Search

We discuss relaxation solutions to the dark matter - baryon coincidence problem in the context of QCD axion dark matter. In relaxation solutions, a moduli dynamically adjusts the mass of dark matter and baryons until their energy densities are $\mathrm{O}(1)$ the same. Because the QCD axion is heavily connected to QCD, scanning the QCD axion mass inherently also scans the proton mass. In the context of relaxation solutions, this implies that the ratio of dark matter to baryon abundances ($\Omega_{\rm DM}/\Omega_{\rm B}$) is a ratio of beta functions showing that these models can only accommodate discrete values of $\Omega_{\rm DM}/\Omega_{\rm B}$ thereby ``predicting" the ratio of the dark matter to baryon abundances. The original composite axion model has only a single integer degree of freedom $N$, the size of the gauge group, and we show that when $N=8$ the observed value of $\Omega_{\rm DM}/\Omega_{\rm B} = 5.36$ is reproduced to within its percent level error bars. Novel tests of this model include more precise measurements of $\Omega_{\rm DM}/\Omega_{\rm B}$, a better lattice determination of the dependence of the proton mass on the high energy QCD gauge coupling, as well as more traditional tests such as fifth force experiments., Comment: 20 pages, 6 figures

We propose a relaxation mechanism for the initial misalignment angle of the pre-inflationary QCD axion with a large decay constant. The proposal addresses the challenges posed to the axion dark matter scenario by an overabundance of axions overclosing the Universe, as well as by isocurvature constraints. Many state-of-the-art experiments are searching for QCD axion dark matter with a decay constant as large as $10^{16}\,\mathrm{GeV}$, motivating the need for a theoretical framework such as ours. In our model, hidden sector magnetic monopoles generated in the early Universe give the axion a large mass via the Witten effect, causing early oscillations that reduce the misalignment angle and axion abundance. As the hidden gauge symmetry breaks, its monopoles confine via cosmic strings, dissipating energy into the Standard Model and leading to monopole-antimonopole annihilation. This removes the monopole-induced mass, leaving only the standard QCD term. We consider the symmetry breaking pattern of $\mathrm{SU}(2)' \to \mathrm{U}(1)' \to 1$, leading to monopole and string formation respectively. We calculate the monopole abundance, their interactions with the axion field, and the necessary conditions for monopole-induced axion oscillations, while accounting for UV instanton effects. We present three model variations based on different symmetry breaking scales and show that they can accommodate an axion decay constant of up to $10^{16}\,\mathrm{GeV}$ with an inflationary scale of $10^{15}\,\mathrm{GeV}$. The required alignment between monopole-induced and QCD axion potentials is achieved through a modest Nelson-Barr mechanism, avoiding overclosure without anthropic reasoning., Comment: 25 pages + references; 5 figures

We study module like objects over categorical quotients of algebras by the action of coalgebras with several objects. These take the form of ``entwined comodules'' and ``entwined contramodules'' over a triple $(\mathscr C,A,\psi)$, where $A$ is an algebra, $\mathscr C$ is a coalgebra with several objects and $\psi$ is a collection of maps that ``entwines'' $\mathscr C$ with $A$. Our objective is to prove Frobenius, separability and Maschke type theorems for functors between categories of entwined comodules and entwined contramodules.

We propose to search for (ultra)-light scalar dark matter (DM) using synchrotron radiation based M\"ossbauer spectroscopy technique. Such DM induces temporal variation in various fundamental constants, which in turn causes time modulation of the nuclear transition energies. When a M\"ossbauer source and absorber is separated by a large baseline, the DM induced shift between their energy levels can be tested by the modulation of the photon absorption spectrum. The narrow M\"ossbauer transitions allow the setup to efficiently probe DM in the high frequency range. We show that the reach of a M\"ossbauer experiment with the existing synchrotron beams is at par with the bounds from various equivalence principle violation searches. An improvement of the synchrotron setup would enable us to probe the hitherto uncharted territory of the DM parameter space upto MHz frequency. The proposed method would extend the DM search beyond the EP limit by several orders of magnitude, and would provide the best bound on DM interaction strength with various standard model fields in the high ($>$kHz) frequency region., Comment: 11 pages, 3 Figures

