Antisymmetric Case Research Articles

Leading large N giant graviton correction to Schur correlators in large representations

We consider 4d N=4U(N) SYM and the leading giant graviton correction at large N to the Schur defect 2-point functions of 12-BPS Wilson lines in rank-k symmetric and antisymmetric representations. We study in particular the large k limit for the symmetric case and the regime 1≪k≪N in the antisymmetric one. In both cases we present exact results for the correction. Wilson lines in symmetric/antisymmetric representations admit a description in terms of D3k and D5k brane probes representing a collection of k fundamental strings. In this picture, giant graviton corrections come from fluctuations of brane probes in the presence of a wrapped D3 brane giant graviton. In the antisymmetric case, our leading correction matches the half-index of the 4d N=4 Maxwell theory living on the disk which is a part of the giant graviton divided out by the D5k probe, as recently proposed in arXiv:2404.08302. For the symmetric case at large k, we derive an explicit exact residue formula for the leading large N correction.

Quest for the golden ratio universality class.

Using mode-coupling theory, the conditions for all allowed dynamical universality classes for the conserved modes in one-dimensional driven systems are presented in closed form as a function of the stationary currents and their derivatives. With an eye on the search for the golden ratio universality class, the existence of some families of microscopic models is ruled out a priori by using an Onsager-type macroscopic current symmetry. In particular, if the currents are symmetric or antisymmetric under the interchange of the conserved densities, then at equal mean densities the golden modes can only appear in the antisymmetric case and if the conserved quantities are correlated, but not in the symmetric case where at equal densities one mode is always diffusive and the second may be either Kardar-Parisi-Zhang (KPZ), modified KPZ, 3/2-Lévy, or also diffusive. We also show that the predictions of mode-coupling theory for a noisy chain of harmonic oscillators are exact.

Interplay of many-body interactions and quasiperiodic disorder in the all-bands-flat diamond chain

We study the effects of quasiperiodic Aubry-Andr\'e (AA) disorder and interactions on a one-dimensional all-band-flat (ABF) diamond chain. We consider the application of disorder in two ways: a symmetric one, where the same disorder is applied to the top and bottom sites of a unit cell, and an antisymmetric one, where the disorder applied to the top and bottom sites are of equal magnitude but with opposite signs. The single-particle wave-packet dynamics for the clean system and when the disorder is applied symmetrically show quantum caging; in the antisymmetric case, the wave-packet spreads over the entire lattice. These results agree with our previous work, where compact localization was observed in the case of the clean system and for symmetrically disordered diamond lattices. In the presence of nearest-neighbour interactions, nonergodic phases are observed in the case of a clean system and symmetrical disorder; at higher disorder strengths, we find an MBL-like phase in the symmetric case. However, many-body non-equilibrium dynamics of the system from carefully engineered initial states exhibit quantum caging. In the antisymmetric case, a nonergodic mixed phase, a thermal phase and an MBL-like phases, respectively, are observed at low, intermediate and high disorder strengths. We observe an absence of caging and initial state dependence (except at the intermediate disorder strength) in the study of non-equilibrium dynamics.

Electrohydrodynamic Liquid Sheet Instability of Moving Viscoelastic Couple-Stress Dielectric Fluid Surrounded by an Inviscid Gas through Porous Medium

Viscoelastic liquid sheet of couple-stress type streaming with relative motion into an inviscid gas through porous molium is studied theoretically and quantitatively in this project. To derive the differential equations that describe liquids, gases, and the electric field, we linearized the governing equations of motion and continuity, Maxwell’s equations in quasi-static approximation, and the appropriate boundary conditions at the two interfaces. Then we used the normal mode method. It was demonstrated analytically that the solutions to these differential equations can be found for both symmetric and antisymmetric disturbances, respectively. We could not obtain an explicit form of the growth rates since we could not solve the dispersion relations for both situations because they were obtained in highly complex forms. The Mathematica program is used to solve the dimensionless forms of the dispersion relations numerically using Gaster’s theorem. Various influences on the stability analysis of the considered system have been studied in detail, and it is determined that the system in the presence of a porous material is more unstable than it would be otherwise. In a two-dimensional system, the antisymmetric disturbance case is found to be more unstable than the corresponding symmetric disturbance situation. Some characteristics, such as Wabe number, Ohnesorge number, and electric field, have destabilizing effects, whereas others, such as porosity, medium permeability, viscoelasticity parameter, gas-to-liquid viscosity ratio, and dielachic constants, have stabilizing effects. Finally, it is discovered that the gas-to-liquid velocity ratio plays a dual role in the stability condition depending on whether the gas-to-liquid velocity ratio U ≶ 1. In the past, we have only found evidence of very few previous studies.

