Article
Mathematics, Applied
Toon Baeyens, Marnix Van Daele
Summary: This paper presents important improvements and additions to a modern technique developed by Ixaru for solving the time-dependent two-dimensional Schrodinger equation with homogeneous Dirichlet boundary conditions over a rectangular domain. The authors refine and extend the algorithm with important features, focusing particularly on new algorithms for determining eigenvalue indices, orthonormalizing eigenfunctions, selecting automatic step sizes, and accurately computing integrals.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Chemistry, Physical
Eli Pollak, Rocco Martinazzo
Summary: Lower bounds are not commonly used in quantum chemistry computations due to inferior quality when compared to Ritz upper bounds. However, by deriving a new eigenvalue equation and introducing a Cauchy-Schwartz inequality, we have successfully improved lower bounds to be competitive with upper bounds. Further, we have shown that methods such as Lehmann's are identical to our recent self-consistent lower bound theory, offering new perspectives for applications to atoms.
JOURNAL OF CHEMICAL THEORY AND COMPUTATION
(2021)
Article
Mathematics, Applied
Toon Baeyens, Marnix Van Daele
Summary: Strands is a new technique that efficiently and accurately finds numerical solutions for the time-independent two-dimensional Schrodinger equation by approximating the eigenfunction as a linear combination of selected basis functions on each grid line, converting the problem into a small sparse eigenvalue problem.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)
Article
Computer Science, Interdisciplinary Applications
Toon Baeyens, Marnix Van Daele
Summary: This paper presents the basic routines of the C++ program Matslise 3.0, which allows for accurate and efficient computation of eigenvalues and eigenfunctions of one dimensional time-independent Schrodinger problems. Compared to Matslise 2.0, Matslise 3.0 is faster and aims to extend to solving 2D, 3D and time-dependent 1D problems in the future.
COMPUTER PHYSICS COMMUNICATIONS
(2021)
Article
Physics, Multidisciplinary
Mark J. Ablowitz, Joel B. Been, Lincoln D. Carr
Summary: This article presents a new class of integrable fractional nonlinear evolution equations that describe dispersive transport in fractional media. These equations can be constructed from nonlinear integrable equations using a widely generalizable mathematical process and have been applied to fractional extensions of the Korteweg-deVries and nonlinear Schrodinger equations.
PHYSICAL REVIEW LETTERS
(2022)
Article
Engineering, Electrical & Electronic
Lanre Akinyemi, Mustafa Inc, Mostafa M. A. Khater, Hadi Rezazadeh
Summary: In this work, the exact traveling wave solutions of the (2 + 1)-dimensional Chiral nonlinear Schrodinger equation were studied using the generalized auxiliary equation method. The results showed that the aforementioned model has wide applications in quantum field theory, and the suggested technique provides various types of solutions.
OPTICAL AND QUANTUM ELECTRONICS
(2022)
Article
Physics, Applied
Ijaz Ali, Aly R. Seadawy, Syed Tahir Raza Rizvi, Muhammad Younis
Summary: By utilizing the Painleve test, this paper aims to analyze integrability of three famous nonlinear models: unstable nonlinear Schrodinger equation (UNLSE), modified UNLSE (MUNLSE), and (2+1)-dimensional cubic NLSE (CNLSE). The non-appearance of certain singularities such as movable branch points suggests a high probability of complete integrability. If an NLSE passes the P-test, the model can be solved using the inverse scattering transformation (IST).
INTERNATIONAL JOURNAL OF MODERN PHYSICS B
(2021)
Article
Mathematics, Applied
Wencai Liu
Summary: In this paper, three rigidity theorems for discrete periodic Schrodinger operators in any dimension d≥3 are proven.
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS
(2023)
Article
Physics, Multidisciplinary
Georgi Gary Rozenman, Wolfgang P. Schleich, Lev Shemer, Ady Arie
Summary: In this study, we theoretically investigate and experimentally observe the evolution of periodic wave trains using surface gravity water wave packets. For low steepness waves, the waves form a Talbot carpet in the linear regime. By increasing the wave steepness and the corresponding nonlinear response, the waves follow the Akhmediev breather solution, resulting in the disappearance of higher frequency periodic patterns at the fractional Talbot distance.
PHYSICAL REVIEW LETTERS
(2022)
Article
Physics, Fluids & Plasmas
A. Bazzani, M. Giovannozzi, C. E. Montanari, G. Turchetti
Summary: The efficient detection of chaotic behavior in orbits of a complex dynamical system is actively researched. Various indicators have been proposed, and new ones have been developed to enhance the performance of chaos detection through numerical simulations. The challenge lies in predicting chaotic behavior based on limited length of orbits. This paper presents a detailed performance analysis of both past and recent chaos indicators in terms of their predictive power, using a dynamical system characterized by a symplectic Henon-like cubic polynomial map.
