Linear Coupling Terms Research Articles

Properties of non-equilibrium steady states for the non-linear BGK equation on the torus

We study the non-linear BGK model in one dimension coupled to a spatially varying thermostat. We show existence, local uniqueness, and linear stability of a steady state when the linear coupling term is large compared to the non-linear self-interaction term. This model possesses a non-explicit spatially dependent non-equilibrium steady state. For the existence and the local uniqueness we utilise a fixed point argument, reducing the study of the non-linear model to the linear BGK model, while for the stability we adapt the L^{2} hypocoercivity theory, yielding existence of a spectral gap for the linearised operator around this non-equilibrium steady state.

Alleviating H 0 and S 8 Tensions Simultaneously in K-essence Cosmology

The present work begins by examining the early-Universe inflationary epoch of a special K-essence model, which incorporates a linear coupling term between the scalar field potential and the canonical Lagrangian. For the power-law potential, we both numerically and analytically prove that the inflationary parameters such as the spectral index and tensor-to-scalar ratio are compatible with the recent BICEP/Keck observations. Continuing this work, our analysis based on comparing early-Universe observations with late-Universe measurements indicates that the tension on the Hubble parameter H 0 and the growth of structure parameter S 8 can be alleviated simultaneously. More precisely, compared to the standard ΛCDM model, our model can reduce H 0 tension to roughly 2.2σ, and the S 8 discrepancy diminishes to 0.82σ.

Classification of Lifshitz invariant in multiband superconductors: An application to Leggett modes in the linear response regime in Kagome lattice models

Multiband superconductors are sources of rich physics arising from multiple order parameters, which show unique collective dynamics including Leggett mode as relative phase oscillations. Previously, it has been pointed out that the Leggett mode can be optically excited in the linear response regime, as demonstrated in a one-dimensional model for multiband superconductors [T. Kamatani , ]. Here we identify the linear coupling term in the Ginzburg-Landau free energy to be the so-called Lifshitz invariant, which takes the form of d·(Ψi*∇Ψj−Ψj*∇Ψi), where d is a constant vector and Ψi and Ψj(i≠j) represent superconducting order parameters. We classify all pairs of irreducible representations of order parameters in the crystallographic point groups that allow for the existence of the Lifshitz invariant. We emphasize that the Lifshitz invariant can appear even in systems with inversion symmetry. The results are applied to a model of s-wave superconductors on a Kagome lattice with various bond orders, for which in some cases we confirm that the Leggett mode appears as a resonance peak in a linear optical conductivity spectrum based on microscopic calculations. We discuss a possible experimental observation of the Leggett mode by a linear optical response in multiband superconductors. Published by the American Physical Society 2024

Quantum dissipation with nonlinear environment couplings: Stochastic fields dressed dissipaton equation of motion approach

Accurate and efficient simulation on quantum dissipation with nonlinear environment couplings remains a challenging task nowadays. In this work, we propose to incorporate the stochastic fields, which resolve just the nonlinear environment coupling terms, into the dissipaton-equation-of-motion (DEOM) construction. The stochastic fields are introduced via the Hubbard-Stratonovich transformation. After the transformation, the resulted stochastic-fields-dressed (SFD) total Hamiltonian contains only linear environment coupling terms. On the basis of that, SFD-DEOM can then be constructed. The resultant SFD-DEOM, together with the ensemble average over the stochastic fields, constitutes an exact and nonperturbative approach to quantum dissipation under nonlinear environment couplings. It is also of relatively high efficiency and stability due to the fact that only nonlinear environment coupling terms are dealt with stochastic fields, while linear couplings are still treated as the usual DEOM. Numerical performance and demonstrations are presented with a two-state model system.

Force sensing in a dual-mode optomechanical system with linear-quadratic coupling and modulated photon hopping.

A weak force sensor scheme is presented in an optomechanical system, in which the two cavity modes couple to a mechanical mode with linear and quadratic coupling. Due to introducing time-dependent hopping, the linear and quadratic coupling terms coexist under the rotating-wave approximation in the interaction picture. Compared with the quantum non-demolition measurement (ignoring the quadratic optomechanical coupling), the current scheme can decrease the additional noise to a lower level. Our proposal provides a promising platform for improving the detection of a weak force.

