Topological Spectral Correlations in 2D Disordered Systems

It is shown that the tail in the two-level spectral correlation function R(s) for particles on 2D closed disordered surfaces is determined entirely by surface topology: $R(s)=-\chi/(6\pi^2\beta s^2)$, where $\beta$ = 1,2 or 4 for the orthogonal, unitary and symplectic ensembles, and $\chi$ = 2(1-p) is the Euler characteristics of the surface with p "handles" (holes). The result is valid for g << s << g^2 for $\beta$=1,4 and for g << s << g^3 for $\beta$=2, where g >> 1 is the dimensionless conductance.Comment: 4 pages, revte

Asymptotic behavior and critical coupling in the scalar Yukawa model from Schwinger-Dyson equations

A sequence of $n$-particle approximations for the system of Schwinger-Dyson equations is investigated in the model of a complex scalar field $\phi$ and a real scalar field $\chi$ with the interaction $g\phi^*\phi\chi$. In the first non-trivial two-particle approximation, the system is reduced to a system of two nonlinear integral equations for propagators. The study of this system shows that for equal masses a critical coupling constant $g^2_c$ exists, which separates the weak- and strong-coupling regions with the different asymptotic behavior for deep Euclidean momenta. In the weak-coupling region ($g^2<g^2_c$), the propagators are asymptotically free, which corresponds to the wide-spread opinion about the dominance of perturbation theory for this model. At the critical point the asymptotics of propagators are $\sim 1/p$. In the strong coupling region ($g^2>g^2_c$), the propagators are asymptotically constant, which corresponds to the ultra-local limit. For unequal masses, the critical point transforms into a segment of values, in which there are no solutions with a self-consistent ultraviolet behavior without Landau singularities.Comment: 19 pages; some points clarified; typos correcte

On Some Peculiarities of Solving Nonstationary Problems of Quantum Mechanics

Exact solutions of several nonstationary problems of quantum mechanics are obtained. It is shown that if the initial conditions of the problem correspond to the localized-in-space particle, then it moves exactly along the classical trajectory, and the wave packet is not spread in time.Comment: 3 page

Direct and Inverse Cascades in the Wind-Driven Sea

We offer a new form for the S(nl) term in the Hasselmann kinetic equation for squared wave amplitudes of wind-driven gravity wave. This form of S(nl) makes possible to rewrite in differential form the conservation laws for energy, momentum, and wave action, and introduce their fluxes by a natural way. We show that the stationary kinetic equation has a family of exact Kolmogorov-type solutions governed by the fluxes of motion constants: wave action, energy, and momentum. The simple "local" model for S(nl) term that is equivalent to the "diffusion approximation" is studied in details. In this case, Kolmogorov spectra are found in the explicit form. We show that a general solution of the stationary kinetic equation behind the spectral peak is described by the Kolmogorov-type solution with frequency-dependent fluxes. The domains of "inverse cascade" and "direct cascade" can be separated by natural way. The spectrum in the universal domain is close to $\omega^{-4}$

Norm of Bethe Wave Function as a Determinant

This is a historical note. Bethe Ansatz solvable models are considered, for example XXZ Heisenberg anti-ferromagnet and Bose gas with delta interaction. Periodic boundary conditions lead to Bethe equation. The square of the norm of Bethe wave function is equal to a determinant of linearized system of Bethe equations (determinant of matrix of second derivatives of Yang action). The proof was first published in Communications in Mathematical Physics, vol 86, page 391 in l982. Also domain wall boundary conditions for 6 vertex model were discovered in the same paper [see Appendix D]. These play an important role for algebraic combinatorics: alternating sign matrices, domino tiling and plane partition. Many publications are devoted to six vertex model with domain wall boundary conditions.Comment: 6 page

A note on (asymptotically) Weyl-almost periodic properties of convolution products

The main aim of this paper is to investigate Weyl-$p$-almost periodic properties and asymptotically Weyl-$p$-almost periodic properties of convolution products. In such a way, we continue several recent research studies of ours which do concern a similar problematic

Network as a Complex System: Information Flow Analysis

A new approach for the analysis of information flow on a network is suggested using protocol parameters encapsulated in the package headers as functions of time. The minimal number of independent parameters for a complete description of the information flow (phase space dimension of the information flow) is found to be about 10 - 12

Multidimensional Network Monitoring for Intrusion Detection

An approach for real-time network monitoring in terms of numerical time-dependant functions of protocol parameters is suggested. Applying complex systems theory for information f{l}ow analysis of networks, the information traffic is described as a trajectory in multi-dimensional parameter-time space with about 10-12 dimensions. The network traffic description is synthesized by applying methods of theoretical physics and complex systems theory, to provide a robust approach for network monitoring that detects known intrusions, and supports developing real systems for detection of unknown intrusions. The methods of data analysis and pattern recognition presented are the basis of a technology study for an automatic intrusion detection system that detects the attack in the reconnaissance stage.Comment: Talk at the International Conference on Complex Systems, June 9-14, 2002, Nashua, N

Charge and spin separation in the 1D Hubbard model

We consider the repulsive Hubbard model in one dimension and show the different mechanisms present in the charge and spin separation phenomena for an electron, at half filling and bellow half filling. We also comment recent experimental results.Comment: revtex, 4 page

New approach for network monitoring and intrusion detection

The approach for a network behavior description in terms of numerical time-dependant functions of the protocol parameters is suggested. This provides a basis for application of methods of mathematical and theoretical physics for information flow analysis on network and for extraction of patterns of typical network behavior. The information traffic can be described as a trajectory in multi-dimensional parameter-time space with dimension about 10-12. Based on this study some algorithms for the proposed intrusion detection system are discussed