Bloch waves

Charles P. Poole, Horácio A. Farach

Wei Qi, Ju-Kui Xue

Bloch band and stabilities of Bloch waves of superfluid Fermi gases in one-dimensional (1D) periodic optical lattices are discussed. Within the hydrodynamical theory and the two-mode approximation, the Bloch band structure, the energetic and dynamical instabilities of Bloch waves at the first Brilliouin zone are presented. The results show that, when the atom density is beyond a critical value, a loop structure in the Bloch band at the zone edge is developed along the BEC-BCS crossover. The Bloch band structure and the stabilities of Bloch waves are modified dramatically when the system crosses from the BEC side to the BCS side, and they can be adjusted to the required characteristics by changing the atom's interaction (with the Feshbach resonance technique), the atom density, and the lattice parameters. The analytical expressions of the critical atom density for exciting the loop structure and maintaining the stabilities of Bloch waves are obtained.

Calvin H. Wilcox

The Bloch waves of the one-electron theory of electronic states in crystals are the eigenfunctions of a family of unbounded selfadjoint operators H(p) that depend holomorphically on the wave momentum p = (p1, p2, p3) elements of R cubed. H(p) has a discrete spectrum, witth corresponding complete orthonormal sequences of eigenfunctions, and it is customary to denote such a sequence by (psi sub n) (p) and speak of the Bloch waves. However, the eigenfunctions are not unique and a separate choice is required for each p. The customary definitionn therefore rests on the axiom of choice and can provide no information about the p-dependence of the Bloch waves. Some information is essential for applications. A minimal requirements is p-measurability.

Joseph V. Pulé

Pieters, Laura ME

Jacek Dziarmaga

Production of Bloch waves during a rapid quench is studied by analytical and numerical methods. The density of Bloch waves decays exponentially with the quench time. It also strongly depends on temperature. Very few textures are produced for temperatures lower than a characteristic temperature proportional to the square of the magnetic field.