Multimode two-dimensional vibronic spectroscopy. II. Simulating and extracting vibronic coupling parameters from polarization-selective spectra.

Experimental demonstrations of polarization-selection two-dimensional Vibrational-Electronic (2D VE) and 2D Electronic-Vibrational (2D EV) spectroscopies aim to map the magnitudes and spatial orientations of coupled electronic and vibrational coordinates in complex systems. The realization of that goal depends on our ability to connect spectroscopic observables with molecular structural parameters. In this paper, we use a model Hamiltonian consisting of two anharmonically coupled vibrational modes in electronic ground and excited states with linear and bilinear vibronic coupling terms to simulate polarization-selective 2D EV and 2D VE spectra. We discuss the relationships between the linear vibronic coupling and two-dimensional Huang-Rhys parameters and between the bilinear vibronic coupling term and Duschinsky mixing. We develop a description of the vibronic transition dipoles and explore how the Hamiltonian parameters and non-Condon effects impact their amplitudes and orientations. Using simulated polarization-selective 2D EV and 2D VE spectra, we show how 2D peak positions, amplitudes, and anisotropy can be used to measure parameters of the vibronic Hamiltonian and non-Condon effects. This paper, along with the first in the series, provides the reader with a detailed description of reading, simulating, and analyzing multimode, polarization-selective 2D EV and 2D VE spectra with an emphasis on extracting vibronic coupling parameters from complex spectra.

Spatial-Variant SAR Range Cell Migration Correction Using Subaperture Strategy

The coupling between range and azimuth dimensions is the main obstacle for highly squinted synthetic aperture radar (SAR) data focusing. Range walk correction (RWC) processing is effective to remove the linear coupling term, but the residual high order range cell migration (RCM) parts are spatial-variant in both range and azimuth dimensions. In this paper, we propose a precise spatial-variant range cell migration correction (RCMC) method with subaperture processing. The method contains two stages. Firstly, the main component of range-variant RCM is corrected in the coarse RCMC stage. Secondly, data are derived into azimuth subapertures (SAs), an SA-image-domain RCMC is developed by interp correction, where the SA image is obtained using a modified spectrum analysis (SPECAN) algorithm by establishing the relationship between Doppler frequency and residual spatial-variant RCM. In the proposed algorithm, precise compensation of space-variant RCM is implemented by SA processing, which is designed for a better practicality in real-time processing system. Simulated and real measured data experiments are designed to validate the effectiveness of the proposed approach for highly squinted SAR imaging.

The large-time behavior of solutions in the critical Lp framework for compressible viscous and heat-conductive gas flows

The $L^{p}$ theory for non-isentropic Navier-Stokes equations governing compressible viscous and heat-conductive gases is not yet proved completely so far, because the critical regularity cannot control all non linear coupling terms. In this paper, we pose an additional regularity assumption of low frequencies in $\mathbb{R}^d(d\geq 3)$, and then the sharp time-weighted inequality can be established, which leads to the time-decay estimates of global strong solutions in the $L^{p}$ critical Besov spaces. Precisely, we show that if the initial data belong to some Besov space $\dot{B}^{-s_{1}}_{2,\infty}$ with $s_{1}\in (1-\frac{d}{2}, s_0](s_0\triangleq \frac{2d}{p}-\frac{d}{2})$, then the $L^{p}$ norm of the critical global solutions admits the time decay $t^{-\frac{s_{1}}{2}-\frac{d}{2}(\frac{1}{2}-\frac{1}{p})}$ (in particular, $t^{-\frac{d}{2p}}$ if $s_1=s_0$), which coincides with that of heat kernel in the $L^p$ framework. In comparison with \cite{DX2}, the low-frequency regularity $s_1$ can be improved to be \textit{the whole range}.

