Academic literature on the topic 'Geometry and topology in quantum mechanics and condensed matter'

The interaction of light with matter provides some of the most important tools for studying structure and dynamics on the microscopic scale. Atomic and molecular spectroscopy in the low pressure gas phase probes this interaction essentially on the single particle level and yields information about energy levels, state symmetries, and intramolecular potential surfaces. Understanding environmental effects in spectroscopy is important both as a fundamental problem in quantum statistical mechanics and as a prerequisite to the intelligent use of spectroscopic tools to probe and analyze molecular interactions and processes in condensed phases. Spectroscopic observables can be categorized in several ways. We can follow a temporal profile or a frequency resolved spectrum; we may distinguish between observables that reflect linear or nonlinear response to the probe beam; we can study different energy domains and different timescales and we can look at resonant and nonresonant response. This chapter discusses some concepts, issues, and methodologies that pertain to the effect of a condensed phase environment on these observables. For an in-depth look at these issues the reader may consult many texts that focus on particular spectroscopies. With focus on the optical response of molecular systems, effects of condensed phase environments can be broadly discussed within four categories: 1. Several important effects are equilibrium in nature, for example spectral shifts associated with solvent induced changes in solute energy levels are equilibrium properties of the solvent–solute system. Obviously, such observables may themselves be associated with dynamical phenomena, in the example of solvent shifts it is the dynamics of solvation that affects their dynamical evolution. Another class of equilibrium effects on radiation– matter interaction includes properties derived from symmetry rules. A solvent can affect a change in the equilibrium configuration of a chromophore solute and consequently the associated selection rules for a given optical transition. Some optical phenomena are sensitive to the symmetry of the environment, for example, surface versus bulk geometry. 2. The environment affects the properties of the radiation field; the simplest example is the appearance of the dielectric coefficient ε in the theory of radiation–matter interaction.