Vortex lattice stability and phase coherence in three-dimensional rapidly rotating Bose condensates

We establish the general equations of motion for the modes of a vortex lattice in a rapidly rotating Bose-Einstein condensate in three dimensions, taking into account the elastic energy of the lattice and the vortex line bending energy. As in two dimensions, the vortex lattice supports Tkachenko and gapped sound modes. In contrast, in three dimensions the Tkachenko mode frequency at long wavelengths becomes linear in the wavevector for any propagation direction out of the transverse plane. We compute the correlation functions of the vortex displacements and the superfluid order parameter for a homogeneous Bose gas of bounded extent in the axial direction. At zero temperature the vortex displacement correlations are convergent at large separation, but at finite temperatures, they grow with separation. The growth of the vortex displacements should lead to observable melting of vortex lattices at higher temperatures and somewhat lower particle number and faster rotation than in current experiments. At zero temperature a system of large extent in the axial direction maintains long range order-parameter correlations for large separation, but at finite temperatures the correlations decay with separation.Comment: 10 pages, 2 figures, Changes include the addition of the particle density - vortex density coupling and the correct value of the shear modulu

Central Charge Extended Supersymmetric Structures for Fundamental Fermions Around non-Abelian Vortices

Fermionic zero modes around non-abelian vortices are shown that they constitute two $N=2$, $d=1$ supersymmetric quantum mechanics algebras. These two algebras can be combined under certain circumstances to form a central charge extended $N=4$ supersymmetric quantum algebra. We thoroughly discuss the implications of the existence of supersymmetric quantum mechanics algebras, in the quantum Hilbert space of the fermionic zero modes

Extended Supersymmetric Quantum Mechanics Algebras in Scattering States of Fermions off Domain Walls

We study the underlying extended supersymmetric structure in a system composed of fermions scattered off an infinitely extended static domain wall in the $xz$-plane. As we shall demonstrate, the fermionic scattered states are associated to two $N=2$ one dimensional supersymmetric quantum mechanical algebras with zero central charge. These two symmetries are combined to form a non-trivial one dimensional $N=4$ superalgebra with various central charges. In addition, we form higher dimensional irreducible representations of the two $N=2$ algebras. Moreover, we study how the Witten index behaves under compact odd and even perturbations, coming from a background magnetic field and some non-renormalizable Yukawa mass terms for the fermions. As we shall demonstrate, the Witten index is invariant only when the magnetic field is taken into account and particularly when only the $z$-component of the field is taken into account. Finally, we study the impact of this supersymmetric structures on the Hilbert space of the fermionic states and also we present a deformed extension of the $N=2$ supersymmetric structure

Quantization of generally covariant systems with extrinsic time

A generally covariant system can be deparametrized by means of an ``extrinsic'' time, provided that the metric has a conformal ``temporal'' Killing vector and the potential exhibits a suitable behavior with respect to it. The quantization of the system is performed by giving the well ordered constraint operators which satisfy the algebra. The searching of these operators is enlightned by the methods of the BRST formalism.Comment: 10 pages. Definite published versio