228 research outputs found

### Differential Form of the Skornyakov--Ter-Martirosyan Equations

The Skornyakov--Ter-Martirosyan three-boson integral equations in momentum
space are transformed into differential equations. This allows us to take into
account quite directly the Danilov condition providing self-adjointness of the
underlying three-body Hamiltonian with zero-range pair interactions. For the
helium trimer the numerical solutions of the resulting differential equations
are compared with those of the Faddeev-type AGS equations.Comment: 4 pages, 2 figure

### 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

### Порядок слов в сочетаниях существительного с прилагательным в предложных и беспредложных группах: Доклад к XV Международному съезду славистов (Минск, 2013)

This paper discusses a statistical correlation between possessive prenominal placement and the presence of a preposition. The data from mediaeval Russian, Czech, and Croatian are validated against standard statistical measures (chisquare (X2) test and phi (φ) coefficient). Different explanations for the correlation are proposed; the most natural and simple one links the syntactic feature with the phonetic chunking of preposition and adjacent possessive, strengthened by their frequent co-occurence.В статье обсуждается статистическая корреляция между препозицией притяжательных местоимений и наличием предлога. Данные средневековых русских, чешских и хорватских памятников оцениваются по стандартным статистическим процедурам (критерий X2 и φ-коэффициент). В статье предложено несколько различных объяснений для этой корреляции; самое естественное и простое объяснение связывает эту синтаксическую особенность с фонетической: предлог со смежным притяжательным местоимением образуют единое фонетическое слово, причем это единство усиливается частым повторением этой пары в текстах

### Poincar\'{e}'s Observation and the Origin of Tsallis Generalized Canonical Distributions

In this paper, we present some geometric properties of the maximum entropy
(MaxEnt) Tsallis- distributions under energy constraint. In the case q > 1,
these distributions are proved to be marginals of uniform distributions on the
sphere; in the case q < 1, they can be constructed as conditional distribu-
tions of a Cauchy law built from the same uniform distribution on the sphere
using a gnomonic projection. As such, these distributions reveal the relevance
of using Tsallis distributions in the microcanonical setup: an example of such
application is given in the case of the ideal gas.Comment: 2 figure

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