The robustness of the macroscopic quantum nature of a superconductor can be characterized by the superfluid stiffness, $\rho_s$, a quantity that describes the energy required to vary the phase of the macroscopic quantum wave function. In unconventional superconductors, such as cuprates, the low-temperature behavior of $\rho_s$ drastically differs from that of conventional superconductors due to quasiparticle excitations from gapless points (nodes) in momentum space. Intensive research on the recently discovered magic-angle twisted graphene family has revealed, in addition to superconducting states, strongly correlated electronic states associated with spontaneously broken symmetries, inviting the study of $\rho_s$ to uncover the potentially unconventional nature of its superconductivity. Here we report the measurement of $\rho_s$ in magic-angle twisted trilayer graphene (TTG), revealing unconventional nodal-gap superconductivity. Utilizing radio-frequency reflectometry techniques to measure the kinetic inductive response of superconducting TTG coupled to a microwave resonator, we find a linear temperature dependence of $\rho_s$ at low temperatures and nonlinear Meissner effects in the current bias dependence, both indicating nodal structures in the superconducting order parameter. Furthermore, the doping dependence shows a linear correlation between the zero temperature $\rho_s$ and the superconducting transition temperature $T_c$, reminiscent of Uemura's relation in cuprates, suggesting phase-coherence-limited superconductivity. Our results provide strong evidence for nodal superconductivity in TTG and put strong constraints on the mechanisms of these graphene-based superconductors.

We construct Fredholm modules over an algebra taking values in generalized Hilbert spaces over a rigid $C^*$-tensor category. Using methods of Connes, we obtain Chern characters taking values in cyclic cohomology. These Chern characters are well behaved with respect to the periodicity operator, and depend only on the homotopy class of the Fredholm module.

We study entanglement activation in a generalized entanglement swapping process involving two Bell pairs and generalized measurements. The conventional understanding posits entangled measurements as both necessary and sufficient for establishing entanglement between distant parties. In this study, we reassess the role of measurement operators in entanglement generation within a generalized entanglement swapping process. We focus on maximally entangled two-qubit initial states and generalized measurements, investigating the necessity and sufficiency conditions for entangled measurement operators. By utilizing two Bell pairs, (1, 2) shared between Alice and Bob, and (3, 4) shared between Bob and Charlie, we demonstrate that while entangled measurements are sufficient, they are not indispensable for establishing entanglement between spatially separated observers. Through a sequential approach, if Bob performs an initial measurement which is not able to establish entanglement then followed by another measurement after post-processing the first measurement it is possible to establish entanglement. We identify specific criteria for different measurement operators that enable the potential for performing a second measurement to establish entanglement. Our findings highlight the feasibility of generating entanglement between distant parties through a combination of measurements, shedding light on entanglement distribution in quantum networks. Additionally, we showcase through illustrative examples how successive measurements enhance entanglement compared to single measurements, underscoring the practical benefits of our approach in enhancing entanglement. Moreover, our protocol extends beyond bipartite qubit states to higher-dimensional maximally entangled states, emphasizing its versatility and applicability., Comment: (v1) Preliminary version. (v2) Rectified the typos and improved the clarity. (v3) Close to the published version, published in Physical Review A

In a quantum change point problem, a source emitting particles in a fixed quantum state (default) switches to a different state at some stage, and the objective is to identify when the change happened by measuring a sequence of particles emitted from such a source. Motivated by entanglement-sharing protocols in quantum information, we study this problem within the paradigm of local operations and classical communication (LOCC). Here, we consider a source that emits entangled pairs in a default state, but starts producing another entangled state (mutation) at a later stage. Then, a sequence of entangled pairs prepared from such a source and shared between distant observers cannot be used for quantum information processing tasks as the identity of each entangled pair remains unknown. We show that identifying the change point using LOCC leads to the distillation of free entangled pairs. In particular, if the default and the mutation are mutually orthogonal, there exists an efficient LOCC protocol that identifies the change point without fail and distills a sufficiently large number of pairs. However, if they are nonorthogonal, there is a probability of failure. In this case, we compute the number of entangled pairs that may be obtained on average. We also consider a relaxation of the two-state problem where the mutation is not known a priori, but instead belongs to a known set. Here we show that local distinguishability plays a crucial role: if the default and the possible mutations are locally distinguishable, the problem reduces to the two-state problem with orthogonal states, but if not, one may still identify the mutation, the change point, and distill entanglement, as we illustrate with a concrete example., Comment: v1: 14 pages, 2 figures; v2: 12 pages + appendix (2 pages), 2 figures, result on non-orthogonal states added, reference added, other revisions to improve clarity; v3: published version

