A self-consistent mode coupling model for supercooled fluids is derived from fluctuating nonlinear hydrodynamics (extended to short wavelengths) with attention to detailed balance constraints. The sharp glass transition predicted by mode coupling models based only on pressure nonlinearities does not occur here. Instead, the long time asymptotic behavior of the density autocorrelation function is determined by additional nonlinearities imposed by the detailed balance constraints.

The influence of frozen-in topological defects in a crystal on the long-wavelength quantum states of a particle is considered. In the continuum limit of a conveniently defined tight-binding model one is led to a covariant Schrödinger equation on a Riemann-Cartan manifold. When the tight-binding transfer energies are assumed to depend on the local lattice deformations caused by the defects, additional noncovariant terms are generated in the Hamiltonian. These terms generate bound states of the particle to edge dislocations and enhance the scattering of particles on screw dislocations. [S0031-9007(98)05432-5]

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