Recent years have seen a growing appreciation for the effects of quantum critical fluctuations on gapless boundary degrees of freedom. Here we consider the boundary dynamics of the non-compact $\mathbb{CP}^{N-1}$ (NCCP$^{N-1}$) model in two spatial dimensions, with $N$ complex boson species coupled to a fluctuating $\mathrm{U}(1)$ gauge field. These models describe quantum phase transitions beyond the Landau paradigm, such as the deconfined quantum critical point between superconducting (SC) and quantum spin Hall (QSH) phases. We show that, in a large-$N$ limit and with the bulk tuned to criticality, boundaries of the NCCP$^{N-1}$ model display logarithmically decaying, or ``extraordinary-log,'' correlations. In particular, when monopole operators exhibit quasi-long-ranged order at the boundary, we find that the extraordinary-log exponent of the NCCP$^{N-1}$ model in the large-$N$ limit is $q=N/4$, signifying a new family of boundary universality classes parameterized by $N$. In the context of the QSH -- SC transition, the quantum critical point inherits helical edge modes from the QSH phase, and this extraordinary-log behavior manifests in their Cooper pair correlations.
Extraordinary acoustic transmission is commonly associated with periodic or multi-aperture structures. In this work, we show that a single subwavelength slit can support strongly enhanced transmission when its boundary response is described by an effective impedance. Using a reduced analytical model together with numerical calculations, we demonstrate that appropriate impedance tuning leads to efficient coupling between the incident field and the slit mode, resulting in transmission levels approaching unity. The observed enhancement is governed by impedance matching rather than geometric periodicity, highlighting a minimal mechanism for extraordinary transmission. This study establishes boundary impedance control as a versatile route for manipulating acoustic wave transport through deeply subwavelength apertures.
We numerically demonstrate a reconfigurable extraordinary terahertz transmission based on a phase-change material of vanadium dioxide (VO2). The proposed hybrid metasurface is composed of an array of subwavelength apertures perforated on a gold film. The holes are partially filled with annular VO2 and gold disks to control the effective aperture area and the modes inside the aperture. Switching between the insulator and the metallic phase of VO2 provides a convenient way to shift the transmission window. We present two designs offering redshift or blueshift of the extraordinary terahertz transmission. Upon phase transition from the insulator to the metallic phase, in the first design, the transmission peak redshifts from 1.02 to 0.82 THz while in the second design the transmission peak blueshifts from 0.71 to 0.77 THz. Furthermore, the transmission level and resonance frequency can be modulated by controlling the partial phase transition of the VO2. The potential applications for the proposed structures are terahertz modulators and reconfigurable filters.
Speech and language are valuable for interacting with technology. It would be ideal to be able to decouple their use from anthropomorphization, which has recently met an important moment of reckoning. In the world of folktales, language is everywhere and talking to extraordinary objects is not unusual. This overview presents examples of the analogies that folktales offer. Extraordinary objects in folktales are diverse and also memorable. Language capacity and intelligence are not always connected to humanness. Consideration of folktales can offer inspiration and insight for using speech and language for interacting with technology.
We study the boundary extraordinary transition of a three-dimensional (3D) tricritical $O(N)$ model. We first compute the mean-field Green's function with a general coupling of $|\vec φ|^{2n}$ (with $n=3$ corresponding to the tricritical model) at the extraordinary phase transition. Then, using layer susceptibility, we obtain the boundary operator expansion for the transverse and longitudinal modes within the $ε=3 - d$ expansion. Based on these results, we demonstrate that the tricritical point exhibits an extraordinary transition characterized by an ordered boundary for any $N$. This provides the first nontrivial example of continuous symmetry breaking in 2D in the context of boundary criticality.
