Showing papers on "Antisymmetric relation published in 2014"

Assessing the accuracy of new geminal-based approaches.

Abstract: We present a systematic theoretical study on the dissociation of diatomic molecules and their spectroscopic constants using our recently presented geminal-based wave function ansatze. Specifically, the performance of the antisymmetric product of rank two geminals (APr2G), the antisymmetric product of 1-reference-orbital geminals (AP1roG) and its orbital-optimized variant (OO-AP1roG) are assessed against standard quantum chemistry methods. Our study indicates that these new geminal-based approaches provide a cheap, robust, and accurate alternative for the description of bond-breaking processes in closed-shell systems requiring only mean-field-like computational cost. In particular, the spectroscopic constants obtained from OO-AP1roG are in very good agreement with reference theoretical and experimental data.

Multiple Fano Resonances Based on Different Waveguide Modes in a Symmetry Breaking Plasmonic System

Abstract: Multiple Fano resonances are numerically investigated based on different waveguide modes in a nanoscale plasmonic waveguide resonator system, which consists of two grooves coupled with a metal–insulator–metal (MIM) waveguide. Simulation results show that by introducing a small structural breaking in the plasmonic resonator, both symmetric and antisymmetric waveguide modes can be excited. Due to the interaction of the symmetric and antisymmetric waveguide modes, the transmission spectra possess a sharp asymmetrical profile. Because of different origins, these Fano resonances exhibit different dependence on the parameters of the structure and can be easily tuned. These characteristics offer flexibility to design the device. This nanosensor yields a sensitivity of $\sim$ 820 nm/RIU and a figure-of-merit of $\sim\! 3.2\times 10^{5}$ . The utilization of the antisymmetric mode in the MIM waveguide provides a new possibility for designing high-performance plasmonic devices.

Strong photon antibunching of symmetric and antisymmetric modes in weakly nonlinear photonic molecules

Abstract: We study the photon statistics of symmetric and antisymmetric modes in a photonic molecule consisting of two linearly coupled nonlinear cavity modes. Our calculations show that strong photon antibunching of both symmetric and antisymmetric modes can be obtained even when the nonlinearity in the photonic molecule is weak. The strong antibunching effect results from the destructive interference between different paths for two-photon excitation. Moreover, we find that the optimal frequency detunings for strong photon antibunching in the symmetric and antisymmetric modes are linearly dependent on the coupling strength between the cavity modes in the photonic molecule. This implies that the photonic molecules can be used to generate tunable single-photon sources by tuning the values of the coupling strength between the cavity modes with weak nonlinearity.

Exact results for Wilson loops in arbitrary representations

Abstract: We compute the exact vacuum expectation value of 1/2 BPS circular Wilson loops of $ \mathcal{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.

Projected seniority-two orbital optimization of the antisymmetric product of one-reference orbital geminal.

Abstract: We present a new, non-variational orbital-optimization scheme for the antisymmetric product of one-reference orbital geminal wave function. Our approach is motivated by the observation that an orbital-optimized seniority-zero configuration interaction (CI) expansion yields similar results to an orbital-optimized seniority-zero-plus-two CI expansion [L. Bytautas, T. M. Henderson, C. A. Jimenez-Hoyos, J. K. Ellis, and G. E. Scuseria, J. Chem. Phys. 135, 044119 (2011)]. A numerical analysis is performed for the C2 and LiF molecules, for the CH2 singlet diradical as well as for the symmetric stretching of hypothetical (linear) hydrogen chains. For these test cases, the proposed orbital-optimization protocol yields similar results to its variational orbital optimization counterpart, but prevents symmetry-breaking of molecular orbitals in most cases.

Irreducible representations of oscillatory and swirling flows in active soft matter.

Abstract: Recent experiments imaging fluid flow around swimming microorganisms have revealed complex time-dependent velocity fields that differ qualitatively from the stresslet flow commonly employed in theoretical descriptions of active matter. Here we obtain the most general flow around a finite sized active particle by expanding the surface stress in irreducible Cartesian tensors. This expansion, whose first term is the stresslet, must include, respectively, third-rank polar and axial tensors to minimally capture crucial features of the active oscillatory flow around translating Chlamydomonas and the active swirling flow around rotating Volvox. The representation provides explicit expressions for the irreducible symmetric, antisymmetric, and isotropic parts of the continuum active stress. Antisymmetric active stresses do not conserve orbital angular momentum and our work thus shows that spin angular momentum is necessary to restore angular momentum conservation in continuum hydrodynamic descriptions of active soft matter.

