Fixed Energy Level Research Articles

Te Cluster Engineering for Tunable Optical Response

AbstractThe construction of active materials with controllable optical response facilitates the development of advanced photonic devices. However, the achievement of robust active materials with wide wavelength tunable and broadband emission remains a great challenge, mainly due to the fixed energy levels of conventional active dopants and limited inhomogeneous broadening in common hosts. Here, the study proposes that the cluster in the mesoscopic scale of ≈1 nm may break this bottleneck issue and demonstrate a strategy for the management of photon emission by engineering the cluster evolution. The amorphous glass as the host to tailor the characteristic configuration of Te clusters from 1 to 2 nm by control of the topological structures in glass is employed. Impressively, it presents a distinct optical response totally different from the conventional active centers and this enables to construct of active photonic glass with continuously tunable emission from 888 to 1064 nm. More importantly, Te cluster‐activated photonic glass fibers are fabricated and the broadband on‐off gain is successfully achieved. Furthermore, benefiting from the unique tunable emission, novel near‐infrared devices are constructed and their application in imaging is demonstrated. The approach of cluster engineering mediated tunable optical response is believed to bring new opportunities for developing advanced photonic devices.

Programmable Heisenberg interactions between Floquet qubits

The trade-off between robustness and tunability is a central challenge in the pursuit of quantum simulation and fault-tolerant quantum computation. In particular, quantum architectures are often designed to achieve high coherence at the expense of tunability. Many current qubit designs have fixed energy levels and consequently limited types of controllable interactions. Here by adiabatically transforming fixed-frequency superconducting circuits into modifiable Floquet qubits, we demonstrate an XXZ Heisenberg interaction with fully adjustable anisotropy. This interaction model can act as the primitive for an expressive set of quantum operations, but is also the basis for quantum simulations of spin systems. To illustrate the robustness and versatility of our Floquet protocol, we tailor the Heisenberg Hamiltonian and implement two-qubit iSWAP, CZ and SWAP gates with good estimated fidelities. In addition, we implement a Heisenberg interaction between higher energy levels and employ it to construct a three-qubit CCZ gate, also with a competitive fidelity. Our protocol applies to multiple fixed-frequency high-coherence platforms, providing a collection of interactions for high-performance quantum information processing. It also establishes the potential of the Floquet framework as a tool for exploring quantum electrodynamics and optimal control.

Conformal transformations and integrable mechanical billiards

In this article we explain that several integrable mechanical billiards in the plane are connected via conformal transformations. We first remark that the free billiards in the plane are conformal equivalent to infinitely many billiard systems defined in central force problems on a particular fixed energy level. We then explain that the classical Hooke-Kepler correspondence can be carried over to a correspondence between integrable Hooke-Kepler billiards. As part of the conclusion we show that any focused conic section gives rise to integrable Kepler billiards, which continues previous works of Panov [26] and Gallavotti-Jauslin [11]. We discuss several generalizations of integrable Stark billiards. We also show that any finite combinations of confocal conic sections give rise to integrable billiard systems of Euler's two-center problems.

CuNCs assisted by carbon dots to construct Z-type heterostructures: Ultra-high photocatalytic performance and peroxidase-like activity

Copper nanoclusters (CuNCs), as novel energy level tunable photocatalysts, have been utilized to combine with various conventional inorganic catalysts to improve catalytic performance. However, conventional photocatalysts generally have fixed energy levels, which are not conducive to bi-directional adjustment of the composite catalyst energy level structure. In this work, CuNCs protected by 3-mercaptopropionic acid (CuNCs@3-MPA) and energy-level controllable carbon dots (CDs) are combined to prepare intelligent photocatalytic materials through electrostatic self-assembly strategy, i.e., CuNCs@3-MPA/CDs. The self-assembled CuNCs@3-MPA have a large specific surface area, and the Z-type heterostructure can be constructed by introducing energy-matched CDs, which can achieve the effective separation of photogenerated electron-hole pairs and directional generation of ·O2− at the same time, enabling the degradation of 98.5 % Methyl Orange (MO, 20 mg/L) in 7 min. The catalytic rate constant is increased to 0.501 min−1, which is equivalent to 3.6 times that of CuNCs@3-MPA alone. Since CuNCs@3-MPA/CDs with rich Cu(I) can perform Fenton-like reaction to catalyze the production of ·OH from H2O2, we use TMB and H2O2 as substrates to probe its peroxidase-like activity. The Km is 0.18 mM when the substrate is TMB, which is lower than that of horseradish peroxidase (HRP) (Km = 0.434 mM), indicating that the affinity between CuNCs@3-MPA/CDs and TMB is higher than that of HRP, which has a high peroxidase-like activity.

