The quantum lifetime of the Davydov soliton

Considering an infinite spine in the Alpha-helix, stationary states should be eigenstates of a translational operator. These states should be nonlocalized in contradiction to a localized soliton. The difference in energy between localized and nonlocalized (Bloch) states is due to zero point motion and gives information about the quantum stability of the Davydov soliton. We develop a theory of statinary states and show that only for the limiting case of a classical lattice the product ansatz by Davydov is exact. Finally, we calculate the width of the soliton band to get information on the lifetime of the localized soliton.     

A directed binding model of motor protein motion on protein filaments

We propose a new mechanism of motor protein motion on protein filaments, treating the heads as extended objects connected by an elastic neck linker region. In our model, ATP hydrolysis provides chemical energy while directed binding is key in force generation coupled with an elastic neck linker region storing elastic energy. Simulations of the differential equation of motion, based on this model, agree with experiment for both kinesin and its analog, Ncd, and can also be applied to myosin. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Perturbation theory for calculating solitary waves in one-dimensional lattices

A systematic method is given to compute solitary waves in one-dimensional lattices. The procedure, based on perturbation theory, leads to an infinite series, which has to be summed up completely. This can be done by the use of Padé approximation or a pseudo-potential method. We obtain exact results in the case of the Toda lattice and good approximations for solitary waves in non-integrable systems. For the Toda lattice also theN-soliton solution is calculated.     

Ein Modell für den Selbstenergieoperator im unendlichen System

We consider the most simple rational model function for the selfenergyoperator exhibiting the properties which are demanded by the general theory of infinite Fermi systems for the asymptotic region and the neighbourhood of the Fermisurface. The occupation number which may be calculated exactly is determined for various parameters.     

Conditions for the weak energy dependency of effective interactions

We discuss the possibilities for the existence of effective interactions depending weakly on the energy in a given interval. These interactions may be used in computing matrixelements of the Greenoperator in a modelspace. To show that the interval in which the model is valid may principally be chosen at random, we introduce effective interactions with poles at the eigenvalues of the operatorH+λV ¹ and consider the necessary properties ofV ¹. The operatorV ¹ determines the modelspace, and there-fore the matrixelements of the Greenoperator which can be computed within the model.     

Nonlinear excitations in the low temperature region of the classical toda lattice

The ideal cnoidal wave gas approximation is presented. It is shown that this approximation is valid for low temperatures.     

Elementary arguments that the Wu-Austin Hamiltonian has no finite ground state (the search for a microscopic foundation of Fr?lichs theory).

The Wu-Austin Hamiltonian as the basis for deriving Fr?hlichs rate equations from a microscopical point of view has been investigated. In addition to an earlier paper we show in a very easy manner that this or similar Hamiltonians have no lower bound and are therefore unphysical. The perturbation expansion which is the tool to derive Fr?hlichs rate equations with this Hamiltonian is not converging. Therefore, the usual derivation of this rate equation is not valid.     

Der Einflu\ einer Spin-Spinwechselwirkung auf das magnetische Moment schwerer Atomkerne

The corrections to the magnetic moments of heavy nuclei on account of a spindependent two-body-interaction of the form (σ ₁ σ ₂)V(r ₁–r ₂) are determined in the Fermi model calculating the second order contribution for the selfenergy part. It is shown using conservation laws that this contribution is connected to the local Vertex T ^ω [σ] of Migdal's theory of finite Fermi systems.     

Solitons in the statistical mechanics of the Toda lattice

Using proper canonical variables of the Toda soliton we develop a formalism to describe a gas of independent solitons. We find that this model gives the exact thermodynamic properties for high temperatures.