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  • 1
    Electronic Resource
    Electronic Resource
    Statistical mechanics of quantum-classical systems (2001)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 115 (2001), S. 5805-5815 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The statistical mechanics of systems whose evolution is governed by mixed quantum-classical dynamics is investigated. The algebraic properties of the quantum-classical time evolution of operators and of the density matrix are examined and compared to those of full quantum mechanics. The equilibrium density matrix that appears in this formulation is stationary under the dynamics and a method for its calculation is presented. The response of a quantum-classical system to an external force which is applied from the distant past when the system is in equilibrium is determined. The structure of the resulting equilibrium time correlation function is examined and the quantum-classical limits of equivalent quantum time correlation functions are derived. The results provide a framework for the computation of equilibrium time correlation functions for mixed quantum-classical systems. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1400129
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  • 2
    Electronic Resource
    Electronic Resource
    Mixed quantum-classical surface hopping dynamics (2000)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 112 (2000), S. 6543-6553 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: An algorithm is presented for the exact solution of the evolution of the density matrix of a mixed quantum-classical system in terms of an ensemble of surface hopping trajectories. The system comprises a quantum subsystem coupled to a classical bath whose evolution is governed by a mixed quantum-classical Liouville equation. The integral solution of the evolution equation is formulated in terms of a concatenation of classical evolution segments for the bath phase space coordinates separated by operators that change the quantum state and bath momenta. A hybrid Molecular Dynamics–Monte Carlo scheme which follows a branching tree of trajectories arising from the action of momentum derivatives is constructed to solve the integral equation. We also consider a simpler scheme where changes in the bath momenta are approximated by momentum jumps. These schemes are illustrated by considering the computation of the evolution of the density matrix for a two-level system coupled to a low dimensional classical bath. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.481225
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  • 3
    Electronic Resource
    Electronic Resource
    Coloring a Lorentz gas (1998)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 109 (1998), S. 6460-6468 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A catalytic site is introduced into a two-dimensional Lorentz gas system consisting of three disks arranged in an equilateral triangle to model reactive dynamics. This system is studied at a microscopic level using an N-cylinder description where the exact dynamics is replaced by a symbolic dynamics which is a generating partition. The Kolmogorov–Sinai entropy and its finite and colored varieties are discussed. These are then related to the colored escape rate, a macroscopic property. Lastly, escape is eliminated by extending the three disk system to an infinite lattice, and the color correlation function is studied. For large catalytic regions the Poisson process rate law expression breaks down. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.477291
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  • 4
    Electronic Resource
    Electronic Resource
    Non-Adiabatic Dynamics in Mixed Quantum-Classical Systems (2000)
    Springer
    Journal of statistical physics 101 (2000), S. 225-242 
    Details
    ISSN: 1572-9613
    Keywords: surface-hopping dynamics ; non-adiabatic dynamics ; mixed quantum-classical dynamics ; density matrix
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Non-adiabatic dynamics in mixed quantum-classical systems is investigated. The mixed quantum-classical system comprises a quantum system coupled to a classical environment. The starting point for the analysis is an evolution equation for the density matrix expressed in a basis of adiabatic quantum states that describes the full quantum dynamics of the subsystem and its coupling to the bath. Since the quantum dynamics influences the evolution of the “classical” degrees of freedom, a description in terms of single Newtonian trajectories is not possible. Through explicit calculations of a two-level quantum system coupled to a low dimensional bath we examine the details of mixed quantum-classical dynamics and its representation in terms of an ensemble of surface-hopping classical trajectory segments.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1026458004345
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    Paper (German National Licenses)
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