Article
Physics, Multidisciplinary
Etienne Granet
Summary: In the Lieb-Liniger model, explicit expressions for dynamical correlations of the field and density operators are derived within an arbitrary eigenstate with a small particle density Dc > 0, and at the leading order of an expansion in D. This expansion is obtained by expressing correlation functions as sums over form factors when decomposed into partial fractions.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2021)
Article
Optics
Jae-Gyun Baak, Uwe R. Fischer
Summary: This study investigates the classical and quantum Fisher information of the interaction coupling in the Lieb-Liniger model, with a focus on the dependence on system size and interaction strength.
Article
Physics, Multidisciplinary
Isabelle Bouchoule, Jerome Dubail, Lea Dubois, Dimitri M. Gangardt
Summary: Motivated by recent experiments, this study investigates the Lieb-Liniger gas initially prepared in an out-of-equilibrium state that is Gaussian in terms of the phonons. The gas relaxes to a stationary state at very long times whose phonon population is different from the initial one. Using the Bethe-ansatz mapping and bosonization techniques, the stationary state of the gas after relaxation is characterized and its phonon population distribution is computed. The results are applied to the case of an excited coherent state for a single phonon mode and compared to exact results obtained in the hard-core limit.
PHYSICAL REVIEW LETTERS
(2023)
Article
Physics, Fluids & Plasmas
Samy Mailoud, Fausto Borgonovi, Felix M. Izrailev
Summary: The study focuses on the spectrum statistics of integrable quantum systems through the analysis of the Lieb-Liniger model, revealing the dependence of energy level properties on model parameters. It is found that the Poisson distribution of spacing between nearest-neighbor energies only occurs for a specific set of energy levels with fixed total momentum, under certain interaction strengths and high energy conditions.
Article
Mathematics, Applied
Matthew Rosenzweig
Summary: This article investigates the Lieb-Liniger model for N bosons interacting pairwise on the line via the delta potential. By assuming suitable asymptotic factorization of the initial wave functions and convergence of the microscopic energy per particle, the authors prove the convergence of the time-dependent reduced density matrices to pure states.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
(2022)
Article
Physics, Multidisciplinary
Run-Tian Li, Song Cheng, Yang-Yang Chen, Xi-Wen Guan
Summary: This paper precisely calculates the dynamical structure factor (DSF) of the Lieb-Liniger model with arbitrary interaction strength using the form factor approach based on algebraic Bethe ansatz theory. The DSF for a system as large as 2000 particles can accurately depict its line-shape and reveals the power-law singularity near spectral thresholds. The results are compared with other methods, confirming the validity of the obtained results.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2023)
Article
Physics, Multidisciplinary
Etienne Granet, Fabian Essler
Summary: In this study, we investigated the time evolution of local observables in the repulsive Lieb-Liniger model after an interaction quench using the Quench Action approach. By deriving a 1/c expansion for various one and two-point functions, we confirmed the typicality assumptions underlying the Quench Action approach. Our results provide a non-trivial confirmation of the typicality assumptions and contribute to our understanding of quantum systems.
Article
Physics, Multidisciplinary
Eldad Bettelheim
Summary: We use the Bethe ansatz technique and functional approach to exactly compute the matrix element of the field operator in the Lieb-Liniger model in the thermodynamic limit for any coupling constant c, and compare our results to known semiclassics at the limit c -> 0.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2021)
Article
Mathematics
Hironori Michihisa
Summary: In this paper, we obtain higher order asymptotic expansions of solutions to the linear damped wave equation Cauchy problem, where the order of expansions depends on the spatial dimension, presenting new hyperbolic effects.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Mathematics, Applied
Yali Zhang, Shuhuang Xiang, Desong Kong
Summary: By utilizing Hilb type formula and generalized van der Corput type Lemmas, this paper establishes optimal decay rates for expansion coefficients of functions expressed as Laguerre polynomial series. It further derives convergence rates for spectral orthogonal projections and provides new estimates on errors in Gauss-Laguerre quadrature. Extensive numerical experiments are conducted to validate the optimality and accuracy of these theoretical findings.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2023)
Article
Mathematics, Applied
Lenka Mihokovic
Summary: On the set M of mean functions, the symmetric mean of M with respect to mean M0 can be defined in several ways. The first one is related to the group structure on M, and the second one is defined through Gauss' functional equation. In this paper, the authors provide an answer to the open question about the matching of these two different mappings called symmetries on the set of mean functions, formulated by B. Farhi. Using techniques of asymptotic expansions, the authors discuss properties of such symmetries and discover a new class of means that interpolates between harmonic, geometric, and arithmetic mean.
