Quantum Phases of Attractive Matter Waves in a Toroidal Trap

Investigating the quantum phase transition in a ring from a uniform attractive Bose-Einstein condensate to a localized bright soliton we find that the soliton undergoes transverse collapse at a critical interaction strength, which depends on the ring dimensions. In addition, we predict the existence of other soliton configurations with many peaks, showing that they have a limited stability domain. Finally, we show that the phase diagram displays several new features when the toroidal trap is set in rotation.Comment: 6 pages, 5 figures. To be published in Phys. Rev.

Superfluidity of metastable bulk glass para-hydrogen at low temperature

Molecular para-hydrogen has been proposed theoretically as a possible candidate for superfluidity, but the eventual superfluid transition is hindered by its crystallization. In this work, we study a metastable non crystalline phase of bulk p-H2 by means of the Path Integral Monte Carlo method in order to investigate at which temperature this system can support superfluidity. By choosing accurately the initial configuration and using a non commensurate simulation box, we have been able to frustrate the formation of the crystal in the simulated system and to calculate the temperature dependence of the one-body density matrix and of the superfluid fraction. We observe a transition to a superfluid phase at temperatures around 1 K. The limit of zero temperature is also studied using the diffusion Monte Carlo method. Results for the energy, condensate fraction, and structure of the metastable liquid phase at T=0 are reported and compared with the ones obtained for the stable solid phase.Comment: 10 pages, accepted for publication in Phys. Rev.

Scalar Field Oscillations Contributing to Dark Energy

We use action-angle variables to describe the basic physics of coherent scalar field oscillations in the expanding universe. These analytical mechanics methods have some advantages, like the identification of adiabatic invariants. As an application, we show some instances of potentials leading to equations of state with $p<-\rho/3$, thus contributing to the dark energy that causes the observed acceleration of the universe.Comment: 17 pages, 6 figures, Latex file. Sec.II reduced, discussion on sound speed added in Sec.IV, new references added. Accepted for publication in Physical Review

Spitzer's Identity and the Algebraic Birkhoff Decomposition in pQFT

In this article we continue to explore the notion of Rota-Baxter algebras in the context of the Hopf algebraic approach to renormalization theory in perturbative quantum field theory. We show in very simple algebraic terms that the solutions of the recursively defined formulae for the Birkhoff factorization of regularized Hopf algebra characters, i.e. Feynman rules, naturally give a non-commutative generalization of the well-known Spitzer's identity. The underlying abstract algebraic structure is analyzed in terms of complete filtered Rota-Baxter algebras.Comment: 19 pages, 2 figure

Asymmetric Synthesis of Secondary Alcohols and 1,2-Disubstituted Epoxides via Organocatalytic Sulfenylation

Enantioenriched secondary alcohols can be prepared via a short reaction sequence involving asymmetric organocatalytic sulfenylation of an aldehyde, organometallic addition, and desulfurization. This process provides access to enantioenriched alcohols with sterically similar groups attached to the alcohol carbon atom. The intermediate β-hydroxysulfides can also serve as precursors to enantioenriched 1,2-disubstituted epoxides via alkylation of the sulfur and subsequent base-mediated ring closure

Condensate fraction in liquid 4He at zero temperature

We present results of the one-body density matrix (OBDM) and the condensate fraction n_0 of liquid 4He calculated at zero temperature by means of the Path Integral Ground State Monte Carlo method. This technique allows to generate a highly accurate approximation for the ground state wave function Psi_0 in a totally model-independent way, that depends only on the Hamiltonian of the system and on the symmetry properties of Psi_0. With this unbiased estimation of the OBDM, we obtain precise results for the condensate fraction n_0 and the kinetic energy K of the system. The dependence of n_0 with the pressure shows an excellent agreement of our results with recent experimental measurements. Above the melting pressure, overpressurized liquid 4He shows a small condensate fraction that has dropped to 0.8% at the highest pressure of p = 87 bar.Comment: 12 pages. 4 figures. Accepted for publication on "Journal of Low Temperature Physics

