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Sep 20, 2013
09/13

by
V. N. Kuzovkov; W. von Niessen

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We discuss here in detail a new analytical random walk approach to calculating the phase-diagram for spatially extended systems with multiplicative noise. We use the Anderson localization problem as an example. The transition from delocalized to localized states is treated as a generalized diffusion with a noise-induced first-order phase transition. The generalized diffusion manifests itself in the divergence of averages of wavefunctions (correlators). This divergence is controlled by the...

Source: http://arxiv.org/abs/cond-mat/0607404v1

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40

Sep 21, 2013
09/13

by
V. N. Kuzovkov; W. von Niessen

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Subsequent to the ideas presented in our previous papers [J.Phys.: Condens. Matter {\bf 14} (2002) 13777 and Eur. Phys. J. B {\bf 42} (2004) 529], we discuss here in detail a new analytical approach to calculating the phase-diagram for the Anderson localization in arbitrary spatial dimensions. The transition from delocalized to localized states is treated as a generalized diffusion which manifests itself in the divergence of averages of wavefunctions (correlators). This divergence is controlled...

Source: http://arxiv.org/abs/cond-mat/0508283v1

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42

Sep 22, 2013
09/13

by
V. N. Kuzovkov; W. von Niessen

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The method proposed by the present authors to deal analytically with the problem of Anderson localization via disorder [J.Phys.: Condens. Matter {\bf 14} (2002) 13777] is generalized for higher spatial dimensions D. In this way the generalized Lyapunov exponents for diagonal correlators of the wave function, $ $, can be calculated analytically and exactly. This permits to determine the phase diagram of the system. For all dimensions $D > 2$ one finds intervals in the energy and the disorder...

Source: http://arxiv.org/abs/cond-mat/0501446v1

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Sep 21, 2013
09/13

by
V. N. Kuzovkov; W. von Niessen

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The method proposed by the present authors to deal analytically with the problem of Anderson localization via disorder [J.Phys.: Condens. Matter {\bf 14} (2002) 13777] is generalized for higher spatial dimensions D. In this way the generalized Lyapunov exponents for diagonal correlators of the wave function, $ $, can be calculated analytically and exactly. This permits to determine the phase diagram of the system. For all dimensions $D > 2$ one finds intervals in the energy and the disorder...

Source: http://arxiv.org/abs/cond-mat/0402463v1

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Sep 18, 2013
09/13

by
V. N. Kuzovkov; W. von Niessen

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Our previous results [J.Phys.: Condens. Matter 14 (2002) 13777] dealing with the analytical solution of the two-dimensional (2-D) Anderson localization problem due to disorder is generalized for anisotropic systems (two different hopping matrix elements in transverse directions). We discuss the mathematical nature of the metal-insulator phase transition which occurs in the 2-D case, in contrast to the 1-D case, where such a phase transition does not occur. In anisotropic systems two...

Source: http://arxiv.org/abs/cond-mat/0611198v1

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Jul 20, 2013
07/13

by
O. Kortlüke; V. N. Kuzovkov; W. von Niessen

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We show the existence of internal stochastic resonance in a microscopic stochastic model for the oscillating CO oxidation on single crystal surfaces. This stochastic resonance arises directly from the elementary reaction steps of the system without any external input. The lattice gas model is investigated by means of Monte Carlo simulations. It shows oscillation phenomena and mesoscopic pattern formation. Stochastic resonance arises once homogeneous nucleation in the individual surface phases...

Source: http://arxiv.org/abs/cond-mat/9906215v1

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Sep 21, 2013
09/13

by
V. N. Kuzovkov; V. Kashcheyevs; W. von Niessen

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We reply to comments by P.Marko$\breve{s}$, L.Schweitzer and M.Weyrauch [preceding paper] on our recent paper [J. Phys.: Condens. Matter 63, 13777 (2002)]. We demonstrate that our quite different viewpoints stem for the different physical assumptions made prior to the choice of the mathematical formalism. The authors of the Comment expect \emph{a priori} to see a single thermodynamic phase while our approach is capable of detecting co-existence of distinct pure phases. The limitations of the...

Source: http://arxiv.org/abs/cond-mat/0402468v1

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Sep 18, 2013
09/13

by
V. N. Kuzovkov; W. von Niessen; V. Kashcheyevs; O. Hein

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The Anderson localization problem in one and two dimensions is solved analytically via the calculation of the generalized Lyapunov exponents. This is achieved by making use of signal theory. The phase diagram can be analyzed in this way. In the one dimensional case all states are localized for arbitrarily small disorder in agreement with existing theories. In the two dimensional case for larger energies and large disorder all states are localized but for certain energies and small disorder...

Source: http://arxiv.org/abs/cond-mat/0212036v1