Molecular dissociation in presence of a catalyst: II. The bond breaking role of the transition from virtual to localized states

Ruderman, Andrés; Dente, Axel D.; Santos, Elizabeth; Pastawski, Horacio M.

doi:10.1088/2053-1591/3/8/085017

Cited by 6 publications

(9 citation statements)

References 32 publications

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“…Instead we refer to the excellent book [17] and to the collection of articles on spectral analysis, stability and bifurcation in modern nonlinear physical systems [18]. Related problems are studied also in molecular physics, see the recent paper [19] where the references to older papers can be found. In quantum physics the problems are studied, unfortunately, in a confusing and often contradictory manner.…”

Section: Introductionmentioning

confidence: 99%

Resonances in open quantum systems

Eleuch¹,

Rotter²

2017

Phys. Rev. A

115

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The Hamilton operator of an open quantum system is non-Hermitian. Its eigenvalues are, generally, complex and provide not only the energies but also the lifetimes of the states of the system. The states may couple via the common environment of scattering wavefunctions into which the system is embedded. This causes an external mixing (EM) of the states. Mathematically, EM is related to the existence of singular (the so-called exceptional) points (EPs). The eigenfunctions of a non-Hermitian operator are biorthogonal, in contrast to the orthogonal eigenfunctions of a Hermitian operator. A quantitative measure for the ratio between biorthogonality and orthogonality is the phase rigidity of the wavefunctions. At and near an EP, the phase rigidity takes its minimum value. The lifetimes of two nearby eigenstates of a quantum system bifurcate under the influence of an EP. At the parameter value of maximum width bifurcation, the phase rigidity approaches the value one, meaning that the two eigenfunctions become orthogonal. However, the eigenfunctions are externally mixed at this parameter value. The S-matrix and therewith the cross section do contain, in the one-channel case, almost no information on the EM of the states. The situation is completely different in the case with two (or more) channels where the resonance structure is strongly influenced by the EM of the states and interesting features of non-Hermitian quantum physics are revealed. We provide numerical results for two and three nearby eigenstates of a nonHermitian Hamilton operator which are embedded in one common continuum and are influenced by two adjoining EPs. The results are discussed. They are of interest for an experimental test of the non-Hermitian quantum physics as well as for applications.2

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Section: Introductionmentioning

confidence: 99%

Resonances in open quantum systems

Eleuch¹,

Rotter²

2017

Phys. Rev. A

115

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“…They give the same conceptual picture as the exact numerical results obtained in Ref. [Ruderman et al, 2015, Ruderman et al, 2016. Those solutions involved the fully non-linear equations and complex forms of the uncertainties, as the Lorentzian tails are naturally truncated by the band edges of the metallic substrate [Dente et al, 2008].…”

Section: Molecular Dissociation Beyond Perfect Symmetrymentioning

confidence: 63%

Simulating a Catalyst induced Quantum Dynamical Phase Transition of a Heyrovsky reaction with different models for the environment

Lozano-Negro,

Ferreyra-Ortega,

Bendersky

et al. 2022

Preprint

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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.

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“…The expression (16) is unitary. According to (16), the resonance structure of the cross section is determined exclusively by the spectroscopic values of the localized part of the system, i.e., by the eigenvalues E = + /2Γ of the non-Hermitian Hamiltonian H. The expression (16) allows us therefore to receive reliable results also in the twochannel case and, moreover, when the phase rigidity of the eigenfunctions of H is reduced, < 1 and when the eigenfunctions of H contain EM, i.e., when they are mixed in the set of eigenfunctions {Φ 0 } of H 0 according to (11).…”

Section: Non-hermitian Hamiltonian and Resonancementioning

confidence: 99%

“…Observable information on the spectroscopic properties of the localized part of the system is contained in the resonance structure of the cross section. Using (16), we have calculated the resonance structure of the cross section at the critical parameter value = cr and at the two values 1 = −3 and 2 = 3 of far from cr .…”

Section: Resonance Structure and Contour Plot Of The Transmissionmentioning

confidence: 99%

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Loss, Gain, and Singular Points in Open Quantum Systems

Eleuch

Rotter

2018

Advances in Mathematical Physics

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Non-Hermitian quantum physics is used successfully for the description of different puzzling experimental results, which are observed in open quantum systems. Mostly, the influence of exceptional points on the dynamical properties of the system is studied. At these points, two complex eigenvalues E ≡ + Γ /2 of the non-Hermitian Hamiltonian H coalesce (where is the energy and Γ is the inverse lifetime of the state ). We show that also the eigenfunctions Φ of the two states play an important role, sometimes even the dominant one. Besides exceptional points, other critical points exist in non-Hermitian quantum physics. At these points = cr in the parameter space, the biorthogonal eigenfunctions of H become orthogonal. For illustration, we show characteristic numerical results.

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Molecular dissociation in presence of a catalyst: II. The bond breaking role of the transition from virtual to localized states

Cited by 6 publications

References 32 publications

Resonances in open quantum systems

Resonances in open quantum systems

Simulating a Catalyst induced Quantum Dynamical Phase Transition of a Heyrovsky reaction with different models for the environment

Loss, Gain, and Singular Points in Open Quantum Systems

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