Diagonal Phase Research Articles

Gait planning based on bionic quadruped robot

Based on the ankylosaurus, a four-legged robot structure with 14 degrees of freedom was designed in this study. The kinematic model was established using the Denavit-Hartenberg (D-H) method. The inverse kinematics of the robot was analyzed, and the angle equations of each leg joint were obtained. In order to reduce the kinetic energy generated when leaving the ground and landing, the compound cycloid was modified. The modified foot curve effectively reduces energy and meets the kinematic requirements. On the basis of the foot trajectory, the diagonal leg phase difference was set to 0.5, and the diagonal gait was adopted as the gait of the bionic quadrupled robot. Simulink software was used to construct the simulation environment, and the maximum error of the simulation results and the theoretical step height was 2.05%, and the step length maximum error was 2.39%. During walking, the thigh joint angle was −92.82° to −80.21°, and the hip joint angle was 22.23° to 43.83°. Compared with the simulation trajectory and the theoretical curve, because the experiment did not consider the balance of the fuselage, there was a certain error when the leg was raised to the highest point. Overall, the gait planning strategy designed in this study basically achieves the expected effect, lays a certain foundation for the practical application of the bionic quadruped dinosaur robot, and also provides a reference for the subsequent research.

Extracting off-diagonal order from diagonal basis measurements

Quantum gas microscopy has developed into a powerful tool to explore strongly correlated quantum systems. However, discerning phases with topological or off-diagonal long range order requires the ability to extract these correlations from site-resolved measurements. Here, we show that a multiscale complexity measure can pinpoint the transition to and from the bond ordered wave phase of the one-dimensional extended Hubbard model with an off-diagonal order parameter, sandwiched between diagonal charge and spin density wave phases, using only diagonal descriptors. We study the model directly in the thermodynamic limit using the recently developed variational uniform matrix product states algorithm, and draw our samples from degenerate ground states related by global spin rotations, emulating the projective measurements that are accessible in experiments. Our results will have important implications for the study of exotic phases using optical lattice experiments. Published by the American Physical Society 2024

Reconfigurable Intelligent Surface Assisted Wireless Network Rate Optimization Design

To enhance the communication rate, we deploy one active reconfigurable intelligent surface (RIS) and one passive RIS to cooperatively assist the downlink communication, while meeting the constraints of base station transmission power, total Active RIS power, and RIS unit modulus constraint. Due to the nonlinear coupling of multiple variables in the objective function, non-convexity is caused. Therefore, an alternating optimization algorithm (AO) is proposed, which uses semi-definite programming (SDP) based algorithm to optimize the transmit beamforming vector, ARIS reflection matrix, and PRIS diagonal phase shift matrix. The simulation results have verified the effectiveness of the proposed algorithm, which indicates that optimizing the coefficients can significantly improve the spectrum efficiency of wireless networks.

Beyond Diagonal Reconfigurable Intelligent Surfaces: A Multi-Sector Mode Enabling Highly Directional Full-Space Wireless Coverage

Reconfigurable intelligent surface (RIS) has gained much traction due to its potential to manipulate the propagation environment via nearly-passive reconfigurable elements. In our previous work, we have analyzed and proposed a beyond diagonal RIS (BD-RIS) model, which is not limited to traditional diagonal phase shift matrices, to unify different RIS modes/architectures. In this paper, we create a new branch of BD-RIS supporting a multi-sector mode. A multi-sector BD-RIS is modeled as multiple antennas connected to a multi-port group-connected reconfigurable impedance network. More specifically, antennas are divided into <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> ≥ 2) sectors and arranged as a polygon prism with each sector covering 1/ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> space. Different from the recently introduced concept of intelligent omni-surface (or simultaneously transmitting and reflecting RIS), the multi-sector BD-RIS not only achieves a full-space coverage, but also has significant performance gains thanks to the highly directional beam of each sector. We derive the constraint of the multi-sector BD-RIS and the corresponding channel model taking into account the relationship between antenna beamwidth and gain. With the proposed model, we first derive the scaling law of the received signal power for a multi-sector BD-RIS-assisted single-user system. We then propose efficient beamforming design algorithms to maximize the sum-rate of the multi-sector BD-RIS-assisted multiuser system. Simulation results verify the effectiveness of the proposed design and demonstrate the performance enhancement of the proposed multi-sector BD-RIS.