Article
Engineering, Mechanical
R. Fuentes, R. Nayek, P. Gardner, N. Dervilis, T. Rogers, K. Worden, E. J. Cross
Summary: This paper presents a new Bayesian approach to equation discovery in nonlinear structural dynamics, combining structure detection and parameter estimation. By using a sparsity-inducing prior and an over-complete dictionary, the method successfully identifies and validates equations for nonlinear dynamic systems. Unlike other sparse learners, this approach utilizes hierarchical Bayesian priors and hyperpriors to achieve accurate results.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2021)
Article
Automation & Control Systems
Han Shu, Xuan Zhang, Na Li, Antonis Papachristodoulou
Summary: This article presents a control reconfiguration approach to improve the performance of two classes of dynamical systems. The approach involves a three-step procedure of reverse-engineering, forward-engineering, and comparing dynamics to redesign and improve the given system. Internet congestion control and distributed proportional-integral control are used as applications to showcase the effectiveness of the proposed approach.
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
(2022)
Article
Engineering, Electrical & Electronic
Chai Wah Wu
Summary: The study shows that a combination of multiple networks can contribute to synchronization even if the coupling in a single network may not be sufficient. The effectiveness of a collection of networks to synchronize the coupled systems depends on the graph topology. If the graph sum is a directed graph whose reversal contains a spanning directed tree, the network synchronizes if the coupling is strong enough.
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS
(2021)
Article
Optics
Wafaa B. Rabie, Aly R. Seadawy, Hamdy M. Ahmed
Summary: In this work, the generalized third-order nonlinear Schrodinger equation is studied using the extended simplest equation method. Various types of solutions such as bright solitons, dark solitons, singular solitons, singular-bright combo solitons, periodic solutions, and other solutions are obtained. Additionally, graphs for some solutions are presented.
Article
Astronomy & Astrophysics
Robin Buehler, Vincent Desjacques
Summary: This work investigates the dynamical friction experienced by circularly moving perturbers in fuzzy dark matter backgrounds. After condensation, fuzzy dark matter can be described by a single wave function satisfying the Schrodinger-Poisson equation. Analytical solutions are derived for both steady-state and finite time perturbation cases, and compared with numerical implementations. The study reveals the diffusive nature of the density wake produced by perturbers in the fuzzy dark matter medium.
Article
Physics, Multidisciplinary
Daniel Leykam, Ekaterina Smolina, Aleksandra Maluckov, Sergej Flach, Daria A. Smirnova
Summary: The modulational instability of nonlinear Bloch waves in topological photonic lattices is influenced by topological band inversions, leading to the creation of topologically nontrivial wave fields. Nonlinear wave mixing plays a role in spreading energy through the entire band and creating wave polarization singularities.
PHYSICAL REVIEW LETTERS
(2021)
Article
Optics
Nana Chang, Sinan Gundogdu, Daniel Leykam, Dimitris G. Angelakis, SuPeng Kou, Sergej Flach, Aleksandra Maluckov
Summary: In the presence of a synthetic magnetic flux, nonlinear Bloch waves in a diamond chain waveguide lattice exhibit sensitivity to wavevector k, leading to bifurcations and instabilities. The instabilities can result in either spontaneous or controlled formation of localized modes, which are immobile due to the synthetic magnetic flux.
Article
Quantum Science & Technology
K. Shulga, I Vakulchyk, Y. Nakamura, S. Flach, M. Fistul
Summary: Numerical evidence is provided for the existence of time molecules (TMs), which exhibit periodic temporal interference in the dynamics of two interacting qubits subject to pi-pulses. The TMs have specific characteristics such as almost zero total polarization, enhanced entanglement entropy, and switching between maximally entangled states. These phenomena are stable with detuned system parameters and can also be observed in dynamics of three interacting qubits.
QUANTUM SCIENCE AND TECHNOLOGY
(2021)
Article
Mathematics, Interdisciplinary Applications
Charalampos Skokos, Enrico Gerlach, Sergej Flach
Summary: We study the evolution of chaos in a one-dimensional nonlinear disordered Klein-Gordon lattice with initially localized energy excitations. We find that chaos is more intense in the central region of the wave packet, where the energy content is higher. The strength of chaotic behavior decreases over time, indicating that chaos is becoming weaker even though the number of chaotic oscillators is constantly growing. In the strong chaos regime, the zones of regular motion at the edges of the wave packet are smaller and the fraction of strongly chaotic oscillators is higher compared to the weak chaos case. Additionally, a significantly larger number of frequencies is excited in the strong chaos regime, even from the beginning stages of the evolution. The fundamental frequencies also shift outside the normal mode frequency band in the selftrapping regime where a large part of the wave packet remains localized.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2022)
Article
Physics, Multidisciplinary
Merab Malishava, Sergej Flach
Summary: This paper proposes a novel framework to characterize the thermalization process of many-body dynamical systems close to integrable limits using the scaling properties of the full Lyapunov spectrum. The study finds that long-range and short-range integrable limits have different effects on the thermalization process.
