Cooperative behavior of qutrits with dipole-dipole interactions

We have identified a class of many body problems with analytic solution beyond the mean-field approximation. This is the case where each body can be considered as an element of an assembly of interacting particles that are translationally frozen multi-level quantum systems and that do not change significantly their initial quantum states during the evolution. In contrast, the entangled collective state of the assembly experiences an appreciable change. We apply this approach to interacting three-level systems.Comment: 5 pages, 3 figures. Minor correction

On Vertex Operator Construction of Quantum Affine Algebras

We describe the construction of the quantum deformed affine Lie algebras using the vertex operators in the free field theory. We prove the Serre relations for the quantum deformed Borel subalgebras of affine algebras, namely the case of $\hat{\it sl}_{2}$ is considered in detail. We provide some formulas for generators of affine algebra.Comment: LaTeX, 9 pages; typos corrected, references adde

Influence of low-frequency vibration on the erythrocytes acid resistance

Досліджено дію низькочастотної вібрації (діапазон частот 8–32 Гц, амплітуди 0,5 ± 0,04 та 0,9 ± 0,08 мм) на кислотну резистентність еритроцитів. Охарактеризовано кінетику окремих стадій гемолізу. Оцінено частотно-часові залежності констант швидкості стадій гемолізу. Вібрація з частотами 8–16 Гц, амплітудою 0,5 ± 0,04 та 8 Гц, амплітудою 0,9 ± 0,08 мм викликає деструктивні перебудови водно-білкового складу цитоплазми, що викликає зниження бар’єру проникності для гемолітичного агента. При вібраційному впливі інтервалу частот 20–32 Гц, в результаті окислювального стресу, переважають реакції модифікувального характеру, що викликають агрегацію клітинних білків, зокрема білка смуги 3.Исследовано действие низкочастотной вибрации (диапазон частот 8–32 Гц, амплитуды 0,5 ± 0,04 и 0,9 ± 0,08 мм) на кислотную резистентность эритроцитов. Охарактеризована кинетика отдельных стадий гемолиза. Оценены частотно-временные зависимости констант скоростей стадий гемолиза. Вибрация с частотами 8–16 Гц, амплитудой 0,5 ± 0,04 мм и 8 Гц, амплитудой 0,9 ± 0,08 мм вызывает деструктивные перестройки водно-белкового состава цитоплазмы, приводящие к снижению барьера проницаемости для гемолитического агента. При вибрационном воздействии интервала частот 20–32 Гц, в результате окислительного стресса, преобладают реакции модифицирующего характера, приводящие к агрегации клеточных белков и, в частности, белка полосы 3.The influence of low-frequency vibration (frequency range 8–32 Hz, amplitudes 0.5 ± 0.04 and 0.9 ± 0.08 mm) on the erythrocytes’ acid resistance was studied. The kinetics of various hemolysis stages was investigated. The time-frequency dependences of the kinetics constants of hemolysis stages were obtained and discussed. It was shown that 8–16 Hz vibration with the 0.5 mm amplitude and 8 Hz with 0.9 mm causes destructive reorganizations of a cytoplasm’s water-protein structure. It leads to decrease in a permeability barrier for a hemolytic agent. As a result of oxidizing stress the vibration in the frequency range of 20–32 Hz causes the modifying reactions leading to the aggregation of cellular proteins and, in particular, the band 3 protein

Probing AdS/CFT correspondence via world-sheet methods and 2d gravity like scaling arguments

We show how some features of the AdS/CFT correspondence for AdS_3 can easily be understood via standard world-sheet methods and 2d gravity like scaling arguments. To do this, we propose a stringy way for perturbing two-dimensional CFT's around their critical points. Our strategy is to start from a stringy (world-sheet) representation of 2d CFT in space-time. Next we perturb a world-sheet action by some marginal operators such that the space-time symmetry becomes finite dimensional. As a result, we get a massive FT in space-time with a scale provided by two-dimensional coupling constant. It turns out that there exists a perturbation that leads to string theory on AdS_3. In this case the scale is equivalently provided by the radial anti-de-Sitter coordinate.Comment: 15 pages; corrected some typo

Invaded cluster algorithm for critical properties of periodic and aperiodic planar Ising models

