The Price of Governance: A Middle Ground Solution to Coordination in Organizational Control

Achieving coordination is crucial in organizational control. This paper investigates a middle ground solution between decentralized interactions and centralized administrations for coordinating agents beyond inefficient behavior. We first propose the price of governance (PoG) to evaluate how such a middle ground solution performs in terms of effectiveness and cost. We then propose a hierarchical supervision framework to explicitly model the PoG, and define step by step how to realize the core principle of the framework and compute the optimal PoG for a control problem. Two illustrative case studies are carried out to exemplify the applications of the proposed framework and its methodology. Results show that by properly formulating and implementing each step, the hierarchical supervision framework is capable of promoting coordination among agents while bounding administrative cost to a minimum in different kinds of organizational control problems

Higher ramification loci over homogeneous spaces

We generalize the Gaffney-Lazarsfeld theorem on higher ramification loci of branched coverings of $\mathbb{P}^n$ to homogeneous spaces with Picard number one.Comment: 7 page

Three Identical Fermions with Resonant p-wave Interactions in Two Dimensions

A new kind of "super-Efimov" states of binding energies scaling as $\ln|E_n|\sim-e^{3n\pi/4}$ were predicted by a field theory calculation for three fermions with resonant $p$-wave interactions in two dimensions [Phys. Rev. Lett. \textbf{110}, 235301 (2013)]. However, the universality of these "super-Efimov" states has not been proved independently. In this Letter, we study the three fermion system through the hyperspherical formalism. Within the adiabatic approximation, we find that at $p$-wave resonances, the low energy physics of states of angular momentum $\ell=\pm1$ crucially depends on the value of an emergent dimensionless parameter $Y$ determined by the detail of the inter-particle potential. Only if $Y$ is exactly zero, the predicted "super-Efimov" states exist. If $Y>0$, the scaling of the bound states changes to $\ln|E_n|\sim-(n\pi)^2/2Y$, while there are no shallow bound states if $Y<0$.Comment: The neglected term $Q_{00}$ has been calculated numerically and found to be non-negligible in the large hyperradius limi

Breathing mode of two-dimensional atomic Fermi gases in harmonic traps

For two-dimensional (2D) atomic Fermi gases in harmonic traps, the SO(2,1) symmetry is broken by the interatomic interaction explicitly via the contact correlation operator. Consequently the frequency of the breathing mode $\omega_B$ of the 2D Fermi gas can be different from $2\omega_0$, with $\omega_0$ the trapping frequency of harmonic potentials. At zero temperature, we use the sum rules of density correlation functions to yield upper bounds for $\omega_B$. We further calculate $\omega_B$ through the Euler equations in the hydrodynamic regime. The obtained value of $\omega_B$ satisfies the upper bounds and shows deviation from $2\omega_0$ which can be as large as about 8%.Comment: 5 pages, 1 figur

The Single Particle Excitation Spectrum of Degenerate Fermi gases in a ring cavity

By considering a spin-$\frac{1}{2}$ degenerate Fermi gases in a ring cavity where strong interaction between atoms and light gives rise to a superradiance, we find the cavity dissipation could cause a severe broadening in some special cases, breaking down the quasi-particle picture which was constantly assumed in mean field theory studies. This broadening happens when the band gap resonant with polariton excitation energy. Interestingly enough, this broadening is highly spin selective depending on how the fermions are filled and the spectrum becomes asymmetric due to dissipation. Further, a non-monotonous dependence of the maximal broadening of the spectrum against cavity decay rate $\kappa$ is found and the largest broadening emerges at $\kappa$ comparable to recoil energy.Comment: 10 pages, 10 figure

Density Wave Superradiance of Photonic Fluid in Frustrated Triangle Lattice Cavity Arrays

The spontaneously broken of translational symmetry is usually due to the competition between local interactions and long-range interactions. However, in this paper, we show how a crystalline order can be generated by the competition between local interaction and long-range correlation by frustration. Here we propose a positive hopping Bose Hubbard model on triangle lattices with a pair creation term which comes from frustrated linked cavity arrays with degenerate quantum gases in them. We find by increasing the strength of pair creation term against local interaction strength, two kinds of density wave ordered superradiant photonic fluid phase can be realized and a first order transition between two different density wave ordered states is found. This proposal shows us a new way to produce coherent "solid" phase without the help of long range interactions.Comment: 5 pages, 4 figure