Integrable magnetic geodesic flows on 2-surfaces *

We study the magnetic geodesic flows on 2-surfaces having an additional first integral which is independent of the Hamiltonian at a fixed energy level. The following two cases are considered: when there exists a quadratic in momenta integral, and also the case of a rational in momenta integral with a linear numerator and denominator. In both cases certain semi-Hamiltonian systems of partial differential equations (PDEs) appear. In this paper we construct exact solutions (generally speaking, local ones) to these systems: in the first case via the generalized hodograph method, in the second case via the Legendre transformation and the method of separation of variables.

Oesophageal Probe Evaluation in Radiofrequency Ablation of Atrial Fibrillation (OPERA): results from a prospective randomized trial.

The aim of the study was to determine the incidence of oesophageal lesions after radiofrequency ablation (RFA) of atrial fibrillation (AF) with or without the use of oesophageal temperature probes. Two hundred patients were prospectively randomized into two groups: the OPERA+ group underwent RFA using oesophageal probes (SensiTherm™); the OPERA- group received RFA using fixed energy levels of 25 W at the posterior wall without an oesophageal probe. All patients underwent post-interventional endoscopy and Holter-electrocardiogram after 6 months. (Clinical.Trials.gov: NCT03246594). One hundred patients were randomized in OPERA+ and 100 patients in OPERA-. The drop-out rate was 10%. In total, 18/180 (10%) patients developed endoscopically diagnosed oesophageal lesions (EDEL). There was no difference between the groups with 10/90 (11%) EDEL in OPERA+ vs. 8/90 (9%) in OPERA- (P = 0.62). Despite the higher power delivered at the posterior wall in OPERA+ [28 ± 4 vs. 25 ± 2 W (P = 0.001)], the average EDEL size was equal [5.7 ± 2.6 vs. 4.5 ± 1.7 mm (P = 0.38)]. The peak temperature did not correlate with EDEL size. During follow-up, no patient died. Only one patient in OPERA- required a specific therapy for treatment of the lesion. Cumulative AF recurrence after 6 (3-13) months was 28/87 (32%) vs. 34/88 (39%), P = 0.541. This first randomized study demonstrates that intraoesophageal temperature monitoring using the SensiTherm™ probe does not affect the probability of developing EDEL. The peak temperature measured by the thermoprobe seems not to correlate with the incidence of EDEL. Empiric energy reduction at the posterior wall did not affect the efficacy of the procedure.

On a quantum Hamiltonian in a unitary magnetic field with axisymmetric potential

We study a magnetic Schrödinger Hamiltonian, with axisymmetric potential in any dimension. The associated magnetic field is unitary and non-constant. The problem reduces to a 1D family of singular Sturm–Liouville operators on the half-line indexed by a quantum number. We study the associated band functions. They have finite limits that are the Landau levels. These limits play the role of thresholds in the spectrum of the Hamiltonian. We provide an asymptotic expansion of the band functions at infinity. Each Landau level concerns an infinity of band functions, and each energy level is intersected by an infinity of band functions. We show that among the band functions that intersect a fixed energy level, the derivative can be arbitrary small. We apply this result to prove that even if they are localized in energy away from the thresholds, quantum states possess a bulk component. A similar result is also true in classical mechanics.

Mechanical oscillations frozen on discrete levels by two optical driving fields

It is intuitively imagined that the energy of a classical object always takes continues values and can hardly be confined to discrete ones like the energy levels of microscopic systems. Here, we demonstrate that such classical energy levels against intuition can be created through a previously unknown synchronization process for nonlinearly coupled macroscopic oscillators driven by two equally strong fields. Given the properly matched frequencies of the two drive fields, the amplitude and phase of an oscillator will be frozen on one of a series of determined trajectories like energy levels, and the phenomenon exists for whatever drive intensity beyond a threshold. Interestingly, the oscillator's motion can be highly sensitive to its initial condition but, unlike the aperiodicity in chaotic motion, it will nonetheless end up on such fixed energy levels. Upon reaching the stability, however, the oscillations on the energy levels are robust against noisy perturbation.

Dynamical structures in a low-thrust, multi-body model with applications to trajectory design

A key challenge in low-thrust trajectory design is generating preliminary solutions that simultaneously detail the evolution of the spacecraft position and velocity vectors, as well as the thrust history. To address this difficulty, dynamical structures within a combined low-thrust circular restricted 3-body problem (CR3BP-LT) are explored as candidate solutions to seed initial low-thrust trajectory designs. Furthermore, insights from dynamical systems theory are leveraged to inform the design process. In the combined model, the addition of a low-thrust force modifies the locations and stability of the equilibria, resulting in flow configurations that differ from the natural behavior in the CR3BP. Families of periodic solutions in the vicinity of the equilibria supply novel geometries that may be employed in initial designs. Additionally, the application of simplifying assumptions yields a conservative, autonomous system with properties that supply useful insights. “Forbidden regions” at fixed energy levels bound low-thrust motion in such a simplified system, and analytical equations are available to guide the navigation through energy space. Periodic orbits and their associated manifolds also possess useful properties and act similarly to separatrices in the simplified regime. These structures and insights are employed to design transit and capture trajectories in the Earth-Moon CR3BP-LT.