We investigate the equation of motion for photons with Weyl corrections in a Kerr black hole spacetime in a small coupling case. Our results show that Weyl corrections yield phenomena of birefringence. The light rays propagating in the spacetime are separated into the ordinary rays and the extraordinary rays, and the propagation of the latter depends on the corrections. We probe the effects of Weyl corrections on the Kerr black hole shadows casted by the extraordinary rays and find that such corrections result in a weak stretching or squeezing in the vertical direction for the black hole shadows. Finally, we also study the change of the length of the Near-Horizon Extremal Kerr line (NHEK line) with Weyl corrections. These features could help us to understand the electrodynamics with Weyl corrections from black hole shadows.
Extraordinary transmission through subwavelength metallic apertures has been extensively studied and demonstrated. At resonance, the coupling between surface plasmons on both surfaces of the metallic film tunnels the photon from the one side to the other through the subwavelength aperture with small transmission efficiency based on the metals dielectric parameters and aperture geometrical dimensions. Here, we report a completely different form of extraordinary transmission, where the two subwavelength complementary apertures when coupled with an optical cavity induce about 100% extraordinary transmission far away from the natural plasmon resonance of the constituent metallic apertures. Such unique cavity phase driven plasmon resonance enables tuning of the extraordinary transmission band across wide spectral range unlike previously reported geometry driven extraordinary transmission.
We study the connection between mutually unbiased bases and mutually orthogonal extraordinary supersquares, a wider class of squares which does not contain only the Latin squares. We show that there are four types of complete sets of mutually orthogonal extraordinary supersquares for the dimension $d=8$. We introduce the concept of physical striation and show that this is equivalent to the extraordinary supersquare. The general algorithm for obtaining the mutually unbiased bases and the physical striations is constructed and it is shown that the complete set of mutually unbiased physical striations is equivalent to the complete set of mutually orthogonal extraordinary supersquares. We apply the algorithm to two examples: one for two-qubit systems ($d=4$) and one for three-qubit systems ($d=8$), by using the Type II complete sets of mutually orthogonal extraordinary supersquares of order 8.
The separate spin evolution (SSE) of electrons causes the existence of the spin-electron acoustic wave. Extraordinary spin-electron acoustic waves (SEAWs) propagating perpendicular to the external magnetic field have large contribution of the transverse electric field. Its spectrum has been studied in the quasi-classical limit at the consideration of the separate spin evolution. The spin-spin interaction and the quantum Bohm potential give contribution in the spectrum extraordinary SEAW. This contribution is studied in this paper. Moreover, it is demonstrated that the spin-spin interaction leads to the existence of the extraordinary SEAWs if the SSE is neglected. The hybridization of the extraordinary SEAW and the lower extraordinary wave in the regime, where the cyclotron frequency is larger then the Langmuir frequency is studied either.
The recent discovery of extraordinary-log universality has generated intense interest in classical and quantum boundary critical phenomena. Despite tremendous efforts, the existence of quantum extraordinary-log universality remains extremely controversial. Here, by utilizing quantum Monte Carlo simulations, we study the quantum edge criticality of a two-dimensional Bose-Hubbard model featuring emergent bulk criticality. On top of an insulating bulk, the open edges experience a Kosterlitz-Thouless-like transition into the superfluid phase when the hopping strength is sufficiently enhanced on edges. At the bulk critical point, the open edges exhibit the special, ordinary, and extraordinary critical phases. In the extraordinary phase, logarithms are involved in the finite-size scaling of two-point correlation and superfluid stiffness, which admit a classical-quantum correspondence for the extraordinary-log universality. Thanks to modern quantum emulators for interacting bosons in lattices, the edge critical phases might be realized in experiments.
To consider a contribution of the spin-orbit interaction in the extraordinary wave spectrum we derive a generalization of the separate spin evolution quantum hydrodynamics. Applying corresponding nonlinear Pauli equation we include Fermi spin current contribution in the spin evolution. We find that the spectrum of extraordinary waves consists of three branches: two of them are well-known extraordinary waves and the third one is the spin-electron acoustic wave (SEAW). Earlier SEAWs have been considered in the electrostatic limit. Here we include the electromagnetic effects in their spectrum at the propagation perpendicular to the external magnetic field. We find that the SEAW spectrum considerably changes at the account of transverse part of electric field. We obtain that the separate spin evolution modifies spectrum of the well-known extraordinary waves either. A change of the extraordinary wave spectrum due to the spin-orbit interaction is obtained as well.
