Symmetric States Research Articles

Limitation analysis of the Hill48 yield model and establishment of its modified model for planar plastic anisotropy

In this paper, the limitations of the original Hill48 yield model in predicting uniaxial tensile yield stresses and r-values were analyzed in detail, and then the necessary and sufficient conditions for judging the applicability of the original Hill48 yield model were proposed. On this basis, the approximate satisfactions of the steel sheet DC04, DP980 and the aluminum alloy AA5754-O to the necessary and sufficient conditions were investigated. The results show that the necessary and sufficient conditions can be used to qualitatively analyze the predicted error of the original Hill48 model. Based on the inherent relationship of Hill48 yield function, the direction of principal stress axis was introduced into the anisotropic parameters, and a modified Hill48 model suitable for plane stress state was developed. According to the variation of the predicted error of the original Hill48 yield model in biaxial tensile stress, an exponential interpolation method including material parameter was proposed to correct the asymmetric biaxial stress between uniaxial stress state and symmetric biaxial stress state. The theoretical predicted results show that the modified model can accurately capture the directional yield stresses, r-values and yield locus. The main advantage of the modified model is that it still maintains a simple quadratic form in the stress tensor, and can significantly improve the predicted accuracy of anisotropic behavior of aluminum alloy and other materials from the use of associated flow rule.

Generating femtosecond visible doughnut beams based on transverse-mode modulation

Ultrafast visible doughnut beams carrying cylindrically symmetric states of polarization or orbital angular momentum provide new capabilities for super-resolution microscopy, visible light communications, and material processing. Visible laser pulses typically originate from solid-state lasers, and the generation of ultrashort visible light beams using an all-fiber layout remains challenging. In addition, the generation of doughnut beams usually relies on free-space optics, which are costly and require precise alignment. Here, an integrated fiber method for producing a femtosecond visible doughnut beam is proposed by integrating nonlinear frequency conversion and in-fiber mode conversion techniques. This approach takes advantage of nonlinear frequency conversion and in-fiber transverse-mode modulation, which creates a new manipulation technique of visible doughnut beams of ultrashort pulses. The dynamic spatial manipulation of vector visible beams enabled by polarization control in a polarization-maintaining fiber (PMF) or by mode conversion through a quarter-wave plate and a polarizer experimentally proves the mode-controllable visible doughnut light generation.

H-Infinity Control With Nearly Symmetric State Matrix

In this paper, we give an upper bound on the deviation from H-infinity optimality of a class of controllers as a function of the deviation from symmetry in the state matrix. We further suggest a scalar measure of symmetry which is shown to be directly relevant for estimating nearness to optimality. In connection to this, we give a simple analytical solution to a class of Lyapunov equations for two dimensional state matrices. Finally, we demonstrate how a well-chosen symmetric part for nearly symmetric state matrices may lead not only to near-optimality, but also to controller sparsity, a desirable property for large-scale systems. In the special case that the state matrix is symmetric and Hurwitz, our main result simplifies to give an H-infinity optimal controller with several benefits, a result which has recently appeared in the literature. In this sense, the above is a significant generalization which considers a much wider class of systems, yet allows one to retain the benefits of symmetric state matrices, while offering means of quantifying the effect of this on the H-infinity norm.

Global Solution to an H-infinity Control Problem for Control-affine Systems

In this paper, we present a global solution to a nonlinear H-infinity optimal control problem for control-affine systems with an associated potential function. We also give a closed-form expression for an optimal controller and demonstrate its potential for sparsity. This paper thus advances a recent result which considers the same problem restricted to systems with symmetric state matrix and nonlinear input matrix. We further apply the main result to obtain a simpler and more intuitive statement for a class of systems capable of modeling nonlinear buffer networks.

On the Existence of Linearly Oscillating Galaxies

We consider two classes of steady states of the three-dimensional, gravitational Vlasov-Poisson system: the spherically symmetric Antonov-stable steady states (including the polytropes and the King model) and their plane symmetric analogues. We completely describe the essential spectrum of the self-adjoint operator governing the linearized dynamics in the neighborhood of these steady states. We also show that for the steady states under consideration, there exists a gap in the spectrum. We then use a version of the Birman-Schwinger principle first used by Mathur to derive a general criterion for the existence of an eigenvalue inside the first gap of the essential spectrum, which corresponds to linear oscillations about the steady state. It follows in particular that no linear Landau damping can occur in the neighborhood of steady states satisfying our criterion. Verification of this criterion requires a good understanding of the so-called period function associated with each steady state. In the plane symmetric case we verify the criterion rigorously, while in the spherically symmetric case we do so under a natural monotonicity assumption for the associated period function. Our results explain the pulsating behavior triggered by perturbing such steady states, which has been observed numerically.