Local available quantum correlations of X states: The symmetric and anti-symmetric cases

Local available quantum correlations (LAQC), as defined by Mundarain et al., are analyzed for two-qubit X states with local Bloch vectors of equal magnitude. Symmetric X-states are invariant under the exchange of subsystems, hence having the same Bloch vector. On the other hand, anti-symmetric X states have Bloch vectors with an equal magnitude but opposite direction. In both cases, we obtain exact analytical expressions for their LAQC quantifier. We present some examples and compare this quantum correlation to concurrence and quantum discord. We have also included Markovian decoherence, with Werner states under amplitude damping decoherence. As is the case for depolarization and phase damping, no sudden death behavior occurs for the LAQC of these states with this quantum channel.

Smart damping of a simply supported laminated CNT-based hybrid composite plate using FE approach

We present the finite element (FE) model using the first-order shear deformation theory (FSDT) to investigate the damping performance of laminated hybrid fiber-reinforced composite (HFRC) smart plates via the active constrained layer damping (ACLD) treatment. A unique feature of the HFRC is that the nanoscale carbon nanotubes (CNTs) are embedded in the matrix phase of carbon fiber composite to improve the overall properties, especially the damping characteristics of the resulting HFRC. Two- and three-phase micromechanical models are employed to determine the effective elastic properties of the base composite and HFRC respectively. The constraining layer of the ACLD treatment is considered to be made of vertically reinforced 1–3 piezoelectric composite (PZC) material. The system consists of a laminated HFRC plate integrated with the two patches of ACLD treatment and the numerical results are computed for three cases: symmetric and anti-symmetric cross-ply, and anti-symmetric angle-ply. The damping performance of the laminated HFRC square plate is significantly enhanced over the laminated base composite plate due to the incorporation of a small amount of CNTs. In particular, the anti-symmetric angle-ply case provides better damping than symmetric/anti-symmetric cross-ply cases. Analysis of the HFRC plate showed that its vibration amplitudes can be attenuated from ∼8 to ∼16% by adding a small amount CNTs. The effect of in-plane and transverse actuation of 1–3 PZC on the damping characteristics of the overall plate was also studied. We found that the transverse actuation significantly influences the damping performance of the overall plate. The outcomes of our study provide substantial evidence that the addition of a small amount of CNTs in the conventional composite structure can improve its damping performance significantly. This is practically possible in view of the recent research activities in the field of fabrication of large-scale CNT-based hybrid composite structures.

On Vector-Valued Characters for Noncommutative Function Algebras

Let A be a closed subalgebra of a $$C^*$$-algebra, that is a norm-closed algebra of Hilbert space operators. We generalize to such operator algebras several key theorems and concepts from the theory of classical function algebras. In particular we consider several problems that arise when generalizing classical function algebra results involving characters (nontrivial homomorphisms from the algebra into the scalars). For example, the Jensen inequality, the related Bishop–Ito–Schreiber theorem, and the theory of Gleason parts. Inspired by Arveson’s work on noncommutative Hardy spaces, we replace characters (classical function algebra case) by D-characters; certain completely contractive homomorphisms $$\Phi : A \rightarrow D$$, where D is a $$C^*$$-subalgebra of A. Using Brown’s measure and a potential theoretic balayage argument we prove a partial noncommutative Jensen inequality appropriate for $$C^*$$-algebras with a tracial state. We also show that this Jensen inequality characterizes D-characters among the module maps. Other advances include a theory of noncommutative Gleason parts appropriate for D-characters, which uses Harris’ noncommutative hyperbolic metric and Schwarz–Pick inequality, and other ingredients. As an application of Gleason parts we show that in the antisymmetric case, one is guaranteed the existence of a ‘quantum’ Wermer embedding function, and also of non-trivial compact Hankel operators, whenever the Gleason part of the canonical trace is rich in tracial states.

