Chern-Simons Particles with Nonstandard Gravitational Interaction

The model of nonrelativistic particles coupled to nonstandard (2+1)-gravity [1] is extended to include Abelian or non-Abelian charges coupled to Chern-Simons gauge fields. Equivalently, the model may be viewed as describing the (Abelian or non-Abelian) anyonic dynamics of Chern-Simons particles coupled, in a reparametrization invariant way, to a translational Chern-Simons action. The quantum two-body problem is described by a nonstandard Schr\"{o}dinger equation with a noninteger angular momentum depending on energy as well as particle charges. Some numerical results describing the modification of the energy levels by these charges in the confined regime are presented. The modification involves a shift as well as splitting of the levels.Comment: LaTeX, 1 figure (included), 14 page

Field Theory on q=−1q=-1 Quantum Plane

We build the $q=-1$ defomation of plane on a product of two copies of algebras of functions on the plane. This algebra constains a subalgebra of functions on the plane. We present general scheme (which could be used as well to construct quaternion from pairs of complex numbers) and we use it to derive differential structures, metric and discuss sample field theoretical models.Comment: LaTeX, 10 page

Spontaneous emission of non-dispersive Rydberg wave packets

Non dispersive electronic Rydberg wave packets may be created in atoms illuminated by a microwave field of circular polarization. We discuss the spontaneous emission from such states and show that the elastic incoherent component (occuring at the frequency of the driving field) dominates the spectrum in the semiclassical limit, contrary to earlier predictions. We calculate the frequencies of single photon emissions and the associated rates in the "harmonic approximation", i.e. when the wave packet has approximately a Gaussian shape. The results agree well with exact quantum mechanical calculations, which validates the analytical approach.Comment: 14 pages, 4 figure

Jordanian Twist Quantization of D=4 Lorentz and Poincare Algebras and D=3 Contraction Limit

We describe in detail two-parameter nonstandard quantum deformation of D=4 Lorentz algebra $\mathfrak{o}(3,1)$, linked with Jordanian deformation of $\mathfrak{sl} (2;\mathbb{C})$. Using twist quantization technique we obtain the explicit formulae for the deformed coproducts and antipodes. Further extending the considered deformation to the D=4 Poincar\'{e} algebra we obtain a new Hopf-algebraic deformation of four-dimensional relativistic symmetries with dimensionless deformation parameter. Finally, we interpret $\mathfrak{o}(3,1)$ as the D=3 de-Sitter algebra and calculate the contraction limit $R\to\infty$ ($R$ -- de-Sitter radius) providing explicit Hopf algebra structure for the quantum deformation of the D=3 Poincar\'{e} algebra (with masslike deformation parameters), which is the two-parameter light-cone $\kappa$-deformation of the D=3 Poincar\'{e} symmetry.Comment: 13 pages, no figure

Statistical properties of energy levels of chaotic systems: Wigner or non-Wigner

For systems whose classical dynamics is chaotic, it is generally believed that the local statistical properties of the quantum energy levels are well described by Random Matrix Theory. We present here two counterexamples - the hydrogen atom in a magnetic field and the quartic oscillator - which display nearest neighbor statistics strongly different from the usual Wigner distribution. We interpret the results with a simple model using a set of regular states coupled to a set of chaotic states modeled by a random matrix.Comment: 10 pages, Revtex 3.0 + 4 .ps figures tar-compressed using uufiles package, use csh to unpack (on Unix machine), to be published in Phys. Rev. Let

Moduli-Space Dynamics of Noncommutative Abelian Sigma-Model Solitons

In the noncommutative (Moyal) plane, we relate exact U(1) sigma-model solitons to generic scalar-field solitons for an infinitely stiff potential. The static k-lump moduli space C^k/S_k features a natural K"ahler metric induced from an embedding Grassmannian. The moduli-space dynamics is blind against adding a WZW-like term to the sigma-model action and thus also applies to the integrable U(1) Ward model. For the latter's two-soliton motion we compare the exact field configurations with their supposed moduli-space approximations. Surprisingly, the two do not match, which questions the adiabatic method for noncommutative solitons.Comment: 1+15 pages, 2 figures; v2: reference added, to appear in JHE

SU(5) Gravitating Monopoles

Spherically symmetric solutions of the SU(5) Einstein-Yang-Mills-Higgs system are constructed using the harmonic map ansatz \cite{IS}. This way the problem reduces to solving a set of ordinary differential equations for the appropriate profile functions.Comment: 12 pages, 3 Figure

Nonuniversality in level dynamics

Statistical properties of parametric motion in ensembles of Hermitian banded random matrices are studied. We analyze the distribution of level velocities and level curvatures as well as their correlation functions in the crossover regime between three universality classes. It is shown that the statistical properties of level dynamics are in general non-universal and strongly depend on the way in which the parametric dynamics is introduced.Comment: 24 pages + 10 figures (not included, avaliable from the author), submitted to Phys. Rev.