Showing papers on "Antisymmetric relation published in 2013"

PT symmetry with a system of three-level atoms.

Abstract: We show that a vapor of multilevel atoms driven by far-off-resonant laser beams, with the possibility of interference of two Raman resonances, is highly efficient for creating parity-time symmetric profiles of the probe-field refractive index, whose real part is symmetric and imaginary part is antisymmetric in space. The spatial modulation of the probe-field susceptibility is achieved by a proper combination of standing-wave strong control fields and of Stark shifts induced by far-off-resonance laser fields. As particular examples we explore a mixture of isotopes of rubidium atoms and design a parity-time symmetric lattice and a parabolic refractive index with a linear imaginary part.

A New Mean-Field Method Suitable for Strongly Correlated Electrons: Computationally Facile Antisymmetric Products of Nonorthogonal Geminals

Abstract: We propose an approach to the electronic structure problem based on noninteracting electron pairs that has similar computational cost to conventional methods based on noninteracting electrons. In stark contrast to other approaches, the wave function is an antisymmetric product of nonorthogonal geminals, but the geminals are structured so the projected Schrodinger equation can be solved very efficiently. We focus on an approach where, in each geminal, only one of the orbitals in a reference Slater determinant is occupied. The resulting method gives good results for atoms and small molecules. It also performs well for a prototypical example of strongly correlated electronic systems, the hydrogen atom chain.

The all-loop integrable spin-chain for strings on AdS_3 x S^3 x T^4: the massive sector

Abstract: We bootstrap the all-loop dynamic S-matrix for the homogeneous psu(1,1|2)^2 spin-chain believed to correspond to the discretization of the massive modes of string theory on AdS_3 x S^3 x T^4. The S-matrix is the tensor product of two copies of the su(1|1)^2 invariant S-matrix constructed recently for the d(2,1;alpha)^2 chain, and depends on two antisymmetric dressing phases. We write down the crossing equations that these phases have to satisfy. Furthermore, we present the corresponding Bethe Ansatz, which differs from the one previously conjectured, and discuss how our construction matches several recent perturbative calculations.

Next-to-next-to-leading order spin?orbit effects in the near-zone metric and precession equations of compact binaries

Abstract: We extend our previous work devoted to the computation of the next-to-next-to-leading order spin–orbit correction (corresponding to 3.5PN order) in the equations of motion of spinning compact binaries by (i) deriving the corresponding spin–orbit terms in the evolution equations for the spins, the conserved integrals of the motion and the metric regularized at the location of the particles (obtaining also the metric all over the near zone but with some lower precision); (ii) performing the orbital reduction of the precession equations, near-zone metric and conserved integrals to the center-of-mass frame and then further assuming quasi-circular orbits (neglecting gravitational radiation reaction). The results are systematically expressed in terms of the spin variables with a conserved Euclidean norm instead of the original antisymmetric spin tensors of the pole–dipole formalism. This work paves the way to the future computation of the next-to-next-to-leading order spin–orbit terms in the gravitational-wave phasing of spinning compact binaries.

Eigenvalue hypothesis for racah matrices and homfly polynomials for 3-strand knots in any symmetric and antisymmetric representations

Abstract: Character expansion expresses extended HOMFLY polynomials through traces of products of finite-dimensional - and Racah mixing matrices. We conjecture that the mixing matrices are expressed entirely in terms of the eigenvalues of the corresponding -matrices. Even a weaker (and, perhaps, more reliable) version of this conjecture is sufficient to explicitly calculate HOMFLY polynomials for all the 3-strand braids in arbitrary (anti)symmetric representations. We list the examples of so obtained polynomials for R = [3] and R = [4], and they are in accordance with the known answers for torus and figure-eight knots, as well as for the colored special and Jones polynomials. This provides an indirect evidence in support of our conjecture.

