Linear response theory around a localized impurity in the pseudogap regime of an anisotropic superconductor: precursor pairing vs the d-density-wave scenario

We derive the polarizability of an electron system in (i) the superconducting phase, with d-wave symmetry, (ii) the pseudogap regime, within the precursor pairing scenario, and (iii) the d-density-wave (dDW) state, characterized by a d-wave hidden order parameter, but no pairing. Such a calculation is motivated by the recent proposals that imaging the effects of an isolated impurity may distinguish between precursor pairing and dDW order in the pseudogap regime of the high-Tc superconductors. In all three cases, the wave-vector dependence of the polarizability is characterized by an azymuthal modulation, consistent with the d-wave symmetry of the underlying state. However, only the dDW result shows the fingerprints of nesting, with nesting wave-vector Q=(pi,pi), albeit imperfect, due to a nonzero value of the hopping ratio t'/t in the band dispersion relation. As a consequence of nesting, the presence of hole pockets is also exhibited by the (q,omega) dependence of the retarded polarizability.Comment: accepted in Phys. Rev.

Size shrinking of composite bosons for increasing density in the BCS to Bose-Einstein crossover

We consider a system of fermions in the continuum case at zero temperature, in the strong-coupling limit of a short-range attraction when composite bosons form as bound-fermion pairs. We examine the density dependence of the size of the composite bosons at leading order in the density ("dilute limit"), and show on general physical grounds that this size should decrease with increasing density, both in three and two dimensions. We then compare with the analytic zero-temperature mean-field solution, which indeed exhibits the size shrinking of the composite bosons both in three and two dimensions. We argue, nonetheless, that the two-dimensional mean-field solution is not consistent with our general result in the "dilute limit", to the extent that mean field treats the scattering between composite bosons in the Born approximation which is known to break down at low energy in two dimensions.Comment: Revised version to be published on Eur. Phys. Jour. B, 7 pages, 1 figur

Internal structure of preformed Cooper pairs

In order to obtain information about the internal structure of the preformed pairs in the pseudogap state of high $T_c$ superconductors, we calculate the propagator of a singlet pair with center of mass coordinate $\mathbf{r}$, and relative distance $\pmb{\rho}$, by solving the Bethe-Salpeter equation, representing the sum over repeated two-particle scattering events due to a distance dependent attraction. We define then a ``pair structure function'' $g_{P}(\mathbf{P},\pmb{\rho})$ that depends on the internal distance $\pmb{\rho}$ between the partners and on the momentum $\mathbf{P}$ of the pair. We calculate this function both for a local potential and $s-$wave symmetry of the order parameter and for a separable potential and $d-$wave symmetry of the order parameter. The influence of the center of mass momentum, strenght of the interaction, temperature, density of particles and of the pseudogap in the one-electron spectrum is studied for both cases.Comment: 12 pages, REVTeX4, 8 EPS figure

Internal structure of fluctuating Cooper pairs

Abstract.: In order to obtain information about the internal structure of fluctuating Cooper pairs in the pseudogap state and below the transition temperature of high Tc superconductors, we solve the Bethe-Salpeter equation for the two-electron propagator in order to calculate a "pair structure function” $g_{P}({\mathbf{P}},\pmb{\rho})$ that depends on the internal distance $\pmb{\rho}$ between the partners and on the center of mass momentum P of the pair. We use an attractive Hubbard model with a local potential for s-wave and a separable potential for d-wave symmetry. The amplitude of gP for small ρ depends on temperature, chemical potential and interaction symmetry, but the ρ dependence itself is rather insensitive to the interaction strength. Asymptotically gP decreases as an inverse power of ρ for weak coupling, but exponentially when a pseudogap develops for stronger interaction. Some possibilities of observing the pair structure experimentally are mentione

Size-shrinking of deuterons in very dilute superfluid nuclear matter

It is shown within the strong-coupling BCS approach that, starting from the zero-density limit of superfluid nuclear matter, with increasing density deuterons first shrink before they start expanding.Comment: 2 pages, Latex, 1 figure included, submitted to Phys. Rev.

