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arXiv:1712.01912 · The Journal of Chemical Physics

Quantum dynamics of the intramolecular vibrational energy redistribution in OCS: From localization to quasi-thermalization

J. B. Pérez, J. C. Arce

Published Jun 5, 2018• 13 citations
arXivHTMLPDF

Abstract

We report a fully quantum-dynamical study of the intramolecular vibrational energy redistribution (IVR) in the electronic ground state of carbonyl sulfide, which is a prototype of an isolated many-body quantum system with strong internal couplings and non-Rice-Ramsperger-Kassel-Marcus (RRKM) behavior. We pay particular attention to the role of many-body localization and the approach to thermalization, which currently are topics of considerable interest, as they pertain to the very foundations of statistical mechanics and thermodynamics. We employ local-mode (valence) coordinates and consider initial excitations localized in one local mode, with energies ranging from low to near the dissociation threshold, where the classical dynamics have been shown to be chaotic. We propagate the nuclear wavepacket on the potential energy surface by means of the numerically exact multiconfiguration time-dependent Hartree method and employ mean local energies, time-dependent and time-averaged populations in quantum number space, energy distributions, entanglement entropies, local population distributions, microcanonical averages, and dissociation probabilities, as diagnostic tools. This allows us to identify a continuous localization → delocalization transition in the energy flow, associated with the onset of quantum chaos, as the excitation energy increases up to near the dissociation threshold. Moreover, we find that at this energy and ∼1 ps the molecule nearly thermalizes. Furthermore, we observe that IVR is so slow that the molecule begins to dissociate well before such quasi-thermalization is complete, in accordance with earlier classical-mechanical predictions of non-RRKM behavior.

