Finite Excitation Research Articles

Collective excitations in cigar-shaped spin-orbit-coupled spin-1 Bose-Einstein condensates

We study theoretically the collective excitations of a spin-orbit-coupled spin-1 Bose-Einstein condensate with antiferromagnetic spin-exchange interactions in a cigar-shaped trapping potential at zero and finite temperatures using the Hartree-Fock-Bogoliubov theory with Popov approximation. The collective modes at zero temperature are corroborated by real-time evolution of the ground state subjected to a perturbation suitable to excite a density or a spin mode. We also calculate a few low-lying modes analytically and find very good agreement with the numerical results. We confirm the presence of excitations belonging to two broad categories, namely, density and spin excitations, based on the calculation of dispersion. The degeneracy between a pair of spin modes is broken by the spin-orbit coupling. At finite temperature, spin and density excitations show qualitatively different behavior as a function of temperature.

Learning-Based Attitude Tracking Control With High-Performance Parameter Estimation

This article aims to handle the optimal attitude tracking control tasks for rigid bodies via a reinforcement-learning-based control scheme, in which a constrained parameter estimator is designed to compensate system uncertainties accurately. This estimator guarantees the exponential convergence of estimation errors and can strictly keep all instant estimates always within predetermined bounds. Based on it, a critic-only adaptive dynamic programming (ADP) control strategy is proposed to learn the optimal control policy with respect to a user-defined cost function. The matching condition on reference control signals, which is commonly employed in relevant ADP design, is not required in the proposed control scheme. We prove the uniform ultimate boundedness of the tracking errors and critic weight’s estimation errors under finite excitation conditions by Lyapunov-based analysis. Moreover, an easy-to-implement initial control policy is designed to trigger the real-time learning process. The effectiveness and advantages of the proposed method are verified by both numerical simulations and hardware-in-the-loop experimental tests.

Polaritonic excitations and Bose-Einstein condensation in the Rabi lattice model

The unitary transformation method is used to study the properties of the polaritonic states and Bose-Einstein condensation in the Rabi lattice model, where the on-site two-level systems (TLSs) are coupled with the intersite hopping photons. It is shown that the counter-rotating coupling (CRC) between TLS and photon, which breaks down the conservation of the excitation numbers, may induce a long-range Ising-like interaction among intersite TLSs. We have shown that the coupled TLSs and photons are hybridized to form the polaritonic states, and the corresponding ground state and polaritonic excitation spectra are calculated by diagonalizing our transformed Hamiltonian. When the photon hopping $J$ is weak, the excitation spectrum is gapped. But the gap decreases with increasing $J$, and at critical value $J={J}_{c}$ the gap becomes zero at the $\mathrm{\ensuremath{\Gamma}}$ point and the ground state becomes instable. Thus, ${J}_{c}$ is the phase transition point where the polaritons are condensed at the $\mathrm{\ensuremath{\Gamma}}$ point to form the delocalized superradiant phase. The results show that the larger detuning between TLS and photon favors the disorder insulator phase, which requires the stronger ${J}_{c}$ to get the long-range order phase. The phase diagram of the delocalized superradiant phase transition has been obtained where there are no Mott lobes since the CRC breaks down the number conservation. The ground state and the excitation spectra of the delocalized superradiant phase are also calculated. It is shown that in the delocalized superradiant state the order parameter is the nonzero ground-state average of the photon annihilation operator. The polaritonic excitation has a finite excitation gap because the CRC breaks down the number conservation but leaves only a discrete symmetry, the parity conservation.

Data-Driven Immersion and Invariance Adaptive Attitude Control for Rigid Bodies With Double-Level State Constraints

This article investigates the attitude control problem of a rigid body subject to attitude and angular rate constraints (double-level state constraints), and inertia uncertainties. A data-driven immersion and invariance (I&I) adaptive control scheme is proposed to tackle this technically challenging problem. As a stepping stone, a novel dynamically scaled I&I adaptive controller is designed to bypass the realizability condition that may not hold in the Lyapunov sense when considering angular rate constraints. Lyapunov stability analysis shows that this controller can enable the attitude errors and angular rates to converge asymptotically to zero for most initial conditions in the accessible space, while strictly obeying double-level state constraints with the help of two judiciously constructed potential functions. After that, to further relax the dependence of parameter convergence on the persistent excitation (PE) condition, the I&I adaptive law is extended to a data-driven counterpart through adding a learning term that is acquired by adopting the regressor filtering in conjunction with the dynamic regressor extension and mixing (DREM) procedure. The extended adaptive controller can not only preserve all the results obtained by the earlier proposed I&I adaptive controller, but also ensure asymptotic parameter convergence under a finite excitation condition much weaker than PE. In addition, benefiting from the DREM method and some special designs, the parameter convergence rates across all the parameter vector components can be flexibly tuned in an explicit way, and moreover, they are independent of the excitation level. Finally, simulation results are given to show the effectiveness of the proposed method.

