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Most probable trajectories of a birhythmic oscillator under random perturbations.
Chaos
December 2024
Research Department Complexity Science, Potsdam Institute for Climate Impact Research, Potsdam 14473, Germany.
Article Synopsis
- - This study focuses on birhythmic oscillators, which have two stable limit cycles with different properties, and examines how stochastic (random) disturbances affect their movement.
- - The researchers used a path integral method to find the most probable paths that these oscillators can take when starting from various initial states, revealing how they transition between their stable cycles.
- - By analyzing noise-induced transitions, the study aims to enhance understanding of complex stochastic systems, presenting a new way to visualize and track the behavior of these oscillators in response to outside influences.
Accurate and Fast Estimation of the Continuum Limit in Path Integral Simulations of Quantum Oscillators and Crystals.
J Chem Theory Comput
November 2024
Department of Engineering Science, Trinity University, San Antonio, Texas 78212, United States.
Convergence of imaginary-time path integral results requires a substantial number of beads () when quantum effects are significant. Traditional Trotter scaling approaches estimate the continuum limit ( → ∞) through extrapolation; however, their validity is restricted to the asymptotic domain of large . We introduce an efficient extrapolation approach for quantum oscillators and crystals with harmonic character.
View Article and Find Full Text PDFNuclear Quantum Effects Have a Significant Impact on UV/Vis Absorption Spectra of Chromophores in Water.
Angew Chem Int Ed Engl
January 2025
Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, 44780, Bochum, Germany.
Despite the broadly acknowledged importance of solvation effects on measured UV/Vis spectra in the context of solvatochromism or chemical reactions in solution, it is still an open challenge to calculate UV/Vis spectra with predictive accuracy. This is particularly true when it comes to the impact of nuclear quantum effects on these experimental observables. In the present work, we calculate the UV/Vis absorption spectrum of indole in aqueous solution with a combination of a correlated wavefunction method for computing electronic excitation energies and enhanced path integral simulations for rigorous sampling of nuclear configurations including the quantum effects in solution.
View Article and Find Full Text PDFPath-filtering in path-integral simulations of open quantum systems using GFlowNets.
J Chem Phys
October 2024
Department of Chemistry, McGill University, Montreal, Quebec H3A 0G4, Canada.
An important class of methods for modeling dynamics in open quantum systems is based on the well-known influence functional (IF) approach to solving path-integral equations of motion. Within this paradigm, path-filtering schemes based on the removal of IF elements that fall below a certain threshold aim to reduce the effort needed to calculate and store the influence functional, making very challenging simulations possible. A filtering protocol of this type is considered acceptable as long as the simulation remains mathematically stable.
View Article and Find Full Text PDFGeneralization to d-dimensions of a fermionic path integral for exact enumeration of polygons on hypercubic lattices.
Sci Rep
September 2024
Physics Department, Federal University of Rio Grande do Norte, Natal, Rio Grande do Norte, 59072-970, Brazil.
The generating function for polygons on the square lattice has been known for many decades and is closely related to the path integral formulation of a free fermion model. On the cubic and hypercubic lattices the generating function is still unknown and the problem remains open. It has been conjectured that the three-dimensional (3D) and higher dimensional problems are not solvable-or, to be more precise, that there are no differentiably finite (D-finite) solutions.
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