Casimir force variability in one-dimensional QED systems

The Casimir force between two short-range charge sources, embedded in a background of one dimensional massive Dirac fermions, is explored by means of the original $\ln\text{[Wronskian]}$ contour integration techniques. For identical sources with the same (positive) charge, we find that in the non-perturbative region the Casimir interaction between them can reach sufficiently large negative values and simultaneously reveal the features of a long-range force in spite of nonzero fermion mass, that could significantly influence the properties of such quasi-one-dimensional QED systems. For large distances $s$ between sources we recover that their mutual interaction is governed first of all by the structure of the discrete spectrum of a single source, in dependence on which it can be tuned to give an attractive, a repulsive, or an (almost) compensated Casimir force with various rates of the exponential fall-down, quite different from the standard $\exp (-2 m s)$ law. By means of the same $\ln\text{[Wronskian]}$ techniques, the case of two $\delta$-sources is also considered in a self-consistent manner with similar results for the variability of the Casimir force. A quite different behavior of the Casimir force is found for the antisymmetric source-anti-source system. In particular, in this case, there is no possibility for a long-range interaction between sources. The asymptotics of the Casimir force follows the standard $\exp (-2 m s)$ law. Moreover, for small separations between sources, the Casimir force for symmetric and antisymmetric cases turns out to be of opposite sign.

Hamiltonian formalism for nonlinear spin wave dynamics under antisymmetric interactions: Application to Dzyaloshinskii-Moriya interaction

A Hamiltonian formalism is applied for the investigation of nonlinear spin wave dynamics under the influence of antisymmetric magnetic interactions. In the framework of this formalism we account not only for symmetric magnetic interactions (exchange, dipole-dipole, magnetocrystalline anisotropy), but also for antisymmetric interactions, such as Dzyaloshinskii-Moriya exchange interaction. The account of antisymmetric exchange, in general, could lead to the appearance of an additive nonreciprocal term in the spin wave dispersion law. We present the generalization of the linear transformation for the diagonalization of quadratic part of the Hamiltonian (so-called ``third Holstein-Primakoff transformation'') for the antisymmetric case, which allowed us to obtain generalized expressions for the coefficients of the nonlinear three- and four-magnon interactions. As an example, nonlinear spin wave interactions in ultrathin ferromagnetic nanowires and films subjected to interfacial Dzyaloshinskii-Moriya interaction (IDMI) are considered. It was found that three-magnon interaction coefficients in the ``Damon-Eshbach'' geometry are nonzero only in the case of the noncollinear interacting spin waves, and vanish in the case of the collinear spin waves. It was also found that the nonlinear spin wave frequency shift caused by the four-magnon interaction is nonreciprocal, and has the sign opposite to that of the nonreciprocal term in linear spin wave dispersion, so that the IDMI-induced nonreciprocity of the spin wave spectrum decreases with the increase of the spin wave amplitude.

Solution of thin rectangular plate vibrations for all combinations of boundary conditions

The equation of motion for thin rectangular plate was formulated in its correct form about 200 years ago. Exact solution, for some cases, and high accuracy solution for few more cases, have been obtained along the years since. For several other cases, high accuracy solutions were composed of separate solutions for symmetric and anti-symmetric cases. In this work a new high accuracy solution, that covers all the possible combinations is presented. It is obtained by using carefully chosen series that solve the partial differential equations of motion, for all possible combinations of edge conditions. Examples of the new solutions are given and compared with approximate solutions for these cases.