Projected seniority-two orbital optimization of the Antisymmetric Product of one-reference orbital Geminal

Abstract: We present a new, non-variational orbital-optimization scheme for the Antisymmetric Product of one-reference orbital Geminal wave function. Our approach is motivated by the observation that an orbital-optimized seniority-zero configuration interaction (CI) expansion yields similar results to an orbital-optimized seniority-zero-plus-two CI expansion [J. Chem. Phys., 135, 044119 (2011)]. A numerical analysis is performed for the C$_2$, LiF and CH$_2$ molecules as well as for the symmetric stretching of hypothetical (linear) hydrogen chains. For these test cases, the proposed orbital-optimization protocol yields similar results to its variational orbital optimization counterpart, but prevents symmetry-breaking of molecular orbitals in most cases.

Discrete solitons and vortices on two-dimensional lattices of PT-symmetric couplers.

Abstract: We introduce a 2D network built of 𝒫𝒯 -symmetric dimers with on-site cubic nonlinearity, the gain and loss elements of the dimers being linked by parallel square-shaped lattices. The system may be realized as a set of 𝒫𝒯 -symmetric dual-core waveguides embedded into a photonic crystal. The system supports 𝒫𝒯 -symmetric and antisymmetric fundamental solitons (FSs) and on-site-centered solitary vortices (OnVs). Stability of these discrete solitons is the central topic of the consideration. Their stability regions in the underlying parameter space are identified through the computation of stability eigenvalues, and verified by direct simulations. Symmetric FSs represent the system’s ground state, being stable at lowest values of the power, while anti-symmetric FSs and OnVs are stable at higher powers. Symmetric OnVs, which are also stable at lower powers, are remarkably robust modes: on the contrary to other 𝒫𝒯 -symmetric states, unstable OnVs do not blow up, but spontaneously rebuild themselves into stable FSs.

Three-dimensional hybrid vortex solitons

Abstract: We show, by means of numerical and analytical methods, that media with a repulsive nonlinearity which grows from the center to the periphery support a remarkable variety of previously unknown complex stationary and dynamical three-dimensional (3D) solitary-wave states. Peanut-shaped modulation profiles give rise to vertically symmetric and antisymmetric vortex states, and novel stationary hybrid states, built of top and bottom vortices with opposite topological charges, as well as robust dynamical hybrids, which feature stable precession of a vortex on top of a zero-vorticity soliton. The analysis reveals stability regions for symmetric, antisymmetric, and hybrid states. In addition, bead-shaped modulation profiles give rise to the first example of exact analytical solutions for stable 3D vortex solitons. The predicted states may be realized in media with a controllable cubic nonlinearity, such as Bose–Einstein condensates.

Dynamics of 3D SUSY gauge theories with antisymmetric matter

Abstract: We investigate the IR dynamics ofN = 2 SUSY gauge theories in 3D with antisymmetric matter. The presence of the antisymmetric elds leads to further splitting of the Coulomb branch. Counting zero modes in the instanton background suggests that more than a single direction along the Coulomb branch may remain unlifted. We examine the case of SU(4) with one or two antisymmetric elds and various avors in detail. Using the results for the corresponding 4D theories, we nd the IR dynamics of the 3D cases via compactication and a real mass deformation. We nd that for the s-conning case with two antisymmetric elds, a second unlifted Coulomb branch direction indeed appears in the low-energy dynamics. We present several non-trivial consistency checks to establish the validity of these results. We also comment on the expected structure of general s-conning theories in 3D, which might involve several unlifted Coulomb branch directions.

Simple and inexpensive perturbative correction schemes for antisymmetric products of nonorthogonal geminals.

Abstract: A new multireference perturbation approach has been developed for the recently proposed AP1roG scheme, a computationally facile parametrization of an antisymmetric product of nonorthogonal geminals. This perturbation theory of second-order closely follows the biorthogonal treatment from multiconfiguration perturbation theory as introduced by Surjan et al., but makes use of the additional feature of AP1roG that the expansion coefficients within the space of closed-shell determinants are essentially correct already, which further increases the predictive power of the method. Building upon the ability of AP1roG to model static correlation, the perturbation correction accounts for dynamical electron correlation, leading to absolute energies close to full configuration interaction results. Potential surfaces for multiple bond dissociation in H2O and N2 are predicted with high accuracy up to bond breaking. The computational cost of the method is the same as that of conventional single-reference MP2.

