Irreducible Representations Research Articles

A combined density functional theory and microkinetics simulations study of electrochemical CO2 reduction on Cu8/SnO2(110): The crucial role of hydrogen coverage

The electrochemical reduction of CO2 (eCO2R) is a promising approach for converting CO2 into valuable chemicals and fuels using renewable energy sources. We investigated the mechanism of eCO2R for a small Cu8 cluster placed on SnO2 containing O vacancies using density functional theory and predicted current density and selectivity by microkinetics simulations within the computational hydrogen electrode model. Low and high H coverages were modeled by Cu8/SnO2-x and Cu8H6/SnO2-x models, using statistical methods to identify their most stable structures. Different CO2 adsorption modes on Cu8/SnO2-x and Cu8H6/SnO2-x surface models, all containing an O vacancy, resulted in distinct reaction pathways, leading to either HCOOH or CO. The preferred formation of HCOOH occurred upon CO2 adsorption on an O vacancy on the Cu8H6/SnO2-x surface, followed by sequential hydrogenation to HCOO and HCOOH. Adsorption of CO2 on Cu8/SnO2-x opened a facile pathway to CO. Electronic structure analysis revealed that differences in charge donation of Cu to the antibonding orbitals of CO2 can explain the predicted selectivity differences. The preferred adsorption mode of CO2 is bidentate at the Cu-SnO2-x interface. Our findings emphasize the role of H coverage on Cu on the selectivity of eCO2R for Cu/SnOx catalysts.

Screen time, mute, mixed messages, and panic: An international auto-ethnographic study of knowledge workers during a pandemic.

The coronavirus pandemic provoked worldwide changes to the workplace, leading to rapid changes in lifestyles and working conditions. While organizations and governments struggled to develop regulations and policies, individuals were forced to find ways to manage work and life. During the pandemic and quarantine, a group of knowledge workers from around the world convened virtually and agreed to use qualitative autoethnographic methods to study how the quarantine disrupted their conventional patterns of work and care. In this article, we apply two communication perspectives-uncertainty reduction theory and re-silience-to participant diaries to understand how participants represent internal and external stressors, the efforts diarists employed to overcome those stressors, and their varying success in doing so. Post-hoc application of these communication concepts suggests that the diarists, though privileged in some ways, were not exempt from the social, professional, and emotional consequences of the pandemic and that their efforts to enact resilience were unevenly successful, especially in relation to their use of communications technology. Diarists reported struggling with uncertainty at numerous levels and that uncertainty contributed to individual emotional and cultural distress. Disruptions to work, home, and communities significantly affected wellbeing and ability to cope with challenges. Added to this were the complex and competing roles that diarists felt as they struggled to work from home, parent, and remain engaged.

Quantum model of galactic halos with an Navarro-Frenk-White dark matter profile

A quantum model of a cold dark matter galactic halo is developed. The model requires specifying the mass and radius of the halo as well as its density profile. The structure of the halo resulting from the theory is predicted and its physical properties are determined. Verification of these theoretical predictions by observations is proposed and discussed. The model is constructed by analytically solving the governing equation and using its time-independent solutions to determine the internal structure of a galactic halo with an Navarro-Frenk-White cold dark matter density profile. The governing equation that is the basis of the developed theory is derived from the irreducible representations of the extended Galilean group. The method of finding the solutions is analytical, even though an Navarro-Frenk-White density profile is used in the calculations. The theory predicts a halo with a core composed of free dark matter particles that move randomly with frequent collisions. It also predicts an envelope in which the particles are confined to their orbits, which are quantized. Except in the close vicinity of the core, the population of the orbits remains fixed, and physical reasons for the nonexistence of quantum jumps between these orbits are presented. A quantum model of a galactic cold dark matter halo with a given Navarro-Frenk-White density profile is constructed. It predicts a quantum structure of the halo that is significantly different than any previously known dark matter model. The quantum model naturally accounts for dark matter being collisionless, and it predicts that dark matter can only emit radiation of one fixed frequency. The values of this frequency are computed for dark matter particles of different masses. A potential observational verification of the theory is also discussed.

