Large Amplitude Dynamics of the Pairing Correlations in a Unitary Fermi Gas

A unitary Fermi gas has a surprisingly rich spectrum of large amplitude modes of the pairing field alone, which defies a description within a formalism involving only a reduced set of degrees of freedom, such as quantum hydrodynamics or a Landau-Ginzburg-like description. These modes are very slow, with oscillation frequencies well below the pairing gap, which makes their damping through quasiparticle excitations quite ineffective. In atomic traps these modes couple naturally with the density oscillations, and the corresponding oscillations of the atomic cloud are an example of a new type of collective mode in superfluid Fermi systems. They have lower frequencies than the compressional collective hydrodynamic oscillations, have a non-spherical momentum distribution, and could be excited by a quick time variation of the scattering length.Comment: 4 pages, 3 figures, published version, updated figures and a number of change

Adjoint Trapping: A New Phenomenon at Strong 't Hooft Coupling

Adding matter of mass m, in the fundamental representation of SU(N), to N=4 supersymmetric Yang-Mills theory, we study ``generalized quarkonium'' containing a (s)quark, an anti(s)quark, and J massless (or very light) adjoint particles. At large 't Hooft coupling $\lambda$ >> 1, the states of spin <= 1 are surprisingly light (Kruczenski et al., hep-th/0304032) and small (hep-th/0312071) with a J-independent size of order $\sqrt{\lambda}/m$. This ``trapping'' of adjoint matter in a region small compared with its Compton wavelength and compared to any confinement scale in the theory is an unfamiliar phenomenon, as it does not occur at small $\lambda$. We explore adjoint trapping further by considering the limit of large J. In particular, for J >> $\sqrt{\lambda}$ >> 1, we expect the trapping phenomenon to become unstable. Using Wilson loop methods, we show that a sharp transition, in which the generalized quarkonium states become unbound (for massless adjoints) occurs at $J \simeq 0.22 \sqrt{\lambda}$. If the adjoint scalars of N=4 are massive and the theory is confining (as, for instance, in N=1* theories) then the transition becomes a cross-over, across which the size of the states changes rapidly from ~$\sqrt{\lambda}/m$ to something of order the confinement scale ~ $\Lambda^{-1}$.Comment: Clarified transition with a better figure and improved presentation; added careful discussion of the small regime of validity of the Born-Oppenheimer computation and adjusted some remarks appropriately; also added two reference

Designing quantitative data representations to support people’s understanding of the risk of Covid-19

Since the COVID-19 outbreak, various forms of data representations (e.g., graphs, tables, and charts) have served to illustrate the diverse risks from the virus. These risks include daily cases, hospitalizations, and deaths and involve numerous and sometimes complex quantified attributes (e.g., numbers, time series, and indices) in their representation. Complicating the matter, even in cases in which people analyze identical data, they often interpret it differently. Everyone interacts with data differently in daily living (Ryan & Evers, 2020) due to varied competence in interpreting quantitative data as well as different applications of quantitative ideas in real-world contexts (Hallett, 2003; Wiest et al., 2007). This project aims to support people’s informed- and evidence-based decisions about the severity of COVID-19 and their behavioral choices by assisting their productive assessment and interpretations of quantitative structures in data representations. In such an effort, this research team has developed interactive applets (available at www.covidtaser.com) with three data representations: Risk Comparison, Projection, and Log scaled Graphs of COVID-19. These representations are based on empirical research designed to investigate and promote people’s understandings of: a) chances of facing the risks from the virus in comparison to those from daily activities (e.g., driving), b) impacts of preventive measures (e.g., social distancing), and c) interpreting linear and log scaled graphs. The project representations are designed in a way that better facilitates people’s quantitative reasonings based on the cognitive models of mathematical thinking found in the project and models from prior research. Conducting task-based clinical interviews, this project is studying how the interactive applets promote people’s in making sense of what COVID-19 data conveys and its implications in their health behavior. The project results contribute to the literature in STEM education by providing insights into the importance and utility of quantitative models. Furthermore, the research-based products also add value to promoting data literate society

On the Couplings of Vector Mesons in AdS/QCD

We address, in the AdS/CFT context, the issue of the universality of the couplings of the rho meson to other hadrons. Exploring some models, we find that generically the rho-dominance prediction f_\rho g_{\rho H H}=m_\rho^2 does not hold, and that g_{\rho H H} is not independent of the hadron H. However, we prove that, in any model within the AdS/QCD context, there are two limiting regimes where the g_{\rho H H}, along with the couplings of all excited vector mesons as well, become H-independent: (1) when H is created by an operator of large dimension, and (2) when H is a highly-excited hadron. We also find a sector of a particular model where universality for the rho coupling is exact. Still, in none of these cases need it be true that f_\rho g_\rho=m_\rho^2, although we find empirically that the relation does hold approximately (up to a factor of order two) within the models we have studied.Comment: 28 pages, 3 figures. ver 2: Comments about the commutability of two universal limits in the D3/D7 case corrected. Typos corrected. ver 3: Substantive revisions of certain calculations, with improved conventions, correction of typos, clarifications, new formulas, new figures; no changes in essential results or conclusion

Quarkonium from the Fifth Dimension

Adding fundamental matter of mass m_Q to N=4 Yang Mills theory, we study quarkonium, and "generalized quarkonium" containing light adjoint particles. At large 't Hooft coupling the states of spin<=1 are anomalously light (Kruczenski et al., hep-th/0304032). We examine their form factors, and show these hadrons are unlike any known in QCD. By a traditional yardstick they appear infinite in size (as with strings in flat space) but we show that this is a failure of the yardstick. All of the hadrons are actually of finite size ~ \sqrt{g^2N}/m_Q, regardless of their radial excitation level and of how many valence adjoint particles they contain. Certain form factors for spin-1 quarkonia vanish in the large-g^2N limit; thus these hadrons resemble neither the observed J/Psi quarkonium states nor rho mesons.Comment: 57 pages, LaTeX, 5 figure

Induced P-wave superfluidity within full energy-momentum dependent Eliashberg approximation in asymmetric dilute Fermi gases

We consider a very asymmetric system of Fermions with an interaction characterized by a positive scattering length only. The minority atoms pair and form a BEC of dimers, while the surplus fermions interact only indirectly through the exchange of Bogoliubov sound modes. This interaction has a finite range, the retardation effects are significant and the surplus fermions will form a P-wave superfluid. We compute the P-wave pairing gap in the BCS and Eliashberg with only energy dependence approximations, and demonstrate their inadequacy in comparison with a full treatment of the momentum and energy dependence of the induced interaction. The pairing gap computed with a full momentum and energy dependence is significantly larger in magnitude and that makes it more likely that this new exotic paired phase could be put in evidence in atomic trap experiments.Comment: 5 pages, 1 figure, updated references and figure, published versio