Walking on a split-belt treadmill induces a higher power output and a shorter step length from the faster leg in healthy subjects, with opposite (after)-effect lasting less than 5 minutes after exercise

Walking on a split-belt treadmill has been claimed as a possible treatment of pathologic step asymmetries: in particular, the step lengthening on the affected side [1]. Placing the paretic limb on the slower belt would increase this asymmetry, reverting to long-lasting symmetry after exposure (after-effect). These studies neglected the underlying dynamics. Recently, it has been demonstrated that this paradigm entails an opposite spatial and dynamic asymmetry in healthy subjects. The stance on the faster belt is shortened, thus mimicking the paretic step temporally. On the contrary, the step is shorter and more muscle power is produced [2]. This challenges the rationale of the previous researches. The present study aims at extending these findings by investigating the after-effect both on spatiotemporal step parameters and power output from the plantar flexors on either belt. METHODS Ten healthy adults (21-34 years, 1.61-1.91 m tall, 5 women) participated in the study. After a brief familiarization, participants walked on a force-sensorized split-belt treadmill with one belt running at 0.4 m s-1 and the other belt running at 1.2 m s-1 (split condition) for 15 minutes and then, with no interruption, with the belts running at the same velocity (0.4 m s-1, tied condition) for other 5 minutes. The dominant lower limb was assigned to the faster belt. Kinematic data were recorded through an optoelectronic system as per the Davis anthropometric model. Joint sagittal power was computed by multiplying the moment generated by the ground reaction forces at the joints, times the rotation speed. All signals were simultaneously recorded [2]. The study was approved by the Local Ethics Committee. RESULTS Consistently with previous studies [3], during the split condition, the step length on the slower belt was longer, reaching gradually about 130% of the opposite step length. Ankle peak power attained about 15% of that observed on the opposite side. During the following tied condition, the step length on the formerly slower belt initially shortened by about 65% (after-effect), compared to the opposite step, and returned to values similar to that of the opposite side within 5 minutes. During this transition phase, ankle peak power gradually increased by up to 50% compared to baseline. On the formerly faster belt, step length did not change, while ankle peak power suddenly dropped to the contralateral level (Figure 1). Figure 1 Stride by stride plots (moving average, time-window 30 strides) of step length (upper panel) and ankle power (lower panel) from one representative subject (woman, 21 years, 1.65 m tall, body mass 60 kg) walking on a split-belt treadmill with the dominant lower limb on the faster belt (red) and the nondominant lower limb on the slower belt (blue). Strides from 1 to 867 refer to the split condition, and stride from 868 to 1025 refer to the following tied condition. DISCUSSION The increase in plantar flexor power on the faster belt, despite the shorter stance period and length, may reflect the priority need to counteract the backward drag from the faster belt, with respect to the slower one. This adaptation does not seem to lead to substantial learning, given that an after-effect, both on step length and ankle peak power, is only seen during the 5 minutes following split walking. In pathologic claudication, placing the affected lower limb on the faster belt might represent an effective form of \u201cforced-use\u201d [4], as far as enhanced power is requested. Long term effects remain questionable

Topological representations of matroid maps

The Topological Representation Theorem for (oriented) matroids states that every (oriented) matroid can be realized as the intersection lattice of an arrangement of codimension one homotopy spheres on a homotopy sphere. In this paper, we use a construction of Engstr\"om to show that structure-preserving maps between matroids induce topological mappings between their representations; a result previously known only in the oriented case. Specifically, we show that weak maps induce continuous maps and that the process is a functor from the category of matroids with weak maps to the homotopy category of topological spaces. We also give a new and conceptual proof of a result regarding the Whitney numbers of the first kind of a matroid.Comment: Final version, 21 pages, 8 figures; Journal of Algebraic Combinatorics, 201