Improved upper bounds on the stabilizer rank of magic states

In this work we improve the runtime of recent classical algorithms for strong simulation of quantum circuits composed of Clifford and T gates. The improvement is obtained by establishing a new upper bound on the stabilizer rank ofmcopies of the magic state|T⟩=2−1(|0⟩+eiπ/4|1⟩)in the limit of largem. In particular, we show that|T⟩⊗mcan be exactly expressed as a superposition of at mostO(2αm)stabilizer states, whereα≤0.3963, improving on the best previously known boundα≤0.463. This furnishes, via known techniques, a classical algorithm which approximates output probabilities of ann-qubit Clifford + T circuitUwithmuses of the T gate to within a given inverse polynomial relative error using a runtimepoly(n,m)2αm. We also provide improved upper bounds on the stabilizer rank of symmetric product states|ψ⟩⊗mmore generally; as a consequence we obtain a strong simulation algorithm for circuits consisting of Clifford gates andminstances of any (fixed) single-qubitZ-rotation gate with runtimepoly(n,m)2m/2. We suggest a method to further improve the upper bounds by constructing linear codes with certain properties.

Probing Two-Electron Multiplets in Bilayer Graphene Quantum Dots.

We report on finite bias spectroscopy measurements of the two-electron spectrum in a gate defined bilayer graphene (BLG) quantum dot for varying magnetic fields. The spin and valley degree of freedom in BLG give rise to multiplets of six orbital symmetric and ten orbital antisymmetric states. We find that orbital symmetric states are lower in energy and separated by ≈ 0.4-0.8 meV from orbital antisymmetric states. The symmetric multiplet exhibits an additional energy splitting of its six states of ≈ 0.15-0.5 meV due to lattice scale interactions. The experimental observations are supported by theoretical calculations, which allow to determine that intervalley scattering and "current-current" interaction constants are of the same magnitude in BLG.

Group theoretic approach to many-body scar states in fermionic lattice models

It has been shown [K. Pakrouski et al., Phys. Rev. Lett. 125, 230602 (2020)] that three families of highly symmetric states are many-body scars for any spin-$\frac{1}{2}$ fermionic Hamiltonian of the form ${H}_{0}+OT$, where $T$ is a generator of an appropriate Lie group. One of these families consists of the well-known $\ensuremath{\eta}$-pairing states. In addition to having the usual properties of scars, these families of states are insensitive to electromagnetic noise and have advantages for storing and processing quantum information. In this paper we show that a number of well-known coupling terms, such as the Hubbard and the Heisenberg interactions, and the Hamiltonians containing them, are of the required form and support these states as scars without fine tuning. The explicit ${H}_{0}+OT$ decomposition for a number of most commonly used models, including topological ones, is provided. To facilitate possible experimental implementations, we discuss the conditions for the low-energy subspace of these models to be comprised solely of scars. Further, we write all the generators $T$ that can be used as building blocks for designing new models with scars, most interestingly including the spin-orbit coupled hopping and superconducting pairing terms. We expand this framework to the non-Hermitian open systems and demonstrate that for them the scar subspace continues to undergo coherent time evolution and exhibit the ``revivals.'' A full numerical study of an extended two-dimensional $tJU$ model explicitly illustrates the novel properties of the invariant scars and supports our findings.

On state instability of the bi-stable flow past a notchback bluff body

The wake of a notchback Ahmed body presenting a bi-stable nature is investigated by performing wind tunnel experiments and large-eddy simulations. Attention is confined to the Reynolds number ( $Re$ ) influence on the wake state instability within $5\times 10^{4}\leq Re \leq 25\times 10^{4}$ . Experimental observations suggest a wake bi-stability with low-frequency switches under low $Re$ . The wake becomes ‘tri-stable’ with the increase of $Re$ with the introduction of a new symmetric state. The higher presence of the symmetric state can be considered as a symmetrization of the wake bi-stability with an increasing $Re$ . The wake symmetry under high $Re$ attributed to the highly frequent switches of the wake is extremely sensitive to small yaw angles, showing the feature of bi-stable flows. The wake asymmetry is confirmed in numerical simulations with both low and high $Re$ . The wake asymmetries are indicated by the wake separation, the reattachment and the wake dynamics identified by the proper orthogonal decomposition. However, the turbulence level is found to be significantly higher with a higher $Re$ . This leads to a higher possibility to break the asymmetric state, resulting in highly frequent switches showing symmetry.

