Generalized Einstein relations between absorption and emission spectra at thermodynamic equilibrium

• 成果类型: Article
• 署名作者: Ryu, Jisu; Yeola, Sarang; Jonas, David M.
• 署名单位: University of Colorado System; University of Colorado Boulder; University of Colorado System; University of Colorado Boulder; University of Colorado System; University of Colorado Boulder
• 刊物名称: PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
• ISSN/ISSBN: 0027-13906
• DOI: 10.1073/pnas.2410280121
• 发表日期: 2024-09-10
• 关键词: electron-transfer; quantum-theory; fluorescence; DYNAMICS; shape

摘要

We present Einstein coefficient spectra and a detailed-balance derivation of generalized Einstein relations between them that is based on the connection between spontaneous and stimulated emission. If two broadened levels or bands overlap in energy, transitions between them need not be purely absorptive or emissive. Consequently, spontaneous emission can occur in both transition directions, and four Einstein coefficient spectra replace the three Einstein coefficients for a line. At equilibrium, the four different spectra obey five pairwise relationships and one lineshape generates all four. These relationships are independent of molecular quantum statistics and predict the Stokes' shift between forward and reverse transitions required by equilibrium with blackbody transitions depend on the formal chemical potential difference between the initial and final bands, which becomes the standard chemical potential difference for ideal solutes. The formal chemical potential of a band replaces both the energy and degeneracy of a quantum level. Like the energies of quantum levels, the formal spontaneous emission, but do not directly obey generalized Einstein relations. Even predominantly absorptive rather than emissive.