Article
Mathematics, Applied
Alexandre R. Nieto, Jesus M. Seoane, Miguel A. F. Sanjuan
Summary: This study reveals a noise-activated escape phenomenon in closed Hamiltonian systems, transforming bounded motion into chaotic scattering. By analyzing average escape time, probability basins, and escape time distribution, it is found that characteristics of scattering in closed systems differ from open systems, with noise-enhanced trapping playing a minor role in escapes and a transition in average escape time evolution with increased noise. This research provides numerical evidence of the destruction of the stickiness of KAM islands as a key factor in changing scaling laws, unlocking the possibility of modeling chaotic scattering problems in noisy closed Hamiltonian systems.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2022)
Article
Physics, Multidisciplinary
Ville J. Harkonen, Ivan A. Gonoskov
Summary: A new method for diagonalizing quadratic Hamiltonians is introduced by changing the frame of reference through a unitary transformation. The paper presents a general approach for diagonalizing any quadratic Hamiltonian and provides detailed derivations for several simplest special cases.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2022)
Article
Astronomy & Astrophysics
Francisco D. Mazzitelli, Leonardo G. Trombetta
Summary: This paper investigates the impact of stochastic fluctuations of the gravitational coupling G on the evolution of binary systems. Working at the elementary level in the Newtonian limit, the focus is mainly on laser ranging. The study demonstrates that observational data can be used to constrain the stochastic fluctuations and reanalyzes previous results on the implications of G fluctuations on cosmological models.
Article
Mathematics, Interdisciplinary Applications
Wadia Faid Hassan Al-shameri, Mohamed El Sayed
Summary: This research article presents a modified algorithm for generating a fractal pattern using the numerical iteration method, which demonstrates the dynamic behavior of the iterations. A nonstandard convergence test was applied to the resulting displayable fractal pattern.
FRACTAL AND FRACTIONAL
(2022)
Article
Multidisciplinary Sciences
Francisco Bento Lustosa, Samuel Colin, Santiago E. Perez Bergliaffa
Summary: Numerical simulations in the context of the de Broglie-Bohm pilot-wave theory show that initial states out of quantum equilibrium usually relax over time to the expected distribution, but the relaxation can be influenced by parameters such as coupling strength. The system tends towards equilibrium, but the speed of relaxation depends on various factors, particularly the interaction strength.
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2021)
Article
Multidisciplinary Sciences
Francisco Bento Lustosa, Nelson Pinto-Neto, Antony Valentini
Summary: In the context of de Broglie-Bohm pilot-wave theory, violations of the Born rule can describe non-equilibrium distributions. We investigate the influence of interactions on quantum relaxation in a system of 1D coupled harmonic oscillators. Our numerical simulations show that interactions can delay or prevent complete relaxation for certain initial states. We also discuss the potential relevance of this effect in cosmological scenarios and the possibility of detecting non-equilibrium in certain models.
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2023)
Article
Physics, Multidisciplinary
Nicolas Martzel
Summary: We first introduce the Zwanzig-Kawasaki version of the generalized Langevin equation and show that the commonly used term for the Markovian approximation of the dissipation is vanishing, necessitating the use of the next-order term. Independently, we provide a comprehensive description of complex coarse-grained molecules and derive their dynamics, which enriches considerably the dynamics at the coarse-grained level and could serve as a foundation for developing more holistic and accurate numerical models for complex molecular systems. This advancement opens up new possibilities for understanding and predicting the behavior of such systems in various scientific and engineering applications.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2023)
Article
Mathematics, Applied
Hongyu Cheng, Shimin Wang
Summary: This paper focuses on quasi-periodically forced nonlinear harmonic oscillators and proves the existence of real analytic response solutions for a given class of frequencies, based on a modified KAM theorem.
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS
(2021)
Article
Chemistry, Multidisciplinary
Monica Sanchez-Barquilla, Johannes Feist
Summary: This article discusses methods for handling the dynamics of open quantum systems, truncating chains to manageable lengths by introducing losses while still maintaining accuracy, and demonstrates that extending the chain mapping can replicate any environment.
Article
Astronomy & Astrophysics
Le-Chen Qu, Jing Chen, Yu-Xiao Liu
Summary: We investigate the circuit complexity and Loschmidt echo for the (inverted) harmonic oscillators using a perturbative approach. Analytical results for the Lyapunov exponent and scrambling time of the inverted harmonic oscillators are derived. Our findings show that the circuit complexity and Loschmidt echo exhibit qualitatively similar behaviors, particularly with respect to the consistent Lyapunov exponent.
Article
Physics, Multidisciplinary
Anupam Kundu
Summary: We study transport in a one-dimensional lattice system with conserved quantities of 'volume' and energy. By considering a slowly evolving local equilibrium state, we estimate the correction to the local equilibrium distribution caused by space-time correlations of local currents. In the continuum limit, we derive drift-diffusion equation for 'volume' and super-diffusion equation for energy, showing a crossover from diffusive to anomalous transport.
Article
Physics, Multidisciplinary
Ole Steuernagel, Andrei B. Klimov
Summary: A polynomial of a harmonic oscillator hamiltonian of degree N can lead to a fully solvable continuous quantum system with customizable energy eigenvalues. The re-ordering of energy eigenfunctions due to this choice does not necessarily result in a monotonic increase in the number of nodes. These systems exhibit 'universal' features and their basic behaviors are studied.
Article
Mathematics, Applied
A. Ugulava, S. Chkhaidze, O. Kharshiladze, G. Mchedlishvili
Summary: The electronic system in an atom is considered Hamiltonian only at times shorter than the spontaneous relaxation time. However, a phenomenon of nonlinear hybrid resonance can be observed in the electronic spectrum when the external electromagnetic field has a specific form.
Article
Mathematics, Applied
Adrian P. Bustamante, Cristel Chandre
Summary: We investigate the critical surfaces for the existence of invariant tori in Hamiltonian systems with two and three degrees of freedom. Two methods, renormalization-group transformations and conjugation in configuration space, are used and compared to compute the critical surfaces. We discover the presence of cusps in the critical surface of three-dimensional invariant tori in Hamiltonian systems with three degrees of freedom, while the critical surface of two-dimensional invariant tori in Hamiltonian systems with two degrees of freedom is expected to be smooth.
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS
(2023)
Article
Physics, Multidisciplinary
Jen-Hsu Chang, Chun-Yan Lin, Ray-Kuang Lee
Summary: By studying quantum particles with probability density-dependent effective mass in harmonic oscillators, we have revealed continuous energy spectra and stable solutions, showing the influence of nonlinear effective mass on the oscillator system and discovering new solutions.