Anisotropic RKKY interactions mediated by j=32 quasiparticles in half-Heusler topological semimetals

We theoretically explore the RKKY interaction mediated by spin-3/2 quasiparticles in half-Heusler topological semimetals in quasi-two-dimensional geometries. We find that while the Kohn-Luttinger terms gives rise to generalized Heisenberg coupling of the form ${\cal H}_{\rm RKKY} \propto {\sigma}_{1,i} {\cal I}_{ij} {\sigma}_{2,j}$ with a symmetric matrix ${\cal I}_{ij}$, addition of small antisymmetric linear spin-orbit coupling term leads to Dzyaloshinskii-Moriya (DM) coupling with an antisymmetric matrix ${\cal I}'_{ij}$. We demonstrate that besides the oscillatory dependence on the distance, all coupling strengths strongly depend on the relative orientation of the two impurities with respect to the lattice. This yields a strongly anisotropic behavior for ${\cal I}_{ij}$ such that by only rotating one impurity around another at a constant distance, we can see further oscillations of the RKKY couplings. This unprecedented effect is unique to our system which combines spin-orbit coupling with strongly anisotropic Fermi surfaces. We further find that all of the RKKY terms have two common features: a tetragonal warping in their map of spatial variations, and a complex beating pattern. Intriguingly, all these features survive in all dopings and we see them in both electron- and hole-doped cases. In addition, due to the lower dimensionality combined with the effects of different spin-orbit couplings, we see that only one symmetric off-diagonal term, ${\cal I}_{xy}$ and two DM components ${\cal I}'_{xz}$ and ${\cal I}'_{yz}$ are nonvanishing, while the remaining three off-diagonal components are identically zero. This manifests another drastic difference of RKKY interaction in half-Heusler topological semimetals compared to the electronic systems with spin-1/2 effective description.

Approximate analytical description for the nonlinear -symmetric coupled-mode equations

In this paper, we present an approximate analytical description of the solutions dynamics of nonlinear -symmetric coupled-mode equations which can be used to realize the nonlinear -symmetric optical configuration. By the multiple-scale analysis, we construct the asymptotic solutions of the coupled-mode equations. In the -symmetry unbroken region, there is a good agreement between the asymptotic solutions and exact numerical solutions, and the higher-order asymptotic series can yield a higher accuracy. However, in the -symmetry broken region, the asymptotic solutions become invalid quickly as z increases. Instead, we neglect one linear coupling term and obtain the approximate analytical solutions which, to some extent, describe the dynamics in the -symmetry broken region when z ≫ 1. This paper may be helpful for undergraduate and graduate students in physics to understand the nonlinear dynamics of -symmetric systems.

A Particle Module for the PLUTO Code. III. Dust

Abstract Implementation of a new particle module describing the physics of dust grains coupled to a gas via drag forces is the subject of this work. The proposed particle–gas hybrid scheme has been designed to work in Cartesian as well as in cylindrical and spherical geometries. The numerical method relies on a Godunov-type second-order scheme for the fluid and an exponential midpoint rule for dust particles, which overcomes the stiffness introduced by the linear coupling term. Besides being time-reversible and globally second-order accurate in time, the exponential integrator provides energy errors that are always bounded, and it remains stable in the limit of arbitrarily small particle stopping times, yielding the correct asymptotic solution. Such properties make this method preferable to the more widely used semi-implicit or fully implicit schemes at a very modest increase in computational cost. Coupling between particles and grid quantities is achieved through particle deposition and field-weighting techniques borrowed from particle-in-cell simulation methods. In this respect, we derive new weight factors in curvilinear coordinates that are more accurate than traditional volume or area weighting. A comprehensive suite of numerical benchmarks is presented to assess the accuracy and robustness of the algorithm in Cartesian, cylindrical, and spherical coordinates. Particular attention is devoted to the streaming instability, which is analyzed in both local and global disk models. The module is part of the PLUTO code for astrophysical gas dynamics, and it is mainly intended for the numerical modeling of protoplanetary disks in which solid and gas interact via aerodynamic drag.

Restricted normal mode analysis and chaotic response of p-mode intrinsic localized mode

Nonlinearities in arrays of discrete oscillators can cause energy localizations called intrinsic localized modes (ILMs). Two spatial physical manifestations of localization within the array are the ST-mode ILM (a symmetric mode) and the P-mode ILM (an asymmetric mode). The free response and forced response of the asymmetric vibratory P-mode are discussed within this paper, with particular attention given to the linear coupling between the oscillators. The free, undamped response is studied by means of the restricted normal mode approach, which gives the amplitude profile of the P-mode ILM. The initial P-mode ILM amplitude profile, as calculated from the restricted normal mode approach, is capable of creating both forced and unforced persistent ILMs. For the unforced and undamped free response, the P-mode ILM is stable with and without linear coupling, and its response frequency is incommensurate with the response of the surrounding oscillators. It was found that the frequency of oscillation of this mode has a strong relationship to the amplitude of vibration. Moreover, the amplitude profiles generated by the restricted normal mode approach are used to generate initial conditions for the forced, damped case. The existence of the damped and forced P-mode ILM is strongly dependent upon the linear coupling term. It is shown that if linear coupling does not exist, then this mode is persistent but chaotic. To the author’s knowledge, this is the first pinned and persistent chaotic ILM to be observed, which is not predicted from local analysis.

