Weak Coupling Region Research Articles

Non trivial solutions for a system of coupled Ginzburg-Landau equations

This article addresses both the existence and properties of non-trivial solutions for a system of coupled Ginzburg-Landau equations derived from nematic-superconducting models. Its main goal is to provide a thorough numerical description of the region in the parameter space containing solutions that behave as a mixed (non trivial) nematic-superconducting state along with a rigorous proof for the existence of this region. More precisely, the rigorous approach establishes that the parameter space is divided into two regions with qualitatively different properties, according to the magnitude of the coupling constant: for small values (weak coupling), there is a unique non-trivial solution, and for large values (strong coupling), only trivial solutions exist. In addition, using a shooting method-based numerical approach, the profiles for the nematic and superconducting components of the non trivial solution are given, together with an algorithm computing the transition values representing the boundaries for the weak coupling region: from superconducting to mixed, and from mixed to nematic. Finally, numerical evidence is given for the existence of a third region, related to neither a small nor a strong coupling parameter (medium coupling) for which multiple non trivial solutions exist.

Ultrahigh Energy Storage Performance of BiFeO3-BaTiO3 Flexible Film Capacitor with High-Temperature Stability via Defect Design.

Nanoengineering polar oxide films have attracted great attention in energy storage due to their high energy density. However, most of them are deposited on thick and rigid substrates, which is not conducive to the integration of capacitors and applications in flexible electronics. Here, an alternative strategy using van der Waals epitaxial oxide dielectrics on ultra-thin flexible mica substrates is developed and increased the disorder within the system through high laser flux. The introduction of defects can efficiently weaken or destroy the long-range ferroelectric ordering, ultimately leading to the emergence of a large numbers of weak-coupling regions. Such polarization configuration ensures fast polarization response and significantly improves energy storage characteristics. A flexible BiFeO3-BaTiO3 (BF-BT) capacitor exhibits a total energy density of 43.5 J cm-3 and an efficiency of 66.7% and maintains good energy storage performance over a wide temperature range (20-200 °C) and under large bending deformation (bending radii ≈ 2mm). This study provides a feasible approach to improve the energy storage characteristics of dielectric oxide films and paves the way for their practical application in high-energy density capacitors.

Preparation of fidelity-robust quantum entanglement with error-detected blocks based on quantum-dot spins inside optical microcavities

Effective schemes are proposed for the generation of bipartite Bell states and theoretically scaling up to arbitrary multiparticle Greenberger–Horne–Zeilinger, cluster, and W states among quantum-dot (QD) spins. They are realized based on the interaction between an single incident photon and single QD spin. Errors from system nonuniformity and defective photon scattering are transformed into detectable photon losses. In the event of a failed experiment, the system allows for the reinjection of a single photon and the reinitiation of the quantum circuit, until a successful outcome is achieved. This loss-prediction and experiment-repeatability approach ensures that the schemes are implemented with uniform and robust fidelity. Compared with the previous methods, these schemes significantly simplify experimental procedures and analysis processes. Furthermore, upon successful execution of the experiment, the use of single-photon detector can faithfully differentiate between various types of entangled states, depending on the initial states of the QD spins. An analysis of the feasibility of the schemes under current experimental parameters suggests high efficiency even in the weak coupling region.

Analysis of Interference Effect in Double Optomechanically Induced Transparency System

We propose a scheme to investigate the interference properties of a double optomechanically induced transparency system, which involves two charged nanomechanical resonators, coupled via Coulomb interaction. The results show that the opening of transparency windows is caused by a destructive interference effect only in the weak optical coupling region. For strong optical coupling, normal mode splitting dominates the transparency phenomenon. In the intermediate region, both destructive interference and normal mode splitting contribute to the transparency windows. When the Coulomb coupling is much weaker than the optical coupling, the Coulomb interaction strength linearly determines the distance between the two transparency windows, and has nearly no influence on the destructive interference effect. Otherwise, the system will work in a nonlinear region.

Autonomous Wireless Power Transfer System with Constant Output Voltage in a Wide Load Range

In this paper, an autonomous wireless power transfer (WPT) system with constant voltage output in a wide load range is presented. Here, combining self-oscillating control and phase-shift control, a new implementation of the autonomous WPT system is proposed. The proposed autonomous WPT system operates using a self-oscillating control method in the strong coupling region, which can automatically maintain the constant output voltage. In the weak coupling region, a phase-shift control method with a fixed frequency and a variable duty cycle is implemented, and a control strategy based on output voltage estimation is proposed to obtain the constant output voltage. In addition, according to the operating frequency characteristic of the proposed autonomous WPT system, a corresponding coupling region judgment method is presented to guarantee the realization of switching between the two control methods. An experimental prototype with a 24 V output voltage is constructed to validate the practicability of the proposed method. The experimental results show the proposed autonomous WPT system can obtain constant output voltage in a wide load range.