Beyond Diagonal Reconfigurable Intelligent Surfaces: From Transmitting and Reflecting Modes to Single-, Group-, and Fully-Connected Architectures

Reconfigurable intelligent surfaces (RISs) are envisioned as a promising technology for future wireless communications. With various hardware realizations, RISs can work under different modes (reflective/transmissive/hybrid) or have different architectures (single/group/fully-connected). However, most existing research focused on single-connected reflective RISs, mathematically characterized by diagonal phase shift matrices, while there is a lack of a comprehensive study for RISs unifying different modes/architectures. In this paper, we solve this issue by analyzing and proposing a general RIS-aided communication model. Specifically, we establish an RIS model not limited to diagonal phase shift matrices, a novel branch referred to as beyond diagonal RIS (BD-RIS), unifying modes and architectures. With the proposed model, we develop efficient algorithms to jointly design transmit precoder and BD-RIS matrix to maximize the sum-rate for RIS-aided systems. We also provide simulation results to compare the performance of BD-RISs with different modes/architectures. Simulation results show that under the same mode, fully- and group-connected RIS can effectively increase the sum-rate performance compared with single-connected RIS, and that hybrid RIS outperforms reflective/transmissive RIS with the same architecture.

Many-body localization in the infinite-interaction limit and the discontinuous eigenstate phase transition

We study many-body localization (MBL) in a spin-chain model mimicking the Rydberg-blockade quantum simulator with infinite-strength projection and moderate quasiperiodic modulation. Employing exact diagonalization, Krylov-typicality technique, and time-evolving block decimation, we identify evidence for a constrained MBL phase stabilized by a pure quasirandom transverse field. Intriguingly, the constrained MBL transition may embody a discontinuous eigenstate phase transition, whose discontinuity nature significantly suppresses finite-size drifts that plague most numerical studies of conventional MBL transition. Through quantum dynamics, we find that rotating the modulated field from parallel toward perpendicular to the projection axis induces an eigenstate transition between diagonal and constrained MBL phases. The entanglement-entropy growth in constrained MBL follows a double-log form, whereas it changes to a power law in approaching the diagonal limit. By unveiling confined nonlocal effects in integrals of motion of constrained MBL, we show this insulating state is not a many-body Anderson insulator. Our predictions are testable in Rydberg experiments.

Geometric phases in neutrino mixing

Neutrinos can acquire both dynamic and geometric phases due to the nontrivial mixing between mass and flavor eigenstates. In this paper, we derive the general expressions for all plausible gauge invariant diagonal and off-diagonal geometric phases in the three- flavor neutrino model using the kinematic approach. We find that diagonal and higher-order off-diagonal geometric phases are sensitive to the mass ordering and the Dirac CP violating phase [Formula: see text]. We show that, third-order off-diagonal geometric phase [Formula: see text] is invariant under any cyclic or non-cyclic permutations of flavor indices when the Dirac CP phase is zero. For nonzero [Formula: see text], we find that [Formula: see text]. We also prove that, only the third-order off-diagonal geometric phase is sensitive to the sign of [Formula: see text]. Further, we explore the effects of matter background using a two-flavor neutrino model and show that the diagonal geometric phase is either [Formula: see text] or [Formula: see text] in the MSW resonance region and takes nontrivial values elsewhere. The transition between zero and [Formula: see text] occurs at the point of complete oscillation inversion called the nodal point, where the diagonal geometric phase is not defined. Also, in two-flavor approximations, two distinct diagonal geometric phases are co-functions with respect to the mixing angle. Finally, in the two-flavor model, we show that the only second-order off-diagonal geometric phase is a topological invariant quantity and is always [Formula: see text].

