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While the role of the environment in the spontaneously broken symmetry in two level systems was early hinted by P. W. Anderson [1], the problem of accurately describe a dynamical phase transition remained a complex problem [2] often dealt phenomenologically [3]. A new impulse appeared when a SWAP gate in NMR was observed to have such a transition [4]. In such cases, the environment degrees of freedom were clearly identified and traced out in a precise renormalization procedure that even accounts for memory effects [5]. While specific symmetries in the relaxation process described by a non-Hermitian Hamiltonian was immediately recognized to have a determining role, the requirement of complete positivity in the evolution (such as Keldysh formalism or a Kossakowski-Lindblad equation) also proved to provide an additional path [5]. Since then, our group has devoted a great deal of effort to determine the conditions for the appearance of such transitions in various experimental contexts. Here we will describe various physically meaningful situations where the phase transition occur as well as other situations that have been investigated by our group that involve vibrational degrees of freedom [6], quantum SWAP gates [7], plasmonic excitations [8], electronic transport [9] and molecular lysis in heterogeneous catalysis [10]. [1] More is Different, P.W. Anderson, Science 177 393 (1972) [2] Dynamics of the Two-State System with Ohmic Dissipation, S. Chakravarty and A. J. Leggett, Phys. Rev. Lett. 52, 5 (1984) [3] A Mathematical Model for the Narrowing of Spectral Lines by Exchange or Motion. P. W. Anderson, J. Phys. Soc. Japan, 9, 316 (1954) [4] Environmentally induced quantum dynamical phase transitionin the spin swapping operation. G. A. Álvarez, E. P. Danieli, P. R. Levstein, and H. M. Pastawski, J. Chem. Phys. 124, 1 (2006) [5] Revisiting the Fermi Golden Rule: Quantum dynamical phase transition as a paradigm shift, H. M. Pastawski, Phys. B 398 278(2007) [6]Dynamical Phase Transition in Vibrational Surface Modes, H. L. Calvo, and H. M. Pastawski, Braz. J. Phys. 36, 963 (2006) [7] Dynamical regimes of a quantum SWAP gate beyond the Fermi Golden Rule, A. D. Dente, R.A. Bustos-Marun, H.M. Pastawski, Phys. Rev. A. 78, 062116 (2008) [8] Buffering plasmons in nanoparticle waveguides at the virtual-localized transition, R. A. Bustos-Marún, E.A. Coronado, and H. M. Pastawski, Phys. Rev. B 82, 035434 (2010) [9] Crucial role of decoherence for electronic transport in molecular wires: Polyaniline as a case study, C.J. Cattena, R.A. Bustos-Marún, and H.M. Pastawski, Phys. Rev. B 82, 144201 (2010); From tunneling to hopping mechanism: demonstration of paradigm shift in molecular wires, D. Nozaki, C. G. Rocha, H. M. Pastawski, and G. Cuniberti (unpublished) [10] Molecular dissociation in Heterogeneous catalysis as a Dynamical Phase Transition. A. Dente, A. Ruderman, E. Santos, W. Schmickler and H. M. Pastawski, (unpublished); A. Ruderman, Lic. Thesis (FaMAF-UNC 2011) |
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