On the renormalization of non-polynomial field theories

A class of scalar models with non-polynomial interaction, which naturally admits an analytical resummation of the series of tadpole diagrams is studied in perturbation theory. In particular, we focus on a model containing only one renormalizable coupling that appear as a multiplicative coefficient of the squared field. A renormalization group analysis of the Green functions of the model shows that these are only approximated solutions of the flow equations, with errors proportional to powers of the coupling, therefore smaller in the region of weak coupling. The final output of the perturbative analysis is that the renormalized model is non-interacting with finite mass and vanishing vertices or, in an effective theory limited by an ultraviolet cut-off, the vertices are suppressed by powers of the inverse cut-off. The relation with some non-polynomial interactions derived long ago, as solutions of the linearized functional renormalization group flow equations, is also discussed.

Autonomous Pulse Frequency Modulation for Wireless Battery Charging With Zero-Voltage Switching

This paper proposes an autonomous pulse frequency modulation (APFM) scheme for wireless battery charging in which the self-excited oscillating (SEO) wireless power transfer (WPT) system can offer output power regulation with reliable zero-voltage switching (ZVS). The key is to utilize the self-excited oscillation feature to adjust the WPT operating frequency autonomously so as to deliver more power in the strong coupling region than the traditional forced-oscillating (FO) WPT system while the transmission efficiency can maintain at a high level. In the weak coupling region, the system becomes equivalent to the FO-WPT system. The pulse frequency modulation enables the system to adjust the output power by changing its duty ratio. Besides, reliable ZVS is achieved by extracting and processing the current signal at the primary side. Both theoretical analysis and experimental verification are provided to support the feasibility of the proposed APFM for SEO-WPT system.

Exact Treatment of the Infinite Square Well in One Dimension with λδ^' (x) Potential

Abstract: This work considered the infinite square well in one dimension with a contact potential. The Dirac delta derivative function potential λδ^' where λ is a coupling constant was used to represent the contact potential. Using Green’s function technique, exact implicit expressions of the energy eigenvalues and eigenfunctions were obtained. The energy eigenvalues were expressed using a transcendental equation. The energy eigenfunctions satisfy the Schrödinger equation and the infinite square well boundary conditions. Also, the eigenfunctions and their first derivative were shown to be discontinuous. The values of these discontinuity jumps agreed with the required conditions for a self-adjoint extension Hamiltonian. In the weak coupling region, the energy eigenvalues are close to that of the even parity solution before adding the contact potential. The energy eigenvalues in the strong coupling regime reveal the energy eigenvalues of the odd parity solution. Keywords: Point interactions, Infinite square well, Green’s function technique. PACS numbers: 03.65.-w, 03.65.Db, 03.65.Ge

Contribution of Processes in SN Electrodes to the Transport Properties of SN-N-NS Josephson Junctions.

In this paper, we present a theoretical study of electronic transport in planar Josephson Superconductor-Normal Metal-Superconductor (SN-N-NS) bridges with arbitrary transparency of the SN interfaces. We formulate and solve the two-dimensional problem of finding the spatial distribution of the supercurrent in the SN electrodes. This allows us to determine the scale of the weak coupling region in the SN-N-NS bridges, i.e., to describe this structure as a serial connection between the Josephson contact and the linear inductance of the current-carrying electrodes. We show that the presence of a two-dimensional spatial current distribution in the SN electrodes leads to a modification of the current-phase relation and the critical current magnitude of the bridges. In particular, the critical current decreases as the overlap area of the SN parts of the electrodes decreases. We show that this is accompanied by a transformation of the SN-N-NS structure from an SNS-type weak link to a double-barrier SINIS contact. In addition, we find the range of interface transparency in order to optimise device performance. The features we have discovered should have a significant impact on the operation of small-scale superconducting electronic devices, and should be taken into account in their design.

Level pinning of anti-PT-symmetric circuits for efficient wireless power transfer.