Stresses in thin-walled composite laminated box-beams with curvilinear fibers: Antisymmetric and symmetric fiber paths

Stress analysis of thin-walled composite laminated box beams having variable stiffness is realized in this study based on an analytical model accounting for flexural-torsional coupling and warping effects. The variable stiffness of the beam is acquired by constructing laminates with curvilinear fibers having certain specific paths. The fiber paths of variable stiffness layers are classified in three groups as antisymmetric, symmetric and asymmetric. A displacement based finite element method is used to solve the analytical model and to calculate the distributions of axial and transverse shear stresses at different locations of the cantilever composite beam subjected to the transverse and the torsional loading at its free end. Numerical results obtained are compared with available results in the literature for specific cases. A detailed investigation is performed to understand the relation between the stress distributions along the cross section of the beam and the shape of curvilinear fibers for antisymmetric and symmetric cases.

Biderivations of the higher rank Witt algebra without anti-symmetric condition

Abstract The Witt algebra 𝔚 d of rank d(≥ 1) is the derivation algebra of Laurent polynomial algebras in d commuting variables. In this paper, all biderivations of 𝔚 d without anti-symmetric condition are determined. As an applications, commutative post-Lie algebra structures on 𝔚 d are obtained. Our conclusions recover and generalize results in the related papers on low rank or anti-symmetric cases.

Relations between the efficiency, power and dissipation for linear irreversible heat engine at maximum trade-off figure of merit

A trade of figure of merit () criterion accounts the best compromise between the useful input energy and the lost input energy of the heat devices. When the heat engine is working at maximum criterion its efficiency increases significantly from the efficiency at maximum power. We derive the general relations between the power, efficiency at maximum criterion and minimum dissipation for the linear irreversible heat engine. The efficiency at maximum criterion has the lower bound and it can reach up to , where is the maximum efficiency. Further, for time-reversal symmetric or anti-symmetric case our results show that the efficiency at maximum criterion is bounded by 3/4 of the Carnot efficiency when the minimum dissipation is zero.

Analysis of DCB test of angle-ply laminates including bending-twisting coupling

Interlaminar fracture of angle-ply symmetric and anti-symmetric laminates by means of the Double Cantilever Beam test has been analyzed. As the cracked arms are symmetric in both cases, bending-twisting coupling occurs. Nevertheless, the effect of that coupling is different in symmetric and anti-symmetric cases. In symmetric cases, it induces a non-uniform aperture of the arms associated to mode I. In anti-symmetric cases, the effect is a sliding of both arms associated to mode III. The analytic approach of the energy release rate includes those coupling effects. Besides the present approach, experimental results are reduced with a previous approach that does not include coupling effects and with the area method.

Experimental study on dependence of streak breakdown on disturbance nature

Instability and breakdown of a low-speed streak initially forced by disturbances with a frequency-spectrum similar to that of wall turbulence were examined experimentally. A single low-speed streak was generated using a small piece of screen set normal to a boundary-layer plate, and disturbances made by two loudspeakers were introduced through two small holes. Turbulent velocity fluctuations with various spanwise coherences were used as driving signals to two loudspeakers to see how strongly the streak breakdown depended on the nature of disturbances. Signals were deduced at two spanwise locations with distance Δz+= 24–149 in the buffer region of a turbulent boundary layer by using a pair of hot-wires. The correlation coefficient Ct of the two turbulent signals ranged from −0.11 to 0.56. Both sinuous and varicose modes were excited but the former became dominant downstream in all cases. Development of the disturbance excited was compared to those for anti-symmetric (Ct=−1) and symmetric (Ct=1) excitations with the same turbulent spectrum. The comparison showed that the magnitude of the sinuous instability mode excited was dependent on the initial disturbances, but not strongly for −1≤Ct≤0. That is, in terms of the rms value of velocity fluctuations, the magnitude of the sinuous instability mode for the initial disturbance with Ct∼0 was about 75% of that in the case of anti-symmetric forcing. Even for Ct∼+0.56, the magnitude of the sinuous mode excited was as large as 50% of that in the anti-symmetric case.

