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Sep 18, 2013
09/13

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V N Kuzovkov

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The analytical approach developed by us for the calculation of the phase diagram for the Anderson localization via disorder [J.Phys.: Condens. Matter 14, 13777 (2002)] is generalized here to the case of a strong magnetic field when $q$ subbands ($q=1,2,3$) arise. It is shown that in a line with the generally accepted point of view, each subband is characterized by a critical point with a divergent localization length $\xi$ which reveals anomaly in energy and disorder parameters. These critical...

Source: http://arxiv.org/abs/0806.1838v1

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Sep 22, 2013
09/13

by
V. N. Kuzovkov

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The goal of this paper is two-fold. First, based on the interpretation of a quantum tight-binding model in terms of a classical Hamiltonian map, we consider the Anderson localization (AL) problem as the Fermi-Pasta-Ulam (FPU) effect in a modified dynamical system containing both stable and unstable (inverted) modes. Delocalized states in the AL are analogous to the stable quasi-periodic motion in FPU; whereas localized states are analogous to thermalization, respectively. The second aim is to...

Source: http://arxiv.org/abs/0811.1832v1

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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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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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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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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

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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 17, 2013
09/13

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R. Salazar; A. P. J. Jansen; V. N. Kuzovkov

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We present a parallel implementation of cellular automata to simulate chemical reactions on surfaces. The scaling of the computer time with the number of processors for this parallel implementation is quite close to the ideal T/P, where T is the computer time used for one single processor and P the number of processors. Two examples are presented to test the algorithm, the simple A+B->0 model and a realistic model for CO oxidation on Pt(110). By using large parallel simulations, it is...

Source: http://arxiv.org/abs/nlin/0207059v1

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Sep 18, 2013
09/13

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R. Salazar; A. P. J. Jansen; V. N. Kuzovkov

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We discuss an alternative to the traditional gas-phase coupling approach in order to explain synchronized global oscillations in CO oxidation on Pt(110). We use a minimalist microscopic model which includes structural Pt surface reconstruction via front propagation, and large diffusion rates for CO. The synchronization mechanism is associated with the formation of a Turing-like structure of the substrate. By using large parallel microscopic simulations we derive a scaling laws which allow us to...

Source: http://arxiv.org/abs/cond-mat/0210699v1

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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