Fluctuations of a swarm of Brownian bees.

The "Brownian bees" model describes an ensemble of N independent branching Brownian particles. When a particle branches into two particles, the particle farthest from the origin is eliminated so as to keep the number of particles constant. In the limit of N→∞, the spatial density of the particles is governed by the solution of a free boundary problem for a reaction-diffusion equation. At long times the particle density approaches a spherically symmetric steady-state solution with a compact support. Here, we study fluctuations of the "swarm of bees" due to the random character of the branching Brownian motion in the limit of large but finite N. We consider a one-dimensional setting and focus on two fluctuating quantities: the swarm center of mass X(t) and the swarm radius ℓ(t). Linearizing a pertinent Langevin equation around the deterministic steady-state solution, we calculate the two-time covariances of X(t) and ℓ(t). The variance of X(t) directly follows from the covariance of X(t), and it scales as 1/N as to be expected from the law of large numbers. The variance of ℓ(t) behaves differently: It exhibits an anomalous scaling (1/N)lnN. This anomaly appears because all spatial scales, including a narrow region near the edges of the swarm where only a few particles are present, give a significant contribution to the variance. We argue that the variance of ℓ(t) can be obtained from the covariance of ℓ(t) by introducing a cutoff at the microscopic time 1/N where the continuum Langevin description breaks down. Our theoretical predictions are in good agreement with Monte Carlo simulations of the microscopic model. Generalizations to higher dimensions are briefly discussed.

Asymptotic softness of a laterally confined sheet in a pressurized chamber.

Elastohydrodynamic models, that describe the interaction between a thin sheet and a fluid medium, have been proven successful in explaining the complex behavior of biological systems and artificial materials. Motivated by these applications we study the quasistatic deformation of a thin sheet that is confined between the two sides of a closed chamber. The two parts of the chamber, above and below the sheet, are filled with an ideal gas. We show that the system is governed by two dimensionless parameters, Δ and η, that account respectively for the lateral compression of the sheet and the ratio between the amount of fluid filling each part of the chamber and the bending stiffness of the sheet. When η≪1 the bending energy of the sheet dominates the system, the pressure drop between the two sides of the chamber increases, and the sheet exhibits a symmetric configuration. When η≫1 the energy of the fluid dominates the system, the pressure drop vanishes, and the sheet exhibits an asymmetric configuration. The transition between these two limiting scenarios is governed by a third branch of solutions that is characterized by a rapid decrease of the pressure drop. Notably, across the transition the energetic gap between the symmetric and asymmetric states scales as δE∼Δ^{2}. Therefore, in the limit Δ≪1 small variations in the energy are accompanied by relatively large changes in the elastic shape.

Intrinsic quantum correlations for Gaussian localized Dirac cat states in phase space

Following the information-based approach to Dirac spinors under a constant magnetic field, the phase-space representation of symmetric and antisymmetric localized Dirac cat states is obtained. The intrinsic entanglement profile implied by the Dirac Hamiltonian is then investigated so as to shed a light on quantum states as carriers of qubits correlated by phase-space variables. Corresponding to the superposition of Gaussian states, cat states exhibit nontrivial elementary information dynamics which include the interplay between intrinsic entanglement and quantum superposition as reported by the corresponding Dirac archetypes. Despite the involved time evolution as nonstationary states, the Wigner function constrains the elementary information quantifiers according to a robust framework which can be consistently used for quantifying the time-dependent $\text{SU}(2)\ensuremath{\bigotimes}\text{SU}(2)$ (spin projection and intrinsic parity) correlation profile of phase-space localized Dirac spinor states. Our results show that the Dirac Wigner functions for cat states---described in terms of generalized Laguerre polynomials---exhibit an almost maximized timely persistent mutual information profile which is engendered by either classical- or quantumlike spin-parity correlations, depending on the magnetic field intensity.

