Gap equation with pairing correlations beyond mean field and its equivalence to a Hugenholtz-Pines condition for fermion pairs

The equation for the gap parameter represents the main equation of the pairing theory of superconductivity. Although it is formally defined through a single-particle property, physically it reflects the pairing correlations between opposite-spin fermions. Here, we exploit this physical connection and cast the gap equation in an alternative form which explicitly highlights these two-particle correlations, by showing that it is equivalent to a Hugenholtz-Pines condition for fermion pairs. At a formal level, a direct connection is established in this way between the treatment of the condensate fraction in condensate systems of fermions and bosons. At a practical level, the use of this alternative form of the gap equation is expected to make easier the inclusion of pairing fluctuations beyond mean field. As a proof-of-concept of the new method, we apply the modified form of the gap equation to the long-pending problem about the inclusion of the Gorkov-Melik-Barkhudarov correction across the whole BCS-BEC crossover, from the BCS limit of strongly overlapping Cooper pairs to the BEC limit of dilute composite bosons, and for all temperatures in the superfluid phase. Our numerical calculations yield excellent agreement with the recently determined experimental values of the gap parameter for an ultra-cold Fermi gas in the intermediate regime between BCS and BEC, as well as with the available quantum Monte Carlo data in the same regime.Comment: 24 pages, 13 figure

Municipal transitions: The social, energy, and spatial dynamics of sociotechnical change in South Tyrol, Italy

With the aim of proposing recommendations on how to use social and territorial specificities as levers for wider achievement of climate and energy targets at local level, this research analyses territories as sociotechnical systems. Defining the territory as a sociotechnical system allows us to underline the interrelations between space, energy and society. Groups of municipalities in a region can be identified with respect to their potential production of renewable energy by means of well-known data-mining approaches. Similar municipalities linking together can share ideas and promote collaborations, supporting clever social planning in the transition towards a new energy system. The methodology is applied to the South Tyrol case study (Italy). Results show eight different spatially-based sociotechnical systems within the coherent cultural and institutional context of South Tyrol. In particular, this paper observes eight different systems in terms of (1) different renewable energy source preferences in semi-urban and rural contexts; (2) different links with other local planning, management, and policy needs; (3) different socio-demographic specificities of individuals and families; (4) presence of different kinds of stakeholders or of (5) different socio-spatial organizations based on land cover. Each energy system has its own specificities and potentialities, including social and spatial dimensions, that can address a more balanced, inclusive, equal, and accelerated energy transition at the local and translocal scale

Comparison between a vector multiport network analyzer and the national S-parameter measurement system

A multiport vector network analyzer based on a new calibration concept, has been compared with the P-port S-parameter National measurement system at IENGF. The measurements were performed on precision 7 mm standard components and exhibited an optimum agreement. These results open the possibility to use the new multiport network analyzer for certification measurements of multiport device

Accuracy of a multiport network analyzer

The accuracy of a multiport vector network analyzer, which uses a new calibration concept, has been compared with a 2-port network analyzer that implements the classical TRL procedure. The accuracy assessment is based on the analysis of the error propagation due to the connectors repeatability, both of the used standards and the measurands. The comparison, performed in the 2-18 GHz band on devices fitted with APC-7 mm connectors, proved the high accuracy reached by a multiport system which can qualify for metrological applications

Entanglement between pairing and screening in the Gorkov-Melik-Barkhudarov correction to the critical temperature throughout the BCS-BEC crossover

The theoretical description of the critical temperature Tc of a Fermi superfluid dates back to the work by Gor'kov and Melik-Barkhudarov (GMB), who addressed it for a weakly-coupled (dilute) superfluid in the BCS (weak-coupling) limit of the BCS-BEC crossover. The point made by GMB was that particle-particle (pairing) excitations, which are responsible for superfluidity to occur below Tc, and particle-hole excitations, which give rise to screening also in a normal system, get effectively disentangled from each other in the BCS limit, thus yielding a reduction by a factor 2.2 of the value of Tc obtained when neglecting screening effects. Subsequent work on this topic, aimed at extending the original GMB argument away from the BCS limit with diagrammatic methods, has kept this disentangling between pairing and screening throughout the BCS-BEC crossover, without realising that the conditions for it to be valid are soon violated away from the BCS limit. Here, we reconsider this problem from a more general perspective and argue that pairing and screening are intrinsically entangled with each other along the whole BCS-BEC crossover but for the BCS limit considered by GMB. We perform a detailed numerical calculation of the GMB diagrammatic contribution extended to the whole BCS-BEC crossover, where the full wave-vector and frequency dependence occurring in the repeated in-medium two-particle scattering is duly taken into account. Our numerical calculations are tested against analytic results available in both the BCS and BEC limits, and the contribution of the GMB diagrammatic term to the scattering length of composite bosons in the BEC limit is highlighted. We calculate Tc throughout the BCS-BEC crossover and find that it agrees quite well with Quantum Monte Carlo calculations and experimental data available in the unitarity regime.Comment: 21 pages, 11 figure

Novel software techniques for automatic microwave measurements

Although many microwave measurement techniques are heavily based on special purpose software, the application of modern software techniques like object oriented programming and new programming language like C++ is seldom used. The impact of such new software solutions can drastically improve the overall design of a microwave test set. The paper presents the design and implementation of a new multiport network analyzer with particular attention to the control program architecture. The use of Object Oriented Programming techniques results in a clear and easy to maintain solution which boosts both the user interface and the overall test set organizatio

Pairing fluctuation effects on the single-particle spectra for the superconducting state

Single-particle spectra are calculated in the superconducting state for a fermionic system with an attractive interaction, as functions of temperature and coupling strength from weak to strong. The fermionic system is described by a single-particle self-energy that includes pairing-fluctuation effects in the superconducting state. The theory reduces to the ordinary BCS approximation in weak coupling and to the Bogoliubov approximation for the composite bosons in strong coupling. Several features of the single-particle spectral function are shown to compare favorably with experimental data for cuprate superconductors.Comment: 4 pages, 4 figure