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We consider a BEC of rigid rotor molecules confined to quasi-2D through harmonic trapping. The molecules are subjected to an external electric field which polarizes the gas, and the molecules interact via dipoleâ€"dipole interactions. We present a description of the ground state and low-energy excitations of the system including an analysis of the mean-field energy, polarization, and stability. Under large electric fields the gas becomes fully polarized and we reproduce a well known density-wave instability which arises in polar BECs. Under smaller applied electric fields the gas develops an in-plane polarization leading to the emergence of a new global instability as the molecules ‘tilt’. The character of these instabilities is clarified by means of momentum-space densityâ€"density structure factors. A peak at zero momentum in the spinâ€"spin structure factor for the in-plane component of the polarization indicates that the tilt instability is a global phonon-like instability. [ABSTRACT FROM AUTHOR]

Two identical objects are simultaneously projected vertically upward with the same initial speed in a uniform gravitational field and then return to their starting point. One object is subject to a resistive force proportional to the nth power of its speed where n ≥ 0 , such as linear (Stokes) drag for n = 1 or quadratic (Newtonian) drag for n = 2. The other object moves through vacuum with no resistance. Which object returns to its starting point first? It is shown analytically that the object subject to drag always wins the race if n ≥ 1 , but that either object can win otherwise, depending on the ratio of the launch speed to the terminal speed of the object subject to drag if 0 < n < 1 or depending on the ratio of the frictional acceleration to the gravitational acceleration if n = 0. These analytical results are confirmed by Euler–Cromer numerical integration of the equations of motion. [ABSTRACT FROM AUTHOR]

We show that, under achievable experimental conditions, a Bose-Einstein condensate of polar molecules can exhibit dielectric character. In particular, we derive a set of self-consistent mean-field equations that couple the condensate density to its electric dipole field, leading to the emergence of polarization modes that are coupled to the rich quasi-particle spectrum of the condensate. While the usual roton instability is suppressed in this system, the coupling can give rise to a phonon-like instability that is characteristic of a dielectric material with a negative static dielectric function. [ABSTRACT FROM AUTHOR]