Article
Mathematics, Applied
Shuhuang Xiang
Summary: By studying the relationship between Jacobi polynomials and Bessel functions, optimal convergence rates on Jacobi, Gegenbauer, and Chebyshev orthogonal projections can be derived, with higher values of parameters leading to higher convergence rates. For interior singularities, the convergence order is independent of specific parameters.
SIAM JOURNAL ON NUMERICAL ANALYSIS
(2021)
Article
Engineering, Multidisciplinary
Pulkit Kumar, Moumita Mahanty, Abhishek Kumar Singh, Amares Chattopadhyay
Summary: This study analyzes the propagation characteristics of shear waves in a spherical layered structure consisting of isotropic sandy material and a concentric layer of transversely isotropic sandy material. The dispersion relation is obtained using analytical treatment and numerical computations are used to illustrate the influence of different parameters on dispersion curves. The impact of anisotropy is exposed through a comparative study with isotropic materials.
APPLIED MATHEMATICAL MODELLING
(2022)
Article
Mathematics, Applied
Qing Han, Lin Zhang
Summary: In this study, we investigate the linear wave equation in Bondi-Sachs coordinates for an asymptotically flat Lorentz metric. We focus on the null-timelike boundary problem and obtain spacetime estimates for r > r(0), deriving an asymptotic expansion of ru as r approaches infinity.
SCIENCE CHINA-MATHEMATICS
(2021)
Article
Mathematics, Applied
Maryam Al-Towailb, Zeinab S. I. Mansour
Summary: This paper examines the characteristics of functions represented by convergent q-Lidstone series expansion. We provide the necessary and sufficient conditions for the entire function f(z) to have such an expansion, ensuring uniform convergence on compact sets.
Article
Multidisciplinary Sciences
Shiqi Xia, Dimitrios Kaltsas, Daohong Song, Ioannis Komis, Jingjun Xu, Alexander Szameit, Hrvoje Buljan, Konstantinos G. Makris, Zhigang Chen
Summary: The study established a nonlinear non-Hermitian topological platform for active tuning of PT symmetry and topological states, revealing the interaction between sensitivity close to exceptional points and the robustness of non-Hermitian topological states. The research provides opportunities for unconventional light manipulation and device applications through single-channel control of global PT symmetry and topology via local nonlinearity.
Article
Optics
Xiuying Liu, Frane Lunic, Daohong Song, Zhixuan Dai, Shiqi Xia, Liqin Tang, Jingjun Xu, Zhigang Chen, Hrvoje Buljan
Summary: Pseudospins arising from valley degrees of freedom in photonic structures have become a powerful tool for manipulating the flow of light, allowing for wavepacket self-rotation induced by Berry phase and resulting in Zitterbewegung oscillations. The frequency of Zitterbewegung is proportional to the gap size, while the helicity of self-rotation is valley-dependent, correlated with the Berry curvature. These findings provide new insights into the Zitterbewegung phenomenon from a topological perspective and have potential applications in other platforms such as 2D Dirac materials and ultracold atoms.
LASER & PHOTONICS REVIEWS
(2021)
Article
Optics
Zhichan Hu, Domenico Bongiovanni, Dario Jukic, Ema Jajtic, Shiqi Xia, Daohong Song, Jingjun Xu, Roberto Morandotti, Hrvoje Buljan, Zhigang Chen
Summary: This study uncovered the interplay of nonlinearity, higher-order topology, and BICs in a photonic platform, where topological corner states that are also BICs were observed. The authors further demonstrated the nonlinear coupling of these states with edge modes under the action of self-focusing and defocusing nonlinearities. Theoretical calculations showed that a topological BIC can be actively tuned by nonlinearity in such a photonic HOTI, with potential applications in emerging topology-driven devices.
