Slavic Relative ČTO/CO: between Pronouns and Conjunctions

This paper presents the key points concerning Slavic relative constructions with a group of kindred invariable lexemes: Russian что, BCS što, Czech, Polish co, Slovak čo, and their cognates. These constructions are classified into two main types, depending on whether the third-person pronoun is used for marking the relative target. Across Slavic languages, the parameters governing the distribution between the two types are closely connected. The interpretation of these parameters (as well as their microvariation) is presented within the functional-typological approach. Syntactic category (part of speech) of the lexemes is discussed in diachronic perspective: in the more innovative construction with third-person pronoun, čto functions more as a complementizer; in the more conservative construction without the pronoun, čto retains some pronoun traits

General relations for quantum gases in two and three dimensions. Two-component fermions

We derive exact relations for $N$ spin-1/2 fermions with zero-range or short-range interactions, in continuous space or on a lattice, in $2D$ or in $3D$, in any external potential. Some of them generalize known relations between energy, momentum distribution $n(k)$, pair distribution function $g^{(2)}(r)$, derivative of the energy with respect to the scattering length $a$. Expressions are found for the second order derivative of the energy with respect to $1/a$ (or to $\ln a$ in $2D$). Also, it is found that the leading energy corrections due to a finite interaction range, are proportional to the effective range $r\_e$ in $3D$ (and to $r\_e^2$ in $2D$) with exprimable model-independent coefficients, that give access to the subleading short distance behavior of $g^{(2)}(r)$ and to the subleading $1/k^6$ tail of $n(k)$. This applies to lattice models for some magic dispersion relations, an example of which is given. Corrections to exactly solvable two-body and three-body problems are obtained. For the trapped unitary gas, the variation of the finite-$1/a$ and finite $r\_e$ energy corrections within each $SO(2,1)$ energy ladder is obtained; it gives the frequency shift and the collapse time of the breathing mode. For the bulk unitary gas, we compare to fixed-node Monte Carlo data, and we estimate the experimental uncertainty on the Bertsch parameter due to a finite $r\_e$.Comment: Augmented version: with respect to published version, subsection V.K added (minorization of the contact by the order parameter). arXiv admin note: text overlap with arXiv:1001.077

Славянское релятивное ŠTO/CO между местоимениями и союзами

This paper presents the key points concerning Slavic relative constructions with a group of kindred invariable lexemes: Russian что, BCS što, Czech, Polish co, Slovak čo, and their cognates. These constructions are classified into two main types, depending on whether the third-person pronoun is used for marking the relative target. Across Slavic languages, the parameters governing the distribution between the two types are closely connected. The interpretation of these parameters (as well as their microvariation) is presented within the functional-typological approach. Syntactic category (part of speech) of the lexemes is discussed in diachronic perspective: in the more innovative construction with third-person pronoun, čto functions more as a complementizer; in the more conservative construction without the pronoun, čto retains some pronoun traits. DOI: 10.31168/2305-6754.2012.1.1.5This paper presents the key points concerning Slavic relative constructions with a group of kindred invariable lexemes: Russian что, BCS što, Czech, Polish co, Slovak čo, and their cognates. These constructions are classified into two main types, depending on whether the third-person pronoun is used for marking the relative target. Across Slavic languages, the parameters governing the distribution between the two types are closely connected. The interpretation of these parameters (as well as their microvariation) is presented within the functional-typological approach. Syntactic category (part of speech) of the lexemes is discussed in diachronic perspective: in the more innovative construction with third-person pronoun, čto functions more as a complementizer; in the more conservative construction without the pronoun, čto retains some pronoun traits. DOI: 10.31168/2305-6754.2012.1.1.

Lower Spectral Branches of a Particle Coupled to a Bose Field

The structure of the lower part (i.e. $\epsilon$-away below the two-boson threshold) spectrum of Fr\"ohlich's polaron Hamiltonian in the weak coupling regime is obtained in spatial dimension $d\geq 3$. It contains a single polaron branch defined for total momentum $p\in G^{(0)}$, where $G^{(0)}\subset {\mathbb R}^d$ is a bounded domain, and, for any $p\in {\mathbb R}^d$, a manifold of polaron + one-boson states with boson momentum $q$ in a bounded domain depending on $p$. The polaron becomes unstable and dissolves into the one boson manifold at the boundary of $G^{(0)}$. The dispersion laws and generalized eigenfunctions are calculated

Crossover in the Efimov spectrum

A filtering method is introduced for solving the zero-range three-boson problem. This scheme permits to solve the original Skorniakov Ter-Martirosian integral equation for an arbitrary large Ultra-Violet cut-off and to avoid the Thomas collapse of the three particles. The method is applied to a more general zero-range model including a finite background two-body scattering length and the effective range. A cross-over in the Efimov spectrum is found in such systems and a specific regime emerges where Efimov states are long-lived

Geometric expansion of the log-partition function of the anisotropic Heisenberg model

We study the asymptotic expansion of the log-partition function of the anisotropic Heisenberg model in a bounded domain as this domain is dilated to infinity. Using the Ginibre's representation of the anisotropic Heisenberg model as a gas of interacting trajectories of a compound Poisson process we find all the non-decreasing terms of this expansion. They are given explicitly in terms of functional integrals. As the main technical tool we use the cluster expansion method.Comment: 38 page