Wireless power transfer (WPT) technology based on magnetic resonance (a basic physical phenomenon) can directly transfer energy from the source to the load without wires and other physical contacts, and has been successfully applied to implantable medical devices, electric vehicles, robotic arms and other fields. However, due to the frequency splitting of near-field coupling, the resonant WPT system has some unique limitations, such as poor transmission stability and low efficiency. Here, we propose anti-resonance with level pinning for high-performance WPT. By introducing the anti-resonance mode into the basic WPT platform, we uncover the competition between dissipative coupling and coherent coupling to achieve novel level pinning, and construct an effective anti-parity-time (anti-PT)-symmetric non-Hermitian system that is superior to previous PT-symmetric WPT schemes. On the one hand, the eigenvalue of the anti-PT-symmetric system at resonance frequency is always pure real in both strong and weak coupling regions, and can be used to overcome the transmission efficiency decrease caused by weak coupling, as brought about by, for example, a large size ratio of the transmitter to receiver, or a long transmission distance. On the other hand, due to the level pinning effect of the two kinds of coupling mechanisms, the working frequency of the system is guaranteed to be locked, so frequency tracking is not required when the position and size of the receiver change. Even if the system deviates from the matching condition, an efficient WPT can be realized, thereby demonstrating the robustness of the level pinning. The experimental results show that when the size ratio of the transmitter coil to the receiver coil is 4.29 (which is in the weak coupling region), the transfer efficiency of the anti-PT-symmetric system is nearly 4.3 (3.2) times higher than that of the PT-symmetric system when the matching conditions are satisfied (deviated). With the miniaturization and integration of devices in mind, a synthetic anti-PT-symmetric system is used to realize a robust WPT. Anti-PT-symmetric WPT technology based on the synthetic dimension not only provides a good research platform for the study of abundant non-Hermitian physics, but also provides a means of going beyond traditional near-field applications with resonance mechanisms, such as resonance imaging, wireless sensing and photonic routing.

Robustness of Wireless Power Transfer Systems with Parity-Time Symmetry and Asymmetry

Recently, wireless power transfer (WPT) technology has attracted much attention and shown rapid development. However, a fundamental challenge emerges in practical applications: how to achieve robust power transfer against the variation of operating conditions, such as the fluctuation of transfer distance, as well as the relative orientation of resonant coils. In this article, we theoretically propose and experimentally demonstrate that the robustness of a parity-time (PT) asymmetric system with unbalanced gain-loss working in a weak coupling region can be improved significantly, compared with that of a PT-symmetric system with balanced gain-loss working in a strong coupling region under the premise that the system works at a fixed optimal frequency. A pure real mode known as bound state in the continuum (BIC) in the weak coupling region of the PT-asymmetric system is adopted to ensure the high efficiency and stability of the WPT and break the limitations of balanced gain-loss of the PT-symmetric system. The better robustness performance originates from the orthogonal state with a pure real eigenmode embedded in the weak coupling region. Further experiments also verify that the PT-asymmetric system can achieve higher efficiency than that of the PT-symmetric system. In addition, we discuss the performance of the WPT system based on the theories of coupled mode theory (CMT) and circuit theory (CT); the BIC in the framework of CMT and a perfect impedance matching condition in the framework of CT for efficient power transfer are consistent. We also conducted power experimental verification of 30 watts, and found the efficiency between the coils can reach over 90% in dynamic scenarios, which meets expectations. The presented framework extends the field of non-Hermitian physics, bridges the gap between the non-ideal PT-symmetric system and a practical engineering application, and introduces a novel WPT mechanism for flexible application scenarios. Our results could provide instructive significance for practical applications of the WPT system in the long term.

Fano-resonant propagating plexcitons and Rabi-splitting local plexcitons of bilayer borophene in TERS

Optical nanocavity provides an opportunity to deeply study the light–matter interaction with notable findings such as Rabi splitting in strong coupling and Fano resonance in weak coupling. Here, we theocratically explore the plexcitons of a bilayer (BL) borophene synthesized on an Ag (1 1 1) film in a tip-enhanced Raman scattering (TERS) system, where the BL borophene is located in the nanocavity between the tip and substrate, stimulated by recent experimental synthesis [Liu et al., Nat. Mater. 21, 35 (2022)]. In the strong-coupling region, the negative real part of the dielectric function of the BL borophene manifests; the BL borophene is of plasmonic properties resulting in Rabi splitting of plexcitons with 310 meV. In the weak-coupling region, the spectra show typical asymmetry with a sharp change between a dip and a peak (Fano resonance). A balanced gain and loss facilitates single-mode lasing in the parity-time symmetry-broken regime, where single-mode lasing with a very narrow half-width is of ultrahigh enhancement factor up to 108. Fano-resonant propagating plexcitons are observed in the dip of Fano resonance, which is extremely sensitive to the excitation wavelength. Our results not only deepen the physical understanding of the plasmon–exciton coupling interaction in the TERS system but also provide a way to manipulate the light–matter interaction in the TERS system.