We consider representations of quivers taking values in monads or comonads over a Grothendieck category $\mathcal C$. We treat these as scheme like objects whose ``structure sheaf'' consists of monads or comonads. By using systems of adjoint functors between Eilenberg-Moore categories, we obtain a categorical framework of modules over monad quivers, and of comodules over comonad quivers. Our main objective is to give conditions for these to be Grothendieck categories, which play the role of noncommutative spaces. As with usual ringed spaces, we have to study two kinds of module categories over a monad quiver. The first behaves like a sheaf of modules over a ringed space. The second consists of modules that are cartesian, which resemble quasi-coherent sheaves. We also obtain an extension of the classical quasi-coherator construction to modules over a monad quiver with values in Eilenberg-Moore categories. We establish similar results for comodules over a comonad quiver. One of our key steps is finding a modulus like bound for an endofunctor $U:\mathcal C\longrightarrow \mathcal C$ in terms of $\kappa(G)$, where $G$ is a generator for $\mathcal C$ and $\kappa(G)$ is a cardinal such that $G$ is $\kappa(G)$-presentable. Another feature of our paper is that we study modules over a monad quiver in two different orientations, which we refer to as ``cis-modules'' and ``trans-modules.'' We conclude with rational pairings of a monad quiver with a comonad quiver, which relate comodules over a comonad quiver to coreflective subcategories of modules over monad quivers., Comment: Minor updates

We introduce heavily separable functors of the second kind and study them in three different situations. The first of these is with restrictions and extensions of scalars for modules over small preadditive categories. The second is with free functors taking values in Eilenberg-Moore categories associated to a monad or a comonad. Finally, we consider entwined modules and give if and only if conditions for heavy separability of the second kind for functors forgetting either the comodule action or the module action.

We show that coupling of ultralight dark matter (UDM) to quarks and gluons would lead to an oscillation of the nuclear charge radius for both the quantum chromodynamics (QCD) axion and scalar dark matter. Consequently, the resulting oscillation of electronic energy levels could be resolved with optical atomic clocks, and their comparisons can be used to investigate UDM-nuclear couplings, which were previously only accessible with other platforms. We demonstrate this idea using the ${}^2S_{1/2} (F=0)\leftrightarrow {}^2F_{7/2} (F=3)$ electric octupole and ${}^2S_{1/2} (F=0)\leftrightarrow \,{}^2D_{3/2} (F=2)$ electric quadrupole transitions in ${}^{171}Yb^+$. Based on the derived sensitivity coefficients for these two transitions and a long-term comparison of their frequencies using a single trapped ${}^{171}Yb^+$ ion, we find bounds on the scalar UDM-nuclear couplings and the QCD axion decay constant. These results are at a similar level compared to the tightest spectroscopic limits, and future investigations, also with other optical clocks, promise significant improvements., Comment: 6+3 pages, 2 figures

In this paper, we consider measurings between Hopf algebroids and show that they induce morphisms on cyclic homology and cyclic cohomology. We also consider comodule measurings between SAYD modules over Hopf algebroids. These give an enrichment of the global category of SAYD modules over comodules. These measurings also induce morphisms on cyclic (co)homology of Hopf algebroids with SAYD coefficients, which are compatible with Hopf-Galois maps. Finally, we consider non-$\Sigma$ operads with multiplication. We obtain an enrichment of cyclic unital comp modules over non-$\Sigma$ operads, as well as morphisms on cyclic homology induced by measurings of comp modules over operads with multiplication., Comment: Several updates

In analogy to conventional semiconductor diodes, the Josephson diode exhibits superconducting properties that are asymmetric in applied bias. The effect has been investigated in number of systems recently, and requires a combination of broken time-reversal and inversion symmetries. We demonstrate a dual of the usual Josephson diode effect, a nonreciprocal response of Andreev bound states to a superconducting phase difference across the normal region of a superconductor-normal-superconductor Josephson junction, fabricated using an epitaxial InAs/Al heterostructure. Phase asymmetry of the subgap Andreev spectrum is absent in the absence of in-plane magnetic field and reaches a maximum at 0.15 T applied in the plane of the junction transverse to the current direction. We interpret the phase diode effect in this system as resulting from finite-momentum Cooper pairing due to orbital coupling to the in-plane magnetic field, without invoking Zeeman or spin-orbit coupling.