We demonstrate that the invaded cluster algorithm, recently introduced by Machta et al, is a fast and reliable tool for determining the critical temperature and the magnetic critical exponent of periodic and aperiodic ferromagnetic Ising models in two dimensions. The algorithm is shown to reproduce the known values of the critical temperature on various periodic and quasiperiodic graphs with an accuracy of more than three significant digits. On two quasiperiodic graphs which were not investigated in this respect before, the twelvefold symmetric square-triangle tiling and the tenfold symmetric T\"ubingen triangle tiling, we determine the critical temperature. Furthermore, a generalization of the algorithm to non-identical coupling strengths is presented and applied to a class of Ising models on the Labyrinth tiling. For generic cases in which the heuristic Harris-Luck criterion predicts deviations from the Onsager universality class, we find a magnetic critical exponent different from the Onsager value. But also notable exceptions to the criterion are found which consist not only of the exactly solvable cases, in agreement with a recent exact result, but also of the self-dual ones and maybe more.Comment: 15 pages, 5 figures; v2: Fig. 5b replaced, minor change

Calogero-Sutherland eigenfunctions with mixed boundary conditions and conformal field theory correlators

We construct certain eigenfunctions of the Calogero-Sutherland hamiltonian for particles on a circle, with mixed boundary conditions. That is, the behavior of the eigenfunction, as neighbouring particles collide, depend on the pair of colliding particles. This behavior is generically a linear combination of two types of power laws, depending on the statistics of the particles involved. For fixed ratio of each type at each pair of neighboring particles, there is an eigenfunction, the ground state, with lowest energy, and there is a discrete set of eigenstates and eigenvalues, the excited states and the energies above this ground state. We find the ground state and special excited states along with their energies in a certain class of mixed boundary conditions, interpreted as having pairs of neighboring bosons and other particles being fermions. These particular eigenfunctions are characterised by the fact that they are in direct correspondence with correlation functions in boundary conformal field theory. We expect that they have applications to measures on certain configurations of curves in the statistical O(n) loop model. The derivation, although completely independent from results of conformal field theory, uses ideas from the "Coulomb gas" formulation.Comment: 35 pages, 9 figure

An information theoretic approach to statistical dependence: copula information

We discuss the connection between information and copula theories by showing that a copula can be employed to decompose the information content of a multivariate distribution into marginal and dependence components, with the latter quantified by the mutual information. We define the information excess as a measure of deviation from a maximum entropy distribution. The idea of marginal invariant dependence measures is also discussed and used to show that empirical linear correlation underestimates the amplitude of the actual correlation in the case of non-Gaussian marginals. The mutual information is shown to provide an upper bound for the asymptotic empirical log-likelihood of a copula. An analytical expression for the information excess of T-copulas is provided, allowing for simple model identification within this family. We illustrate the framework in a financial data set.Comment: to appear in Europhysics Letter

Liouville Field Theory of Fluctuating Loops

Effective field theories of two-dimensional lattice models of fluctuating loops are constructed by mapping them onto random surfaces whose large scale fluctuations are described by a Liouville field theory. This provides a geometrical view of conformal invariance in two-dimensional critical phenomena and a method for calculating critical properties of loop models exactly. As an application of the method, the conformal charge and critical exponents for two mutually excluding Hamiltonian walks on the square lattice are calculated.Comment: 4 RevTex pages, 1 eps figur

Critical behavior of weakly-disordered anisotropic systems in two dimensions

The critical behavior of two-dimensional (2D) anisotropic systems with weak quenched disorder described by the so-called generalized Ashkin-Teller model (GATM) is studied. In the critical region this model is shown to be described by a multifermion field theory similar to the Gross-Neveu model with a few independent quartic coupling constants. Renormalization group calculations are used to obtain the temperature dependence near the critical point of some thermodynamic quantities and the large distance behavior of the two-spin correlation function. The equation of state at criticality is also obtained in this framework. We find that random models described by the GATM belong to the same universality class as that of the two-dimensional Ising model. The critical exponent $\nu$ of the correlation length for the 3- and 4-state random-bond Potts models is also calculated in a 3-loop approximation. We show that this exponent is given by an apparently convergent series in $\epsilon=c-\frac{1}{2}$ (with $c$ the central charge of the Potts model) and that the numerical values of $\nu$ are very close to that of the 2D Ising model. This work therefore supports the conjecture (valid only approximately for the 3- and 4-state Potts models) of a superuniversality for the 2D disordered models with discrete symmetries.Comment: REVTeX, 24 pages, to appear in Phys.Rev.