Linear Response Theory Around a Localized Impurity in the Pseudogap Regime of an Anisotropic Superconductor

We compare and contrast the polarizability of a d-wave superconductor in the pseudogap regime, within the precursor pairing scenario (dPG), and of a d-density-wave (dDW) state, characterized by a d-wave hidden order parameter, but no pairing. Our study is motivated by STM imaging experiments around an isolated impurity, which may in principle distinguish between precursor pairing and dDW order in the pseudogap regime of the high-$$T_{c}$$ superconductors. In both cases, the $${\bf q}$$-dependence of the polarizability is characterized by an azimuthal modulation, consistent with the d-wave symmetry of the underlying state. However, only the dDW result shows the fingerprints of nesting, with nesting wave vector $${{\bf Q}}=(\pi,\pi)$$, albeit imperfect, due to a nonzero value of the hopping ratio $$t^\prime /t$$ in the band dispersion relation. As a consequence of nesting, the presence of hole pockets is also reflected by the $$({\bf q},\omega)$$ dependence of the retarded polarizabilit

Good trouble in the academy: inventing design-focused case studies about public management as an archetype of policy design research

Speaking archetypically, public organizations are practical means for implementing policy interventions. In this regard, their purposeful roles include furnishing operational capacity, while also sustaining support and legitimacy for the interventions as implemented. Contributions to fulfilling these roles are made by myriad practices and systems that are situated organizationally. Organizationally situated practices and systems are matters of concern for professional practitioners concerned with public organizations and their management. As they engage in creating and adapting such working phenomena, design-oriented professional practitioners bring professional knowledge into play. From this standpoint, there's a need for professional practitioners to acquire such professional knowledge, which implies a need for researchers to furnish it. At present, there's no good off the shelf solution for meeting that particular need. This chapter deals with the question of what to do about that gap. Dealing with it makes for good trouble

Density-induced BCS to Bose-Einstein crossover

We investigate the zero-temperature BCS to Bose-Einstein crossover at the mean-field level, by driving it with the attractive potential and the particle density. We emphasize specifically the role played by the particle density in this crossover. Three different interparticle potentials are considered for the continuum model in three spatial dimensions, while both s- and d-wave solutions are analyzed for the attractive ~extended! Hubbard model on a two-dimensional square lattice. For this model the peculiar behavior of the crossover for the d-wave solution is discussed. In particular, in the strong-coupling limit when approaching half-filling we evidence the occurrence of strong correlations among antiparallel-spin fermions belonging to different composite bosons, which give rise to a quasi-long-range antiferromagnetic order in this limit

NB-IoT via LEO satellites: An efficient resource allocation strategy for uplink data transmission

In this paper, we focus on the use of Low-Eart Orbit (LEO) satellites providing the Narrowband Internet of Things (NB-IoT) connectivity to the on-ground user equipment (UEs). Conventional resource allocation algorithms for the NBIoT systems are particularly designed for terrestrial infrastructures, where devices are under the coverage of a specific base station and the whole system varies very slowly in time. The existing methods in the literature cannot be applied over LEO satellite-based NB-IoT systems for several reasons. First, with the movement of the LEO satellite, the corresponding channel parameters for each user will quickly change over time. Delaying the scheduling of a certain user would result in a resource allocation based on outdated parameters. Second, the differential Doppler shift, which is a typical impairment in communications over LEO, directly depends on the relative distance among users. Scheduling at the same radio frame users that overcome a certain distance would violate the differential Doppler limit supported by the NB-IoT standard. Third, the propagation delay over a LEO satellite channel is around 4-16 times higher compared to a terrestrial system, imposing the need for message exchange minimization between the users and the base station. In this work, we propose a novel uplink resource allocation strategy that jointly incorporates the new design considerations previously mentioned together with the distinct channel conditions, satellite coverage times and data demands of various users on Earth. The novel methodology proposed in this paper can act as a framework for future works in the field.Comment: Tis work has been submitted to the IEEE IoT Journal for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl