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 $G_0V$ 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 $(a_n)$ and $(b_n)$ of positive integers, we define a game $G$ by setting $\{\{a_n, b_n\}\}$ as invariant moves. We then introduce the invariant game $G^\star$, whose moves are all non-zero $P$-positions of $G$. Provided the set of non-zero $P$-positions of $G^\star$ equals $\{\{a_n,b_n\}\}$, 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 $T$ 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 $T$ 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