Reconfigurable Intelligent Surfaces Relying on Non-Diagonal Phase Shift Matrices

Reconfigurable intelligent surfaces (RIS) have been actively researched as a potential technique for future wireless communications, which intelligently ameliorate the signal propagation environment. In the conventional design, each RIS element configures and reflects its received signal independently of all other RIS elements, which results in a diagonal phase shift matrix. By contrast, we propose a novel RIS architecture, where the incident signal impinging on one element can be reflected from another element after an appropriate phase shift adjustment, which increases the flexibility in the design of RIS phase shifts, hence, potentially improving the system performance. The resultant RIS phase shift matrix also has off-diagonal elements, as opposed to the pure diagonal structure of the conventional design. Compared to the state-of-art fully-connected/group-connected RIS structures, our proposed RIS architecture has lower complexity, while attaining a higher channel gain than the group-connected RIS structure, and approaching that of the fully-connected RIS structure. We formulate and solve the problem of maximizing the achievable rate of our proposed RIS architecture by jointly optimizing the transmit beamforming and the non-diagonal phase shift matrix based on alternating optimization and semi-define relaxation (SDR) methods. Moreover, the closed-form expressions of the channel gain, the outage probability and bit error ratio (BER) are derived. Simulation results demonstrate that our proposed RIS architecture results in an improved performance in terms of the achievable rate compared to the conventional architecture, both in single-user as well as in multi-user scenarios.

Lower Bound on the Capacity of the Continuous-Space SSFM Model of Optical Fiber

The capacity of a discrete-time model of optical fiber described by the split-step Fourier method (SSFM) as a function of the signal-to-noise ratio SNR and the number of segments in distance K is considered. It is shown that if K ≥ SNR2/3 and SNR → ∞, the capacity of the resulting continuous-space lossless model is lower bounded by 1/2 log2(1 + SNR) - 1/2 + o(1), where o(1) tends to zero with SNR. As K → ∞, the inter-symbol interference (ISI) averages out to zero due to the law of large numbers and the SSFM model tends to a diagonal phase noise model. It follows that, in contrast to the discrete-space model where there is only one signal degree-of-freedom (DoF) at high powers, the number of DoFs in the continuous-space model is at least half of the input dimension n. Intensity-modulation and direct detection achieves this rate. The pre-log in the lower bound when K=δ√SNR is generally characterized in terms of δ. It is shown that if the nonlinearity parameter γ → ∞, the capacity of the continuous-space model is 1/2 log2(1 + SNR) + o(1). The SSFM model when the dispersion matrix does not depend on K is considered. It is shown that the capacity of this model when K=δ√SNR, δ > 3, and SNR → ∞ is 1/2n log2(1 + SNR) + O(1). Thus, there is only one DoF in this model. Finally, it is found that the maximum achievable information rates (AIRs) of the SSFM model with back-propagation equalization obtained using numerical simulation follows a double-ascent curve. The AIR characteristically increases with SNR, reaching a peak at a certain optimal power, and then decreases as SNR is further increased. The peak is attributed to a balance between noise and stochastic ISI. However, if the power is further increased, the AIR will increase again, approaching the lower bound 1/2 log(1 + SNR) - 1/2 + o(1). The second ascent is because the ISI averages out to zero with K → ∞ sufficiently fast.