Piezoelectricity and Topological Quantum Phase Transitions in Two-Dimensional Spin-Orbit Coupled Crystals with Time-Reversal Symmetry

Finding new physical responses that signal topological quantum phase transitions is of both theoretical and experimental importance. Here, we demonstrate that the piezoelectric response can change discontinuously across a topological quantum phase transition in two-dimensional time-reversal invariant systems with spin-orbit coupling, thus serving as a direct probe of the transition. We study all gap closing cases for all 7 plane groups that allow non-vanishing piezoelectricity and find that any gap closing with 1 fine-tuning parameter between two gapped states changes either the $Z_2$ invariant or the locally stable valley Chern number. The jump of the piezoelectric response is found to exist for all these transitions, and we propose the HgTe/CdTe quantum well and BaMnSb$_2$ as two potential experimental platforms. Our work provides a general theoretical framework to classify topological quantum phase transitions and reveals their ubiquitous relation to the piezoelectric response.Comment: Close to the published versio

Note on acoustic black holes from black D3-brane

In this paper, we study the acoustic black hole emerged from the nonextremal black D3-brane, based on the holographic approaches in constructing the acoustic black hole in asymptotically Anti de-Sitter spacetime (AAdS) and the effective hydrodynamic description of the nonextremal black D3-brane. We show that the holographic dual description of the acoustic black hole appeared on the timelike cutoff surface in the nonextremal black D3-brane also exist. The duality includes the dynamical connection between the acoustic black hole and the bulk gravity, a universal equation relating the Hawking-like temperature and the Hawking temperature, and a phonon/scalar channel quasinormal mode correspondence.Comment: 14 pages, no figure

Spin Susceptibility, Upper Critical Field and Disorder Effect in j=32j=\frac{3}{2} Superconductors with Singlet-Quintet Mixing

Recently, a new pairing state with the mixing between s-wave singlet channel and isotropic d-wave quintet channel induced by centrosymmetric spin-orbit coupling has been theoretically proposed in the superconducting materials with $j=\frac{3}{2}$ electrons. In this work, we derive the expressions of the zero-temperature spin susceptibility, the upper critical field close to the zero-field critical temperature $T_c$ and the critical temperature with weak random non-magnetic disorders for the singlet-quintet mixed state based on the Luttinger model. Our study revealed the following features of the singlet-quintet mixing. (1) The zero-temperature spin susceptibility remains zero for the singlet-quintet mixed state if only the centrosymmetric spin-orbit coupling is taken into account, and will deviate from zero when the non-centrosymmetric spin-orbit coupling is introduced. (2) The singlet-quintet mixing can help enhance the upper critical field roughly because it can increase $T_c$. (3) Although the quintet channel is generally suppressed by the non-magnetic disorder scattering, we find the strong mixing between singlet and quintet channels can help to stabilize the quintet channel. As a result, we still find a sizable quintet component mixed into the singlet channel in the presence of weak random non-magnetic disorders. Our work provides the guidance for future experiments on spin susceptibility and upper critical field of the singlet-quintet mixed superconducting states, and illustrates the stability of the singlet-quintet mixing against the weak random non-magnetic disorder.Comment: 23 pages and 6 figure

Gravitational waves and extra dimensions: a short review

We give a brief review on the recent development of gravitational waves in extra-dimensional theories of gravity. Studying extra-dimensional theories with gravitational waves provides a new way to constrain extra dimensions. After a flash look at the history of gravitational waves and a brief introduction to several major extra-dimensional theories, we focus on the sources and spectra of gravitational waves in extra-dimensional theories. It is shown that one can impose limits on the size of extra dimensions and the curvature of the universe by researching the propagations of gravitational waves and the corresponding electromagnetic waves. Since gravitational waves can propagate throughout the bulk, how the amplitude of gravitational waves decreases determines the number of extra dimensions for some models. In addition, we also briefly present some other characteristics of gravitational waves in extra-dimensional theories.Comment: 35 pages, 1 figur