Quantum dynamics of a binary mixture of BECs in a double well potential: an Holstein-Primakoff approach

We study the quantum dynamics of a binary mixture of Bose-Einstein condensates (BEC) in a double-well potential starting from a two-mode Bose-Hubbard Hamiltonian. Focussing on the regime where the number of atoms is very large, a mapping onto a SU(2) spin problem together with a Holstein-Primakoff transformation is performed. The quantum evolution of the number difference of bosons between the two wells is investigated for different initial conditions, which range from the case of a small imbalance between the two wells to a coherent spin state. The results show an instability towards a phase-separation above a critical positive value of the interspecies interaction while the system evolves towards a coherent tunneling regime for negative interspecies interactions. A comparison with a semiclassical approach is discussed together with some implications on the experimental realization of phase separation with cold atoms.Comment: 12 pages, 7 figures, accepted for publication in J. Phys.

Majorana and the theoretical problem of photon-electron scattering

Relevant contributions by Majorana regarding Compton scattering off free or bound electrons are considered in detail, where a (full quantum) generalization of the Kramers-Heisenberg dispersion formula is derived. The role of intermediate electronic states is appropriately pointed out in recovering the standard Klein-Nishina formula (for free electron scattering) by making recourse to a limpid physical scheme alternative to the (then unknown) Feynman diagram approach. For bound electron scattering, a quantitative description of the broadening of the Compton line was obtained for the first time by introducing a finite mean life for the excited state of the electron system. Finally, a generalization aimed to describe Compton scattering assisted by a non-vanishing applied magnetic field is as well considered, revealing its relevance for present day research.Comment: latex, amsart, 10 pages, 1 figur

Quantum tricriticality in transverse Ising-like systems

The quantum tricriticality of d-dimensional transverse Ising-like systems is studied by means of a perturbative renormalization group approach focusing on static susceptibility. This allows us to obtain the phase diagram for 3<d<4, with a clear location of the critical lines ending in the conventional quantum critical points and in the quantum tricritical one, and of the tricritical line for temperature T \geq 0. We determine also the critical and the tricritical shift exponents close to the corresponding ground state instabilities. Remarkably, we find a tricritical shift exponent identical to that found in the conventional quantum criticality and, by approaching the quantum tricritical point increasing the non-thermal control parameter r, a crossover of the quantum critical shift exponents from the conventional value \phi = 1/(d-1) to the new one \phi = 1/2(d-1). Besides, the projection in the (r,T)-plane of the phase boundary ending in the quantum tricritical point and crossovers in the quantum tricritical region appear quite similar to those found close to an usual quantum critical point. Another feature of experimental interest is that the amplitude of the Wilsonian classical critical region around this peculiar critical line is sensibly smaller than that expected in the quantum critical scenario. This suggests that the quantum tricriticality is essentially governed by mean-field critical exponents, renormalized by the shift exponent \phi = 1/2(d-1) in the quantum tricritical region.Comment: 9 pages, 2 figures; to be published on EPJ

Two steps one pot process for the conversion of dimethylfuran to pyrrole compounds with almost null E factor

The replacement of the oil-based chemicals with those derived from biomasses is one of the most exciting challenges of the last decades. For example, 1,4-dicarbonyl compounds have a great importance in chemical synthesis, thanks to their high chemoselectivity and there is an increasing interest for preparing them from biomasses. In particular, 2,5-hexanedione could be synthesized starting from lignocellulosic sources, through the acid-ring opening reaction of 2,5-dimethylfuran as the bio-based feedstock.[1] The reaction of 2,5-hexanedione and a generic primary amine leads to pyrrole compounds. Many examples have been reported by some of the authors.[2] In this work a sustainable process for the preparation of pyrrole compounds starting from a bio-based reagent has been developed. The selected starting material was 2,5-dimethyl furan. In this work, the ring opening reaction of 2,5-dimethylfuran was optimized by tuning parameters such as the amount of water, type and amount of acid, time and temperature. 2,5-hexanedione was obtained with a high yield (95%) without the need of purification. Then, different primary amines, in particular biosourced, have been used to prepare a variety of pyrrole compounds, with high yield (at least 90%) and with high carbon efficiency, without producing waste. The pyrrole compounds have then been used for the functionalization of a nanosized graphite, promoting the exfoliation to few layers graphene

Quantum phase excitations in Ginzburg-Landau superconductors

We give a straightforward generalization of the Ginzburg-Landau theory for superconductors where the scalar phase field is replaced by an antisymmetric Kalb-Ramond field. We predict that at very low temperatures, where quantum phase effects are expected to play a significant role, the presence of vortices destroys superconductivity.Comment: revtex, 4 pages, no figure

A bio-sourced molecule as carbon black coupling agent in rubber compounds with low hysteresis

The prime application of rubber composites is represented by tire compounds. To achieve the desired tire performances an equilibrium between dynamic rigidity and hysteresis must be acquired. Amorphous precipitated silica is the preferred reinforcing filler to have low energy dissipations and thus low fuel consumption. Indeed, silica is characterized by nano dimensions and by the possibility of establishing chemical bonds with rubber chains allowing the achievement of high hysteresis at low temperatures, to promote wet traction, and low hysteresis at medium-high temperatures, for low fuel consumption. Carbon black (CB) is the main filler for tire compounds, but it does not have functional groups able to promote chemical bonds with the rubber matrix, though it would be highly desirable. In this work, a pyrrole compound (PyC) containing a thiol group, and which can be synthesized starting from bio-based building blocks was used to functionalize CB by the socalled “pyrrole methodology”. The thiol group was expected to react with the sulphurbased crosslinking system and/or with rubber chains, thus forming strong bonds with the rubber matrix. Results The synthesis of the PyC and the functionalization reaction were characterized by high atom efficiency. A poly(styrene-co-butadiene) copolymer from anionic solution polymerization was used as the main rubber for the compound preparation. The crosslinked composite material filled with functionalized CB revealed substantial improvements with respect to the composite with pristine CB, in particular: high rigidity and low hysteresis at high temperature. Composite properties were even comparable to those of silica-based rubber composites. The formation of the expected rubber-filler chemical bond via the thiol group of the selected PyC was confirmed studying such functionalizing agent in a squalene-based model compound. The results here reported pave the way to CB-based rubber composites with a low environmental impact

Topological order in Josephson junction ladders with Mobius boundary conditions

We propose a CFT description for a closed one-dimensional fully frustrated ladder of quantum Josephson junctions with Mobius boundary conditions, in particular we show how such a system can develop topological order. Such a property is crucial for its implementation as a "protected" solid state qubit.Comment: 14 pages, 3 figures, to appear in JSTA

Point-like topological defects in bilayer quantum Hall systems

Following a suggestion given in Phys. Lett. B 571 (2003) 250, we show how a bilayer Quantum Hall system at fillings nu =m/pm+2 can exhibit a point-like topological defect in its edge state structure. Indeed our CFT theory for such a system, the Twisted Model (TM), gives rise in a natural way to such a feature in the twisted sector. Our results are in agreement with recent experimental findings (cond-mat/0503478) which evidence the presence of a topological defect in the bilayer system.Comment: 9 pages, 3 figure