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Nettesheim, Peter [Author] ; Peter Deuflhard [Contributor]; Christian Lubich [Contributor]

Mixed quantum-classical dynamics: A unified approach to mathematical modelling and numerical simulation ; Gemischt quanten-klassische Dynamik: Ein einheitlicher Zugang zur mathematischen Modellierung und numerischen Simulation

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  • Media type: E-Book; Doctoral Thesis; Electronic Thesis
  • Title: Mixed quantum-classical dynamics: A unified approach to mathematical modelling and numerical simulation ; Gemischt quanten-klassische Dynamik: Ein einheitlicher Zugang zur mathematischen Modellierung und numerischen Simulation
  • Contributor: Nettesheim, Peter [Author]
  • imprint: Freie Universität Berlin: Refubium (FU Berlin), 2000
  • Language: English
  • DOI: https://doi.org/10.17169/refubium-11307
  • Keywords: 81V55 ; 81Q05 ; 65L20 ; 35Q40 ; mixed quantum-classical models ; 81Q20 ; 65L70 ; quantum-classical molecular dynamics ; short wave asymptotics ; 92C40 ; 81Q15
  • Origination:
  • Footnote: Diese Datenquelle enthält auch Bestandsnachweise, die nicht zu einem Volltext führen.
  • Description: 1. Introduction 1 A. Modelling 5 2. The quantum-classical molecular dynamics model 8 § 1 Full quantum dynamics 8 § 2 QCMD 8 § 3 Appropriate scaling 10 § 4 Spatial discretization 10 § 5 Application problems 11 3. Mathematical Derivation of QCMD 16 § 1 First Approximation Step: Separation 16 § 2 Second Approximation Step: Short Wave Asymptotics 18 § 3 Discussion and Examples 21 § 4 Concluding Remarks 23 4. Adiabatic limits 27 § 1 Three methods to compute the adiabatic limit 27 § 2 Adiabatic limit of QD 38 § 3 Adiabatic limit of QCMD 39 § 4 Multivalued adiabatic limit: Takens chaos 41 5. Non-Adiabatic dynamics 43 § 1 Non-Adiabaticity in QD 43 § 2 An Avoided Crossing Example 44 § 3 Non-Adiabaticity in QCMD 46 § 4 QCMD-based Surface Hopping 49 § 5 Quantum-classical Liouville equation 52 B. Numerical Algorithms 57 6. Structure Conserving Integration Schemes 60 § 1 The structure of QCMD 60 § 2 Liouville formalism 61 § 3 Symplectic Integrators 62 § 4 Symmetric Integration Schemes 64 7. Exponential Integrators 66 § 1 Evaluating the matrix exponential 66 § 2 Exponential schemes for QCMD 67 § 3 Adaptive Methods 70 8. Algorithms for almost adiabatic dynamics 73 § 1 Approximating highly oscillatory phases 73 § 2 Inheriting asymptotic dynamics 75 9. Averaging integrators for classical dynamics 77 § 1 Pointwise and averaging force evaluation 77 § 2 The highly oscillatory perturbed Hamiltonian test system 79 § 3 Novel construction technique for averaging methods 96 C. Appendix 100 10. Weak convergence 100 Bibliography 102 Zusammenfassung 109 Lebenslauf 110 ; The present thesis is devoted to a mathematical analysis of mixed quantum- classical simulations. Since a fully quantum dynamical description of realistic biomolecular systems is by far beyond the scope of simulations, quantum classicl models have attracted considerable attention. They describe most atoms by the means of classical mechanics but an important, small portion of the underlying system by quantum mechanics. Thus, two mathematical topics arise: 1. the analysis of ...
  • Access State: Open Access