Implicit-correction-based immersed boundary-lattice Boltzmann method with two relaxation times.

Abstract: In the present paper, we verify the effectiveness of the two-relaxation-time (TRT) collision operator in reducing boundary slip computed by the immersed boundary--lattice Boltzmann method (IB-LBM). In the linear collision operator of the TRT, we decompose the distribution function into symmetric and antisymmetric components and define the relaxation parameters for each part. The Chapman-Enskog expansion indicates that one relaxation time for the symmetric component is related to the kinematic viscosity. Rigorous analysis of the symmetric shear flows reveals that the relaxation time for the antisymmetric part controls the velocity gradient, the boundary velocity, and the boundary slip velocity computed by the IB-LBM. Simulation of the symmetric shear flows, the symmetric Poiseuille flows, and the cylindrical Couette flows indicates that the profiles of the numerical velocity calculated by the TRT collision operator under the IB-LBM framework exactly agree with those of the multirelaxation time (MRT). The TRT is as effective in removing the boundary slip as the MRT. We demonstrate analytically and numerically that the error of the boundary velocity is caused by the smoothing technique using the $\ensuremath{\delta}$ function used in the interpolation method. In the simulation of the flow past a circular cylinder, the IB-LBM based on the implicit correction method with the TRT succeeds in preventing the flow penetration through the solid surface as well as unphysical velocity distortion. The drag coefficient, the wake length, and the separation points calculated by the present IB-LBM agree well with previous studies at Re = 10, 20, and 40.

Singularities and Gauge Theory Phases II

Abstract: We present a simple algebraic construction of all the small resolutions for the SU(5) Weierstrass model. Each resolution corresponds to a subchamber on the Coulomb branch of the five-dimensional N=1 SU(5) gauge theory with matter fields in the fundamental and two-index antisymmetric representations. This construction unifies all previous resolutions found in the literature in a single framework.

Angular energy quantization for linear elliptic systems with antisymmetric potentials and applications

Abstract: We establish a quantization result for the angular part of the energy of solutions to elliptic linear systems of Schrodinger type with antisymmetric potentials in two dimensions. This quantization is a consequence of uniform Lorentz‐Wente type estimates in degenerating annuli. Moreover this result is optimal in the sense that we exhibit a sequence of functions satisfying our hypothesis whose radial part of the energy is not quantized. We derive from this angular quantization the full energy quantization for general critical points to functionals which are conformally invariant or also for pseudoholomorphic curves on degenerating Riemann surfaces.

Unbreakable PT-symmetry of solitons supported by inhomogeneous defocusing nonlinearity

Abstract: We consider bright solitons supported by a symmetric inhomogeneous defocusing nonlinearity growing rapidly enough toward the periphery of the medium, combined with an antisymmetric gain-loss profile. Despite the absence of any symmetric modulation of the linear refractive index, which is usually required to establish a PT-symmetry in the form of a purely real spectrum of modes, we show that the PT-symmetry is never broken in the present system, and that the system always supports stable bright solitons, fundamental and multi-pole ones. Such phenomenon is connected to non-linearizability of the underlying evolution equation. The increase of the gain-losses strength results, in lieu of the PT-symmetry breaking, in merger of pairs of different soliton branches, such as fundamental and dipole, or tripole and quadrupole ones. The fundamental and dipole solitons remain stable for all values of the gain-loss coefficient.

Chern-Simons and RG flows: contact with dualities

Abstract: Contact terms in two point functions of global symmetry currents have recently been proposed as a check of Seiberg-like duality in three dimensional supersymmetric field theories. In this paper we compute the contact terms for various $$ \mathcal{N} $$ = 2 dual pairs in flat space. We show that the results of this computation agree with the ones obtained from localization. We study dual pairs of gauge theories with (anti-)fundamental matter fields, and some special examples of dual pairs with adjoint and antisymmetric matter fields. We also propose a duality between unitary and symplectic gauge theories.

