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Range00:59

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The range is one of the measures of variation. It can be defined as the difference between a dataset's highest and lowest values. For example, in the study of seven 16-ounce soda cans, the filled volume of soda was measured, thus producing the following amount (in ounces) of soda:
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The genomes of eukaryotes are punctuated by long stretches of sequence which do not code for proteins or RNAs. Although some of these regions do contain crucial regulatory sequences, the vast majority of this DNA serves no known function. Typically, these regions of the genome are the ones in which the fastest change, in evolutionary terms, is observed, because there is typically little to no selection pressure acting on these regions to preserve their sequences.
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The coupling interactions of nuclei across four or more bonds are usually weak, with J values less than 1 Hz. While these are usually not observed in spectra, the presence of multiple bonds along the coupling pathway can result in observable long-range coupling.
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Atoms and molecules interact through bonds (or forces): intramolecular and intermolecular. The forces are electrostatic as they arise from interactions (attractive or repulsive) between charged species (permanent, partial, or temporary charges) and exist with varying strengths between ions, polar, nonpolar, and neutral molecules. The different types of intermolecular forces are ion–dipole, dipole–dipole, hydrogen bonds, and dispersion; among these, dipole–dipole, hydrogen...
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Electricity is generated by either electrons or ions flowing through a solution or a conducting medium. This flow of electrons or specifically electrical charge is defined as an electric current. When electrons move through a wire, they generate an electric current. It can be recalled  that in a redox reaction, electrons are lost and gained. In the spontaneous redox reaction of zinc  with copper, when zinc is immersed in a copper ion solution, a transfer of electrons from one substance to...
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Updated: Jan 29, 2026

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
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Slow dynamics and subdiffusion in a non-Hamiltonian system with long-range forces.

Romain Bachelard1, Nicola Piovella2, Shamik Gupta3

  • 1Departamento de Fisica, Universidade Federal de São Carlos, Rodovia Washington Luis, km 235, S/n Jardim Guanabara, São Carlos, São Paulo 13565-905, Brazil.

Physical Review. E
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PubMed
Summary

Molecular dynamics of non-Hamiltonian systems with long-range forces exhibit slow, diverging timescales. Single-particle behavior resembles Brownian motion, driven by noise and leading to subdiffusive momentum fluctuations.

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Area of Science:

  • Statistical mechanics
  • Non-Hamiltonian dynamics
  • Complex systems

Background:

  • Investigating dynamics of non-Hamiltonian systems with long-range forces.
  • Inspired by one-dimensional light-particle systems.

Purpose of the Study:

  • To investigate the dynamics of a non-Hamiltonian system with long-range forces.
  • To understand the macroscopic and single-particle behaviors.
  • To model the evolution using Vlasov and Fokker-Planck equations.

Main Methods:

  • Molecular dynamics simulations.
  • Approximation by Vlasov equation in the thermodynamic limit.
  • Modeling single-particle evolution with noise.
  • Analysis of nonlinear Fokker-Planck equation.

Main Results:

  • Molecular dynamics does not reach equilibrium.
  • Vlasov equation shows stable stationary solutions in the thermodynamic limit.
  • Macroscopic dynamics evolve on a slow timescale diverging with system size.
  • Single-particle evolution driven by incoherent interactions modeled as noise.
  • Subdiffusive behavior of momentum fluctuations observed.

Conclusions:

  • Macroscopic behavior of non-Hamiltonian systems can be approximated by Vlasov equation.
  • Single-particle dynamics exhibit Brownian-like momentum evolution due to self-generated noise.
  • Nonlinearity in Fokker-Planck equation leads to subdiffusion, consistent with numerical findings.