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By K. Lindenberg, Y. Zhao, D. W. Brown (auth.), Pedro L. Garrido, Joacquín Marro (eds.)

ISBN-10: 3662141485

ISBN-13: 9783662141489

ISBN-10: 3662141507

ISBN-13: 9783662141502

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Example text

Any point in the parameter space can be approached from various points close to it, which we shall call A Variational Approach to Exciton-Phonon Coupling 21 its "neighbors". A completely reversible point is one that survives all the reversibility tests of its various neighbors. Most of the regions in our problem are found to be reversible except for a thin tongue (see Fig. 2 and Fig. 14) constituting a "phase boundary" between two types of polaron states. Within that tongue, two solutions are obtained depending on whether those points are reached from above or below the tongue.

There are only two surfaces because both amplitudes in Fourier space turn out to be real. We have not proved this analytically, but it turns out this way numerically for all parameter values studied; this is one compelling reason for exhibiting these results in Fourier space. The surfaces shown are typical of the strong-coupling region. , reflect states of motion or polaron dynamics. Consider first the exciton amplitude, and let us perform a "mental inverse Fourier transform" in k to real space.

Compared with previous work we have imposed no restrictions on the forms of the variational surfaces other than those implicit in each variational Ansatz itself. Relaxation techniques are efficient iteration methods for identifying energy minima of complex variational systems. The principal difficulties with 20 K. Lindenberg, Y. W. Brown this approach lie in the stability of the iteration and the quality of the convergence. Though a proper solution obtained by this or any other variational method must be stable relative to small changes in the variational parameters, and though the search for such solutions relies upon this stability property, it is possible for errors in a fraction of the total solution to spread and destabilize the iteration or otherwise limit the quality of the convergence.

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Fourth Granada Lectures in Computational Physics: Proceedings of the 4th Granada Seminar on Computational Physics Held at Granada, Spain, 9–14 September 1996 by K. Lindenberg, Y. Zhao, D. W. Brown (auth.), Pedro L. Garrido, Joacquín Marro (eds.)


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