Master equation for dissipative interacting qubits in a common environment

Abstract: In this paper, we derive a microscopic master equation for a pair of $XY$-coupled two-level systems interacting with the same memoryless reservoir. In particular, we apply this master equation to the case of a pair of two-level atoms in free space where we can clearly contrast the predictions made with the microscopic master equation obtained here and the phenomenological approaches where the atom-atom coupling is included just a posteriori, i.e., not taking into account in the derivation of the open system equation of motion. We show, for instance, that the phenomenological approach fails completely in the assessment of the role played by the symmetric and antisymmetric decay channels. As a consequence, the predictions related to collective effects such as superradiance, for instance, are misleading in the phenomenological approach. We also obtain the fluorescence spectrum using the microscopic model developed here.

Exact Polynomial Solutions of Schrödinger Equation with Various Hyperbolic Potentials

Abstract: The Schrodinger equation with hyperbolic potential V(x) = -V(0)sinh(2q)(x/d)/cosh(6)(x/d) (q = 0, 1, 2, 3) is studied by transforming it into the confluent Heun equation We obtain general symmetric and antisymmetric polynomial solutions of the Schrodinger equation in a unified form via the Functional Bethe ansatz method Furthermore, we discuss the characteristic of wavefunction of bound state with varying potential strengths Particularly, the number of wavefunction's nodes decreases with the increase of potential strengths, and the particle tends to the bottom of the potential well correspondingly

Symmetric and Antisymmetric Convection Signals in the Madden–Julian Oscillation. Part I: Basic Modes in Infrared Brightness Temperature

Abstract: This work studies the significance of north–south asymmetry in convection associated with the 20–90-day Madden–Julian oscillation (MJO) propagating across the equatorial Indo-Pacific warm pool region. Satellite infrared brightness temperature data in the tropical belt for the period 1983–2006 were decomposed into components symmetric and antisymmetric about the equator. Using a recent nonlinear objective method called nonlinear Laplacian spectral analysis, modes of variability were extracted representing symmetric and antisymmetric features of MJO convection signals, along with a plethora of other modes of tropical convective variability spanning diurnal to interannual time scales. The space–time reconstruction of these modes during the 1992/93 Tropical Ocean Global Atmosphere Coupled Ocean–Atmosphere Response Experiment (TOGA COARE) period is described in detail. In particular, the boreal winter MJO emerges as a single pair of modes in both symmetric and antisymmetric convection signals. Both sig...

Symmetric Monge–Kantorovich problems and polar decompositions of vector fields

Abstract: We address the problem of whether a bounded measurable vector field from a bounded domain Ω into \({\mathbb{R}^d}\) is N-cyclically monotone up to a measure preserving N-involution, where N is any integer larger than 2. Our approach involves the solution of a multidimensional symmetric Monge–Kantorovich problem, which we first study in the case of a general cost function on a product domain ΩN. The polar decomposition described above corresponds to a special cost function derived from the vector field in question (actually N − 1 of them). The problem amounts to showing that the supremum in the corresponding Monge–Kantorovich problem when restricted to those probability measures on ΩN which are invariant under cyclic permutations and with a given first marginal μ, is attained on a probability measure that is supported on a graph of the form x → (x, Sx, S2x,..., SN-1x), where S is a μ-measure preserving transformation on Ω such that SN = I a.e. The proof exploits a remarkable duality between such involutions and those Hamiltonians that are N-cyclically antisymmetric.

Hygrothermal analysis of antisymmetric cross-ply laminates using a refined plate theory

Abstract: The effect of hygrothermal conditions on the antisymmetric cross-ply laminates has been investigated using a unified shear deformation plate theory. The present plate theory enables the trial and testing of different through-the-thickness transverse shear-deformation distributions and, among them, strain distributions do not involve the undesirable implications of the transverse shear correction factors. The differential equations of laminated plates whose deformations are governed by either the shear deformation theories or the classical one are derived. Displacement functions that identically satisfy boundary conditions are used to reduce the governing equations to a set of coupled ordinary differential equations with variable coefficients. A wide variety of results is presented for the static response of simply supported rectangular plates under non-uniform sinusoidal hygrothermal/thermal loadings. The influence of material anisotropy, aspect ratio, side-to-thickness ratio, thermal expansion coefficients ratio and stacking sequence on the hygrothermally induced response is studied.

