Quantum Monte Carlo determinantal algorithm without Hubbard-Stratonovich transformation: a general consideration

Continuous-time determinantal algorithm is proposed for the quantum Monte Carlo simulation of the interacting fermions. The scheme does not invoke Hubbard-Stratonovich transformation. The fermionic action is divided into two parts. One of them contains the interaction and certain additional terms; another one is purely Gaussian. The first part is considered as a perturbation. Terms of the series expansion for the partition function are generated in a random walk process. The sign problem and the complexity of the algorithm are analyzed. We argue that the scheme should be useful particularly for the systems with non-local interaction.Comment: 5 Page

Regular realizability problems and regular languages

We investigate regular realizability (RR) problems, which are the problems of verifying whether intersection of a regular language -- the input of the problem -- and fixed language called filter is non-empty. We consider two kind of problems depending on representation of regular language. If a regular language on input is represented by a DFA, then we obtain (deterministic) regular realizability problem and we show that in this case the complexity of regular realizability problem for an arbitrary regular filter is either L-complete or NL-complete. We also show that in case of representation regular language on input by NFA the problem is always NL-complete

Analytical model for a crossover between uncorrelated and fractal behaviour of a self-repulsive chain

The thermodynamics of a long self-repulsive chain is studied. In $D<4$ dimensions it shows two distinctly different regimes, corresponding to weak and strong correlations in the system. A simple microscopic analytical model is presented which successfully describes both the regimes. The self-consistent scheme is used, in which the center of mass of a chain is fixed explicitly. This allows to take correlations into account in an indirect manner.Comment: 9 pages, 3 figure

Small parameter for lattice models with strong interaction

Diagram series expansion for lattice models with a localized nonlinearity can be renormalized so that diagram vertexes become irreducible vertex parts of certain impurity model. Thus renormalized series converges well in the very opposite cases of tight and weak binding and pretends to describe in a regular way strong-correlated systems with localized interaction. Benchmark results for the classical O(N) models on a cubic lattice are presented.Comment: 5 page

Dualities in integrable systems: geometrical aspects

We discuss geometrical aspects of different dualities in the integrable systems of the Hitchin type and its various generalizations. It is shown that T duality known in the string theory context is related to the separation of variables procedure in dynamical system. We argue that there are analogues of S duality as well as mirror symmetry in the many-body systems of Hitchin type. The different approaches to the double elliptic systems are unified using the geometry behind the Mukai-Odesskii algebra.Comment: Latex, 29 pages, Contribution to the Proceedings of NATO Advanced Research Workshop, Kiev, September 200

Polynomilal Poisson algebras with regular structure of symplectic leaves

We study polynomial Poisson algebras with some regularity conditions. Linear (Lie-Berezin-Kirillov) structures on dual spaces of semi-simple Lie algebras, quadratic Sklyanin elliptic algebras of \cite{FO1},\cite{FO2} as well as polynomial algebras recently described by Bondal-Dubrovin-Ugaglia (\cite{Bondal},\cite{Ug}) belong to this class. We establish some simple determinantal relations between the brackets and Casimirs in this algebras. These relations imply in particular that for Sklyanin elliptic algebras the sum of Casimir degrees coincides with the dimension of the algebra. We are discussing some interesting examples of these algebras and in particular we show that some of them arise naturally in Hamiltonian integrable systems. Among these examples is a new class of two-body integrable systems admitting an elliptic dependence both on coordinates and momenta.Comment: 21 pages, LaTe

Integrable systems associated with elliptic algebras

We construct some new Integrable Systems (IS) both classical and quantum associated with elliptic algebras. Our constructions are partly based on the algebraic integrability mechanism given by the existence of commuting families in skew fields and partly - on the internal properties of the elliptic algebras and their representations. We give some examples to make an evidence how these IS are related to previously studied.Comment: 24 pages, Late

Optical properties of a disordered metallic film: local vs. collective phenomena

We apply the dual-varibles approach to the problem of the optical response of an disordered film of metal particles with dipole-dipole interaction. Long range dipole-dipole interaction makes the effect of spatial correlations significant, so that dual-variables technique provides a desirable improvement of the coherent-potential results. It is shown that the effect of nonlocality is more pronounced for a medium-range concentration of the particles. The result is compared with the non-local cluster approach. It is shown that short-range correlations accounted in the cluster method reveal themselves in the spectral properties of the response, whereas long-range phenomena kept in the dual technique are more pronounced in the k-dependence of the Green's function.Comment: 8 pages, 3 figure

Constraining the star formation rate with the extragalactic background light

The present day spectrum of the extragalactic background light (EBL) in UV, optical and IR wavelengths is the integral result of multiple astrophysical processes going on throughout the evolution of the Universe. The relevant processes include star formation, stellar evolution, light absorption and emission by the cosmic dust. The properties of these processes are known with uncertainties which contribute to the EBL spectrum precision. In the present paper we develop a numerical model of the EBL spectrum while maintaining the explicit dependence on the astrophysical parameters involved. We constructed a Markov Chain in the parameter space by using the likelihood function built with the up-to-date upper and lower bounds on the EBL intensity. The posterior distributions built with the Markov Chain Monte Carlo method are used to determine an allowed range of the individual parameters of the model. Consequently, the star formation rate multiplication factor is constrained in the range 1.01 < C_{\mbox{sfr}} < 1.69 at $68\%$ C.L. The method also results in the bounds on the lifetime, radius, dust particle density and opacity of the molecular clouds that have large ambiguity otherwise. It is shown that there is a reasonable agreement between the model and the intensity bounds while the astrophysical parameters of the best fit model are close to their estimates from literature.Comment: Submitted to MNRA

Thermodynamic Properties of the Discommensuration Point for Incommensurate Structures: A "Third-Order" Phase Transition

The consequences of the opening of a phason gap in incommensurate systems are studied on a simple model, the discrete frustrated $\phi^4$-model. Analytical considerations and numerical results show that there is a very weak phase transition that can be characterized as third order.Comment: 5 page