Revisiting double Dirac delta potential

We study a general double Dirac delta potential to show that this is the simplest yet still versatile solvable potential to introduce double wells, avoided crossings, resonances and perfect transmission (T = 1). Perfect transmission energies turn out to be the critical property of symmetric and anti-symmetric cases wherein these discrete energies are found to correspond to the eigenvalues of a Dirac delta potential placed symmetrically between two rigid walls. For well(s) or barrier(s), perfect transmission (or zero reflectivity, ) at energy is non-intuitive. However, this has been found earlier and called the ‘threshold anomaly’. Here we show that it is a critical phenomenon and we can have when the parameters of the double delta potential satisfy an interesting condition. We also invoke a zero-energy and zero curvature eigenstate () of the delta well between two symmetric rigid walls for . We resolve that the resonant energies and the perfect transmission energies are different and they arise differently.

Collective Dynamics on a Two-Lane Asymmetrically Coupled TASEP with Mutually Interactive Langmuir Kinetics

Motivated by the recent experimental observations on clustering of motor proteins on microtubule filament, we study an open system of two parallel totally asymmetric simple exclusion processes under asymmetric coupling conditions, which incorporates the mutual interaction with the surrounding environment through Langmuir Kinetics in both the lanes. In the modified Langmuir Kinetics, the attachment and detachment rates depends on the configuration of nearest neighboring sites. We analyse the model within the framework of continuum mean-field theory and the phase diagrams along with density profiles are obtained using boundary layer analysis. The effect of mutual interactions on the phase diagram for two different situations of attachment and detachment (LK) rates is discussed. Under the symmetric LK dynamics, the topological structure of the phase diagram remains similar to the one in without mutual interaction; while for the antisymmetric case, after a certain critical value of attractive/repulsive mutual attraction, significant changes are found in the qualitative nature of phase diagram. Moreover, it is shown that the type of mutual interaction affects the dynamic properties of motor proteins. The theoretical findings are examined by extensive Monte-Carlo simulations.

On 3D problems of thermoelastostatics for transversely isotropic solids with anticracks

Abstract A general method is proposed for the solution of uncoupled thermoelasticity problems for a transversely isotropic space containing a rigid sheet-like inclusion (an anticrack) in the isotropy plane under some thermal actions. An analogy between the thermal anticrack problems and their mechanical counterparts is exploited and used to reduce the resulting boundary-value problems in the symmetric and antisymmetric cases to the mixed problems of potential theory. The governing boundary integral equations for a planar anticrack of arbitrary shape are obtained with the unknown stress jumps across the inclusion. As an application of the theory, complete solutions in elementary functions are given and discussed for a circular rigid disc-inclusion whose surfaces are exposed to uniform cooling temperatures or temperature gradients.

All possible permutational symmetries of a quantum system

We investigate the intermediate permutational symmetries of a system of qubits, that lie in between the perfect symmetric and antisymmetric cases. We prove that, on average, pure states of qubits picked at random with respect to the uniform measure on the unit sphere of the Hilbert space are almost as antisymmetric as they are allowed to be. We then observe that multipartite entanglement, measured by the generalized Meyer- Wallach measure, tends to be larger in subspaces that are more antisymmetric than the complete symmetric one. Eventually, we prove that all states contained in the most antisymmetric subspace are relevant multipartite entangled states in the sense that their 1-qubit reduced states are all maximally mixed.

Landau damping of the dust-acoustic surface waves in a Lorentzian dusty plasma slab

Landau damping of a dust-acoustic surface wave propagating at the interfaces of generalized Lorentzian dusty plasma slab bounded by a vacuum is kinetically derived as the surface wave displays the symmetric and the anti-symmetric mode in a plasma slab. In the limiting case of small scaled wave number, we have found that Landau damping is enhanced as the slab thickness is increased. In particular, the damping of anti-symmetric mode is much stronger for a Lorentzian plasma than for a Maxwellian plasma. We have also found that the damping is more affected by superthermal particles in a Lorentzian plasma than by a Maxwellian plasma for both of the symmetric and the anti-symmetric cases. The variations of Landau damping with various parameters are also discussed.