Description In Terms Of Equations Research Articles

Multiple superconducting phases in heavy-fermion metals

Symmetry breaking beyond a global U(1) phase is the key signature of unconventional superconductors. As prototypical strongly correlated materials, heavy-fermion metals provide ideal platforms for realizing unconventional superconductivity. In this article, we review heavy-fermion superconductivity, with a focus on those materials with multiple superconducting phases. In this context, we highlight the role of orbital-selective (matrix) pairing functions, which are defined as matrices in the space of effective orbital degrees of freedom such as electronic orbitals and sublattices as well as equivalent descriptions in terms of intra- and inter-band pairing components in the band basis. The role of quantum criticality and the associated strange-metal physics in the development of unconventional superconductivity is emphasized throughout. We discuss in some detail the recent experimental observations and theoretical perspectives in the illustrative cases of UTe2, CeRh2As2, and CeCu2Si2, where applied magnetic fields or pressure induce a variety of superconducting phases. We close by providing a brief overview of overarching issues and implications for possible future directions.

Disformal transformations and the motion of a particle in semi-classical gravity

The approach to incorporate quantum effects in gravity by replacing free particle geodesics with Bohmian non-geodesic trajectories has an equivalent description in terms of a conformally related geometry, where the motion is force free, with the quantum effects inside the conformal factor, i.e., in the geometry itself. For more general disformal transformations relating gravitational and physical geometries, we show how to establish this equivalence by taking the quantum effects inside the disformal degrees of freedom. We also show how one can solve the usual problems associated with the conformal version, namely the wrong continuity equation, indefiniteness of the quantum mass, and wrong description of massless particles in the singularity resolution argument, by using appropriate disformal transformations.

Holographic boundary states and dimensionally reduced braneworld spacetimes

Recently it was proposed that microscopic models of braneworld cosmology could be realized in the context of anti--de Sitter/conformal field theory ($\mathrm{AdS}/\mathrm{CFT}$) correspondence using black hole microstates containing an end-of-the-world brane. Motivated by a desire to establish the microscopic existence of such microstates, which so far have been discussed primarily in bottom-up models, we have studied similar microstates in a simpler version of $\mathrm{AdS}/\mathrm{CFT}$. On one side, we define and study boundary states in the charged Sachdev-Ye-Kitaev model and show that these states typically look thermal with a certain pattern of symmetry breaking. On the other side, we study the dimensional reduction of microstates in Einstein-Maxwell theory featuring an end-of-the-world brane and show that they have an equivalent description in terms of 2D Jackiw-Teitelboim gravity coupled to an end-of-the-world particle. In particular, the same pattern of symmetry breaking is realized in both sides of the proposed duality. These results give significant evidence that such black hole microstates have a sensible microscopic realization.

Wikipedia for multilingual COVID-19 vaccine education at scale

We present the design of a project to develop Wikipedia content on general vaccine safety and the COVID-19 vaccines, specifically. This proposal describes what a team would need to distribute public health information in Wikipedia in multiple languages in response to a disaster or crisis, and to measure and report the communication impact of the same. Researchers at the School of Data Science at the University of Virginia made this proposal in response to a February 2021 call from a sponsor which was seeking to share public health information to respond globally to vaccine hesitancy related to the COVID-19 vaccines. This proposal was not selected for funding, and now the research team is sharing the proposal here with an open copyright license for anyone to reuse and remix. Most of the text here is from the original proposal, but there are modifications to remove the names of the funder, named partners, and for other details to make this text more reusable. The budget in this proposal has been converted from a dollar amount to equivalent descriptions in terms of labor hours, and the timeline was adapted from absolute to relative months.

Quantum crystals, Kagome lattice, and plane partitions fermion-boson duality

In this work, we study quantum crystal melting in three space dimensions. Using an equivalent description in terms of dimers in a hexagonal lattice, we recast the crystal melting Hamiltonian as an occupancy problem in a Kagome lattice. The Hilbert space is spanned by states labeled by plane partitions and writing them as a product of interlaced integer partitions, we define a fermion-boson duality for plane partitions. Finally, based upon the latter result we conjecture that the growth operators for the quantum Hamiltonian can be represented in terms of the affine Yangian ${\cal Y}[\widehat{\mathfrak{gl}}(1)]$.

