Horndeski fermion-boson stars

We establish the existence of static and spherically symmetric fermion-boson stars, in a low energy effective model of (beyond) Horndeski theories. These stars are in equilibrium, and are composed by a mixing of scalar and fermionic matters that only interact gravitationally one with each other. Properties such as mass, radius, and compactness are studied, highlighting the existence of two families of configurations defined by the parameter c4. These families have distinctive properties, although in certain limits both are reduced to their counterparts in General Relativity. Finally, by assuming the same conditions used in General Relativity, we find the maximum compactness of these hybrid stars and determine that it remains below the so-called Buchdahl's limit.

Unconventional Superconductivity in Samarium Nitride

<p>We have studied the nature of unconventional superconductivity in the rare-earth nitride (REN) samarium nitride (SmN) for the purposes of providing a deeper understanding of the mechanisms that lead to such a phenomenon in an already extremely interesting material. An approximate low energy model has been introduced for SmN based on previous bandstructure calculation and recent experimental results. This consists of the non-dispersive 4f band associated with the samarium ion crossing through the dispersive 5d band associated with the nitrogen ion. Due to large spin polarisation in the bandstructure we need only consider the majority-spin 5d and 4f bands which lead to an essentially spinless two band system. Starting from this two band system, we apply the k dot p method to it in order to create an effective model for the system. This effective model for the material acts as the platform from which we study the possible triplet superconducting pairing. Basing our pairing on the electron-phonon interaction we have postulated the existence of triplet pairing in the 5d band, from which we have successfully characterised the pair potential in this system through the self-consistency equation. The pair potential Delta_d could be solved analytically in a special case where the Fermi level was equal to the 4f band. In this case we find that above a threshold effective coupling strength the superconducting state is established and analytically known. In contrast to this result for the more general case where the Fermi level is different to the 4f band we numerically recover a solution that was exponential in the effective coupling strength which is similar to the pairing as we expect from the single band case. Analytic solutions in this case were not able to be found, however, we know that from our numerical investigations there will exist a solution for any effective coupling strength, contrasting with the special case where the pairing amplitude can disappear below a certain threshold. In conjunction to these results we also examined the situation where the 5d and 4f bands have hybridised together in order to search for unique pairing that may be resistant to disorder. By keeping the triplet pairing only in the 5d band, this translates to hybrid pairing between electrons in the two hybridised bands. Results from the hybridised bands system show a new singlet-like pairing Delta_S which is even in k and singlet in the hybridised band indices. Preliminary numerical results suggest that this pairing indeed exists and occurs only near the avoided crossing of the hybridised bands. The existence of such a pairing, originating from triplet pairing, has exciting implications for the robustness of the superconductivity in the presence of disorder and/or impurities.</p>

Unconventional Superconductivity in Samarium Nitride

<p>We have studied the nature of unconventional superconductivity in the rare-earth nitride (REN) samarium nitride (SmN) for the purposes of providing a deeper understanding of the mechanisms that lead to such a phenomenon in an already extremely interesting material. An approximate low energy model has been introduced for SmN based on previous bandstructure calculation and recent experimental results. This consists of the non-dispersive 4f band associated with the samarium ion crossing through the dispersive 5d band associated with the nitrogen ion. Due to large spin polarisation in the bandstructure we need only consider the majority-spin 5d and 4f bands which lead to an essentially spinless two band system. Starting from this two band system, we apply the k dot p method to it in order to create an effective model for the system. This effective model for the material acts as the platform from which we study the possible triplet superconducting pairing. Basing our pairing on the electron-phonon interaction we have postulated the existence of triplet pairing in the 5d band, from which we have successfully characterised the pair potential in this system through the self-consistency equation. The pair potential Delta_d could be solved analytically in a special case where the Fermi level was equal to the 4f band. In this case we find that above a threshold effective coupling strength the superconducting state is established and analytically known. In contrast to this result for the more general case where the Fermi level is different to the 4f band we numerically recover a solution that was exponential in the effective coupling strength which is similar to the pairing as we expect from the single band case. Analytic solutions in this case were not able to be found, however, we know that from our numerical investigations there will exist a solution for any effective coupling strength, contrasting with the special case where the pairing amplitude can disappear below a certain threshold. In conjunction to these results we also examined the situation where the 5d and 4f bands have hybridised together in order to search for unique pairing that may be resistant to disorder. By keeping the triplet pairing only in the 5d band, this translates to hybrid pairing between electrons in the two hybridised bands. Results from the hybridised bands system show a new singlet-like pairing Delta_S which is even in k and singlet in the hybridised band indices. Preliminary numerical results suggest that this pairing indeed exists and occurs only near the avoided crossing of the hybridised bands. The existence of such a pairing, originating from triplet pairing, has exciting implications for the robustness of the superconductivity in the presence of disorder and/or impurities.</p>

Deep double descent: where bigger models and more data hurt*

We show that a variety of modern deep learning tasks exhibit a ‘double-descent’ phenomenon where, as we increase model size, performance first gets worse and then gets better. Moreover, we show that double descent occurs not just as a function of model size, but also as a function of the number of training epochs. We unify the above phenomena by defining a new complexity measure we call the effective model complexity and conjecture a generalized double descent with respect to this measure. Furthermore, our notion of model complexity allows us to identify certain regimes where increasing (even quadrupling) the number of train samples actually hurts test performance.