Existence and nonexistence of bound state solutions for Schrödinger systems with linear and nonlinear couplings

We study the Schrödinger systems with linear and nonlinear coupling terms (doubly coupled nonlinear Schrödinger system for short) which arise naturally in nonlinear optics, and in the Hartree–Fock theory for Bose–Einstein condensates, among other physical problems. First, for small linear coupling constant, we get existence of a nontrivial bound state solution to the system via perturbation method, furthermore, we prove each component of the bound state solution is nonnegative by energy estimate. Second, we establish a version of Pohozaev–Nehari identity and prove a nonexistence result for the more general system when the spatial dimension N ≥ 4 .

Signatures of vibronic coupling in two-dimensional electronic-vibrational and vibrational-electronic spectroscopies.

Two-Dimensional Electronic-Vibrational (2D EV) spectroscopy and Two-Dimensional Vibrational-Electronic (2D VE) spectroscopy are new coherent four-wave mixing spectroscopies that utilize both electronically resonant and vibrationally resonant field-matter interactions to elucidate couplings between electronic and vibrational degrees of freedom. A system Hamiltonian is developed here to lay a foundation for interpreting the 2D EV and 2D VE signals that arise from a vibronically coupled molecular system in the condensed phase. A molecular system consisting of one anharmonic vibration and two electronic states is modeled. Equilibrium displacement of the vibrational coordinate and vibrational frequency shifts upon excitation to the first electronic excited state are included in our Hamiltonian through linear and quadratic vibronic coupling terms. We explicitly consider the nuclear dependence of the electronic transition dipole moment and demonstrate that these spectroscopies are sensitive to non-Condon effects. A series of simulations of 2D EV and 2D VE spectra obtained by varying parameters of the system, system-bath, and interaction Hamiltonians demonstrate that one of the following conditions must be met to observe signals: (1) non-zero linear and/or quadratic vibronic coupling in the electronic excited state, (2) vibrational-coordinate dependence of the electronic transition dipole moment, or (3) electronic-state-dependent vibrational dephasing dynamics. We explore how these vibronic interactions are manifested in the positions, amplitudes, and line shapes of the peaks in 2D EV and 2D VE spectroscopies.

Jahn-Teller effect and large-amplitude motion in [formula omitted] studied by high-resolution photoelectron spectroscopy of CH4

This article presents the current status of the knowledge of the rovibronic energy-level structure of CH4+ obtained by high-resolution photoelectron spectroscopy. The results of previous investigations are summarized and extended by new results obtained by double-resonance experiments involving vacuum-ultraviolet and mid-infrared laser radiation. These experiments have led to assignments of the nuclear-spin symmetry of 303 rovibrational levels of CH4+ with up to 3575cm−1 of internal excitation. A two-dimensional model of the pseudorotational motion of CH4+ is also presented, with which the positions and vibronic symmetry of the low-lying vibronic levels of CH4+ can be predicted. The model maps the F⊗(f⊕e) Jahn-Teller problem for the e and f2 modes corresponding to the CH bending motion onto a sphere, including the effects of both linear and quadratic Jahn-Teller coupling terms. The pseudorotation eigenstates are obtained by solving the two-dimensional Schrödinger equation using a basis of spherical harmonics.

Tunable Mode Coupling in Nanocontact Spin-Torque Oscillators

Recent experiments on spin torque oscillators have revealed interactions between multiple magnetodynamic modes, including mode-coexistence, mode-hopping, and temperature-driven cross-over between modes. Initial multimode theory has indicated that a linear coupling between several dominant modes, arising from the interaction of the subdynamic system with a magnon bath, plays an essential role in the generation of various multimode behaviors, such as mode hopping and mode coexistence. In this work, we derive a set of rate equations to describe the dynamics of coupled magnetodynamic modes in a nano-contact spin torque oscillator. Expressions for both linear and nonlinear coupling terms are obtained, which allow us to analyze the dependence of the coupled dynamic behaviors of modes on external experimental conditions as well as intrinsic magnetic properties. For a minimal two-mode system, we further map the energy and phase difference of the two modes onto a two-dimensional phase space, and demonstrate in the phase portraits, how the manifolds of periodic orbits and fixed points vary with external magnetic field as well as with temperature.

