Shi-Hai Dong

The motivation for this paper is that phonons embedded in proteins in light-harvesting systems appear to exhibit an asymmetric distribution, leading to asymmetric spectral densities and lineshapes. Although the spectral density consisted of a half-Lorentzian and a half-Gaussian distribution (G—L), each with a width that fit the experimental data, was examined thoroughly before, the lognormal distribution function spectral density (also assumes an asymmetric distribution), sufficing to say that its performance is optimum in modeling spectra) has been used without an in-depth analysis. Beyond its asymmetric shape, it proves useful for interpreting spectra and dynamics of pigment-protein complexes. However, a disadvantage of the G—L spectral density is its long tail, which can cause dynamical and spectral errors, albeit often unnoticed. For this reason, Kell et al. [Kell, A.; Feng, X.; Reppert, M.; Jankowiak, R., J. Phy. Chem. B 2013, 117, 7317] have introduced the lognormal distribution function to represent an asymmetric spectral density to resolve the long-tail issue in proteins. However, working with lognormal spectral density in the time domain using cumulant expansion is numerically challenging, making this paper a useful commodity that would be numerically inaccessible without it. The lognormal spectral density is a functional and has branch cuts due to the log function in the Gaussian exponential, resulting in divergence when directly Fourier transformed because the uniform convergence criterion is not met. The Fourier transform of this spectral density, used to obtain the phonon relaxation function in the time domain and, in turn, the electronic transition dipole moment time-correlation function, diverges. This work employs the Lambert W function saddle expansion to second order, thereby circumventing the branch cuts and contour-integration requirements. This allows us to derive a manageable electronic transition dipole moment time-correlation function, which may be utilized to compute linear homogeneous absorption, hole-burned, line-narrowing fluorescence (FLN), and difference line-narrowing fluorescence (DFLN) spectra. Calculation of linear and nonlinear spectra of model and real systems, e.g., Rps. viridis bacterial reaction center and CP29 chlorophyll-protein antenna complex of green from time domain through the electronic transition dipole moment time-correlation function.

We investigate chaotic dynamics in nonlinear Schrödinger equations with higher-order dispersion and cubic–quintic nonlinearities under small dispersive perturbations. Through suitable transformations, the model is reduced to a four-dimensional near-integrable system with a normally hyperbolic invariant manifold. The homoclinic structure is analyzed in a rotating frame, and an extended multiscale Melnikov method is developed to quantify transversal manifold splitting and derive explicit thresholds for Smale horseshoe chaos. Numerical computations of Lyapunov exponents and Poincaré sections confirm the analysis. These results provide explicit geometric criteria for perturbation-induced chaos and extend Melnikov theory beyond classical two-dimensional reductions.

This paper is aimed at investigating a codimension‐one thick brane with cuscuton dynamics within the framework of modified symmetric teleparallel gravity, where is the nonmetricity scalar and is the energy‐momentum tensor trace. The brane is generated by a scalar field with noncanonical dynamics containing a cuscuton term, which modifies the structure of the scalar sector without introducing additional propagating degrees of freedom. By employing the first‐order formalism, analytical solutions for the scalar field, warp factor, scalar potential, and energy density are obtained for different choices of superpotentials, including sine‐Gordon, polynomial, and linear forms. We analyze how the parameters controlling the nonmetricity corrections and the matter coupling affect the internal structure and localization properties of the brane. In addition, the localization of spin‐ fermions is studied through a minimal Yukawa coupling between the fermionic field and the background scalar field. The resulting Schrödinger‐like equations exhibit a supersymmetric structure that guarantees the stability of the fermionic spectrum and allows the localization of the chiral zero mode on the brane. Furthermore, we investigate the spectrum of massive fermionic modes and identify resonant states through the relative probability method. The appearance of these quasi‐localized modes indicates the presence of metastable fermionic excitations associated with the internal structure of the brane.