Secrecy rate analysis for reconfigurable intelligent surface-assisted mimo communications with statistical CSI

In this paper, a reconfigurable intelligent surface (RIS)-assisted MIMO wireless secure communication system is considered, in which a base station (BS) equipped with multiple antennas exploits statistical channel state information to communicate with a legitimate multi-antenna user, in the presence of an eavesdropper, also equipped with multiple antennas. We firstly obtain an analytical expression of the ergodic secrecy rate based on the results of large-dimensional random matrix theory. Then, a jointly alternating optimization algorithm with the method of Taylor series expansion and the projected gradient ascent method is proposed to design the transmit covariance matrix at the BS, as well as the diagonal phase- shifting matrix to maximize the ergodic secrecy rate. Simulations are conducted to demonstrate the accuracy of the derived analytical expressions, as well as the superior performance of our proposed algorithm.

Generalizations of exactly solvable quantum spin models

Several generalizations of one-dimensional and two-dimensional exactly solvable low-dimensional quantum spin-1/2 models, some of which contain off-diagonal terms of the exchange tensor, are proposed. It is shown that off-diagonal terms of the exchange (symmetric or nonsymmetric with respect to the exchange of spins) yield renormalization of the diagonal ones and phase shifts. The latter can be moved to eigenfunctions of the models and do not affect eigenvalues for open geometries of the lattices. For closed geometries of the lattices the phase shifts manifest themselves in the finite size corrections. The advantage of the proposed models is in their simplicity and in possible realizations of the models in a number of applications, e.g., for the description of the wide variety of correlated electron systems, ultracold atoms, and in the theory of topological quantum computation.

Investigating the Sterile Neutrino Parameters with QLC in 3 + 1 Scenario

In the scenario with four generation quarks and leptons and using a 3+1 neutrino model having one sterile and the three standard active neutrinos with a 4×4 unitary transformation matrix, UPMNS4, we perform a model-based analysis using the latest global data and determine bounds on the sterile neutrino parameters i.e., the neutrino mixing angles. Motivated by our previous results, where, in a quark-lepton complementarity (QLC) model we predicted the values of θ13PMNS=9−2+2° and θ23PMNS=40.60−0.3+0.1°. In the QLC model the nontrivial correlation between CKM4 and PMNS4 mixing matrix is given by the correlation matrix Vc4. Monte Carlo simulations are performed to estimate the texture of Vc4 followed by the calculation of PMNS4 using the equation, UPMNS4=UCKM4·ψ4−1·Vc4, where ψ4 is a diagonal phase matrix. The sterile neutrino mixing angles, θ14PMNS, θ24PMNS and θ34PMNS are assumed to be freely varying between 0−π/4 and obtained results which are consistent with the data available from various experiments, like NovA, MINOS, SuperK, Ice Cube-DeepCore. In further investigation, we analytically obtain approximately similar ranges for various neutrino mixing parameters Uμ42 and Uτ42.

Electrical and magnetic properties of thin films of the spin-filter material CrVTiAl

The spin-filter material CrVTiAl is a promising candidate for producing highly spin-polarized currents at room temperature in a nonmagnetic architecture. Thin films of compensated-ferrimagnetic CrVTiAl have been grown and their electrical and magnetic properties have been studied. The resistivity shows two-channel semiconducting behavior with one disordered gapless channel and a gapped channel with activation energy $\Delta E$=~0.1~-~0.2~eV. Magnetoresistance measurements to B~=~35~T provide values for the mobilities of the gapless channel, leading to an order of magnitude difference in the carrier effective masses, which are in reasonable accord with our density-functional-theory based results. The density of states and electronic band structure is computed for permutations of the four sublattices arranged differently along the (111) body diagonal, yielding metallic (Cr-V-Al-Ti), spin-gapless (Cr-V-Ti-Al) and spin-filtering (Cr-Ti-V-Al) phases. Robustness of the spin-gapless phase to substitutional disorder is also considered.

