In condensed phases, intermolecular interactions and collective motions act to modify the state of a molecule in a time-dependent fashion. Liquids, polymers, and other soft matter experience intermolecular interactions that lead to electronic and structural motions. Atoms and molecules in solid form are subject to fluctuations that result from thermally populated phonons and defect states that influence electronic, optical, and transport properties. As a result, the properties and dynamics of an internal variable that we may observe in an experiment are mixed with its surroundings. In studying mixed states we cannot write down an exact Hamiltonian for these problems; however, we can describe the influence of the surroundings in a statistical manner. This requires a conceptual change.
- 9.1: Concepts and Definitions
- Perhaps the most significant change between isolated states and condensed matter is the dynamics. From the time-dependent Schrödinger equation, we see that the laws governing the time evolution of isolated quantum mechanical systems are invariant under time reversal. That is, there is no intrinsic directionality to time. If one reverses the sign of time and thereby momenta of objects, we should be able to exactly reverse the motion and propagate the system to where it was at an earlier time.
- 9.2: Thermal Equilibrium
- For a statistical mixture at thermal equilibrium, individual molecules can occupy a distribution of energy states.
- 9.3: Fluctuations
- Systems at thermal equilibrium are macroscopically time-invariant; however, they are microscopically dynamic, with molecules exploring the range of microstates that are thermally accessible. Local variations in energy result in changes in molecular position, orientation, and structure, and are responsible for the activation events that allow chemical equilibria to be established.