Biomembranes undergo complex, non-axisymmetric deformations governed by Kirchhoff-Love kinematicsand revealed by a three-dimensional computational framework.

Biomembranes play a central role in various phenomena like locomotion of cells, cell-cell interactions, packaging and transport of nutrients, transmission of nerve impulses, and in maintaining organelle morphology and functionality. During these processes, the membranes undergo significant morphological changes through deformation, scission, and fusion. Modelling the underlying mechanics of such morphological changes has traditionally relied on reduced order axisymmetric representations of membrane geometry and deformation. Axisymmetric representations, while robust and extensively deployed, suffer from their inability to model-symmetry breaking deformations and structural bifurcations. To address this limitation, a three-dimensional computational mechanics framework for high fidelity modelling of biomembrane deformation is presented. The proposed framework brings together Kirchhoff–Love thin-shell kinematics, Helfrich-energy-based mechanics, and state-of-the-art numerical techniques for modelling deformation of surface geometries. Lipid bilayers are represented as spline-based surface discretizations immersed in a three-dimensional space; this enables modelling of a wide spectrum of membrane geometries, boundary conditions, and deformations that are physically admissible in a three-dimensional space. The mathematical basis of the framework and its numerical machinery are presented, and their utility is demonstrated by modelling three classical, yet non-trivial, membrane deformation problems: formation of tubular shapes and their lateral constriction, Piezo1-induced membrane footprint generation and gating response, and the budding of membranes by protein coats during endocytosis. For each problem, the full three-dimensional membrane deformation is captured, potential symmetry-breaking deformation paths identified, and various case studies of boundary and load conditions are presented. Using the endocytic vesicle budding as a case study, we also present a ‘phase diagram’ for its symmetric and broken-symmetry states.

Distant emitters in ultrastrong waveguide QED: Ground-state properties and non-Markovian dynamics

Starting from the paradigmatic spin-boson model (SBM), we investigate the static and dynamical properties of a system of two distant two-level emitters coupled to a one-dimensional Ohmic waveguide beyond the rotating wave approximation. Employing static and dynamical polaron Ans\"atze we study the effects of finite separation distance on the behavior of the photon-mediated Ising-like interaction, qubit frequency renormalization, ground-state magnetization, and entanglement entropy of the two-qubit system. Based on previous works we derive an effective approximate Hamiltonian for the two-impurity SBM that preserves the excitation-number and thus facilitates the analytical treatment. In particular, it allows us to introduce non-Markovianity arising from delay-feedback effects in two distant emitters in the so-called ultrastrong coupling (USC) regime. We test our results with numerical simulations performed over a discretized circuit-QED model, finding perfect agreement with previous results, and showing interesting dynamical effects arising in ultrastrong waveguide QED with distant emitters. In particular, we revisit the Fermi two-atom problem showing that, in the USC regime, initial correlations yield two different evolutions for symmetric and antisymmetric states even before the emitters become causally connected. Finally, we demonstrate that the collective dynamics, e.g., superradiance or subradiance, are affected not only by the distance between emitters, but also by the coupling, due to significant frequency renormalization. This constitutes another dynamical consequence of the USC regime.

Spontaneous decay-induced quantum dynamics in Rydberg-blockaded Λ-type atoms

Strongly Rydberg-blockaded two-level atoms form a Rydberg superatom which is excited only to a collective symmetrical Dicke state. However, emerging often in the alkali-earth atoms, spontaneous decay from the Rydberg state to an additional pooling state renders the ensemble no longer a closed superatom. Herein we present a computationally efficient model to characterize the interaction between a fully Rydberg-blockaded ensemble of N Λ-type three-level atoms and a strong probe light field in a coherent state. The model enables us to achieve a decomposition of the coupled dynamics in the strong field limit, which significantly reduces the complexity of computing the N-body system evolution and paves the way for practical analysis in experiments. A quasi-steady-state power spectrum with multiple sidebands is found in the scattered field. The relative heights of the sidebands show a time-dependence determined by the atomic relaxation, which illuminates potential applications of using the system in information transfer of quantum networks. With negligible dissipative flipping to the unsymmetrical states, the atomic relaxation time, indicating a linearly increasing pooling state fraction, is derived analytically as a function of the number of atoms.