A Natural Orbital Functional Based on an Explicit Approach of the Two-Electron Cumulant

Abstract: The cumulant expansion gives rise to an useful decomposition of the two-matrix in which the pair correlated matrix (cumulant) is disconnected from the antisymmetric product of the onematrices. The cumulant can be approximated in terms of two matrices, � and � , which are explicit functions of the occupation numbers of the natural orbitals. It produces a natural orbital functional (NOF) that reduces to the exact expression for the total energy in two-electron systems.The N-representability positivity necessaryconditionsofthetwo-matriximposeseveralboundson

Fluctuation theorem for hidden entropy production.

Abstract: Elimination of seemingly unnecessary variables in Markovian models may cause a difference in the value of irreversible entropy production between the original and reduced dynamics. We show that such difference, which we call the hidden entropy production, obeys an integral fluctuation theorem if all variables are time-reversal invariant, or if the density function is symmetric with respect to the change of sign of the time-reversal antisymmetric variables. The theorem has wide applicability, since the proposed condition is mostly satisfied in the case where the hidden fast variables are equilibrated. The main consequence of this theorem is that the entropy production decreases by the coarse-graining procedure. By contrast, in the case where a stochastic process is obtained by coarse-graining a deterministic and reversible dynamics, the entropy production may increase, implying that the integral fluctuation theorem should not hold for such reductions. We reveal, with an explicit example, that the nonequilibrated time-reversal antisymmetric variables play a crucial role in distinguishing these two cases, thus guaranteeing the consistency of the presented theorem.

Measuring the quantum geometry of Bloch bands with current noise

Abstract: Single-particle states in electronic Bloch bands form a Riemannian manifold whose geometric properties are described by two gauge invariant tensors, one being symmetric and the other being antisymmetric, that can be combined into the so-called Fubini-Study metric tensor of the projective Hilbert space. The latter directly controls the Hall conductivity. Here we show that the symmetric part of the Fubini-Study metric tensor also has measurable consequences by demonstrating that it enters the current noise spectrum. In particular, we show that a nonvanishing equilibrium current noise spectrum at zero temperature is unavoidable whenever Wannier states have nonzero minimum spread, the latter being quantifiable by the symmetric part of the Fubini-Study metric tensor. We illustrate our results by three examples: (1) atomic layers of hexagonal boron nitride, (2) graphene, and (3) the surface states of three-dimensional topological insulators when gapped by magnetic dopants.

The Jastrow antisymmetric geminal power in Hilbert space: Theory, benchmarking, and application to a novel transition state

Abstract: The Jastrow-modified antisymmetric geminal power (JAGP) ansatz in Hilbert space successfully overcomes two key failings of other pairing theories, namely, a lack of inter-pair correlations and a lack of multiple resonance structures, while maintaining a polynomially scaling cost, variational energies, and size consistency. Here, we present efficient quantum Monte Carlo algorithms that evaluate and optimize the JAGP energy for a cost that scales as the fifth power of the system size. We demonstrate the JAGP’s ability to describe both static and dynamic correlation by applying it to bond stretching in H2O, C2, and N2 as well as to a novel, multi-reference transition state of ethene. JAGP’s accuracy in these systems outperforms even the most sophisticated single-reference methods and approaches that of exponentially scaling active space methods.

A4 flavor symmetry model for Dirac neutrinos and sizable Ue3

Abstract: Models based on flavor symmetries are the most often studied approaches to explain the unexpected structure of lepton mixing. In many flavor symmetry groups a product of two triplet representations contains a symmetric and an antisymmetric contraction to a triplet. If this product of two triplets corresponds to a Majorana mass term, then the antisymmetric part vanishes, and in economic models tribimaximal mixing is achieved. If neutrinos are Dirac particles, the antisymmetric part is, however, present and leads to deviations from tribimaximal mixing, in particular, nonzero ${U}_{e3}$. Thus, the nonvanishing value of ${U}_{e3}$ and the nature of the neutrino are connected. We illustrate this with a model based on ${A}_{4}$ within the framework of a neutrinophilic two Higgs doublet scenario.

