Simulating a Catalyst induced Quantum Dynamical Phase Transition of a Heyrovsky reaction with different models for the environment
arxiv(2022)
摘要
Through an appropriate election of the molecular orbital basis, we show
analytically that the molecular dissociation occurring in a Heyrovsky reaction
can be interpreted as a Quantum Dynamical Phase Transition, i.e., an analytical
discontinuity in the molecular energy spectrum induced by the catalyst. The
metallic substrate plays the role of an environment that produces an energy
uncertainty on the adatom. This broadening induces a critical behavior not
possible in a quantum closed system. We use suitable approximations on
symmetry, together with both Lanczos and canonical transformations, to give
analytical estimates for the critical parameters of molecular dissociation.
This occurs when the bonding to the surface is (√(2)) times the molecular
bonding. This value is slightly weakened for less symmetric situations. However
simple, this conclusion involves a high order perturbative solution of the
molecule-catalyst system. This model is further simplified to discuss how an
environment-induced critical phenomenon can be evaluated through an idealized
perturbative tunneling microscopy set-up. In this case, the energy
uncertainties in one or both atoms are either Lorentzian or Gaussian. The
former results from the Fermi Golden Rule, i.e., a Markovian approximation. The
Gaussian uncertainty, associated with non-Markovian decoherent processes,
requires the introduction of a particular model of a spin bath. The partially
coherent tunneling current is obtained from the Generalized Landauer-Büttiker
Equations. The resonances observed in these transport parameters reflect, in
many cases, the critical properties of the resonances in the molecular
spectrum.
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