LIGHT-SCIENCE & APPLICATIONS
(2021)
News Item
Physics, Multidisciplinary
Hrvoje Buljan, Dario Jukic, Zhigang Chen
Article
Physics, Multidisciplinary
Domenico Bongiovanni, Dario Jukic, Zhichan Hu, Frane Lunic, Yi Hu, Daohong Song, Roberto Morandotti, Zhigang Chen, Hrvoje Buljan
Summary: In the evolving Su-Schrieffer-Heeger lattices made of interacting soliton arrays, dynamical topological phase transitions occur entirely driven by nonlinearity. The transitions involve a periodic shift from topologically trivial-to-nontrivial phases, with crossovers from topologically nontrivial-to-trivial regimes. The signature of the phase transition is the closing and reopening of the gap, where extended states become localized topological edge states through decoupling from the lattice bulk.
PHYSICAL REVIEW LETTERS
(2021)
Article
Physics, Multidisciplinary
Ziteng Wang, Xiangdong Wang, Zhichan Hu, Domenico Bongiovanni, Dario Jukic, Liqin Tang, Daohong Song, Roberto Morandotti, Zhigang Chen, Hrvoje Buljan
Summary: Some topological boundary states are protected by sub-symmetry, even if the full symmetry and topological invariant are destroyed. By introducing a weaker sub-symmetry requirement, researchers find that the nature of boundary state protection is more complex than previously believed. Experimental demonstrations in photonic lattices show the sub-symmetry protection of topological states and the resolution of debates on the higher-order topological nature of corner states in breathing kagome lattices. These findings have implications beyond photonics and can be applied to explore symmetry-protected topological phases in different physical contexts.
Article
Optics
Yahui Zhang, Domenico Bongiovanni, Ziteng Wang, Xiangdong Wang, Shiqi Xia, Zhichan Hu, Daohong Song, Dario Jukic, Jingjun Xu, Roberto Morandotti, Hrvoje Buljan, Zhigang Chen
Summary: The orbital degrees of freedom play a pivotal role in understanding fundamental phenomena in solid-state materials as well as exotic quantum states of matter. High orbitals in higher-order topological insulators (HOTIs) have not been realized, but p-orbital corner states have been demonstrated in a photonic HOTI, unveiling their underlying topological invariant and symmetry protection.
Article
Physics, Multidisciplinary
Ioannis Komis, Dimitrios Kaltsas, Shiqi Xia, Hrvoje Buljan, Zhigang Chen, Konstantinos G. Makris
Summary: This article studies the properties of non-Hermitian topological systems under different perturbations. By studying the non-Hermitian Su-Schrieffer-Heeger lattice, it is found that the topological modes around the underlying third-order exceptional point are robust against chiral perturbations but sensitive to diagonal perturbations.
PHYSICAL REVIEW RESEARCH
(2022)
Article
Optics
Bruno Klajn, Silvije Domazet, Dario Jukic, Hrvoje Buljan
Summary: An exactly solvable model for synthetic anyons carrying non-Abelian flux is proposed in this study. The system, which corresponds to a two-dimensional electron gas in a magnetic field with specific spin interaction, displays twofold degeneracy in the ground state subspace. Perturbing the system with identical solenoids carrying a non-Abelian gauge potential reveals the dynamics of ground state behaving as anyons with non-Abelian flux. This system serves as a middle ground between ordinary Abelian anyons and fully non-Abelian anyons.
Article
Optics
Karlo Lelas, Ozana Celan, David Prelogovic, Hrvoje Buljan, Dario Jukic
Summary: In this study, we investigated the modulation instability of systems obeying the nonlinear Schrödinger equation under the influence of an external homogeneous synthetic magnetic field. The choice of gauge used to describe the magnetic field affects the stability regions in momentum space and the time evolution in real space. Despite appearances, the gauge invariance is not actually broken, as evolving the system from identical initial conditions in different gauges is equivalent to suddenly turning on the synthetic magnetic field at t = 0, resulting in different effects on the wave packet.