Subhomogeneous Operator Systems and Classification of Operator Systems Generated by Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}-Commuting Unitaries

A unital C∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C^*$$\\end{document}-algebra is called N-subhomogeneous if its irreducible representations are finite dimensional with dimension at most N. We extend this notion to operator systems, replacing irreducible representations by boundary representations. This is done by considering UCP(S)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext {UCP }(\\mathcal {S})$$\\end{document} which is the matrix state space associated with an operator system S\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {S}$$\\end{document} and identifying the boundary representations as absolute matrix extreme points. We show that two N-subhomogeneous operator systems are completely order equivalent if and only if they are N-order equivalent. Moreover, we show that a unital N-positive map into a finite dimensional N-subhomogeneous operator system is completely positive. We apply these tools to classify pairs of q-commuting unitaries up to ∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$*$$\\end{document}-isomorphism. Similar results are obtained for operator systems related to higher dimensional non-commutative tori.

Magnetic structure of Tb[formula omitted]NbO[formula omitted] determined using neutron diffraction experiments and magnetic anisotropy calculations

We determined the magnetic structure of Tb3NbO7 based on powder neutron diffraction experiments and magnetic anisotropy calculations. We calculated the energy levels split by crystalline electric fields, and the magnetic moments using McPhase. The c axis is the easy axis for Tb1 moments, and magnetic anisotropy is small for Tb2 moments. Magnetic reflections were observed at low temperatures. The propagation vector is k1=(0,0,0) at 1.8 K and k2=(1/2,1/2,0) at 2.5 K between transition temperatures TN1=2.0 K and TN2=3.2 K. We selected candidates for an irreducible representation (IR) of the magnetic structures using magnetic anisotropy. From Rietveld refinements, we determined the following: The IRs are mΓ4 and mS2 at 1.8 K and 2.5 K, respectively. The main component of Tb1 ordered moments is w at 1.8 K. The order of the main components in each chain along the c axis is antiferromagnetic. Tb1 moments are disordered at 2.5 K. Tb2 moments form noncollinear magnetic structures in the ab plane perpendicular to Tb1 chains with a small w component at both the 1.8 K and 2.5 K. The magnetic structure at 1.8 K is consistent with the magnetic anisotropies obtained using McPhase calculations. Only Tb2 moments are ordered at 2.5 K, indicating the appearance of a partially disordered state. We also considered the origin of the two magnetic transitions.

Universal fine grained asymptotics of free and weakly coupled quantum field theory

We give a rigorous proof that in any free quantum field theory with a finite group global symmetry G, on a compact spatial manifold, at sufficiently high energy, the density of states ρα(E) for each irreducible representation α of G obeys a universal formula as conjectured by Harlow and Ooguri. We further prove that this continues to hold in a weakly coupled quantum field theory, given an appropriate scaling of the coupling with temperature. This generalizes similar results that were previously obtained in (1 + 1)-D to higher spacetime dimension. We discuss the role of averaging in the density of states, and we compare and contrast with the case of continuous group G, where we prove a universal, albeit different, behavior.

On the Product Functor on Inner forms of the General Linear Group Over A Non-Archimedean Local Field

AbstractLet $$G_n$$ G n be an inner form of a general linear group over a non-Archimedean local field. We fix an arbitrary irreducible representation $$\sigma $$ σ of $$G_n$$ G n . Building on the work of Lapid-Mínguez on the irreducibility of parabolic inductions, we show how to define a full subcategory of the category of smooth representations of some $$G_m$$ G m , on which the parabolic induction functor $$\tau \mapsto \tau \times \sigma $$ τ ↦ τ × σ is fully-faithful. A key ingredient of our proof for the fully-faithfulness is constructions of indecomposable representations of length 2. Such result for a special situation has been previously applied in proving the local non-tempered Gan-Gross-Prasad conjecture for non-Archimedean general linear groups. In this article, we apply the fully-faithful result to prove a certain big derivative arising from Jacquet functor satisfies the property that its socle is irreducible and has multiplicity one in the Jordan-Hölder sequence of the big derivative.