The effects of scalar and pseudoscalar ultralight bosonic dark matter (UBDM) were searched for by comparing the frequency of a quartz oscillator to that of a hyperfine-structure transition in $^{87}$Rb, and an electronic transition in $^{164}$Dy. We constrain linear interactions between a scalar UBDM field and Standard-Model (SM) fields for an underlying UBDM particle mass in the range $1\times10^{-17}-8.3\times10^{-13} $ eV and quadratic interactions between a pseudoscalar UBDM field and SM fields in the range $5\times10^{-18}- 4.1\times10^{-13} $ eV. Within regions of the respective ranges, our constraints on linear interactions significantly improve on results from previous, direct searches for oscillations in atomic parameters, while constraints on quadratic interactions surpass limits imposed by such direct searches as well as by astrophysical observations.

We discuss models of ultralight scalar Dark Matter (DM) with linear and quadratic couplings to the Standard Model (SM). In addition to studying the phenomenology of linear and quadratic interactions separately, we examine their interplay. We review the different experiments that can probe such interactions and present the current and expected future bounds on the parameter space. In particular, we discuss the scalar field solution presented in [A. Hees, O. Minazzoli, E. Savalle, Y. V. Stadnik and P. Wolf, Phys.Rev.D 98 (2018) 6, 064051], and extend it to theories that capture both the linear and the quadratic couplings of the DM field to the SM. Furthermore, we discuss the theoretical aspects and the corresponding challenges for natural models in which the quadratic interactions are of phenomenological importance., Comment: 73 pages, 17 figures; v2: References added. Matches the JHEP accepted version

Inverter-dominated microgrids are quickly becoming a key building block of future power systems. They rely on centralized controllers that can provide reliability and resiliency in extreme events. Nonetheless, communication failures due to cyber-physical attacks or natural disasters can make autonomous operation of islanded microgrids challenging. This paper examines a unified decentralized secondary control scheme that is robust to inverter clock synchronization errors and can be seamlessly applied to grid-following or grid-forming control architectures. The proposed scheme overcomes the well-known stability problem that arises from parallel operation of local integral controllers. Theoretical guarantees for stability are provided along with criteria to appropriately tune the secondary control gains to achieve good frequency regulation performance while ensuring fair power sharing. The efficacy of our approach in eliminating the steady-state frequency deviation is demonstrated through simulations on a 5-bus microgrid with four grid-forming inverters., Comment: 7 pages, 9 figures

We highlight general issues associated with quality and naturalness problems in theories of light QCD-axions, axion-like particles, and relaxions. We show the presence of Planck-suppressed operators generically lead to scalar coupling of axions with the Standard model. We present a new class of $\mathbb Z_{N}$ QCD relaxion models that can address both the QCD relaxion CP problem as well as its quality problem. This new class of models also leads to interesting experimental signatures, which can be searched for at the precision frontier., Comment: 17 pages, 4 figures; v2: previously ignored effects related to higher harmonics included, available parameter space updated, discussion extended; v3: matches the PRD accepted version

We develop the categorical algebra of the noncommutative base change of a comodule category by means of a Grothendieck category $\mathfrak S$. We describe when the resulting category of comodules is locally finitely generated, locally noetherian or may be recovered as a coreflective subcategory of the noncommutative base change of a module category. We also introduce the category ${_A}\mathfrak S^H$ of relative $(A,H)$-Hopf modules in $\mathfrak S$, where $H$ is a Hopf algebra and $A$ is a right $H$-comodule algebra. We study the cohomological theory in ${_A}\mathfrak S^H$ by means of spectral sequences. Using coinduction functors and functors of coinvariants, we study torsion theories and how they relate to injective resolutions in ${_A}\mathfrak S^H$. Finally, we use the theory of associated primes and support in noncommutative base change of module categories to give direct sum decompositions of minimal injective resolutions in ${_A}\mathfrak S^H$., Comment: Minor updates

Andreev bound states with opposite phase-inversion asymmetries are observed in local and non-local tunneling spectra at the two ends of a superconductor-semiconductor-superconductor planar Josephson junction in the presence of a perpendicular magnetic field. Spectral signatures agree with a theoretical model, yielding a physical picture in which phase textures in superconducting leads localize and control the position of Andreev bound states in the junction, demonstrating a simple means of controlling the position and size of Andreev states within a planar junction.

