1,099,394 research outputs found
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 , supersymmetric quantum mechanics algebras. These
two algebras can be combined under certain circumstances to form a central
charge extended 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 -plane. As we shall demonstrate, the fermionic scattered states are
associated to two one dimensional supersymmetric quantum mechanical
algebras with zero central charge. These two symmetries are combined to form a
non-trivial one dimensional superalgebra with various central charges. In
addition, we form higher dimensional irreducible representations of the two
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 -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 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
- …