Two types of Witten zeta functions

We define two types of Witten’s zeta functions according to Cartan’s classification of compact symmetric spaces. The type II is the original Witten zeta function constructed by means of irreducible representations of the simple compact Lie group U. The type I Witten zeta functions, we introduce here, are related to the irreducible spherical representations of U. They arise in the harmonic analysis on compact symmetric spaces of the form U/K, where K is the maximal subgroup of U. To construct the type I zeta function we calculate the partition functions of 2d YM theory with broken gauge symmetry using the Migdal–Witten approach. We prove that for the rank one symmetric spaces the generating series for the values of the type I functions with integer arguments can be defined in terms of the generating series of the Riemann zeta-function.

SO(2,2) representations in polar coordinates and Pöschl-Teller potentials

This work is devoted to show the interest of polar coordinates in the description of some unitary irreducible representations (or uir’s) of the SO(2,2) group where the support space are functions on the three dimensional pseudosphere HR2,2 . We will show that the differential equations associated to such uir’s can be interpreted as quantum systems including centrifugal terms; in our case these equations lead to one-dimensional Pöschl-Teller systems. The solutions to these equations are computed and the uir’s are characterized in terms of polar coordinates. We will also discuss briefly the more standard pseudospherical coordinates on HR2,2 in order to appreciate some of the differences. We will consider as well the (maximally superintegrable) free classical systems defined on the real pseudosphere HR2,2 symmetric under SO(2,2) . The constants of motion are found and they are applied to find some bounded (therefore periodic) and unbounded orbits also in terms of polar coordinates.

Weil zeta functions of group representations over finite fields

In this article we define and study a zeta function ζG\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\zeta _G$$\\end{document}—similar to the Hasse-Weil zeta function—which enumerates absolutely irreducible representations over finite fields of a (profinite) group G. This Weil representation zeta function converges on a complex half-plane for all UBERG groups and admits an Euler product decomposition. Our motivation for this investigation is the observation that the reciprocal value ζG(k)-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\zeta _G(k)^{-1}$$\\end{document} at a sufficiently large integer k coincides with the probability that k random elements generate the completed group ring of G. The explicit formulas obtained so far suggest that ζG\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\zeta _G$$\\end{document} is rather well-behaved. A central object of this article is the Weil abscissa, i.e., the abscissa of convergence a(G) of ζG\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\zeta _G$$\\end{document}. We calculate the Weil abscissae for free abelian, free abelian pro-p, free pro-p, free pronilpotent and free prosoluble groups. More generally, we obtain bounds (and sometimes explicit values) for the Weil abscissae of free pro-C\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathfrak {C}}$$\\end{document} groups, where C\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathfrak {C}}$$\\end{document} is a class of finite groups with prescribed composition factors. We prove that every real number a≥1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a \\ge 1$$\\end{document} is the Weil abscissa a(G) of some profinite group G. In addition, we show that the Euler factors of ζG\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\zeta _G$$\\end{document} are rational functions in p-s\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p^{-s}$$\\end{document} if G is virtually abelian. For finite groups G we calculate ζG\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\zeta _G$$\\end{document} using the rational representation theory of G.

From port-based teleportation to Frobenius reciprocity theorem: partially reduced irreducible representations and their applications

In this paper, we present the connection of two concepts as induced representation and partially reduced irreducible representations (PRIR) appear in the context of port-based teleportation protocols. Namely, for a given finite group G with arbitrary subgroup H, we consider a particular case of matrix irreducible representations, whose restriction to the subgroup H, as a matrix representation of H, is completely reduced to diagonal block form with an irreducible representation of H in the blocks. The basic properties of such representations are given. Then as an application of this concept, we show that the spectrum of the port-based teleportation operator acting on n systems is connected in a very simple way with the spectrum of the corresponding Jucys–Murphy operator for the symmetric group S(n-1)⊂S(n)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S(n-1)\\subset S(n)$$\\end{document}. This shows on the technical level relation between teleporation and one of the basic objects from the point of view of the representation theory of the symmetric group. This shows a deep connection between the central object describing properties of deterministic PBT schemes and objects appearing naturally in the abstract representation theory of the symmetric group. In particular, we present a new expression for the eigenvalues of the Jucys–Murphy operators based on the irreducible characters of the symmetric group. As an additional but not trivial result, we give also purely matrix proof of the Frobenius reciprocity theorem for characters with explicit construction of the unitary matrix that realizes the reduction in the natural basis of induced representation to the reduced one.