A hydrogen atom on curved noncommutative space

Abstract: We have calculated the hydrogen atom spectrum on curved noncommutative space defined by the commutation relations , where θ is the parameter of noncommutativity. The external antisymmetric field which determines the noncommutativity is chosen as ωij(x) = eijkxkf(xixi). In this case, the rotational symmetry of the system is conserved, preserving the degeneracy of the energy spectrum. The contribution of the noncommutativity appears as a correction to the fine structure. The corresponding nonlocality is calculated: , where m is a magnetic quantum number.

Mixed-symmetry tensor conserved currents and AdS/CFT correspondence

Abstract: We present the full list of conserved currents built of two massless spinor fields in Minkowski space and their derivatives multiplied by Clifford algebra elements. The currents have particular mixed-symmetry type described by Young diagrams with one row and one column of arbitrary lengths and heights. Along with Yukawa-like totally antisymmetric currents, the complete set of constructed currents exactly matches the spectrum of AdS mixed-symmetry fields arising in the generalized Flato?Fr?nsdal theorem for two spinor singletons. As a by-product, we formulate and study general properties of primary fields and conserved currents of mixed-symmetry type.This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ?Higher spin theories and holography?.

Supertropical linear algebra

Abstract: The objective of this paper is to lay out the algebraic theory of supertropical vector spaces and linear algebra, utilizing the key antisymmetric relation of “ghost surpasses”. Special attention is paid to the various notions of “base”, which include d-base and s-base, and these are compared to other treatments in the tropical theory. Whereas the number of elements in various d-bases may differ, it is shown that when an s-base exists, it is unique up to permutation and multiplication by scalars, and can be identified with a set of “critical” elements. Then we turn to orthogonality of vectors, which leads to supertropical bilinear forms and a supertropical version of the Gram matrix, including its connection to linear dependence. We also obtain a supertropical version of a theorem of Artin, which says that if g-orthogonality is a symmetric relation, then the underlying bilinear form is (supertropically) symmetric.

An enhanced beam-theory model of the mixed-mode bending (MMB) test—Part I: Literature review and mechanical model

Abstract: The paper presents a mechanical model of the mixed-mode bending (MMB) test used to assess the mixed-mode interlaminar fracture toughness of composite laminates. The laminated specimen is considered as an assemblage of two sublaminates partly connected by an elastic–brittle interface. The problem is formulated through a set of 36 differential equations, accompanied by suitable boundary conditions. Solution of the problem is achieved by separately considering the two subproblems related to the symmetric and antisymmetric parts of the loads, which for symmetric specimens correspond to fracture modes I and II, respectively. Explicit expressions are determined for the interfacial stresses, internal forces, and displacements.

Nonlocal electron-phonon coupling in organic semiconductor crystals: the role of acoustic lattice vibrations.

Abstract: We discuss, in the context of a tight-binding description, how the electronic and charge-transport properties in single crystals of molecular organic semiconductors are affected by the nonlocal electron-phonon coupling to both acoustic and optical lattice vibrations. While the nonlocal electron-phonon interactions can in general be divided into contributions from symmetric modes and antisymmetric modes, we show that only the antisymmetric coupling mechanism is operational in the case of acoustic vibrations. Interestingly, when the quantum nature of the phonons can be neglected, the effect of electron-phonon interactions with acoustic phonons is found to be equivalent to that of the electron-phonon interactions with optical phonons, in the case where contributions from symmetric and antisymmetric modes are equal.

Exact results for Wilson loops in arbitrary representations

Abstract: We compute the exact vacuum expectation value of 1/2 BPS circular Wilson loops of ${\cal N}$=4 U(N) super Yang-Mills in arbitrary irreducible representations. By localization arguments, the computation reduces to evaluating certain integrals in a Gaussian matrix model, which we do using the method of orthogonal polynomials. Our results are particularly simple for Wilson loops in antisymmetric representations; in this case, we observe that the final answers admit an expansion where the coefficients are positive integers, and can be written in terms of sums over skew Young diagrams. As an application of our results, we use them to discuss the exact Bremsstrahlung functions associated to the corresponding heavy probes.