The effect of critical coupling constants on superconductivity enhancement

In this study, we propose a phenomenological model to extend McMillan's results on a coupling strength equal to 2. We investigate possible strategies to enhance superconductivity by tuning the phonon frequency, carrier number, or pressure. In particular, we show that the critical coupling constants corresponding to the phonon frequency, carrier number, or pressure determine whether the variation of the critical temperature is positive or negative. These observations explain the contrasting behavior between weak and strong coupling superconductors and are consistent with experimental observations. We also demonstrate the dome observed in the carrier number effect and pressure effect. Additionally, these critical coupling constants systematically separate superconductivity into three regions: weak, intermediate, and strong coupling. We find that the enhancement strategies for weak and strong coupling regions are opposite, but both inevitably bring superconductivity into the intermediate coupling region. Finally, we propose general zigzag methods for intermediate coupling superconductors to further enhance the critical temperature.

Spontaneous crystallization of chiral active colloidal particles

The crystallization dynamics of chiral active colloids are explored numerically. It is found that chiral colloids with large angular velocity could be localized by self-trapping, which promotes the formation of hexagonal crystal structures. The competition between chirality and coupling strength leads to the transition between liquid and solid regimes. Comparing to the achiral particles, the transition points shift towards the weak coupling region greatly with the increasing degree of chirality. The hexagonal structure seems more tenacious and more difficult to melt. Therefore, the solid–liquid coexistence region shrinks in the phase diagram. In the low rotational speed region, active particles swap neighbors rapidly, the system becomes globally ordered but undergoes a nonnegligible diffusion, leading to the structural ordering occurrence before dynamical freezing.

Local multiplet formation around a single vacancy in graphene: An effective Anderson model analysis based on the block-Lanczos DMRG method

To better understand the electronic structure of a single vacancy in graphene, we study the ground state property of an effective Anderson model, consisting of three dangling $sp^2$ orbitals of the surrounding carbon atoms around the vacancy and the $\pi$ orbitals of carbon atoms that form the honeycomb lattice with a single vacancy. Employing the block-Lanczos density-matrix renormalization group method, we show that there are two phases in the relevant parameter space, i.e., a nonmagnetic phase in the weak coupling region and a free magnetic moment phase in the realistic parameter region. The systematic analysis finds that, in the free magnetic moment phase, local multiplets of the doubly degenerate irreducible representation of the $\mathcal{C}_3$ point group with spin 1 become dominant in the ground state, and approximately half of this local spin 1 is screened by electrons in the surrounding $\pi$ orbitals, indicating the emergence of the residual spin-1/2 free magnetic moment. Furthermore, we find that the emergence of the free magnetic moment is robust against carrier doping, which is in sharp contrast to the case of graphene with an adatom, thus explaining the qualitative difference observed experimentally in these two classes of systems. We also find the enhancement of the spin correlation function between $\pi$ electrons around the vacancy and those in the conduction band away from the vacancy in the undoped case, as compared to that in the doped case, while the spin correlation function between the $\sigma$ electrons in the $sp^2$ dangling orbitals around the vacancy and the $\pi$ electrons in the conduction band remains large in both undoped and doped cases. Our calculations thus support qualitatively the previous experiment that suggests the emergence of free magnetic moment with two distinct origins.

Exact WKB and the quantum Seiberg-Witten curve for 4d N = 2 pure SU(3) Yang-Mills. Abelianization

We investigate the exact WKB method for the quantum Seiberg-Witten curve of 4d N = 2 pure SU(3) Yang-Mills in the language of abelianization. The relevant differential equation is a third-order equation on ℂℙ1 with two irregular singularities. We employ the exact WKB method to study the solutions to such a third-order equation and the associated Stokes phenomena. We also investigate the exact quantization condition for a certain spectral problem. Moreover, exact WKB analysis leads us to consider new Darboux coordinates on a moduli space of flat SL(3,ℂ)-connections. In particular, in the weak coupling region we encounter coordinates of the higher length-twist type generalizing Fenchel-Nielsen coordinates. The Darboux coordinates are conjectured to admit asymptotic expansions given by the formal quantum periods series and we perform numerical analysis supporting this conjecture.