BRST in the exact renormalization group

AbstractWe show, explicitly within perturbation theory, that the quantum master equation and the Wilsonian renormalization group flow equation can be combined such that for the continuum effective action, quantum BRST invariance is not broken by the presence of an effective ultraviolet cutoff $\Lambda$, despite the fact that the structure demands quantum corrections that naïvely break the gauge invariance, such as a mass term for a non-Abelian gauge field. Exploiting the derivative expansion, BRST cohomological methods fix the solution up to choice of renormalization conditions, without inputting the form of the classical, or bare, interactions. Legendre transformation results in an equivalent description in terms of solving the modified Slavnov–Taylor identities and the flow of the Legendre effective action under an infrared cutoff $\Lambda$ (i.e. effective average action). The flow generates a canonical transformation that automatically solves the Slavnov–Taylor identities for the wavefunction renormalization constants. We confirm this structure in detail at tree level and one loop. Under flow of $\Lambda$, the standard results are obtained for the beta function, anomalous dimension, and physical amplitudes, up to the choice of the renormalization scheme.

Synchronization and anti-synchroniztion of dynamically coupled networks

We consider the coupling between two networks, each having N nodes whose individual dynamics is modeled by a two-state master equation. The intra-network interactions are all-to-all, whereas the inter-network interactions involve only a small percentage of the total number of nodes. We demonstrate that the dynamics of the mean field for a single network has an equivalent description in terms of a Langevin equation for a particle in a double-well potential. The coupling of two networks or equivalent coupling of two Langevin equations demonstrates synchronization or anti-synchronization between two systems, depending on the sign of the interaction. The anti-synchronized behavior is explained in terms of the potential function and the inter-network interaction. The relative entropy is used to establish that the conditions for maximum information transfer between the networks are consistent with the principle of complexity management and occurs when one system is near the critical state. The limitations of the Langevin modeling of the network coupling are also discussed.

Asymptotics for a Class of Meandric Systems, via the Hasse Diagram of NC(n)

We consider closed meandric systems, and their equivalent description in terms of the Hasse diagrams of the lattices of non-crossing partitions $NC(n)$. In this equivalent description, the number of components of a random meandric system of order $n$ translates into the distance between two partitions in $NC(n)$. We focus on a class of couples $(\pi,\rho)\in NC(n)^2$ -- namely the ones where $\pi$ is conditioned to be an interval partition -- for which it turns out to be tractable to study distances in the Hasse diagram. As a consequence, we observe a non-trivial class of meanders (i.e. connected meandric systems), which we call "meanders with shallow top", and which can be explicitly enumerated. Moreover, the expected number of components for a random "meandric system with shallow top", is asymptotically $(9n+28)/27$. Our calculations concerning expected number of components are related to the idea of taking the derivative at $t=1$ in a semigroup for the operation $\boxplus$ of free probability (but the underlying considerations are presented in a self-contained way, and can be followed without assuming a free probability background). Let $c_{n}'$ denote the expected number of components of a general, unconditioned, meandric system of order $n$. A variation of the methods used in the shallow-top case allows us to prove that $\mathrm{lim\ inf}_{n\to\infty}c_{n}'/n\geq0.17$. We also note that, by a direct elementary argument, one has $\mathrm{lim\ sup}_{n\to\infty}c_{n}'/n\leq0.5$. These bounds support the conjecture that $c_{n}'$ follows a regime of "constant times $n$" (where numerical experiments suggest that the constant should be $\approx0.23$).

Revisiting the O(3) Non‐linear Sigma Model and Its Pohlmeyer Reduction

AbstractIt is well known that sigma models in symmetric spaces accept equivalent descriptions in terms of integrable systems, such as the sine‐Gordon equation, through Pohlmeyer reduction. In this paper, we study the mapping between known solutions of the Euclidean O(3) non‐linear sigma model, such as instantons, merons and elliptic solutions that interpolate between the latter, and solutions of the Pohlmeyer reduced theory, namely the sinh‐Gordon equation. It turns out that instantons do not have a counterpart, merons correspond to the ground state, while the class of elliptic solutions is characterized by a two to one correspondence between solutions in the two descriptions.