Integral Concurrent Learning for Admittance Control of a Hybrid Exoskeleton

Hybrid exoskeletons are a technology used by people with neurological injuries (e.g., spinal cord injury) for rehabilitation. Hybrid exoskeletons are a hallmark example of physical human-robot interaction because they combine functional electrical stimulation (FES) with a powered exoskeleton. Due to the physical contact between the human and the robot, these exoskeletons must be well controlled to regulate the physical interaction that occurs. In this paper, the exoskeleton is actuated with an integral concurrent learning (ICL) controller to regulate an admittance error system and the human is actuated (via FES) with a robust controller to regulate a position error system. By separating the human dynamics from the hybrid exoskeleton dynamics via the interaction torque, ICL can address structured uncertainties in the exoskeleton dynamics. A Lyapunov-based stability analysis is conducted to prove that the admittance error system is globally exponentially stable under finite excitation. Moreover, the admittance controller is able to ensure bounded position errors, regardless of the FES (i.e., position) controller. A passivity analysis is leveraged to show that the position error system is output feedback passive with respect to the interaction torque, yet is bounded due to the admittance controller.

Super-short fission mode in fermium isotopes

The so-called super-short fission mode, in which a nucleus divides nearly symmetrically into two unusually energetic fragments, competes favorably with the standard asymmetric fission mode for spontaneous fission of a limited number of nuclei near $^{264}\mathrm{Fm}$ but it quickly fades away at finite excitations. We investigate the energy-dependent competition between those two fission modes for even fermium isotopes from $^{254}\mathrm{Fm}$ to $^{268}\mathrm{Fm}$, using the Metropolis method to simulate the strongly damped fission dynamics being driven by shape- and energy-dependent level densities. The origin of the super-short mode is discussed and its effects on the fragment mass distribution, the total fragment kinetic energy, and the neutron multiplicity are calculated. Generally good agreement with the available data is obtained.

Finite excitation based robust adaptive observer for MIMO LTI systems

SummaryThe article addresses the problem of a robust adaptive observer design for multi‐input multi‐output linear time‐invariant plants subjected to bounded disturbances in the system dynamics and the output relation. An adaptive observer design is proposed based on the finite excitation leading to a switched estimation strategy thus relaxing persistence of excitation (PE) condition. The novel finite persistence excitation (f‐PE) condition introduced in this work is significantly milder than the PE condition in terms of excitation requirement and online verifiability. The switched estimator uses the finite excitation via input signal and ensures uniformly ultimately bounded stability of the estimation error dynamics. A multiple switching strategy, which continuously tracks the information richness (about the unknown parameters), is utilized to reduce the intermediate bounds and is proved to be instrumental in improving the result.

Reinforcement Learning-Based Approximate Optimal Control for Attitude Reorientation Under State Constraints

This article addresses the attitude reorientation problems of rigid bodies under multiple state constraints. A novel reinforcement learning (RL)-based approximate optimal control method is proposed to make the tradeoff between control cost and performance. The novelty lies in that it guarantees constraint handling abilities on attitude forbidden zones and angular velocity limits. To achieve this, barrier functions are employed to encode the constraint information into the cost function. Then, an RL-based learning strategy is developed to approximate the optimal cost function and control policy. A simplified critic-only neural network (NN) is employed to replace the conventional actor–critic structure once adequate data are collected online. This design guarantees the uniform boundedness of reorientation errors and NN weight estimation errors subject to the satisfaction of a finite excitation condition, which is a relaxation compared with the persistent excitation condition that is typically required for this class of problems. More importantly, all underlying state constraints are strictly obeyed during the online learning process. The effectiveness and advantages of the proposed controller are verified by both numerical simulations and experimental tests based on a comprehensive hardware-in-loop testbed.

