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  • 1
    Electronic Resource
    Electronic Resource
    Theory of activated rate processes for arbitrary frequency dependent friction: Solution of the turnover problem (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 91 (1989), S. 4073-4087 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: An analytical theory is formulated for the thermal (classical mechanical) rate of escape from a metastable state coupled to a dissipative thermal environment. The working expressions are given solely in terms of the quantities entering the generalized Langevin equation for the particle dynamics. The theory covers the whole range of damping strength and is applicable to an arbitrary memory friction. This solves what is commonly known as the Kramers turnover problem. The basic idea underlying the approach is the observation that the escape dynamics is governed by the unstable normal mode coordinate—and not the particle system coordinate. An application to the case of a particle moving in a piecewise harmonic potential with an exponentially decaying memory-friction is presented. The comparison with the numerical simulation data of Straub, Borkovec, and Berne [J. Chem. Phys. 84, 1788 (1986)] exhibits good agreement between theory and simulation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.456837
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  • 2
    Electronic Resource
    Electronic Resource
    Exact and semiclassical density matrix of a particle moving in a barrier potential with bound states (1996)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 104 (1996), S. 7526-7538 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We present a barrier potential with bound states that is exactly solvable and determine the eigenfunctions and eigenvalues of the Hamiltonian. The equilibrium density matrix of a particle moving at temperature T in this nonlinear barrier potential field is determined. The exact density matrix is compared with the result of the path integral approach in the semiclassical approximation. For opaque barriers the simple semiclassical approximation is found to be sufficient at high temperatures while at low temperatures the fluctuation paths may have a caustic depending on temperature and endpoints. Near the caustics the divergence of the simple semiclassical approximation of the density matrix is removed by a nonlinear fluctuation potential. For opaque barriers the improved semiclassical approximation is again in agreement with the exact result. In particular, bound states and the form of resonance states are described accurately by the semiclassical approach. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.471462
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  • 3
    Electronic Resource
    Electronic Resource
    Semiclassical theory of vibrational energy relaxation (1998)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 108 (1998), S. 4972-4983 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A theory of vibrational energy relaxation based on a semiclassical treatment of the quantum master equation is presented. Using new results on the semiclassical expansion of dipole matrix elements, we show that in the classical limit the master equation reduces to the Zwanzig energy diffusion equation. The leading quantum corrections are determined and discussed for the harmonic and Morse potentials. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.475906
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  • 4
    Electronic Resource
    Electronic Resource
    Single charge tunneling: A brief introduction (1991)
    Springer
    The European physical journal 85 (1991), S. 319-325 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The field of single charge tunneling comprises of phenomena where the tunneling of a microscopic charge, usually carried by an electron or a Cooper pair, leads to macroscopically observable effects. The basic principles governing this area of research are briefly outlined and the present state of the art is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01307626
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  • 5
    Electronic Resource
    Electronic Resource
    Fluctuations in nonlinear Markovian systems (1979)
    Springer
    The European physical journal 34 (1979), S. 107-116 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We study nonlinear irreversible processes by statistical mechanical methods from a general point of view. Assuming that the macroscopic variables behave approximatively Markovian we derive evolution equations for the mean values as well as for the fluctuations about the mean. The mean values obey nonlinear transport equations and the fluctuations obey linear nonstationary Langevin equations. The equations of motion are completely specified by the entropy and the transport coefficients as functions of the macroscopic state. The theory provides a statistical mechanical basis for some phenomenological approaches put forward recently.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01362784
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  • 6
    Electronic Resource
    Electronic Resource
    Renormalized transport equations for the bistable potential model (1980)
    Springer
    The European physical journal 36 (1980), S. 283-293 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Renormalized transport equations for general Fokker-Planck systems are derived and applied to the bistable potential model. The exact equation for the expectation value 〈x〉 t can be evaluated in both domains 〈D〉∈x ± and 〈x〉∈D 0 outside and between the potential minima, leading to drastic differences of the dynamics prevailing inD ± andD 0, respectively.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01325292
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  • 7
    Electronic Resource
    Electronic Resource
    Low-temperature and long-time anomalies of a damped quantum particle (1987)
    Springer
    Journal of statistical physics 49 (1987), S. 767-810 
    Details
    ISSN: 1572-9613
    Keywords: Dissipative quantum systems ; Brownian motion ; localization ; anomalous diffusion ; memory effects ; functional integral techniques
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The time evolution of a damped quantum particle is discussed. Dissipation is modeled by the bilinear coupling to a set of harmonic oscillators. Using a functional integral technique that accounts for initial correlations between the particle and the reservoir, one can express the dynamics of the damped particle entirely in terms of equilibrium correlation functions. The long-time behavior of these correlations is determined for memory damping arising from the coupling to a reservoir with spectral densityI(ω) ∞ω α at low frequencies, where α 〉 0. The time evolution of nonequilibrium initial states of the damped particle is discussed. At finite temperatures an initially localized state is found to spread subdiffusively or superdiffusively, depending on α. For α 〉 2 the damping becomes ineffective for long times, and the width of a state grows kinematically. At zero temperature and for α 〈 1, an initially localized state remains localized for all times. For α ≥ 1 the state spreads, but with a slower rate than at finite temperatures. Study of arbitrary initial states indicates that the process is ergodic at finite temperatures only for α ≤ 2 and at zero temperature for 1 ≤ α ≤ 2.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01009356
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  • 8
    Electronic Resource
    Electronic Resource
    Quantum theory of the damped harmonic oscillator (1984)
    Springer
    The European physical journal 55 (1984), S. 87-94 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A phenomenological stochastic modelling of the process of thermal and quantal fluctuations of a damped harmonic oscillator is presented. The divergence of the momentum dispersion associated with the Markovian limit is removed by a Drude regularization. The variances of position and momentum are evaluated in closed form at arbitrary temperature and for arbitrary damping. Properties of real and imaginary time correlation functions are discussed, and a spectral decomposition of the equilibrium density matrix is given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01307505
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  • 9
    Electronic Resource
    Electronic Resource
    Single electron tunneling rates in multijunction circuits (1991)
    Springer
    The European physical journal 84 (1991), S. 143-155 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The rate of electron tunneling through normal metal tunnel junctions is calculated for the case of ultrasmall junction capacitances. The so-called Coulomb blockade of electron tunneling at low temperatures is shown to be strongly affected by the external electrical circuit. Under the common experimental condition of a low impedance environment the Coulomb blockade is suppressed for single tunnel junctions. However, a Coulomb gap structure emerges for junctions embedded in a high impedance environment. For a double junction setup a Coulomb blockade of tunneling arises even for low impedance environments due to the charge quantization on the metallic island between the junctions. An approach using circuit analysis is presented which allows to reduce the calculation of tunneling rates in multijunction circuits to those of a single junction in series with an effective capacitance. The range of validity of the socalled local rule and global rule rates is clarified. It is found that the tunneling rate tends towards the global rule rate as the number of junctions is increased. Some specific results are given for a one-dimensional array of tunnel junctions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01453767
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  • 10
    Electronic Resource
    Electronic Resource
    Renormalized transport equations for the bistable potential model (1980)
    Springer
    The European physical journal 39 (1980), S. 88-88 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01292642
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