Equivalent Transmission Line Model With a Lumped X-Circuit for a Metalayer Made of Pairs of Planar Conductors

Abstract: We present an equivalent X-shaped lumped circuit network to be interposed in the transmission line (TL) modelling reflection and transmission through a recently proposed metalayer in planar technology. The metalayer consists of arrayed pairs of planar conductors that support two main resonant modes, corresponding to either a symmetric or an antisymmetric current distribution in the pairs. The antisymmetric mode is associated with artificial magnetism. We show that reflection and transmission features of a metalayer are accurately predicted by this simple but effective TL model. We also make a clear distinction for the first time between transmission peaks and resonance frequencies, and their relations are investigated in detail. This paper clearly defines the concept of magnetic resonance and identifies the analytical conditions corresponding to total reflection and transmission through a metalayer made of pairs of conductors supporting symmetric and antisymmetric modes.

Symmetry breaking in dipolar matter-wave solitons in dual-core couplers

Abstract: We study the effects of spontaneous symmetry breaking (SSB) in solitons composed of a dipolar Bose-Einstein condensate trapped in a dual-core system with dipole-dipole interactions (DDIs) and hopping between the cores. Two realizations of such a matter-wave coupler are introduced: weakly and strongly coupled. The former is based on two parallel pipe-shaped traps, whereas the latter is represented by a single pipe sliced by an external field into parallel layers. The dipoles are oriented along the axes of the pipes. In these systems, the dual-core solitons feature SSB of the supercritical and subcritical types, respectively. Stability regions are identified for symmetric and asymmetric solitons and nonbifurcating antisymmetric solitons, as well as for symmetric flat states, which may also be stable in the strongly coupled system due to competition between the attractive and repulsive intracore and intercore DDIs. The effects of the contact interactions are considered too. Collisions between moving asymmetric solitons in the weakly symmetric system feature an elastic rebound, a merger into a single breather, and passage accompanied by excitation of intrinsic vibrations of the solitons for small, intermediate, and large collision velocities, respectively. A $\mathcal{PT}$-symmetric version of the weakly coupled system is considered briefly, which may be relevant for matter-wave lasers. Stability boundaries for $\mathcal{PT}$-symmetric and -antisymmetric solitons are identified.

Similarity renormalization group evolution of three-nucleon forces in a hyperspherical momentum representation

Abstract: A new framework for computing the similarity renormalization group (SRG) evolution of three-nucleon forces (3NF) in momentum representation is presented. The use of antisymmetric three-particle hyperspherical momentum states ensures unitary evolutions within certain basis truncations, much like antisymmetric harmonic oscillator SRG evolutions. Additionally, in each partial wave the ${\mathbit{T}}_{\mathrm{rel}}$-SRG regulator is exactly represented, similar to recent 3NF momentum representation evolutions. Unitary equivalence is demonstrated for the triton using several chiral two- plus three-nucleon interactions. This method allows for a clean visualization of the evolution of the three-nucleon forces, which manifests the SRG decoupling pattern and low-momentum universality.

Schunck Classes of Soluble Leibniz Algebras

Abstract: I set out the theory of Schunck classes and projectors for soluble Leibniz algebras, parallel to that for Lie algebras. Primitive Leibniz algebras come in pairs, one (Lie) symmetric, the other antisymmetric. A Schunck formation containing one member of a pair also contains the other. If ℌ is a Schunck formation and H is an ℌ-projector of the Leibniz algebra L, then H is intravariant in L. An example is given to show that the assumption that the Schunck class ℌ is a formation cannot be omitted.

A novel Gaussian Binning (1GB) analysis of vibrational state distributions in highly excited H2O from reactive quenching of OH∗ by H2.