A Robust Parity-Time-Symmetric WPT System With Extended Constant-Power Range for Cordless Kitchen Appliances

Cordless kitchen appliances powered by wireless power transfer (WPT) technology can operate without the clutter of cords, making them safer and easier to clean. In order to allow cordless kitchen appliances to be placed more freely, this article proposed a parity-time (PT) symmetric WPT system with stable output power in the whole coupling range. Here, a new implementation of a PT-symmetric circuit using a combination of self-oscillating methods and pulsewidth modulation (SO-PWM) is presented. The self-oscillating mode is activated in the strong coupling region, which guarantees a constant output power and constant transfer efficiency against the coupling coefficient variation. In the weak coupling region, the PWM mode with a fixed frequency and a variable duty cycle is adopted, and a control strategy based on primary-side-only parameters is presented to obtain stable power transmission. Besides, a corresponding coupling-region detection method based on the reflected resistance is proposed to ensure smooth switching between SO mode and PWM mode. The advantage is that the stable output power can be maintained in the whole coupling region without any extra dc–dc converter and dual-side communication requirements, while maintaining the same transfer efficiency as the standard PT-symmetric WPT system. A 500-W experimental prototype is built to verify the theoretical analysis. The results show that with a transfer efficiency of over 91.6%, the misalignment tolerance can be increased by 172%.

Nonreciprocal two-photon transmission and statistics in a chiral waveguide QED system

We study the nonreciprocal properties of transmitted photons in a chiral waveguide quantum electrodynamics (QED) system, including single- and two-photon transmissions and second-order correlations. For the single-photon transmission, the nonreciprocity is induced by the effects of chiral coupling and atomic dissipation in the weak coupling region. It vanishes in the strong coupling regime when the effect of atomic dissipation becomes ignorable. In the case of two-photon transmission, there exist two ways of going through the emitter: independently as plane waves and formation of bound state. Besides the nonreciprocal behavior of plane waves, the bound state that differs in two directions also alters transmission probabilities. In addition, the second-order correlation of transmitted photons depends on the interference between plane wave and bound state. The destructive interference leads to the strong antibunching in the weak coupling region, while the effective formation of bound state leads to the strong bunching in the intermediate coupling region. However, the negligible interactions for left-propagating photons hardly change the statistics of the input coherent state.

Three-dimensional charge density wave observed by angle-resolved photoemission spectroscopy in 1T −VSe2

We apply high-resolution angle-resolved photoemission spectroscopy to explore the layered transition-metal dichalcogenide $1T\ensuremath{-}{\mathrm{VSe}}_{2}$ with various photon energies to investigate the three-dimensional (3D) charge-density wave (CDW) transition. Here, we provide quite comprehensive evidence of 3D Fermi surface nesting in $1T\ensuremath{-}{\mathrm{VSe}}_{2}$. The observed Fermi surface (FS) largely overlaps with the in-plane nesting vector reported by the electron-diffraction results. Comparing the CDW gaps below and above ${T}_{c}$, we find that the gaps open along the ellipsoidal FS around the $\overline{M}$ point, in agreement with the in-plane nesting vector. With varying the photon energy, a warping of FS and the nesting condition along ${k}_{z}$ are observed. We further observe the gap variation along the ${k}_{z}$ direction consistent with the out-of-plane nesting conditions. Although it was believed to be a layered two-dimensional material, the satisfaction of the 3D nesting condition of the FS and the variation of gap distribution suggest a 3D character of CDW in $1T\ensuremath{-}{\mathrm{VSe}}_{2}$. Meanwhile, a larger value of $2\mathrm{\ensuremath{\Delta}}/{k}_{B}{T}_{c}$ = 14.76 suggests CDW in $1T\ensuremath{-}{\mathrm{VSe}}_{2}$ beyond the weak-coupling region, the nesting condition and the gap correspondence implies a combined effort in the formation of CDW in this material.

Color confinement and Bose-Einstein condensation

We propose a unified description of two important phenomena: color confinement in large-N gauge theory, and Bose-Einstein condensation (BEC). We focus on the confinement/deconfinement transition characterized by the increase of the entropy from N0 to N2, which persists in the weak coupling region. Indistinguishability associated with the symmetry group — SU(N) or O(N) in gauge theory, and SN permutations in the system of identical bosons — is crucial for the formation of the condensed (confined) phase. We relate standard criteria, based on off-diagonal long range order (ODLRO) for BEC and the Polyakov loop for gauge theory. The constant offset of the distribution of the phases of the Polyakov loop corresponds to ODLRO, and gives the order parameter for the partially-(de)confined phase at finite coupling. We demonstrate this explicitly for several quantum mechanical systems (i.e., theories at small or zero spatial volume) at weak coupling, and argue that this mechanism extends to large volume and/or strong coupling. This viewpoint may have implications for confinement at finite N, and for quantum gravity via gauge/gravity duality.