17,924 research outputs found
BEC-BCS Crossover in Neutron Matter with Renormalization Group based Effective Interactions
We study pure neutron matter in the BEC-BCS crossover regime using
renormalization group based low-momentum interactions within the
Nozi\`eres-Schmitt-Rink framework. This is an attempt to go beyond the mean
field description for low-density matter. We work in the basis of so-called
Weinberg eigenvectors where the operator is diagonal, which proves to be
an excellent choice that allows one to use non-local interactions in a very
convenient way. We study the importance of correlations as a function of
density. We notice that there is a significant reduction of the BCS critical
temperature at low-densities as the neutron matter approaches the unitary
limit.Comment: 10 pages and 8 figures, Figs 6 and 7 now includes higher cut-offs,
discussion of the cut-off dependence improved, new Summary and Outlook
section and new references adde
Three-magnetic fields
A completely new mechanism to generate the observed amount of large-scale
cosmological magnetic fields is introduced in the context of three-form
inflation. The amplification of the fields occurs via fourth order dynamics of
the vector perturbations and avoids the backreaction problem that plagues most
previously introduced mechanisms.Comment: 4 pages, 2 figures -- v2 as published (title changed in the published
version to "Cosmic magnetization in three-form inflation"
Doubly-boosted vector cosmologies from disformal metrics
A systematic dynamical system approach is applied to study the cosmology of
anisotropic Bianchi I universes in which a vector field is assumed to operate
on a disformal frame. This study yields a number of new fixed points, among
which anisotropic scaling solutions. Within the simplifying assumption of
(nearly) constant-slope potentials these are either not stable attractors, do
not describe accelerating expansion or else they feature too large anisotropies
to be compatible with observations. Nonetheless, some solutions do have an
appeal for cosmological applications in that isotropy is retained due to rapid
oscillations of the vector field.Comment: 11 pages, 4 figures, prepared during the NORDITA Extended Theories of
Gravity program. arXiv admin note: substantial text overlap with
arXiv:1407.344
Invariant and dual subtraction games resolving the Duch\^e-Rigo conjecture
We prove a recent conjecture of Duch\^ene and Rigo, stating that every
complementary pair of homogeneous Beatty sequences represents the solution to
an \emph{invariant} impartial game. Here invariance means that each available
move in a game can be played anywhere inside the game-board. In fact, we
establish such a result for a wider class of pairs of complementary sequences,
and in the process generalize the notion of a \emph{subtraction game}. Given a
pair of complementary sequences and of positive integers, we
define a game by setting as invariant moves. We then
introduce the invariant game , whose moves are all non-zero
-positions of . Provided the set of non-zero -positions of
equals , this \emph{is} the desired invariant game. We give
sufficient conditions on the initial pair of sequences for this 'duality' to
hold.Comment: 11 pages, 2 figure
Activation volume of selected liquid crystals in the density scaling regime
In this paper, we demonstrate and thoroughly analyze the activation volumetric properties of selected liquid crystals in the nematic and crystalline E phases in comparison with those reported for glass-forming liquids. In the analysis, we have employed and evaluated two entropic models (based on either total or configurational entropies) to describe the longitudinal relaxation times of the liquid crystals in the density scaling regime. In this study, we have also exploited two equations of state: volumetric and activation volumetric ones. As a result, we have established that the activation volumetric properties of the selected liquid crystals are quite opposite to such typical properties of glass-forming materials, i.e., the activation volume decreases and the isothermal bulk modulus increases when a liquid crystal is isothermally compressed. Using the model based on the configurational entropy, we suggest that the increasing pressure dependences of the activation volume in isothermal conditions and the negative curvature of the pressure dependences of isothermal longitudinal relaxation times can be related to the formation of antiparallel doublets in the examined liquid crystals. A similar pressure effect on relaxation dynamics may be also observed for other material groups in case of systems, the molecules of which form some supramolecular structures
Collective modes of trapped Fermi gases with in-medium interaction
Due to Pauli blocking of intermediate states, the scattering matrix (or
matrix) of two fermionic atoms in a Fermi gas becomes different from that of
two atoms in free space. This effect becomes particularly important near a
Feshbach resonance, where the interaction in free space is very strong but
becomes effectively suppressed in the medium. We calculate the in-medium
matrix in ladder approximation and study its effects on the properties of
collective modes of a trapped gas in the normal-fluid phase. We introduce the
in-medium interaction on both sides of the Boltzmann equation, namely in the
calculation of the mean field and in the calculation of the collision rate.
This allows us to explain the observed upward shift of the frequency of the
quadrupole mode in the collisionless regime. By including the mean field, we
also improve considerably the agreement with the measured temperature
dependence of frequency and damping rate of the scissors mode, whereas the use
of the in-medium cross section deteriorates the description, in agreement with
previous work.Comment: 17 page
Automated Reasoning and Presentation Support for Formalizing Mathematics in Mizar
This paper presents a combination of several automated reasoning and proof
presentation tools with the Mizar system for formalization of mathematics. The
combination forms an online service called MizAR, similar to the SystemOnTPTP
service for first-order automated reasoning. The main differences to
SystemOnTPTP are the use of the Mizar language that is oriented towards human
mathematicians (rather than the pure first-order logic used in SystemOnTPTP),
and setting the service in the context of the large Mizar Mathematical Library
of previous theorems,definitions, and proofs (rather than the isolated problems
that are solved in SystemOnTPTP). These differences poses new challenges and
new opportunities for automated reasoning and for proof presentation tools.
This paper describes the overall structure of MizAR, and presents the automated
reasoning systems and proof presentation tools that are combined to make MizAR
a useful mathematical service.Comment: To appear in 10th International Conference on. Artificial
Intelligence and Symbolic Computation AISC 201
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