A mechanism for pair formation in strongly correlated systems

We start from a Hamiltonian describing non-interacting fermions and add bosons to the model, with a Jaynes-Cummings-like interaction between the bosons and fermions. Because of the specific form of the interaction the model can be solved exactly. In the ground state, part of the electrons form bound pairs with opposite momentum and spin. The model also shows a gap in the kinetic energy of the fermions, but not in the spectrum of the full Hamiltonian. This gap is not of a mean-field nature, but is due to the Pauli exclusion principle.Comment: 13 pages, corrected some notations and made some clarification

Counting operator analysis of the discrete spectrum of some model Hamiltonians

The first step in the counting operator analysis of the spectrum of any model Hamiltonian H is the choice of a Hermitean operator M in such a way that the third commutator with H is proportional to the first commutator. Next one calculates operators R and R^\dagger which share some of the properties of creation and annihilation operators, and such that $M$ becomes a counting operator. The spectrum of H is then decomposed into multiplets, not determined by the symmetries of H, but by those of a reference Hamiltonian H_ref, which is defined by H_ref=H-R-R^\dagger, and which commutes with M. Finally, we introduce the notion of stable eigenstates. It is shown that under rather weak conditions one stable eigenstate can be used to construct another one.Comment: Added references, improved presentatio

Entanglement of a microcanonical ensemble

We replace time-averaged entanglement by ensemble-averaged entanglement and derive a simple expression for the latter. We show how to calculate the ensemble average for a two-spin system and for the Jaynes-Cummings model. In both cases the time-dependent entanglement is known as well so that one can verify that the time average coincides with the ensemble average.Comment: 10 page

Ensemble averaged entanglement of two-particle states in Fock space

Recent results, extending the Schmidt decomposition theorem to wavefunctions of identical particles, are reviewed. They are used to give a definition of reduced density operators in the case of two identical particles. Next, a method is discussed to calculate time averaged entanglement. It is applied to a pair of identical electrons in an otherwise empty band of the Hubbard model, and to a pair of bosons in the the Bose-Hubbard model with infinite range hopping. The effect of degeneracy of the spectrum of the Hamiltonian on the average entanglement is emphasised.Comment: 19 pages Latex, changed title, references added in the conclusion

Analysis of the N=4 Hubbard ring using a counting operator

We prove three theorems about the use of a counting operator to study the spectrum of model Hamiltonians. We analytically calculate the eigenvalues of the Hubbard ring with four lattice positions and apply our theorems to describe the observed level crossings.Comment: reference added tot the work of Schumann, small corrections mad

A multiplet analysis of spectra in the presence of broken symmetries

We introduce the notion of a generalised symmetry M of a hamiltonian H. It is a symmetry which has been broken in a very specific manner, involving ladder operators R and R*. In Theorem 1 these generalised symmetries are characterised in terms of repeated commutators of H with M. Breaking supersymmetry by adding a term linear in the supercharges is discussed as a motivating example. The complex parameter gamma which appears in the definition of a generalised symmetry is necessarily real when the spectrum of M is discrete. Theorem 2 shows that gamma must also be real when the spectrum of H is fully discrete and R and R* are bounded operators. Any generalised symmetry induces a partitioning of the spectrum of H in what we call M-multiplets. The hydrogen atom in the presence of a symmetry breaking external field is discussed as an example. The notion of stability of eigenvectors of H relative to the generalised symmetry M is discussed. A characterisation of stable eigenvectors is given in Theorem 3

pilot ionosonde network for identification of traveling ionospheric disturbances

Travelling Ionospheric Disturbances (TIDs) are the ionospheric signatures of atmospheric gravity waves (AGWs). Their identification and tracking is important because the TIDs affect all services that rely on predictable ionospheric radio wave propagation. Although various techniques have been proposed to measure TID characteristics, their real-time implementation still has several difficulties. In this contribution, we present a new technique, based on the analysis of oblique Digisonde-to-Digisonde (D2D) "skymap" observations, to directly identify TIDs and specify the TID wave parameters based on the measurement of angle-of-arrival, Doppler frequency, and time-of-flight of ionospherically reflected high-frequency (HF) radio pulses. The technique has been implemented for the first time for the Net-TIDE project with data streaming from the network of European Digisonde DPS4D observatories. The performance is demonstrated during a period of moderate auroral activity, assessing its consistency with independent measurements such as data from auroral magnetometers and electron density perturbations from Digisondes and GNSS stations. Given that the different types of measurements used for this assessment were not made at exactly the same time and location, and that there was insufficient coverage in the area between the AGW sources and the measurement lo cations, we can only consider our interpretation as plausible and indicative for the reliability of the extracted TID characteristics. In the framework of the new TechTIDE project (European Commission H2020), a retrospective analysis of the Net-TIDE results in comparison with those extracted from GNSS TEC-based methodologies is currently being attempted, and the results will be the objective of a follow up paper

Early Fasting Is Long Lasting: Differences in Early Nutritional Conditions Reappear under Stressful Conditions in Adult Female Zebra Finches

Conditions experienced during early life can have profound effects on individual development and condition in adulthood. Differences in nutritional provisioning in birds during the first month of life can lead to differences in growth, reproductive success and survival. Yet, under natural conditions shorter periods of nutritional stress will be more prevalent. Individuals may respond differently, depending on the period of development during which nutritional stress was experienced. Such differences may surface specifically when poor environmental conditions challenge individuals again as adults. Here, we investigated long term consequences of differences in nutritional conditions experienced during different periods of early development by female zebra finches (Taeniopygia guttata) on measures of management and acquisition of body reserves. As nestlings or fledglings, subjects were raised under different nutritional conditions, a low or high quality diet. After subjects reached sexual maturity, we measured their sensitivity to periods of food restriction, their exploration and foraging behaviour as well as adult resting metabolic rate (RMR). During a short period of food restriction, subjects from the poor nutritional conditions had a higher body mass loss than those raised under qualitatively superior nutritional conditions. Moreover, subjects that were raised under poor nutritional conditions were faster to engage in exploratory and foraging behaviour. But RMR did not differ among treatments. These results reveal that early nutritional conditions affect adult exploratory behaviour, a representative personality trait, foraging and adult's physiological condition. As early nutritional conditions are reflected in adult phenotypic plasticity specifically when stressful situations reappear, the results suggest that costs for poor developmental conditions are paid when environmental conditions deteriorate