Utilization of the high spatial-frequency component in adaptive beam shaping by using a virtual diagonal phase grating

A square flattop beam is a fundamental shape that is in high demand in various applications, such as ultra-high-power lasers, uniform surface processing and medical engineering. In this experiment, a new and simple scheme of the adaptive beam shaping system to generate a square flattop shape with high uniformity and edge steepness using virtual diagonal phase grating encoded on a spatial-light modulator and a 4f system is proposed. The grating vector kg is non-parallel to the normal vectors kx and ky of the objective beam profile to be extracted; thus, the residual and extracted components hit separately on the Fourier plane of the 4f system. Consequently, using a spatial-frequency filter passing components parallel to kx and ky, the residual components are blocked by the filter without loss of the high spatial-frequency domain of the extracted component. When the width of the filter was 1.0 mm, the edge of the shaped beam increased in height within 20 μm, which is less than 20% of that obtained with conventional vertical phase grating.

Disordering, clustering, and laning transitions in particle systems with dispersion in the Magnus term.

We numerically examine a two-dimensional system of repulsively interacting particles with dynamics that are governed by both a damping term and a Magnus term. The magnitude of the Magnus term has one value for half of the particles and a different value for the other half of the particles. In the absence of a driving force, the particles form a triangular lattice, while when a driving force is applied, we find that there is a critical drive above which a Magnus-induced disordering transition can occur even if the difference in the Magnus term between the two particle species is as small as one percent. The transition arises due to the different Hall angles of the two species, which causes their motion to decouple at the critical drive. At higher drives, the disordered state can undergo both species and density phase separation into a density-modulated stripe that is oriented perpendicular to the driving direction. We observe several additional phases that occur as a function of drive and Magnus force disparity, including a variety of density-modulated diagonal-laned phases. In general, we find a much richer variety of states compared to systems of oppositely driven overdamped Yukawa particles. We discuss the implications of our work for skyrmion systems, where we predict that even for small skyrmion dispersities, a drive-induced disordering transition can occur along with clustering phases and pattern-forming states.

Competition between spin-induced charge instabilities in underdoped cuprates

We study the static charge correlation function in an one-band model on a square lattice. The Hamiltonian consist of effective hoppings of the electrons between the lattice sites and the Heisenberg Hamiltonian. Approximating the irreducible charge correlation function by a single bubble yields the ladder approximation for the charge correlation function. In this approximation one finds in general three charge instabilities, two of them are due to nesting, the third one is the flux phase instability. Since these instabilities cannot explain the experiments in hole-doped cuprates we have included in the irreducible charge correlation function also Aslamasov-Larkin (AL) diagrams where charge fluctuations interact with products of spin fluctuations. We then find at high temperatures a nematic or $d$-wave Pomeranchuk instability with a very small momentum. Its transition temperature decreases roughly linearly with doping in the underdoped region and vanishes near optimal doping. Decreasing the temperature further a secondary axial charge-density wave (CDW) instability appears with mainly $d$-wave symmetry and a wave vector somewhat larger than the distance between nearest neighbor hot spots. At still lower temperatures the diagonal flux phase instability emerges. A closer look shows that the AL diagrams enhance mainly axial and not diagonal charge fluctuations in our one-band model. This is the main reason why axial and not diagonal instabilities are the leading ones in agreement with experiment. The two instabilities due to nesting vanish already at very low temperatures and do not play any major role in the phase diagram. Remarkable is that the nematic and the axial CDW instabilities show a large reentrant behavior.

Experimental quantum information processing with the Talbot effect

We report a proof of concept experiment illustrating the implementation of several simple quantum logic gates on D-level quantum systems (quDits) using the Talbot effect. A number of QuDit states are encoded into the transverse profile of a paraxial laser beam using a spatial light modulator. These states are transformed through a diagonal phase element and then free-propagation via the fractional Talbot effect, demonstrating the realization of some well-known single quDit gates in quantum computation. Our classical optics experiment allows us to identify several important technical details, and serves as a first experimental step in performing D-dimensional quantum operations with single photons or other quantum systems using this scheme.

The biomechanical construction of the horse's body and activity patterns of three important muscles of the trunk in the walk, trot and canter.