Abstract: As shown in experiments by Lester and co-workers [J. Chem. Phys. 110, 11117 (1999)], the reactive quenching of OH∗ by H2 produces highly excited H2O. Previous limited analysis of quasiclassical trajectory calculations using standard Histogram Binning (HB) was reported [B. Fu, E. Kamarchik, and J. M. Bowman, J. Chem. Phys. 133, 164306 (2010)]. Here, we examine the quantized internal state distributions of H2O in more detail, using two versions of Gaussian Binning (denoted 1GB). In addition to the standard version of 1GB, which relies on the harmonic energies of the states (1GB-H), we propose a new and more accurate technique based on exact quantum vibrational energies (1GB-EQ). Data from about 42,000 trajectories from previous calculations that give excited water molecules are used in the two versions of 1GB as well as HB. For the vibrationally hot molecules considered in this study, the classical internal energy distribution serves as a benchmark to estimate the accuracy of the different binning methods analyzed. The 1GB discretization methods, especially the one using exact quantum energies, reconstruct the classical distribution much more accurately than HB and also the original, more elaborate Gaussian Binning method. Detailed quantum state distributions are presented for pure overtone excitations as well as several antisymmetric stretch distributions. The latter are focused on because the antisymmetric stretch has the largest emission oscillator strength of the three water modes.

Energy quantization for biharmonic maps

Abstract: In the present work we establish an energy quantization (or energy identity) result for solutions to scaling invariant variational problems in dimension 4 which includes biharmonic maps (extrinsic and intrinsic) To that aim we first establish an angular energy quantization for solutions to critical linear 4th order elliptic systems with antisymmetric potentials The method is inspired by the one introduced by the authors previously in [LaR] for 2nd order problems

A Self-Dual Polar Factorization for Vector Fields

Abstract: We show that any nondegenerate vector field u in , where Ω is a bounded domain in , can be written as }, where S is a measure-preserving point transformation on Ω such that a.e. (an involution), and is a globally Lipschitz antisymmetric convex-concave Hamiltonian. Moreover, u is a monotone map if and only if S can be taken to be the identity, which suggests that our result is a self-dual version of Brenier's polar decomposition for the vector field as , where ϕ is convex and S is a measure-preserving transformation. We also describe how our polar decomposition can be reformulated as a (self-dual) mass transport problem. © 2012 Wiley Periodicals, Inc.

Accelerating Convergence in the Antisymmetric Product of Strongly Orthogonal Geminals Method

Abstract: Antisymmetric product of strongly orthogonal geminals (APSG) method is a wavefunction theory that can effectively treat the static electron correlation using twoelectron wavefunctions, called geminals. However, the APSG method has the problem of slow convergence in the optimization of the geminal function. In this study, we introduced the direct inversion in the iterative subspace (DIIS) method, for both closed- and open-shell systems, for accelerating its convergence. Two types of error vectors, that is, unitary transformation and orbital gradient, were examined for the DIIS procedure. Numerical assessments revealed that the orbital-gradient error vector shows better performance than the unitary-transformation one. V C 2012

Matching LBO eigenspace of non-rigid shapes via high order statistics

Abstract: A fundamental tool in shape analysis is the virtual embedding of the Riemannian manifold describing the geometry of a shape into Euclidean space. Several methods have been proposed to embed isometric shapes in flat domains while preserving distances measured on the manifold. Recently, attention has been given to embedding shapes into the eigenspace of the Lapalce-Beltrami operator. The Laplace-Beltrami eigenspace preserves the diffusion distance, and is invariant under isometric transformations. However, Laplace-Beltrami eigenfunctions computed independently for different shapes are often incompatible with each other. Applications involving multiple shapes, such as pointwise correspondence, would greatly benefit if their respective eigenfunctions were somehow matched. Here, we introduce a statistical approach for matching eigenfunctions. We consider the values of the eigenfunctions over the manifold as sampling of random variables, and try to match their multivariate distributions. Comparing distributions is done indirectly, using high order statistics. We show that the permutation and sign ambiguities of low order eigenfunctions, can be inferred by minimizing the difference of their third order moments. The sign ambiguities of antisymmetric eigenfunctions can be resolved by exploiting isometric invariant relations between the gradients of the eigenfunctions and the surface normal. We present experiments demonstrating the success of the proposed method applied to feature point correspondence.