Soliton solutions for coupled nonlinear Schrödinger equations with linear self and cross coupling terms

In this paper, coupled nonlinear Schrödinger equations with linear self and cross coupling terms are investigated analytically. We obtain the exact soliton solutions which exist a periodic-wave background for this system, including one-, two- and N-soliton solutions. We find the period of oscillation for periodic wave background is related to the coupling terms. In addition, by adjusting other parameters we can get many types of mixed soliton solutions on the plane-wave background. Moreover, the interactions of the two and three solitons have been discussed through a detailed analysis for the asymptotic behavior and it displays that they are all elastic.

Escape of a vector matter–wave soliton from a parabolic trap

We show that a vector matter–wave soliton in a Bose–Einstein condensate (BEC) loaded into an optical lattice can escape from a trap formed by a parabolic potential, resembling a Hawking emission. The particle–antiparticle pair is emulated by a low-amplitude bright–bright soliton in a two-component BEC with effective masses of opposite signs. It is shown that the parabolic potential leads to a spatial separation of BEC components. One component with chemical potential in a semi-infinite gap exerts periodical oscillations, while the other BEC component, with negative effective mass, escapes from the trap. The mechanism of atom transfer from one BEC component to another by spatially periodic linear coupling term is also discussed.

Persistent quasiplanar nematic texture: Its properties and topological defects.

In the so-called quasiplanar texture of a nematic layer confined between parallel plates with homeotropic anchoring conditions, the director field rotates by π between limit surfaces so that field lines have the shape of a dowsing Y-shaped wooden tool. The orientation of the director field at midheight of the layer is arbitrary for symmetry reasons and is thus very sensitive to perturbations. We point out that contrary to accepted ideas the quasiplanar texture can be preserved infinitely in spite of its metastability with respect to the homogeneous homeotropic texture. We propose to call such a long-lived version of the quasiplanar texture the dowser texture. We demonstrate both experimentally and theoretically that in samples of variable thickness, the director field is sensitive to the gradient of the sample thickness through a linear coupling term. As a result, it has a tendency to follow the direction of the thickness gradient. Because of its sensitivity to perturbations we propose to call the midplane director field the dowser field and its tendency to follow the thickness gradient cuneitropism. Under effect of the gradient field, the dowser field obeys the sine-Gordon equation and exhibits domain walls that correspond to the well-known solitonic solutions of the sine-Gordon model.

High-Frequency Dynamic Overshoot in Linear and Nonlinear Periodic Media

We study the transient responses of linear and nonlinear semi-infinite periodic media on linear elastic foundations under suddenly applied, high-frequency harmonic excitations. We show that “dynamic overshoot” phenomena are realized whereby, due to the high-rate of application of the high-frequency excitations, coherent traveling responses are propagating to the far fields of these media; and this, despite the fact that the high frequencies of the suddenly applied excitations lie well within the stop bands of these systems. For the case of a linear one-dimensional (1D) spring-mass lattice, a leading-order asymptotic approximation in the high frequency limit of the suddenly applied harmonic excitation shows that the transient dynamic overshoot is expressed in terms of the Green's function at its free end. Then, a two-dimensional (2D) strongly nonlinear granular network is considered, composed of two semi-infinite, ordered homogeneous granular lattices mounted on linear elastic foundations and coupled by weak linear coupling terms. A high-frequency harmonic excitation is applied to one of the granular lattices—designated as the “excited lattice”, with the other lattice designated as the “absorbing” one. The resulting dynamic overshoot phenomenon consists of a “pure” traveling breather, i.e., of a single propagating oscillatory wavepacket with a localized envelope, resulting from the balance of discreteness, dispersion, and strong nonlinearity. The pure breather is asymptotically studied by a complexification/averaging technique, showing nearly complete but reversible energy exchanges between the excited and absorbing lattices as the breather propagates to the far field. Verification of the analytical approximations with direct numerical simulations is performed.