Deformed Carroll particle from 2+1 gravity

We consider a point particle coupled to 2+1 gravity, with de Sitter gauge group SO(3,1). We observe that there are two contraction limits of the gauge group: one resulting in the Poincare group, and the second with the gauge group having the form AN(2) \ltimes \an(2)^*. The former case was thoroughly discussed in the literature, while the latter leads to the deformed particle action with de Sitter momentum space, like in the case of kappa-Poincare particle. However, the construction forces the mass shell constraint to have the form p_0^2 = m^2, so that the effective particle action describes the deformed Carroll particle.Comment: 10 page

Coherent states for the q-deformed quantum mechanics on a circle

The q-deformed coherent states for a quantum particle on a circle are introduced and their properties investigated.Comment: 11 pages, 2 PostScript figure

On the definition of velocity in doubly special relativity theories

We discuss the definition of particle velocity in doubly relativity theories. The general formula relating velocity and four-momentum of particle is given.Comment: 7 page

Quantum mechanics on a circle: Husimi phase space distributions and semiclassical coherent state propagators

We discuss some basic tools for an analysis of one-dimensionalquantum systems defined on a cyclic coordinate space. The basic features of the generalized coherent states, the complexifier coherent states are reviewed. These states are then used to define the corresponding (quasi)densities in phase space. The properties of these generalized Husimi distributions are discussed, in particular their zeros.Furthermore, the use of the complexifier coherent states for a semiclassical analysis is demonstrated by deriving a semiclassical coherent state propagator in phase space.Comment: 29 page

Discrete Accidental Symmetry for a Particle in a Constant Magnetic Field on a Torus

A classical particle in a constant magnetic field undergoes cyclotron motion on a circular orbit. At the quantum level, the fact that all classical orbits are closed gives rise to degeneracies in the spectrum. It is well-known that the spectrum of a charged particle in a constant magnetic field consists of infinitely degenerate Landau levels. Just as for the $1/r$ and $r^2$ potentials, one thus expects some hidden accidental symmetry, in this case with infinite-dimensional representations. Indeed, the position of the center of the cyclotron circle plays the role of a Runge-Lenz vector. After identifying the corresponding accidental symmetry algebra, we re-analyze the system in a finite periodic volume. Interestingly, similar to the quantum mechanical breaking of CP invariance due to the $\theta$-vacuum angle in non-Abelian gauge theories, quantum effects due to two self-adjoint extension parameters $\theta_x$ and $\theta_y$ explicitly break the continuous translation invariance of the classical theory. This reduces the symmetry to a discrete magnetic translation group and leads to finite degeneracy. Similar to a particle moving on a cone, a particle in a constant magnetic field shows a very peculiar realization of accidental symmetry in quantum mechanics.Comment: 25 pages, 2 figure

Electronic band structure and exchange coupling constants in ACr2X4 spinels

We present the results of band structure calculations for ACr2X4 (A=Zn, Cd, Hg and X=O, S, Se) spinels. Effective exchange coupling constants between Cr spins are determined by fitting the energy of spin spirals to a classical Heisenberg model. The calculations reproduce the change of the sign of the dominant nearest-neighbor exchange interaction J1 from antiferromagnetic in oxides to ferromagnetic in sulfides and selenides. It is verified that the ferromagnetic contribution to J1 is due to indirect hopping between Cr t2g and eg states via X p states. Antiferromagnetic coupling between 3-rd Cr neighbors is found to be important in all the ACr2X4 spinels studied, whereas other interactions are much weaker. The results are compared to predictions based on the Goodenough-Kanamori rules of superexchange.Comment: 15 pages, 10 figures, 3 table