Unraveling the longitudinal relationships between connectedness to nature, depressive symptoms, and learning burnout in adolescents.

Following the conservation of resource theoryand natural stress reduction theory,the current study investigated mediated pathways, reverse mediated pathways, and reciprocal pathways between connectedness to nature, depressive symptoms, and adolescent learning burnout via a half-longitudinal analysis, and discussed gender differences in the three models. Two waves of data were collected in December 2022 (T1) and June 2023 (T2) for this study. The sample consisted of 1092 Chinese adolescents (52.20% girls, Mage = 13.03, SD = 1.43). Semi-longitudinal analyses were conducted to examine the relationship between connectedness to nature, depressive symptoms, and adolescent academic burnout. The results indicated that connectedness to nature can serve as a positive resource to alleviate the levels of depressive symptoms among adolescents and thereby decrease learning burnout. However, the protective effect of connectedness to nature was smaller, and the decreasing effect of learning burnout on connectedness to nature was stronger than the alleviating effect of connectedness to nature on learning burnout. Additionally, the study found that depressive symptoms and academic burnout have a mutually reinforcing effect over time and that the effects of this interaction are more pronounced in females. The present study emphasizes the protective role of nature connectedness and the detrimental effects of learning burnout in adolescents.

Irreducible representations of the Poincaré group with reflections and two-fold Wigner degeneracy

Not all complete set of spinors can be used as expansion coefficients of a quantum field. In fact, Steven Weinberg established the uniqueness of Dirac spinors for this purpose provided: (a) one paid due attention to the multiplicative phases for each of the spinors, and (b) one paired these to creation and annihilation operators in a specific manner. This is implicit in his implementation of the rotational symmetry for the spin half quantum field. Among the numerous complete set of spinors that are available to a physicist, Elko occupies a unique status that allows it to enter as expansion coefficients of a quantum field without violating Weinberg’s no go theorem. How this paradigm changing claim arises is the primary subject of this communication. Weinberg’s no go theorem is evaded by exploiting a uniquely special feature of Elko that allows us to introduce a doubling of the particle-antiparticle degrees of freedom from four to eight. Weinberg had dismissed this degeneracy on the ground that, “no examples are known of particles that furnish unconventional representations of inversions.” Here we will find that this degeneracy, once envisioned by Eugene Wigner, in fact gives rise to a quantum field that has all the theoretical properties required of dark matter.

Exact Diagonalization of SU(N) Fermi-Hubbard Models.

We show how to perform exact diagonalizations of SU(N) Fermi-Hubbard models on L-site clusters separately in each irreducible representation (irrep) of SU(N). Using the representation theory of the unitary group U(L), we demonstrate that a convenient orthonormal basis, on which matrix elements of the Hamiltonian are very simple, is given by the set of semistandard Young tableaux (or, equivalently, the Gelfand-Tsetlin patterns) corresponding to the targeted irrep. As an application of this color factorization, we study the robustness of some SU(N) phases predicted in the Heisenberg limit upon decreasing the on-site interaction U on various lattices of size L≤12 and for 2≤N≤6. In particular, we show that a long-range color ordered phase emerges for intermediate U for N=4 at filling 1/4 on the triangular lattice.

Paley Wiener Theorem on a Reductive Lie Group

Let G be a locally compact group, K a maximal compact subgroup of G and δ on arbitrary class of irreducible unitary representations of K. The spherical Grassmannian Gp,δ is an equivalence class of spherical functions of type δ−positive of height p. In this work, we give an extension of orbital integral with respect to δ, when G is reductive Lie group. Moreover, if the discret serie is not empty, we give an extension of Paley-Wiener theorem using a compact Cartan subgroup of G.