Extraordinary Invariants are elements of the BRST Cohomology Space which are irrevocably dependent on Zinn sources. The existence of an Extraordinary Invariant means that the symmetry is broken in that sector, and that the field equations can almost rescue the invariance. Adding the Extraordinary Invariant to the action results in a new theory with constraints on the starting theory. So Extraordinary Invariants are seeds from which a theory can grow. For a simple example, it is shown in this paper how Yang Mills theory is implicitly contained in the BRST Cohomology of Free Gauge Theory. It comes from an Extraordinary Invariant which can be added to the free gauge action. The Jacobi Identities are generated by requiring that the BRST Poisson Bracket be zero. Since the mechanism is a general one, it can be used to construct new theories. Some of these, for example in Supersymmetric theories, have not yet been noticed using other methods.
The results of experimental and theoretical study of anomalous attenuation of probe extraordinary waves in experiments on modification of ionosphere by powerful HF waves on "Sura" heating facility are presented. The experimental data indicate significant attenuation of extraordinary waves which can be explained as a result of multiple scattering of extraordinary waves on small-scale random irregularities. The possibility of diagnostics of spectrum of artificial irregularities from measurements of anomalous attenuation of extraordinary waves is demonstrated.
Our purpose is to determine the complete set of mutually orthogonal squares of order $d$, which are not necessary Latin. In this article, we introduce the concept of supersquare of order $d$, which is defined with the help of its generating subgroup in $\mathbb{F}_d\times \mathbb{F}_d$. We present a method of construction of the mutually orthogonal supersquares. Further, we investigate the orthogonality of extraordinary supersquares, a special family of squares, whose generating subgroups are extraordinary. The extraordinary subgroups in $\mathbb{F}_d\times \mathbb{F}_d$ are of great importance in the field of quantum information processing, especially for the study of mutually unbiased bases. We determine the most general complete sets of mutually orthogonal extraordinary supersquares of order 4, which consist in the so-called Type I and Type II. The well-known case of $d-1$ mutually orthogonal Latin squares is only a special case, namely Type I.
Analysis-suitable T-splines (AST-splines) are a promising candidate to achieve a seamless integration between the design and the analysis of thin-walled structures in industrial settings. In this work, we generalize AST-splines to allow multiple extraordinary points within the same face. This generalization drastically increases the flexibility to build geometries using AST-splines; e.g., much coarser meshes can be generated to represent a certain geometry. The AST-spline spaces detailed in this work have $C^1$ inter-element continuity near extraordinary points and $C^2$ inter-element continuity elsewhere. We mathematically show that AST-splines with multiple extraordinary points per face are linearly independent and their polynomial basis functions form a non-negative partition of unity. We numerically show that AST-splines with multiple extraordinary points per face lead to optimal convergence rates for second- and fourth-order linear elliptic problems. To illustrate a possible isogeometric framework that is already available, we design the B-pillar and the side outer panel of a car using T-splines with the commercial software Autodesk Fusion360, import the control nets into our
Resonances and enhancements in meson-meson scattering can be divided into two classes distinguished by their behavior as the number of colors N_c in QCD becomes large: The first are ordinary mesons that become stable as N_c goes to infinity. This class includes textbook q-bar q mesons as well as glueballs and hybrids. The second class, extraordinary mesons, are enhancements that disappear as N_c goes to infinity; they subside into the hadronic continuum. This class includes indistinct and controversial objects that have been classified as q-bar q-bar q q mesons or meson-meson molecules. Pelaez's study of the N_c dependence of unitarized chiral dynamics illustrates both classes: the p-wave pi-pi and K-pi resonances, the rho(770) and K*(892), behave as ordinary mesons; the s-wave pi-pi and K-pi enhancements, the sigma(600) and kappa(800), behave like extraordinary mesons. Ordinary mesons resemble Feshbach resonances while extraordinary mesons look more like effects due to potentials in meson-meson scattering channels. I build and explore toy models along these lines. Finally I discuss some related dynamical issues affecting the interpretation of extraordinary mesons.