DOI
10.1063/1.5026318

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We report a fully quantum-dynamical study of the intramolecular vibrational energy redistribution (IVR) in the electronic ground state of carbonyl sulfide, which is a prototype of an isolated many-body quantum system with strong internal couplings and non-Rice-Ramsperger-Kassel-Marcus (RRKM) behavior. We pay particular attention to the role of many-body localization and the approach to thermalization, which currently are topics of considerable interest, as they pertain to the very foundations of statistical mechanics and thermodynamics. We employ local-mode (valence) coordinates and consider initial excitations localized in one local mode, with energies ranging from low to near the dissociation threshold, where the classical dynamics have been shown to be chaotic. We propagate the nuclear wavepacket on the potential energy surface by means of the numerically exact multiconfiguration time-dependent Hartree method and employ mean local energies, time-dependent and time-averaged populations in quantum number space, energy distributions, entanglement entropies, local population distributions, microcanonical averages, and dissociation probabilities, as diagnostic tools. This allows us to identify a continuous localization → delocalization transition in the energy flow, associated with the onset of quantum chaos, as the excitation energy increases up to near the dissociation threshold. Moreover, we find that at this energy and ∼1 ps the molecule nearly thermalizes. Furthermore, we observe that IVR is so slow that the molecule begins to dissociate well before such quasi-thermalization is complete, in accordance with earlier classical-mechanical predictions of non-RRKM behavior.
We investigate the effect of inter-mode coupling on the vibrational relaxation dynamics of molecules in weak dissipative environments. The simulations are performed within the reduced density matrix formalism in the Markovian regime, assuming a Lindblad form for the system-bath interaction. The prototypical two-dimensional model system representing two CO molecules approaching a Cu(100) surface is adapted from an ab initio potential, while the diatom-diatom vibrational coupling strength is systematically varied. In the weak system-bath coupling limit and at low temperatures, only first order non-adiabatic uni-modal coupling terms contribute to surface-mediated vibrational relaxation. Since dissipative dynamics is non-unitary, the choice of representation will affect the evolution of the reduced density matrix. Two alternative representations for computing the relaxation rates and the associated operators are thus compared: the fully coupled spectral basis, and a factorizable ansatz. The former is well-established and serves as a benchmark for the solution of Liouville-von Neumann equation. In the latter, a contracted grid basis of potential-optimized discrete variable representation is tailored to incorporate most of the inter-mode coupling, while the Lindblad operators are represented as tensor products of one-dimensional operators, for consistency. This procedure results in a marked reduction of the grid size and in a much more advantageous scaling of the computational cost with respect to the increase of the dimensionality of the system. The factorizable method is found to provide an accurate description of the dissipative quantum dynamics of the model system, specifically of the time evolution of the state populations and of the probability density distribution of the molecular wave packet. The influence of intra-molecular vibrational energy redistribution appears to be properly taken into account by the new model on the whole range of coupling strengths. It demontrates that most of the mode mixing during relaxation is due to the potential part of the Hamiltonian and not to the coupling among relaxation operators.
A theory of the photon echo is presented for excitation of the vibrational–rotational transitions in a polyatomic molecule followed by the process of intramolecular vibrational redistribution (IVR). A model is considered that includes a description of IVR using the general statistical properties of chaotic states rather than phenomenological. Special attention is paid to the echo signals at the delay times that are considerably larger than the characteristic times of IVR. It is shown that echo measurements for the far plateau of the IVR curve can provide, directly or indirectly, determination of the so-called dilution factors; their values are of primary importance for estimating effective density of the molecular states that participate in IVR. Differences between the echo and anti-Stokes Raman scattering, really used for the same purposes, are discussed.
Abstract The decoherence is one of the most crucial obstacles for quantum computing, entanglement, and quantum information science, as, for example, the quantum computing is usually processed in pure state. Therefore, from the chemical interest, it is very important to investigate one of the most important decoherence mechanisms of molecules, intramolecular vibrational redistribution (IVR), from the viewpoint of quantum computing and entanglement in detail. We have found that the molecules well described by local mode picture is more suitable to maintain coherence than those well described by normal mode picture for quantum computing if the vibrational modes of polyatomic molecules are utilized for qubits. A representative light–heavy–light molecule that can be well described by local mode picture, water molecule (H2O), is adopted for calculation examples and discussion. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009
Using the ergodicity principle for the expectation values of several types of observables, we investigate the thermalization process in isolated fermionic systems. These are described by the two-body random ensemble, which is a paradigmatic model to study quantum chaos and especially the dynamical transition from integrability to chaos. By means of exact diagonalizations we analyze the relevance of the eigenstate thermalization hypothesis as well as the influence of other factors, such as the energy and structure of the initial state, or the dimension of the Hilbert space. We also obtain analytical expressions linking the degree of thermalization for a given observable with the so-called number of principal components for transition strengths originating at a given energy, with the dimensions of the whole Hilbert space and microcanonical energy shell, and with the correlations generated by the observable. As the strength of the residual interaction is increased, an order-to-chaos transition takes place, and we show that the onset of Wigner spectral fluctuations, which is the standard signature of chaos, is not sufficient to guarantee thermalization in finite systems. When all the signatures of chaos are fulfilled, including the quasicomplete delocalization of eigenfunctions, the eigenstate thermalization hypothesis is the mechanism responsible for the thermalization of certain types of observables, such as (linear combinations of) occupancies and strength function operators. Our results also suggest that fully chaotic systems will thermalize relative to most observables in the thermodynamic limit.
The emergence of statistical mechanics from quantum dynamics is conventionally understood through quantum chaos, the Eigenstate Thermalization Hypothesis (ETH), and canonical typicality, which together explain the thermal behavior of local observables in quantum many-body systems. We provide a distinct mechanism in which, for a quantum many-body system under strong random perturbation, the chaotic behavior of the system's eigenvectors and a constraint on the total energy directly generate a canonical ensemble for the entire system. The canonical ensemble occurs as the first moment of the Porter-Thomas distribution of the system's chaotic eigenstates, and the constraint on the total energy sets the temperature in the ensemble. This yields canonically distributed expectation values without invoking ETH, a microcanonical ensemble, or a subsystem-bath partition for local and global observables. We numerically demonstrate the mechanism for the 1D transverse-field Ising model by showing canonically distributed eigenstate projectors and spin-spin correlators with distinctive temperature dependence of the correlation length. An implementation of this thermalization approach on a quantum computer can be utilized for thermal state preparation.
Using the ergodicity principle for the expectation values of several types of observables, we investigate the thermalization process in isolated fermionic systems.These are described by the two-body random ensemble, which is a paradigmatic model to study quantum chaos and especially the dynamical transition from integrability to chaos.By means of exact diagonalizations we analyze the relevance of the eigenstate thermalization hypothesis as well as the influence of other factors, such as the energy and structure of the initial state, or the dimension of the Hilbert space.We also obtain analytical expressions linking the degree of thermalization for a given observable with the so-called number of principal components for transition strengths originating at a given energy, with the dimensions of the whole Hilbert space and microcanonical energy shell, and with the correlations generated by the observable.As the strength of the residual interaction is increased, an order-to-chaos transition takes place, and we show that the onset of Wigner spectral fluctuations, which is the standard signature of chaos, is not sufficient to guarantee thermalization in finite systems.When all the signatures of chaos are fulfilled, including the quasicomplete delocalization of eigenfunctions, the eigenstate thermalization hypothesis is the mechanism responsible for the thermalization of certain types of observables, such as (linear combinations of) occupancies and strength function operators.Our results also suggest that fully chaotic systems will thermalize relative to most observables in the thermodynamic limit.