A novel first-order shear deformation theory for laminated composite plates

Abstract: In the present study, a new simple first-order shear deformation theory is presented for laminated composite plates. Moreover, the number of unknowns of this theory is the least one comparing with the traditional first-order and the other higher-order shear deformation theories. Equations of motion and boundary conditions are derived from Hamilton's principle. Analytical solutions of simply supported antisymmetric cross-ply and angle-ply laminates are obtained and the results are compared with the exact three-dimensional (3D) solutions and those predicted by existing theories. It can be concluded that the proposed theory is accurate and simple in solving the static bending and free vibration behaviors of laminated composite plates.

Constraining torsion in maximally symmetric (sub)spaces

Abstract: We look into the general aspects of space-time symmetries in presence of torsion, and how the latter is affected by such symmetries. Focusing in particular to space-times which either exhibit maximal symmetry on their own, or could be decomposed to maximally symmetric subspaces, we work out the constraints on torsion in two different theoretical schemes. We show that at least for a completely antisymmetric torsion tensor (for example the one motivated from string theory), an equivalence is set between these two schemes, as the non-vanishing independent torsion tensor components turn out to be the same.

Water wave scattering by a rectangular trench

Abstract: Assuming linear theory, the two-dimensional problem of water wave scattering by a rectangular submarine trench is reinvestigated here employing the multiterm Galerkin approximations involving ultraspherical Gegenbauer polynomials for solving the integral equations arising in the mathematical analysis. Because of the geometrical symmetry of the rectangular trench about the $$y$$ -axis, the problem is split into two separate problems involving symmetric and antisymmetric potential functions. Very accurate numerical estimates for the reflection and transmission coefficients for various values of different parameters are obtained, and these are seen to satisfy the energy identity. These coefficients are computed numerically and depicted graphically against the wave number in a number of figures. Some figures available in the literature drawn using different mathematical methods and laboratory experiments are also recovered following the present analysis, thereby confirming the correctness of the results presented here. It is also observed that the reflection and transmission coefficients depend significantly on the width of the trench.

Variance reduction for diffusions

Abstract: The most common way to sample from a probability distribution is to use Monte-Carlo methods. For distributions on a continuous state space, one can find diffusions with the target distribution as equilibrium measure, so that the state of the diffusion after a long time provides a good sample from the desired distribution. There exist many diffusions with a common equilibrium, and one would naturally like to choose those that make the convergence to equilibrium faster. One way to do this is to consider a reversible diffusion, and add to it an antisymmetric drift which preserves the invariant measure. It has been proven that, in general, the irreversible algorithm performs better than the reversible one, in that the spectral gap is larger. In the present work, asymptotic variance is used as the criterion to compare these algorithms. We first provide a general comparison result, and then apply it to the specific cases of a diffusion on $\mathbb{R}^d$, or on a compact Riemannian manifold. We prove that, in general, adding an antisymmetric drift to a reversible diffusion reduces the asymptotic variance. We also provide some extensions of this result concerning strict inequality, the worst-case analysis, and the behavior of the asymptotic variance when the drift goes to infinity.

Multi-objective optimization of hygro-thermally curvature-stable antisymmetric laminates with extension-twist coupling

Abstract: This paper investigates hygro-thermally curvature-stable (HTCS) antisymmetric laminates with extension-twist coupling. Stacking sequences are designed to obtain optimal extension-twist coupling and buckling strength. A new objective function that maximizes both extension-twist coupling and buckling strength is established by using the weighted sum method. Multi-objective optimization of HTCS antisymmetric laminates is performed for T300/976 graphite/epoxy laminates. Results are presented for the laminates that consist of 6–14 even plies. The effects of the weighting coefficients on the extension-twist coupling and buckling load are analyzed. The robustness of the optimization method is verified by using Monte Carlo simulation for laminates with fiber orientation that slightly deviates from the theoretically designed direction.

Stationary black diholes

Abstract: In this paper, we present and analyze the simplest physically meaningful model for stationary black diholes---a binary configuration of counterrotating Kerr-Newman black holes endowed with opposite electric charges---elaborated in a physical parametrization on the basis of one of the Ernst-Manko-Ruiz equatorially antisymmetric solutions of the Einstein-Maxwell equations. The model saturates the Gabach-Clement inequality for interacting black holes with struts, and in the absence of rotation, it reduces to the Emparan-Teo electric dihole solution. The physical characteristics of each dihole constituent satisfy identically the well-known Smarr's mass formula.