Experiences, Choice and Well-Being: An Economics of Psychological Energy

This paper proposes an economic model of psychological energy used toward the production of experiences. A review of ideas at the nexus of economics and psychology, and how they lead to the thesis of this paper, is presented. A simple mathematical economic model is developed, with two main uses of psychological energy toward well-being. These are the generation of impressions (inward experiences that are sense-like) and expression (outward experiences that are action-like). Choosing is understood as investing energy to change the probabilities of an outcome. The model optimizes energy use between intensity of impressions and capacity for expression. For a fixed energy level, as experiential intensity increases resources are substituted out of decision making and implementation, leading to choices of lower utility. If the material losses are substantial during an experience, the share of psychological energy used to modify impressions will increase, and away from influencing seemingly random external outcomes. Over multiple periods, this generates a feedback loop where the person feels increasingly disempowered, and thus less concerned about making better choices. This feedback loop can be stopped by an external entity providing sufficient resources for the person to experience greater expression.

Engineering Efficient Photon Upconversion in Semiconductor Heterostructures.

Photon upconversion is a photophysical process in which two low-energy photons are converted into one high-energy photon. Photon upconversion has broad appeal for a range of applications from biomedical imaging and targeted drug release to solar energy harvesting. Current upconversion nanosystems, including lanthanide-doped nanocrystals and triplet-triplet annihilation molecules, have achieved upconversion quantum yields on the order of 10-30%. However, the performance of these materials is hampered by inherently narrow absorption cross sections and fixed energy levels originating in atomic, ionic, or molecular states. Semiconductors, on the other hand, have inherently wide absorption cross sections. Moreover, recent advances enable the synthesis of colloidal semiconductor nanoparticles with complex heterostructures that can control band alignments and tune optical properties. We synthesize and characterize a three-component heterostructure that successfully upconverts photons under continuous-wave illumination and solar-relevant photon fluxes. The heterostructure is composed of two cadmium selenide quantum dots (QDs), an absorber and emitter, spatially separated by a cadmium sulfide nanorod (NR). We demonstrate that the principles of semiconductor heterostructure engineering can be applied to engineer improved upconversion efficiency. We first eliminate electron trap states near the surface of the absorbing QD and then tailor the band gap of the NR such that charge carriers are funneled to the emitting QD. When combined, these two changes result in a 100-fold improvement in photon upconversion performance.

Bulk universality for generalized Wigner matrices with few moments

In this paper we consider $$N \times N$$ real generalized Wigner matrices whose entries are only assumed to have finite $$(2 + \varepsilon )$$ th moment for some fixed, but arbitrarily small, $$\varepsilon > 0$$ . We show that the Stieltjes transforms $$m_N (z)$$ of these matrices satisfy a weak local semicircle law on the nearly smallest possible scale, when $$\eta = \mathfrak {I}(z)$$ is almost of order $$N^{-1}$$ . As a consequence, we establish bulk universality for local spectral statistics of these matrices at fixed energy levels, both in terms of eigenvalue gap distributions and correlation functions, meaning that these statistics converge to those of the Gaussian orthogonal ensemble in the large N limit.

Deformed supersymmetric quantum mechanics with spin variables

We quantize the one-particle model of the SU(2|1) supersymmetric multiparticle mechanics with the additional semi-dynamical spin degrees of freedom. We find the relevant energy spectrum and the full set of physical states as functions of the mass-dimension deformation parameter m and SU(2) spin qin left({mathrm{mathbb{Z}}}_{>0,}1/2+{mathrm{mathbb{Z}}}_{ge 0}right) . It is found that the states at the fixed energy level form irreducible multiplets of the supergroup SU(2|1). Also, the hidden superconformal symmetry OSp(4|2) of the model is revealed in the classical and quantum cases. We calculate the OSp(4|2) Casimir operators and demonstrate that the full set of the physical states belonging to different energy levels at fixed q are unified into an irreducible OSp(4|2) multiplet.

Topology, singularities and integrability in Hamiltonian systems with two degrees of freedom

We consider the problem of the existence of first integrals that are polynomial in momenta for Hamiltonian systems with two degrees of freedom on a fixed energy level (conditional Birkhoff integrals). It is assumed that the potential has several singular points. We show that in the presence of conditional polynomial integrals, the sum of degrees of the singularities does not exceed twice the Euler characteristic of the configuration space. The proof is based on introducing a complex structure on the configuration space and estimating the degree of the divisor corresponding to the leading term of the integral with respect to the momentum. We also prove that the topological entropy is positive under certain conditions.