Effective magnetic Hamiltonian at finite temperatures for rare-earth chalcogenides

Alkali metal rare-earth chalcogenide $ARECh2$ (A=alkali or monovalent metal, RE=rare earth, Ch=O, S, Se, Te), is a large family of quantum spin liquid (QSL) candidates we discovered recently. Unlike $YbMgGaO4$, most members in the family except for the oxide ones, have relatively small crystalline electric-field (CEF) excitation levels, particularly the first ones. This makes the conventional Curie-Weiss analysis at finite temperatures inapplicable and CEF excitations may play an essential role in understanding the low-energy spin physics. Here we considered an effective magnetic Hamiltonian incorporating CEF excitations and spin-spin interactions, to accurately describe thermodynamics in such a system. By taking $NaYbSe2$ as an example, we were able to analyze magnetic susceptibility, magnetization under pulsed high fields and heat capacity in a systematic and comprehensive way. The analysis allows us to produce accurate anisotropic exchange coupling energies and unambiguously determine a crossover temperature ($\sim$25 K in the case of $NaYbSe2$), below which CEF effects fade away and pure spin-spin interactions stand out. We further validated the effective picture by successfully explaining the anomalous temperature dependence of electron spin resonance (ESR) spectral width. The effective scenario in principle can be generalized to other rare-earth spin systems with small CEF excitations.

Dual-color up-conversion luminescence and temperature sensing of novel Na3Y(VO4)2: Yb3+, Er3+ phosphor under multi-wavelength excitation

Multi-color up-conversion luminescence materials with broad emission range are scarce extremely due to the finite excitation wavelength, thin types of activators, and inappropriate emission levels. Yb3+, Er3+ dual-sensitized system is established in the text, green and red dual-color luminescence are successfully achieved in novel Na3Y(VO4)2:Yb3+, Er3+ phosphor. The phosphors show green luminescence under 980 nm excitation and high color purity red luminescence under 1550 nm excitation, a wide range of emission colors can be tuned by changing various concentration of Yb3+. The up-conversion luminescence properties and mechanisms of Yb3+, Er3+ co-doping phosphor under 980 and 1550 nm excitation are discussed in detail. Moreover, the temperature performance of the Na3Y(VO4)2:Yb3+, Er3+ phosphors are investigated based on Boltzmann-type population distribution theory. Temperature dependence of the two green emissions ratio of Er3+ is obtained and the maximum temperature sensing sensitivity is 6.7×10−3 K-1 at 406 K.

Dynamical topological excitations in parafermion chains

Topological excitations in many-body systems are one of the paradigmatic cornerstones of modern condensed matter physics. In particular, parafermions are elusive fractional excitations potentially emerging in fractional quantum Hall-superconductor junctions, and represent one of the major milestones in fractional quantum matter. Here, by using a combination of tensor network and kernel polynomial techniques, we demonstrate the emergence of zero modes and finite energy excitations in many-body parafermion chains. We show the appearance of zero energy modes in the many-body spectral function at the edge of a topological parafermion chain, their relation with the topological degeneracy of the system, and we compare their physics with the Majorana bound states of topological superconductors. We demonstrate the robustness of parafermion topological modes with respect to a variety of perturbations, and we show how weakly coupled parafermion chains give rise to in-gap excitations. Our results exemplify the versatility of tensor network methods for studying dynamical excitations of interacting parafermion chains, and highlight the robustness of topological modes in parafermion models.

Non-vanishing zero-temperature normal density in holographic superfluids

The low energy and finite temperature excitations of a d + 1-dimensional system exhibiting superfluidity are well described by a hydrodynamic model with two fluid flows: a normal flow and a superfluid flow. In the vicinity of a quantum critical point, thermodynamics and transport in the system are expected to be controlled by the critical exponents and by the spectrum of irrelevant deformations away from the quantum critical point. Here, using gauge-gravity duality, we present the low temperature dependence of thermodynamic and charge transport coefficients at first order in the hydrodynamic derivative expansion in terms of the critical exponents. Special attention will be paid to the behavior of the charge density of the normal flow in systems with emergent infrared conformal and Lifshitz symmetries, parameterized by a Lifshitz dynamical exponent z > 1. When 1 ≤ z < d + 2, we recover (z = 1) and extend (z > 1) previous results obtained by relativistic effective field theory techniques. Instead, when z > d + 2, we show that the normal charge density becomes non-vanishing at zero temperature. An extended appendix generalizes these results to systems that violate hyperscaling as well as systems with generalized photon masses. Our results clarify previous work in the holographic literature and have relevance to recent experimental measurements of the superfluid density on cuprate superconductors.

