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  <doc>
    <id>381</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>1998-12-21</completedDate>
    <publishedDate>1998-12-21</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Non-Adiabatic Effects in Quantum-Classical Molecular Dynamics</title>
    <abstract language="eng">In molecular dynamics applications there is a growing interest in mixed quantum-classical models. The article is concerned with the so-called QCMD model. This model describes most atoms of the molecular system by the means of classical mechanics but an important, small portion of the system by the means of a wavefunction. We review the conditions under which the QCMD model is known to approximate the full quantum dynamical evolution of the system. In most quantum-classical simulations the {\em Born-Oppenheimer model} (BO) is used. In this model, the wavefunction is adiabatically coupled to the classical motion which leads to serious approximation deficiencies with respect to non-adiabatic effects in the fully quantum dynamical description of the system. In contrast to the BO model, the QCMD model does include non-adiabatic processes, e.g., transitions between the energy levels of the quantum system. It is demonstrated that, in mildly non-adiabatic scenarios, so-called {\em surface hopping} extensions of QCMD simulations yield good approximations of the non-adiabatic effects in full quantum dynamics. The algorithmic strategy of such extensions of QCMD is explained and the crucial steps of its realization are discussed with special emphasis on the numerical problems caused by highly oscillatory phase effects.</abstract>
    <identifier type="serial">SC-98-38</identifier>
    <identifier type="opus3-id">382</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-3817</identifier>
    <enrichment key="SourceTitle">Appeared in: F. Keil, W. Mackens et al. Scientific Computing in Chemical Engineering II, Computational Fluid Dynamics, Reaction Engineering and Molecular Properties. Springer (1999) pp. 42-56</enrichment>
    <author>Christof Schütte</author>
    <author>Peter Nettesheim</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-98-38</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>quantum-classical molecular dynamics</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>non-adiabatic processes</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Schrödinger equation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>highly oscillatory phase</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>adiabatic limit</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>quantum adiabati</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="81Q15">Perturbation theories for operators and differential equations</collection>
    <collection role="msc" number="81Q20">Semiclassical techniques, including WKB and Maslov methods</collection>
    <collection role="msc" number="81S25">Quantum stochastic calculus</collection>
    <collection role="msc" number="81V55">Molecular physics [See also 92E10]</collection>
    <collection role="msc" number="92E10">Molecular structure (graph-theoretic methods, methods of differential topology, etc.)</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/381/SC-98-38.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/381/SC-98-38.pdf</file>
  </doc>
  <doc>
    <id>398</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
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    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>1999-04-12</completedDate>
    <publishedDate>1999-04-12</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Partial Wigner Transforms and the Quantum--Classical Liouville Equation</title>
    <abstract language="eng">In molecular dynamics applications there is a growing interest in mixed quantum-classical models. The {\em quantum-classical Liouville equation} (QCL) describes most atoms of the molecular system under consideration by means of classical phase space density but an important, small portion of the system by means of quantum mechanics. The QCL is derived from the full quantum dynamical (QD) description by applying the Wigner transform to the classical part'' of the system only. We discuss the conditions under which the QCL model approximates the full QD evolution of the system. First, analysis of the asymptotic properties of the Wigner transform shows that solving the QCL yields a first order approximation of full quantum dynamics. Second, we discuss the adiabatic limit of the QCL. This discussion shows that the QCL solutions may be interpretated as classical phase space densities, at least near the adiabatic limit. Third, it is demonstrated that the QCL yields good approximations of {\em non-adiabatic quantum effects,} especially near so-called {\em avoided crossings} where most quantum-classical models fail.</abstract>
    <identifier type="serial">SC-99-10</identifier>
    <identifier type="opus3-id">399</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-3983</identifier>
    <author>Christof Schütte</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-99-10</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>QCMD</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>quantum-classical Liouville equation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>surface hopping</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Wigner transform</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>asymptotic expansion</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>nonadiabatic effects</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="81Q15">Perturbation theories for operators and differential equations</collection>
    <collection role="msc" number="81Q20">Semiclassical techniques, including WKB and Maslov methods</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/398/SC-99-10.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/398/SC-99-10.pdf</file>
  </doc>
</export-example>