There is more to quantum interferometry than entanglement

Entanglement has long stood as one of the characteristic features of quantum mechanics, yet recent developments have emphasized the importance of quantumness beyond entanglement for quantum foundations and technologies. We demonstrate that entanglement cannot entirely capture the worst-case sensitivity in quantum interferometry, when quantum probes are used to estimate the phase imprinted by a Hamiltonian, with fixed energy levels but variable eigenbasis, acting on one arm of an interferometer. This is shown by defining a bipartite entanglement monotone tailored to this interferometric setting and proving that it never exceeds the so-called interferometric power, a quantity which relies on more general quantum correlations beyond entanglement and captures the relevant resource. We then prove that the interferometric power can never increase when local commutativity-preserving operations are applied to qubit probes, an important step to validate such a quantity as a genuine quantum correlations monotone. These findings are accompanied by a room-temperature nuclear magnetic resonance experimental investigation, in which two-qubit states with extremal (maximal and minimal) interferometric power at fixed entanglement are produced and characterized.

The Foucault Pendulum (with a Twist)

A Foucault pendulum is supposed to precess in a direction opposite to the earth's rotation, but nonlinear terms in the equations of motion can also produce precession. The goal of this paper is to study the motion of a nonlinear, spherical pendulum on a rotating planet. It turns out that the problem on a fixed energy level reduces to the study of a monotone twist map of an annulus. For certain values of the parameters, this leads to existence proofs for orbits which do not precess or else precess in the wrong direction. In fact, there will be nonprecessing periodic solutions which return to their initial state after swinging back and forth just once. For pendulums of modest size, these nonprecessing periodic solutions can be very nearly planar.

The Speed of Light in a Novel Gravitational Environment

In this paper, a review of the experiments, developments and ideas which have been presented on this topic together with its natural extension to the description of gravity, the ultimate dominating mystery of the universe, was taken out. A parallel mechanism was proposed between the emission of light and of neutrino by quantum leaps of electrons between the fixed energy levels of atomic orbits. The analysis of the neutron-proton mix of existing nuclides provides a rule for the calculation of the neutrino flux from matter and suggests both a medium for the transmission of light and a solution to the problem of gravitation.

Computed tomographic beam-hardening artefacts: mathematical characterization and analysis.

This paper presents a mathematical characterization and analysis of beam-hardening artefacts in X-ray computed tomography (CT). In the field of dental and medical radiography, metal artefact reduction in CT is becoming increasingly important as artificial prostheses and metallic implants become more widespread in ageing populations. Metal artefacts are mainly caused by the beam-hardening of polychromatic X-ray photon beams, which causes mismatch between the actual sinogram data and the data model being the Radon transform of the unknown attenuation distribution in the CT reconstruction algorithm. We investigate the beam-hardening factor through a mathematical analysis of the discrepancy between the data and the Radon transform of the attenuation distribution at a fixed energy level. Separation of cupping artefacts from beam-hardening artefacts allows causes and effects of streaking artefacts to be analysed. Various computer simulations and experiments are performed to support our mathematical analysis.

Global minimizers for Tonelli Lagrangians on the 2-torus

We study action-minimizing orbits in Tonelli Lagrangian systems on the 2-torus on fixed energy levels above Mañé's strict critical value. Our work generalizes the results of Morse, Hedlund and Bangert on minimal geodesics in Riemannian 2-tori. The techniques in the proofs involve classical variational ones, as well as the theories of Mather, Mañé and Fathi, which allow the step from reversible to non-reversible dynamics.

Invariant tori and topological entropy in Tonelli Lagrangian systems on the 2-torus

We study the Euler–Lagrange flow of a Tonelli Lagrangian on the 2-torus$\mathbb{T}^{2}$at a fixed energy level${\mathcal{E}}\subset T\mathbb{T}^{2}$strictly above Mañé’s strict critical value. We prove that, if for some rational direction${\it\zeta}\in S^{1}$there is no invariant graph${\mathcal{T}}\subset {\mathcal{E}}$over$\mathbb{T}^{2}$for the Euler–Lagrange flow with the property that all orbits on${\mathcal{T}}$have an asymptotic direction equal to${\it\zeta}$, then there are chaotic dynamics in${\mathcal{E}}$. This implies that, if the topological entropy of the Euler–Lagrange flow in${\mathcal{E}}$vanishes, then in${\mathcal{E}}$there are invariant graphs for all asymptotic directions${\it\zeta}\in S^{1}$and integrable-like behavior on a large scale.