Renormalization theory for the Fulde-Ferrell-Larkin-Ovchinnikov states at T>0T>0

Within the renormalization group framework we study the stability of superfluid density wave states, known as Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phases, with respect to thermal order-parameter fluctuations in two and three-dimensional ($d\in \{2,3\}$) systems. We analyze the renormalization-group flow of the relevant ordering wave-vector $\vec{Q_0}$. The calculation indicates an instability of the FFLO-type states towards either a uniform superfluid or the normal state in $d\in\{2,3\}$ and $T>0$. In $d=2$ this is signaled by $\vec{Q_0}$ being renormalized towards zero, corresponding to the flow being attracted either to the usual Kosterlitz-Thouless fixed-point or to the normal phase. We supplement a solution of the RG flow equations by a simple scaling argument, supporting the generality of the result. The tendency to reduce the magnitude of $\vec{Q_0}$ by thermal fluctuations persists in $d=3$, where the very presence of long-range order is immune to thermal fluctuations, but the effect of attracting $\vec{Q_0}$ towards zero by the flow remains observed at $T>0$

The application of the Schur-Weyl duality in the one-dimensional Hubbard model

We present the application of the Schur-Weyl duality in the one-dimensional Hubbard model in the case of half-filled system of any numer of atoms. We replace the actions of the dual symmetric and unitary groups in the whole Hilbert space by the actions of the dual groups in the spin and pseudo-spin spaces. The calculations significantly reduce the dimension of the eigenproblem of the one-dimensional Hubbard model.Comment: 16 pages, 2 table

Dimensional crossovers and Casimir forces for the Bose gas in anisotropic optical lattices

We consider the Bose gas on a $d$-dimensional anisotropic lattice employing the imperfect (mean-field) gas as a prototype example. We study the dimensional crossover arising as a result of varying the dispersion relation at finite temperature $T$. We analyze in particular situations where one of the relevant effective dimensionalities is located at or below the lower critical dimension, so that the Bose-Einstein condensate becomes expelled from the system by anisotropically modifying the lattice parameters controlling the kinetic term in the Hamiltonian. We clarify the mechanism governing this phenomenon. Subsequently we study the thermodynamic Casimir effect occurring in this system. We compute the exact profile of the scaling function for the Casimir energy. As an effect of strongly anisotropic scale invariance, the Casimir force below or at the critical temperature $T_c$ may be repulsive even for periodic boundary conditions. The corresponding Casimir amplitude is universal only in a restricted sense, and the power law governing the decay of the Casimir interaction becomes modified. We also demonstrate that, under certain circumstances, the scaling function is constant for suffciently large values of the scaling variable, and in consequence is not an analytical function. At $T > T_c$ the Casimir-like interactions reflect the structure of the correlation function, and, for certain orientations of the confining walls, show exponentially damped oscillatory behavior so that the corresponding force is attractive or repulsive depending on the distance.Comment: 12 pages, 5 figures, major changes in the manuscrip

Altmanʼs Model as an Instrument for the Evaluation of the Financial Situation of the Alma Market S.A.

Using a set of standard financial statements, you can designate a large number of economic and financial indicators that show the condition of the company. A large number of indicators gives a lot of opportunities to assess the health of the company. However, there is a risk of introduction of information chaos, which instead help in the assessment of the economic and social situation of the firm may make it harder for making analyses. Comes with the help of LDA, which is becoming more and more popular method to synthetic evaluation of the financial health of enterprises on the basis of the available financial statements. It not only allows for the simultaneous and consistent use, at least a couple of economic and financial information, but also takes into account the ability of certain indicators of financial and economic bankruptcy predictor. The essence of this method involves applying a discriminatory function linear, often called discriminatory model. The calculated value to the total health assessment by subject classification of it to one of two groups, businesses operating without any visible signs of problems in the economic sphere or at risk of bankruptcy. The main objective of the article was reached to Alma Market S.A. not threatened bankruptcy in the test for years to come. The article has been following the research hypothesis: An Alma Market S.A. does not run the risk of bankruptcy in all the years of the period considered. This hypothesis is confirmed, because throughout the period, the level of this indicator was higher than Altmanʼs equation, and therefore we can bankruptcy 2,60 except in accordance with the theory of Altman

Fast loans – method of raising liqyudity

This article describes the essence of fast, instant cash loans which can raise liquidity or be the cause of growing indebtedness. The purpose of this article is to show the advantages and disadvantages of fast loans and attempt to compare different loan options available to the client on the Polish market. In this paper an analysis of the costs, repayment terms and specificities loan offers, which showed that fast loans perfect solution for those conscious consequences borrowings

The influence of droplet size on line tension

Within the effective interfacial Hamiltonian approach we evaluate the excess line free energy associated with cylinder-shaped droplets sessile on a stripe-like chemical inhomogeneity of a planar substrate. In the case of short-range intermolecular forces the droplet morphology and the corresponding expression for the line tension - which includes the inhomogeneity finite width effects - are derived and discussed as functions of temperature and increasing width. The width-dependent contributions to the line tension change their structure at the stripe wetting temperature T_W1: for T<T_W1 they decay exponentially while for T>T_W1 the decay is algebraic. In addition, a geometric construction of the corresponding contact angle is carried out and its implications are discussed