Comprehension of the phenomenon of consciousness within the framework of quantum approach (on the example of the concepts of M. Mensky and R. Penrose – S. Hameroff)

The article considers two modern concepts of consciousness: M. Menski's quantum theory of consciousness and R. Penrose-S. Hameroff's theory of objective reduction of states. Key aspects of the concept of consciousness within the framework of quantum approach are identified and both advantages and disadvantages of each concept are noted. Further prospects for the development of these concepts are presented, the philosophical analysis of which, of course, reflects certain trends in the development of modern science.

Quantization of locally compact groups associated with essentially bijective 1-cocycles

Given an extension [Formula: see text] of locally compact groups, with [Formula: see text] abelian, and a compatible essentially bijective [Formula: see text]-cocycle [Formula: see text], we define a dual unitary [Formula: see text]-cocycle on [Formula: see text] and show that the associated deformation of [Formula: see text] is a cocycle bicrossed product defined by a matched pair of subgroups of [Formula: see text]. We also discuss an interpretation of our construction from the point of view of Kac cohomology for matched pairs. Our setup generalizes that of Etingof and Gelaki for finite groups and its extension due to Ben David and Ginosar, as well as our earlier work on locally compact groups satisfying the dual orbit condition. In particular, we get a locally compact quantum group from every involutive nondegenerate set-theoretical solution of the Yang–Baxter equation, or more generally, from every brace structure. On the technical side, the key new points are constructions of an irreducible projective representation of [Formula: see text] on [Formula: see text] and a unitary quantization map [Formula: see text] of Kohn–Nirenberg type.

Optimal external forces of the lock-in phenomena for flow past an inclined plate in uniform flow.

We theoretically studied the optimal control, frequency lock-in, and phase lock-in phenomena due to the spatially localized periodic forcing in flow past an inclined plate. Although frequency lock-in is evident in many fluid phenomena, especially fluid-structure interactions, not many researchers have investigated it using a theoretical approach based on flow details. We obtained detailed information on the lock-in phenomena to external periodic forcing using phase reduction theory, a mathematical method for extracting the dynamics near the limit cycle. Furthermore, the optimal forces applied to the velocity field were determined under the condition of the minimum forcing energy and maximum lock-in range. The study of uniform periodic forces applied within spatially confined regions led to the conclusion that the effective lock-in position, which includes both the upstream and downstream areas of the plate, depends on the principal frequency of the force. The frequency lock-in range of these forces was analyzed and compared with theoretical predictions.

Realization of unitary representations of the Lorentz group on de Sitter space

This paper builds on our previous work in which we showed that, for all connected semisimple linear Lie groups G acting on a non-compactly causal symmetric space M=G/H, every irreducible unitary representation of G can be realized by boundary value maps of holomorphic extensions in distributional sections of a vector bundle over M. In the present paper we discuss this procedure for the connected Lorentz group G=SO1,d(R)e acting on de Sitter space M=dSd. We show in particular that the previously constructed nets of real subspaces satisfy the locality condition. Following ideas of Bros and Moschella from the 1990’s, we show that the matrix-valued spherical function that corresponds to our extension process extends analytically to a large domain Gℂcut in the complexified group Gℂ=SO1,d(ℂ), which for d=1 specializes to the complex cut plane ℂ∖(−∞,0]. A number of special situations is discussed specifically: (a) The case d=1, which closely corresponds to standard subspaces in Hilbert spaces, (b) the case of scalar-valued functions, which for d>2 is the case of spherical representations, for which we also describe the jump singularities of the holomorphic extensions on the cut in de Sitter space, (c) the case d=3, where we obtain rather explicit formulas for the matrix-valued spherical functions.

Local Galois representations associated to additive polynomials

For an additive polynomial and a positive integer, we define an irreducible smooth representation of a Weil group of a non-archimedean local field. We study several invariants of this representation. We obtain a necessary and sufficient condition for it to be primitive.