Quantum Systems: A Mathematical Journey from Few to Many Particles

Dipolar Gross-Pitaevskii equation in lower dimensions

Yongyong Cai

Purdue University


Bose-Einstein condensate (BEC) with dipole-dipole interaction has received considerable research interests recently. At zero temperature, the dipolar BEC is well-described by a three dimensional (3D) Gross-Pitaevskii equation (GPE) with a nonlocal dipole-dipole interaction term. With strongly anisotropic confining potentials, the three dimensional dipolar GPE will result in effective two-dimensional (2D) equation for disk-shaped BEC or effective one-dimensional (1D) equation for cigar-shaped BEC . Upon a new formulation of the 3D dipolar GPE, we obtain the corresponding effective lower dimensional equations. Ground state and dynamics for the 3D and lower dimensional equations are discussed. Extensions to multi-layered dipolar condensate will be also discussed.