PHYSICAL REVIEW LETTERS
(2022)
Article
Mathematics, Applied
Merab Malishava, Sergej Flach
Summary: We study the thermalization process of weakly nonintegrable nonlinear unitary lattice dynamics. Two distinct thermalization regimes close to the integrable limits of either linear dynamics or disconnected lattice dynamics are identified. The almost conserved actions correspond to extended observables coupled into a long-range network for weak nonlinearity, while the corresponding local observables are coupled into a short-range network for weakly connected lattices. The evolution of the variance sigma(2) ( T ) of finite time average distributions is computed for extended and local observables. The ergodization time scale T E that marks the onset of thermalization is extracted, and the type of network is determined through the subsequent decay of sigma(2) ( T ). The Lyapunov spectra analysis is used to compare the Lyapunov time T lambda with T E. The spatial properties of the tangent vector are characterized to arrive at a complete classification picture of weakly nonintegrable macroscopic thermalization dynamics.
Article
Materials Science, Multidisciplinary
Sanghoon Lee, Alexei Andreanov, Sergej Flach
Summary: We study the effect of quasiperiodic perturbations on one-dimensional all-bands-flat lattice models. By varying the parameters of the quasiperiodic potentials, we observe localized insulating states and an entire parameter range hosting critical states. The critical-to-insulating transition becomes energy dependent with what we term fractality edges separating localized from critical states.
Article
Materials Science, Multidisciplinary
Arindam Mallick, Alexei Andreanov, Sergej Flach
Summary: We investigate the transport properties of tight-binding single-particle models on simple Bravais lattices in space dimension d=2 under the influence of a DC field and find the complete absence of transport due to the formation of Wannier-Stark flatbands. By introducing interaction among two particles, the localization is partially lifted and metallic two-particle bound states that propagate perpendicular to the DC field are formed.
Article
Optics
Arindam Mallick, Sergej Flach
Summary: This study investigates the quantum corrections to subdiffusion in Anderson localization and observes the saturation of cloud expansion and an intermediate logarithmic expansion regime. The growth rate of the temporal window of this regime is exponential with the localization length.
Article
Optics
Arindam Mallick, Nana Chang, Alexei Andreanov, Sergej Flach
Summary: We consider tight-binding single-particle lattice Hamiltonians with anti-PT symmetry and derive their constraints to generate examples of generalized kagome networks. We also show that the anti-PT symmetry persists in the presence of uniform DC fields and ensures the presence of flatbands in the corresponding irreducible Wannier-Stark band structure.
Article
Materials Science, Multidisciplinary
Carlo Danieli, Alexei Andreanov, Sergej Flach
Summary: Translationally invariant flatband Hamiltonians with interactions lead to a many-body localization transition. The interaction fine-tuning results in local conserved charges originating from the flatband, inducing a transition between ergodic and localized phases.
Article
Materials Science, Multidisciplinary
Ihor Vakulchyk, Carlo Danieli, Alexei Andreanov, Sergej Flach
Summary: Robust ergodicity breaking can occur in interacting many-body systems based on disorder-free many-body localization in any Euclidian dimension. Heat transport can be completely suppressed in one dimension, while in higher dimensions there exists a universal bound on the filling fraction below which heat transport is suppressed. Above this bound, heat transport is affected by bulk disorder and edge scattering, possibly keeping ergodicity breaking above the universal bound.
Article
Physics, Multidisciplinary
Sergej Flach
Summary: The study revisits and explains the Fermi-Pasta-Ulam-Tsingou paradox, addressing the excitation of normal modes in a one-dimensional nonlinear string and quantitatively analyzing the weak excitation of normal modes in the tail using resonances and secular avalanches. A comparison with previous numerical data shows extremely good agreement.
Article
Optics
Yagmur Kati, Mikhail V. Fistul, Alexander Yu. Cherny, Sergej Flach
Summary: We investigate the one-dimensional Gross-Pitaevskii lattice at zero temperature in the absence of correlated disorder. Analytical expressions for the thermodynamic properties of the ground state field are obtained and compared with numerical simulations in both low-density and high-density regimes. Weak excitations above the ground state are analyzed, and the localization properties of Bogoliubov-de Gennes modes are computed. In the long-wavelength limit, these modes delocalize, consistent with the extended nature of the ground state.
Article
Materials Science, Multidisciplinary
Tilen Cadez, Yeongjun Kim, Alexei Andreanov, Sergej Flach
Summary: We study the effect of infinitesimal onsite disorder on d-dimensional all bands flat lattices, finding that localization persists for any choice of local unitaries in d = 1 and d = 2, and the localization length can be maximized for specific values of theta i. However, in d = 3, we identify a nonperturbative metal-insulator transition upon varying all bands' flat manifold angles.