Bethe strings in the dynamical structure factor of the spin-1/2 Heisenberg XXX chain

Recently there has been a renewed interest in the spectra and role in dynamical properties of excited states of the spin-1/2 Heisenberg antiferromagnetic chain in longitudinal magnetic fields associated with Bethe strings. The latter are bound states of elementary magnetic excitations described by Bethe-ansatz complex non-real rapidities. Previous studies on this problem referred to finite-size systems. Here we consider the thermodynamic limit and study it for the isotropic spin-1/2 Heisenberg XXX chain in a longitudinal magnetic field. We confirm that also in that limit the most significant spectral weight contribution from Bethe strings leads to (k,ω)-plane gapped continua in the spectra of the spin dynamical structure factors S+−(k,ω) and Sxx(k,ω)=Syy(k,ω). The contribution of Bethe strings to Szz(k,ω) is found to be small at low spin densities m and to become negligible upon increasing that density above m≈0.317. For S−+(k,ω), that contribution is found to be negligible at finite magnetic field. We derive analytical expressions for the line shapes of S+−(k,ω), Sxx(k,ω)=Syy(k,ω), and Szz(k,ω) valid in the (k,ω)-plane vicinity of singularities located at and just above the gapped lower thresholds of the Bethe-string states's spectra. As a side result and in order to provide an overall physical picture that includes the relative (k,ω)-plane location of all spectra with a significant amount of spectral weight, we revisit the general problem of the line-shape of the transverse and longitudinal spin dynamical structure factors at finite magnetic field and excitation energies in the (k,ω)-plane vicinity of other singularities. This includes those located at and just above the lower thresholds of the spectra that stem from excited states described by only real Bethe-ansatz rapidities.

Nucleon momentum distribution extracted from the experimental scaling function

The connection between the scaling function, directly extracted from the analysis of electron scattering data, and the nuclear spectral function or nuclear momentum density is investigated at depth. The dependence of the scaling function on the two independent variables in the scattering process, the transfer momentum (q) and the scaling variable (y), is taken into account, and the analysis is extended to both, positive and negative y-values, i.e., below and above the center of the quasielastic peak, respectively. Analytical expressions for the derivatives of the scaling function, evaluated at the finite limits of integration dealing with the kinematically allowed region, are connected with the spectral function. Here, contributions corresponding to zero and finite excitation energies are included. The scaling function is described by the Gumbel density distribution, whereas short-range correlations are incorporated in the spectral function by using some simple models. Also different parameterizations for the nucleon momentum distribution, that are compatible with the general properties of the scaling function, have been considered.

Selective generation of ultrasonic guided waves for damage detection in rectangular bars

Ultrasonic guided waves are used in non-destructive testing and structural health monitoring solutions for long-range inspection, in applications ranging from Civil Engineering to Aerospace. In order to ease the inspection process, it is generally preferable to generate a carefully selected single mode. Although single mode Lamb wave generation is not difficult to achieve in infinite plate-like structures, with carefully polarized or sized piezoceramic elements, for example, such selective generation is much more difficult in a rectangular bar. In this article, we consider the propagation along a thin plate of finite rectangular cross section, which corresponds to a rectangular bar. The finite lateral width leads to a greater density of modes compared to an infinite plate. The authors have previously addressed this matter and developed a methodology for the selective generation of modes in the harmonic regime. This article extends this methodology to selective mode generation for finite time excitation, such as bursts. Results are presented for single mode generation of A0,0 and A0,1 in an aluminum bar instrumented with eight piezoelectric transducers. The waveguide modal basis is calculated with the two-dimensional semi-analytical finite element method, and measurements are conducted using a three-dimensional laser-Doppler vibrometer. To illustrate the potential of the method for structural health monitoring purposes, the detection of a defect simulated by a pair of magnets placed at various positions over the bar width is demonstrated.

Topological Bose-Mott insulators in one-dimensional non-Hermitian superlattices

We study the topological properties of Bose-Mott insulators in one-dimensional non-Hermitian superlattices, which may serve as effective Hamiltonians for cold atomic optical systems with either two-body loss or one-body loss. We find that in the strongly repulsive limit, the Mott insulator states of the Bose-Hubbard model with a finite two-body loss under integer fillings are topological insulators characterized by a finite charge gap, nonzero integer Chern numbers, and nontrivial edge modes in a low-energy excitation spectrum under an open boundary condition. The two-body loss suppressed by the strong repulsion results in a stable topological Bose-Mott insulator which has shares features similar to the Hermitian case. However, for the non-Hermitian model related to the one-body loss, we find the non-Hermitian topological Mott insulators are unstable with a finite imaginary excitation gap. Finally, we also discuss the stability of the Mott phase in the presence of two-body loss by solving the Lindblad master equation.