Equation-free analysis of agent-based models and systematic parameter determination

Abstract Agent based models (ABM)s are increasingly used in social science, economics, mathematics, biology and computer science to describe time dependent systems in circumstances where a description in terms of equations is difficult. Yet few tools are currently available for the systematic analysis of ABM behaviour. Numerical continuation and bifurcation analysis is a well-established tool for the study of deterministic systems. Recently, equation-free (EF) methods have been developed to extend numerical continuation techniques to systems where the dynamics are described at a microscopic scale and continuation of a macroscopic property of the system is considered. To date, the practical use of EF methods has been limited by; (1) the over-head of application-specific implementation; (2) the laborious configuration of problem-specific parameters; and (3) large ensemble sizes (potentially) leading to computationally restrictive run-times. In this paper we address these issues with our tool for the EF continuation of stochastic systems, which includes algorithms to systematically configuration problem specific parameters and enhance robustness to noise. Our tool is generic and can be applied to any ‘black-box’ simulator and determines the essential EF parameters prior to EF analysis. Robustness is significantly improved using our convergence-constraint with a corrector-repeat (C3R) method. This algorithm automatically detects outliers based on the dynamics of the underlying system enabling both an order of magnitude reduction in ensemble size and continuation of systems at much higher levels of noise than classical approaches. We demonstrate our method with application to several ABM models, revealing parameter dependence, bifurcation and stability analysis of these complex systems giving a deep understanding of the dynamical behaviour of the models in a way that is not otherwise easily obtainable. In each case we demonstrate our systematic parameter determination stage for configuring the system specific EF parameters.

Modular operads and the quantum open-closed homotopy algebra

We verify that certain algebras appearing in string field theory are algebras over Feynman transform of modular operads which we describe explicitly. Equivalent description in terms of solutions of generalized BV master equations are explained from the operadic point of view.

Teleparallelism by inhomogeneous dark fluid

In this paper, we investigate \(f(T)\) cosmology and find an exact solution for \(f\) which gives a Little Rip cosmology. Also, considering accelerating cosmology with dark matter, the time-dependent solution is found. For these cases, by using solutions obtained from \(f(T)\) gravity we find expressions for \(\omega\) and \(\varLambda\) defined as time functions via equivalent description in terms of inhomogeneous fluid. This puts the question: which theoretical model describes the observational cosmology?

Inhomogeneous Dark Fluid and Dark Matter, Leading to a Bounce Cosmology

The purpose of this short review is to describe cosmological models with a linear inhomogeneous time-dependent equation of state (EoS) for dark energy, when dark fluid is coupled with dark matter. This may lead to a bounce cosmology. We consider equivalent descriptions in terms of the EoS parameters for an exponential, a power-law, or a double-exponential law for the scale factor a. Stability issues are discussed by considering small perturbations around the critical points for the bounce, in the early as well as in the late, universe. The latter part of the paper is concerned with dark energy coupled with dark matter in viscous fluid cosmology. We allow the bulk viscosity ζ = ζ(H, t) to be a function of the Hubble parameter and the time, and consider the Little Rip, the Pseudo Rip, and the bounce universe. Analytic expressions for characteristic properties of these cosmological models are obtained.

On a space of entire functions rapidly decreasing on Rn and its Fourier transform

AbstractA space of entire functions of several complex variables rapidly decreasing on Rn and such that their growth along iRn is majorized with the help of a family of weight functions is considered in this paper. For such space an equivalent description in terms of estimates on all of its partial derivatives as functions on Rn and a Paley-Wiener type theorem are obtained.

Bounce universe induced by an inhomogeneous dark fluid coupled with dark matter

We investigate cosmological models with a linear inhomogeneous time-dependent equation-of-state (EoS) for the dark energy, coupled with dark matter, leading to a bounce cosmology. Equivalent descriptions in terms of the EoS parameters for an exponential, a power-law, or a double exponential form of the scale factor a is obtained. The stability of the solutions is explored, by considering small perturbations around the critical points for the bounce in the early and in the late-time universe.