Superdense coding in the resource theory of asymmetry

We consider a task in which classical information is encoded into a quantum system by an operation restricted by symmetry. The maximum amount of classical information that can be encoded under this restriction, namely the symmetry-restricted classical information capacity, depends on the initial state of the system. Our focus is on whether the capacity of an asymmetric state can be strictly larger than that of any symmetric states, whereas the latter is a strictly positive constant. That is, we ask whether an analog of superdense coding is implementable in the resource theory of asymmetry. We prove that superdense coding is implementable if and only if the unitary representation of the symmetry is non-Abelian and reducible. Thereby we provide an information theoretical classification of symmetries of quantum systems.

Entangled symmetric states and copositive matrices

Entanglement in symmetric quantum states and the theory of copositive matrices are intimately related concepts. For the simplest symmetric states, i.e., the diagonal symmetric (DS) states, it has been shown that there exists a correspondence between exceptional (non-exceptional) copositive matrices and non-decomposable (decomposable) Entanglement Witnesses (EWs). Here we show that EWs of symmetric, but not DS, states can also be constructed from extended copositive matrices, providing new examples of bound entangled symmetric states, together with their corresponding EWs, in arbitrary odd dimensions.

Free versus bound entanglement, a NP-hard problem tackled by machine learning

Entanglement detection in high dimensional systems is a NP-hard problem since it is lacking an efficient way. Given a bipartite quantum state of interest free entanglement can be detected efficiently by the PPT-criterion (Peres-Horodecki criterion), in contrast to detecting bound entanglement, i.e. a curious form of entanglement that can also not be distilled into maximally (free) entangled states. Only a few bound entangled states have been found, typically by constructing dedicated entanglement witnesses, so naturally the question arises how large is the volume of those states. We define a large family of magically symmetric states of bipartite qutrits for which we find 82% to be free entangled, 2% to be certainly separable and as much as 10% to be bound entangled, which shows that this kind of entanglement is not rare. Via various machine learning algorithms we can confirm that the remaining 6% of states are more likely to belonging to the set of separable states than bound entangled states. Most important we find via dimension reduction algorithms that there is a strong two-dimensional (linear) sub-structure in the set of bound entangled states. This revealed structure opens a novel path to find and characterize bound entanglement towards solving the long-standing problem of what the existence of bound entanglement is implying.

A 4-Bit Multistate Frequency-Selective Surface With Dual-Band Multifunction Response

In this letter, a novel 4 b multistate frequency-selective surface is proposed. Four p-i-n diodes are used to maneuver multifunction behavior of the structure with seven different functional states. The 4 b binary state operations 0000, 1100, 0011, and 1111 offer transverse electric (TE)/transverse magnetic (TM) waves both transmit, TE transmit/TM shield, TM transmit/TE shield, and TE/TM both shield, respectively, at 2 GHz frequency. The passband at 2 GHz frequency has <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$-\text{10}$</tex-math></inline-formula> dB fractional bandwidth of 117%. The binary states 1101 and 1110 are symmetric, which select the TE wave transmit/TM wave shield to the passband at 3.45 GHz frequency with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$-\text{10}$</tex-math></inline-formula> dB fractional bandwidth of 49%, whereas binary states 1011 and 0111 allow the TM wave to transmit at 3.45 GHz and shield the TE wave. The four symmetric binary states 0101, 0110, 1010, and 1001 provide transmission band at 3.45 GHz frequency for dual-polarized plane wave incidence. The transmission of both the passbands can be shielded by selecting the binary state equal to 1111. An equal circuit model is used to elaborate the contribution of different passive structural elements in terms of lumped components. A prototype of the structure is fabricated, and transmission coefficients for different states at normal and oblique incidence of the electromagnetic plane wave are measured, which verifies the simulated responses of the structure.

Vulnerabilities of quantum cryptography on geometrically uniform coherent states

It is shown that the quantum cryptography protocol on geometrically uniform coherent states, which uses the restriction for unambiguous discrimination of a set of symmetric coherent states and allows resisting an unambiguous state discrimination attack (USD attack), is not secure to a number of other attacks. The key length formula from the work of ] and the key generation rate for a number of constructive attacks of the eavesdropper are compared and it is shown that the key generation rate in this work is significantly overestimated. This leads to the fact that the distributed key is not secret.