With simple, exact arguments we show that the surface magnetization $m_1$ at the extraordinary and normal transitions and the surface energy density $ε_1$ at the ordinary, extraordinary, and normal transitions of semi-infinite $d$-dimensional Ising systems have leading thermal singularities $B_\pm |t|^{2-α}$, with the same critical exponent and amplitude ratio as the bulk free energy $f_b(t,0)$. The derivation is carried out in three steps: (i) By tracing out the surface spins, the semi-infinite Ising model with supercritical surface enhancement $g$ and vanishing surface magnetic field $h_1$ is mapped exactly onto a semi-infinite Ising model with subcritical surface enhancement, a nonzero surface field, and irrelevant additional surface interactions. This establishes the equivalence of the extraordinary ($h_1=0, g>0$) and normal ($h_1 eq 0, g<0$) transitions. (ii) The magnetization $m_1$ at the interface of an infinite system with uniform temperature $t$ and a nonzero magnetic field $h$ in the half-space $z>0$ only is shown to be proportional to $f_b(t,0)-f_b(t,h)$. (iii) The energy density $ε_1$ at the interface of an infinite system with temperatures $t_+$ and $t$ in the
Extraordinary magnetoresistance (EMR) is a geometric magnetoresistance effect occurring in hybrid devices consisting of a high-mobility material joined by a metal. The change in resistance can exceed 107% at room temperature when a magnetic field of 5 T is applied. Magnetic field sensors based on EMR hold the potential formeasuring weak magnetic fields with an unprecedented sensitivity, yet, to date this potential is largely unmet. In this work, we provide an extensive review of the current state-of-the-art in EMR sensors with a focus on the hybrid device geometries, the constituent material properties and applications of EMR. We present a direct comparison of the best devices in literature across magnetoresistance, sensitivity and noise equivalent field for different materials and geometric designs. The compilation of studies collected in this review illustrates the extremely rich possibilities for tuning the magnetoresistive behavior varying the device geometry and material properties. In addition, we aim to improve the understanding of the EMR effect and its interplay with geometry and material properties. Finally, we discuss recent trends in the field and future perspectives fo
In this paper, we model the cash surplus (or equity) of a risky business with a Brownian motion. Owners can take cash out of the surplus in the form of "dividends", subject to transaction costs. However, if the surplus hits 0 then ruin occurs and the business cannot operate any more. We consider two types of dividend distributions: (i) periodic, regular ones (that is, dividends can be paid only at countable many points in time, according to a specific arrival process); and (ii) extraordinary dividend payments that can be made immediately at any time (that is, the dividend decision time space is continuous and matches that of the surplus process). Both types of dividends attract proportional transaction costs, and extraordinary distributions also attracts fixed transaction costs, a realistic feature. A dividend strategy that involves both types of distributions (periodic and extraordinary) is qualified as "hybrid". We determine which strategies (either periodic, immediate, or hybrid) are optimal, that is, we show which are the strategies that maximise the expected present value of dividends paid until ruin, net of transaction costs. Sometimes, a liquidation strategy (which pays out
In a contemporary world, people become dependent on electronic devices. Technologies help to clarification and structure life in many ways to meet the need of the children oriented requirements. The children suffering from disabilities (e.g. autism) has desperate needs for elucidation and structures their life. MumIES is a research based system facilitates to support and manage their living. This paper works on MumIES system to evaluate usability of the system in extraordinary environment for extraordinary people. The paper shows from the survey observation users need supporting tools to access the children's potential and challenges and to give the full support to overcome disabilities. Usability evaluation has been considered one of the key challenges to MumIES system. The paper represents analysis, design of usability studies for the extraordinary user in environment.