A K3 sigma model with $ \mathbb{Z}_2^8 $ : $ {{\mathbb{M}}_{20 }} $ symmetry

The K3 sigma model based on the Z_2-orbifold of the D_4-torus theory is studied. It is shown that it has an equivalent description in terms of twelve free Majorana fermions, or as a rational conformal field theory based on the affine algebra su(2)^6. By combining these different viewpoints we show that the N=(4,4) preserving symmetries of this theory are described by the discrete symmetry group Z_2^8:M_{20}. This model therefore accounts for one of the largest maximal symmetry groups of K3 sigma models. The symmetry group involves also generators that, from the orbifold point of view, map untwisted and twisted sector states into one another.

Turbulence accelerating cosmology from an inhomogeneous dark fluid

Specific dark energy models with a linear inhomogeneous time-dependent equation of state, within the framework of 4d Friedman-Robertson-Walker (FRW) cosmology, are investigated. It is demonstrated that such 4d inhomogeneous fluid models may lead to a turbulence FRW cosmology. Both one-component and two-component models from 4d inhomogeneous dark fluid models are considered. In the one-component model the universe may develop from a viscous era with, for instance, a constant bulk viscosity, into a turbulent era. In the two-component model the fluid can be decomposed into two components, one non-turbulent (ideal) and another turbulent part, obeying two different equations of state. Conditions for the appearance of the turbulent dark energy universe in terms of the parameters in the equation of state (EoS) without introducing the turbulence concept explicitly are are obtained. An equivalent description in terms of an inhomogeneous fluid for the viscous Little Rip (LR) cosmology is also developed.

Analytic solution of Bremsstrahlung TBA

We consider the quark-anti-quark potential on the three sphere or the generalized cusp anomalous dimension in planar $ \mathcal{N}=4 $ SYM. We concentrate on the vacuum potential in the near BPS limit with L units of R-charge. Equivalently, we study the anomalous dimension of a super-Wilson loop with L local fields inserted at a cusp. The system is described by a recently proposed infinite set of non-linear integral equations of the Thermodynamic Bethe Ansatz (TBA) type. That system of TBA equations is very similar to the one of the spectral problem but simplifies a bit in the near BPS limit. Using techniques based on the Y-system of functional equations we first reduced the infinite system of TBA equations to a Finite set of Nonlinear Integral Equations (FiNLIE). Then we solve the FiNLIE system analytically, obtaining a simple analytic result for the potential! Surprisingly, we find that the system has equivalent descriptions in terms of an effective Baxter equation and in terms of a matrix model. At L = 0, our result matches the one obtained before using localization techniques. At all other L’s, the result is new. Having a new parameter, L, allows us to take the large L classical limit. We use the matrix model description to solve the classical limit and match the result with a string theory computation. Moreover, we find that the classical string algebraic curve matches the algebraic curve arising from the matrix model.

Non-metric chaotic inflation

We consider inflation within the context of what is arguably the simplest non-metric extension of Einstein gravity. There non-metricity is described by a single graviscalar field with a non-minimal kinetic coupling to the inflaton field Ψ, parameterized by a single parameter γ. There is a simple equivalent description in terms of a massless field and an inflaton with a modified potential. We discuss the implications of non-metricity for chaotic inflation and find that it significantly alters the inflaton dynamics for field values Ψ≳MP/γ, dramatically changing the qualitative behaviour in this regime. In the equivalent single-field description this is described as a cuspy potential that forms of barrier beyond which the inflation becomes a ghost field. This imposes an upper bound on the possible number of e-folds. For the simplest chaotic inflation models, the spectral index and the tensor-to-scalar ratio receive small corrections dependent on the non-metricity parameter. We also argue that significant post-inflationary non-metricity may be generated.

Schwarzschild horizon dynamics andSU(2)Chern-Simons theory

We discuss the effect of different choices in partial gauge fixing of bulk local Lorentz invariance, on the description of the horizon degrees of freedom of a Schwarzschild black hole as an $SU(2)$ Chern-Simons theory with specific sources. A classically equivalent description in terms of an $ISO(2)$ Chern-Simons theory is also discussed. Further, we demonstrate that both of these descriptions can be partially gauge fixed to a horizon theory with $U(1)$ local gauge invariance, with the solder form sources being subject to extra constraints in directions orthogonal to an internal vector field left invariant by $U(1)$ transformations. Seemingly disparate approaches on characterization of the horizon theory for the Schwarzschild black hole (as well as spherical isolated horizons in general) are thus shown to be equivalent physically.