Effects of disorder on magnetotransport oscillations in a two-dimensional electron gas terminated by superconductors

The coupling of superconductivity in a two-dimensional electron gas (2DEG) generates a number of magnetotransport oscillations. For instance, an Aharonov–Bohm-type oscillation at intermediate magnetic fields and an Altshuler–Aronov–Spivak-like oscillation around zero magnetic field appear under the circumstance of the coexistence of Andreev and normal reflections from the interface between the normal-conductor and the superconductor. The presence and the characteristics of such magnetotransport oscillations are investigated in this work by carrying out fully quantum-mechanical simulations. The significant role of the quantum interference is thereby demonstrated. It is also shown how the oscillations are affected by the presence of a potential disorder and finite excitation biases. Shubnikow–de Haas oscillations of the 2DEG are not always suppressed by the disorder under the influence of superconductivity, making their distinction from the Aharonov–Bohm-type oscillation possibly ambiguous.

Inversion method of bubble size distribution based on acoustic nonlinear coefficient measurement**Project supported by the National Natural Science Foundation of China (Grant Nos. 11674074 and 61701133).

Measurements of bubble size distribution require the understanding of the acoustic characteristics of the medium. The bubbles show highly nonlinear properties under finite amplitude acoustic excitation, so the acoustic fields from bubble population are easily observed at the second harmonics as well as at the fundamental frequency, which shows that the nonlinear coefficient increases obviously. The inversion method of bubble size distribution based on nonlinear acoustic effects can peel off the influence of complex environment and obtain the size distribution coefficient information of bubbles more accurately. The previous nonlinear inversion methods of bubble size distribution are mostly based on the nonlinear scattering cross-section characteristics of bubbles. However, the stability of inversion is not high enough. In this paper, we introduce a new acoustic inversion method for bubble size distribution, which is based on the nonlinear coefficients of bubble medium. Compared with other inversion methods based on linear or nonlinear scattering cross section, the inversion method based on nonlinear coefficients of bubble medium proposed in this paper shows good robustness in both simulation and experiment.

Novel Undamped Gapless Plasmon Mode in a Tilted Type-II Dirac Semimetal.

We predict the existence of a novel long-lived gapless plasmon mode in a type-II Dirac semimetal (DSM). This gapless mode arises from the out-of-phase oscillations of the density fluctuations in the electron and the hole pockets of a type-II DSM. It originates beyond a critical wave vector along the direction of the tilt axis, owing to the momentum separation of the electron and hole pockets. A similar out-of-phase plasmon mode arises in other multicomponent charged fluids as well, but generally, it is Landau damped and lies within the particle-hole continuum. In the case of a type-II DSM, the open Fermi surface prohibits low-energy finite momentum single-particle excitations, creating a "gap" in the particle-hole continuum. The gapless plasmon mode lies within this particle-hole continuum gap and, thus, it is protected from Landau damping.

Topological approach to quantum liquid ground states on geometrically frustrated Heisenberg antiferromagnets

We have formulated a twist operator argument for the geometrically frustrated quantum spin systems on the kagome and triangular lattices, thereby extending the application of the Lieb–Schultz–Mattis and Oshikawa–Yamanaka–Affleck theorems to these systems. The equivalent large gauge transformation for the geometrically frustrated lattice differs from that for non-frustrated systems due to the existence of multiple sublattices in the unit cell and non-orthogonal basis vectors. Our study for the S = 1/2 kagome Heisenberg antiferromagnet at zero external magnetic field gives a criterion for the existence of a two-fold degenerate ground state with a finite excitation gap and fractionalized excitations. At finite field, we predict various plateaux at fractional magnetisation, in analogy with integer and fractional quantum Hall states of the primary sequence. These plateaux correspond to gapped quantum liquid ground states with a fixed number of singlets and spinons in the unit cell. A similar analysis for the triangular lattice predicts a single fractional magnetization plateau at 1/3. Our results are in broad agreement with numerical and experimental studies.