The purpose of this paper is to study local cohomology in the noncommutative algebraic geometry framework of Artin and Zhang. The noncommutative spaces are obtained by base change of a Grothendieck category that is locally noetherian or strongly locally noetherian. Using what we call elementary objects and their injective hulls, we develop a theory of supports and associated primes in these categories. We apply our theory to study a general functorial setup that requires certain conditions on the injective hulls of elementary objects and gives us spectral sequences for derived functors associated to local cohomology objects, as well as generalized local cohomology and also generalized Nagata ideal transforms., Comment: Some parts shortened, some new results added

Recently, Dotsenko and Tamaroff have shown that a morphism of $T\longrightarrow S$ of monads over a category $\mathscr C$ satisfies the PBW-property if and only if it makes $S$ into a free right $T$-module. We consider an adjunction $\Psi=(G,F)$ between categories $\mathscr C$, $\mathscr D$, a monad $S$ on $\mathscr C$ and a monad $T$ on $\mathscr D$. We show that a morphism $\phi:(\mathscr C,S)\longrightarrow (\mathscr D,T)$ that is well behaved with respect to the adjunction $\Psi$ has a PBW-property if and only if it makes $S$ satisfy a certain freeness condition with respect to $T$-modules with values in $\mathscr C$.

We present a search for fundamental constant oscillations in the range $20$~kHz-$100$ MHz, that may arise within models for ultralight dark matter (UDM). Using two independent, significantly upgraded optical-spectroscopy apparatus, we achieve up to $\times$1000 greater sensitivity in the search relative to previous work. We report no observation of UDM and thus constrain respective couplings to electrons and photons within the investigated UDM particle mass range $8\cdot 10^{-11}-4\cdot 10^{-7}$ eV. The constraints significantly exceed previously set bounds, and as we show, may surpass in future experiments those provided by equivalence-principle experiments in a specific case regarding the combination of UDM couplings probed by the latter., Comment: 13 pages, 11 figures

In this paper, we use the language of monads, comonads and Eilenberg-Moore categories to describe a categorical framework for $A_\infty$-algebras and $A_\infty$-coalgebras, as well as $A_\infty$-modules and $A_\infty$-comodules over them respectively. The resulting formalism leads us to investigate relations between representation categories of $A_\infty$-algebras and $A_\infty$-coalgebras. In particular, we relate $A_\infty$-comodules and $A_\infty$-modules by considering a rational pairing between an $A_\infty$-coalgebra $C$ and an $A_\infty$-algebra $A$. The categorical framework also motivates us to introduce $A_\infty$-contramodules over an $A_\infty$-coalgebra $C$., Comment: Paper significantly expanded with two new sections

Dietrich Braess while working on traffic modelling, noticed that traffic flow in a network can be worsened by adding extra edges to an existing network. This seemingly counterintuitive phenomenon is known as the Braess paradox. We consider a quantum network, where edges represent shared entangled states between spatially separated parties(nodes). The goal is to entangle two previously uncorrelated nodes using entanglement swappings. The amount of entanglement between the distant nodes is quantified by the average concurrence of the states established, as a result of the entanglement swappings. We then introduce an additional edge of maximally entangled Bell states in the network. We show that the introduction of the additional maximally entangled states to this network leads to lower concurrence between the two previously un-correlated nodes. Thus we demonstrate the occurrence of a phenomenon in a quantum network that is analogous to the Braess' paradox in traffic networks., Comment: Accepted for publication in PRA, close to final version

We study and relate categories of modules, comodules and contramodules over a representation of a small category taking values in (co)algebras, in a manner similar to modules over a ringed space. As a result, we obtain a categorical framework which incorporates all the adjoint functors between these categories in a natural manner. Various classical properties of coalgebras and their morphisms arise naturally within this theory. We also consider cartesian objects in each of these categories, which may be viewed as counterparts of quasi-coherent sheaves over a scheme. We study their categorical properties using cardinality arguments. Our focus is on generators for these categories and on Grothendieck categories, because the latter may be treated as replacements for noncommutative spaces., Comment: Several updates