange Narrowing in Paramagnetic Resonance, P. W. Anderson and P. R. Weiss, Rev. Mod. Phys. 25, 269 (1953) [2] A Mathematical Model for the Narrowing of Spectral Lines by Exchange or Motion. P. W. Anderson, J. Phys. Soc. Japan, 9, 316 (1954) [3] Attenuation of polarization echoes in NMR: A test for the emergence of Dynamical Irreversibility in Many-Body Quantum Systems. P.R. Levstein, G. Usaj, H.M.Pastawski,J. Chem. Phys. 108, 2718 (1998) [4] Environmentally induced quantum dynamical phase transition in the spin swapping operation G. A. Alvarez, E. P. Danieli, P. R. Levstein, and H. M. Pastawski, J. Chem. Phys. 124, 1 (2006) [5] Isotropic and anisotropic spin-spin interactions and a quantum phase transition in a dinuclear Cu(II) compound L. B. Napolitano, O. R. Nascimento, S. Cabaleiro, J. Castro and R. Calvo, Phys.Rev. B 77, 214423 (2008) |
|