The activity patterns of trunk muscles are commonly neglected, in spite of their importance for maintaining body shape. Analysis of the biomechanics of the trunk under static conditions has led to predictions of the activity patterns. These hypotheses are tested experimentally by surface electromyography (EMG). Five horses, with and without a rider, were examined in the walk, trot and canter. Footfall was synchronised with EMG by an accelerometer. Averages of ten consecutive cycles were calculated and compared by statistical methods. The start and stop times of the muscle activities of 5-10 undisturbed EMG plots were determined and the averages and standard deviations calculated. In walking, muscle activities are minor. Electromyography (EMG) activity was increased in the m. rectus during the three-limb support. When the bending moments assume their greatest values, for example while the horses' mass is accelerated upward (two times earth acceleration) in the diagonal support phases in trot and canter the m. rectus, connecting the sternum with the pubic bone is most active. The m. obl. externus is most active when the torsional and bending moments are greatest during the same support phases, but not bilaterally, because the forces exerted on one side by the (recorded) m. obl. externus are transmitted on the other side by the (not recorded) m. obl. internus. While the hindlegs touch the ground in the trot and canter, ground reaction forces tend to flex the hip joint and the lumbar spine. Therefore, the vertebral column needs to be stabilised by the ipsilateral m. longissimus dorsi, which in fact can be observed. As a whole, our EMG data confirm exactly what has been predicted by theoretical analysis.

Ab initio calculation of Hubbard parameters for Rydberg-dressed atoms in a one-dimensional optical lattice

We obtain ab initio the Hubbard parameters for Rydberg-dressed atoms in a one-dimensional (1D) sinusoidal optical lattice on the basis of maximally-localized Wannier states. Finite range, soft-core interatomic interactions become the trait of Rydberg admixed atoms, which can be extended over many neighboring lattice sites. In contrast to dipolar gases, where the interactions follow an inverse cubic law, the key feature of Rydberg-dressed interactions is the possibility of making neighboring couplings to the same magnitude as that of the onsite ones. The maximally-localized Wannier functions (MLWFs) are typically calculated via a spread-minimization procedure (Marzari N and Vanderbilt D 1997 Phys. Rev. B 56 12847) and are always found to be real functions apart from a trivial global phase when an isolated set of Bloch bands are considered. For an isolated single Bloch band, the above procedure reduces to a simple quasi-momentum-dependent unitary phase transformation. Here, instead of minimizing the spread, we employ a diagonal phase transformation which eliminates the imaginary part of the Wannier functions. The resulting Wannier states are found to be maximally localized and in exact agreement with those obtained via a spread-minimization procedure. Using these findings, we calculate the Hubbard couplings from the Rydberg admixed interactions, including dominant density-assisted tunneling (DAT) coefficients. Finally, we provide realistic lattice parameters for the state-of-the-art experimental Rydberg-dressed rubidium setup.

Postural changes and their effects in elite riders when actively influencing the horse versus sitting passively at trot

The objectives were to compare sagittal plane posture of the pelvis, trunk and head of elite dressage riders when they ride actively to train the horse versus sitting passively and following the horses’ movements at trot, and to evaluate the effects of these changes in rider posture on load distribution on the horse’s back. Synchronised motion capture and saddle mat data of seven elite dressage riders were used to measure minimal and maximal angles and range of motion (ROM) for the pelvic, trunk and head segments, the angle between pelvis and trunk segments, phase-shift between pitching motions of pelvis and trunk, and pelvic translation relative to the saddle. Non-parametric statistical tests compared variables between the two rider postures. In the passive rider posture the pelvis, trunk and head showed two pitching cycles per stride. Maximal posterior and anterior pelvic rotation occurred, respectively, early and late in the horse’s diagonal stance phase. Compared with pelvic movements, trunk movements were slightly delayed and head movements were out-of-phase. In the active rider posture the pelvis and trunk pitched further posteriorly throughout the stride. Most of the riders showed similar sagittal plane movements of the axial body segments but with some notable individual variations.