N=1 Supersymetric Quantum Mechanics in a Scenario with Lorentz-Symmetry Violation

We show in this paper that the dynamics of a non-relativistic particle with spin, coupled to an external electromagnetic field and to a background that breaks Lorentz symmetry, is naturally endowed with an N=1-supersymmetry. This result is achieved in a superspace approach where the particle coordinates and the spin degrees of freedom are components of the same supermultiplet.Comment: 6 pages, no figure

A Comment on the Topological Phase for Anti-Particles in a Lorentz-violating environment

Recently, a scheme to analyse topological phases in Quantum Mechanics by means of the non-relativistic limit of fermions non-minimally coupled to a Lorentz-breaking background has been proposed. In this letter, we show that the fixed background, responsible for the Lorentz-symmetry violation, may induce opposite Aharonov-Casher phases for a particle and its corresponding antiparticle. We then argue that such a difference may be used to investigate the asymmetry for particle/anti-particle as well as to propose bounds on the associated Lorentz-symmetry violating parameters.Comment: 4 pages - A published versio

Running Gauge Couplings and Thresholds in the Type II Superstring

A distinctive feature of string unification is the possibility of unification by a non-simply-laced group. This occurs most naturally in four dimensional type~II string models where the gauge symmetry is realized by Kac-Moody algebras at different levels. We investigate the running coupling constants and the one-loop thresholds for such general models. As a specific case, we examine a $\rm SU(3)\times U(1)\times U(1)$ model and find that the threshold corrections lead to a small $6\%$ increase in the unification scale.Comment: 12 pages, IFP-432-UN

The Integrability of Pauli System in Lorentz Violating Background

We systematically analyze the integrability of a Pauli system in Lorentz violating background at the non-relativistic level both in two- and three-dimensions. We consider the non-relativistic limit of the Dirac equation from the QED sector of the so-called Standard Model Extension by keeping only two types of background couplings, the vector a_mu and the axial vector b_mu. We show that the spin-orbit interaction comes as a higher order correction in the non-relativistic limit of the Dirac equation. Such an interaction allows the inclusion of spin degree non-trivially, and if Lorentz violating terms are allowed, they might be comparable under special circumstances. By including all possible first-order derivative terms and considering the cases a\ne 0, b\ne 0, and b_0\ne 0 one at a time, we determine the possible forms of constants of motion operator, and discuss the existence or continuity of integrability due to Lorentz violating background.Comment: 19 page

Edge-Magnetoplasmon Wave-Packet Revivals in the Quantum Hall Effect

The quantum Hall effect is necessarily accompanied by low-energy excitations localized at the edge of a two-dimensional electron system. For the case of electrons interacting via the long-range Coulomb interaction, these excitations are edge magnetoplasmons. We address the time evolution of localized edge-magnetoplasmon wave packets. On short times the wave packets move along the edge with classical E cross B drift. We show that on longer times the wave packets can have properties similar to those of the Rydberg wave packets that are produced in atoms using short-pulsed lasers. In particular, we show that edge-magnetoplasmon wave packets can exhibit periodic revivals in which a dispersed wave packet reassembles into a localized one. We propose the study of edge-magnetoplasmon wave packets as a tool to investigate dynamical properties of integer and fractional quantum-Hall edges. Various scenarios are discussed for preparing the initial wave packet and for detecting it at a later time. We comment on the importance of magnetoplasmon-phonon coupling and on quantum and thermal fluctuations.Comment: 18 pages, RevTex, 7 figures and 2 tables included, Fig. 5 was originally 3Mbyte and had to be bitmapped for submission to archive; in the process it acquired distracting artifacts, to upload the better version, see http://physics.indiana.edu/~uli/publ/projects.htm

Long-Term Evolution and Revival Structure of Rydberg Wave Packets for Hydrogen and Alkali-Metal Atoms

This paper begins with an examination of the revival structure and long-term evolution of Rydberg wave packets for hydrogen. We show that after the initial cycle of collapse and fractional/full revivals, which occurs on the time scale $t_{\rm rev}$, a new sequence of revivals begins. We find that the structure of the new revivals is different from that of the fractional revivals. The new revivals are characterized by periodicities in the motion of the wave packet with periods that are fractions of the revival time scale $t_{\rm rev}$. These long-term periodicities result in the autocorrelation function at times greater than $t_{\rm rev}$ having a self-similar resemblance to its structure for times less than $t_{\rm rev}$. The new sequence of revivals culminates with the formation of a single wave packet that more closely resembles the initial wave packet than does the full revival at time $t_{\rm rev}$, i.e., a superrevival forms. Explicit examples of the superrevival structure for both circular and radial wave packets are given. We then study wave packets in alkali-metal atoms, which are typically used in experiments. The behavior of these packets is affected by the presence of quantum defects that modify the hydrogenic revival time scales and periodicities. Their behavior can be treated analytically using supersymmetry-based quantum-defect theory. We illustrate our results for alkali-metal atoms with explicit examples of the revival structure for radial wave packets in rubidium.Comment: To appear in Physical Review A, vol. 51, June 199

Gravitational physics with antimatter

The production of low-energy antimatter provides unique opportunities to search for new physics in an unexplored regime. Testing gravitational interactions with antimatter is one such opportunity. Here a scenario based on Lorentz and CPT violation in the Standard- Model Extension is considered in which anomalous gravitational effects in antimatter could arise.Comment: 5 pages, presented at the International Conference on Exotic Atoms (EXA 2008) and the 9th International Conference on Low Energy Antiproton Physics (LEAP 2008), Vienna, Austria, September 200

Minimum-Uncertainty Angular Wave Packets and Quantized Mean Values

Uncertainty relations between a bounded coordinate operator and a conjugate momentum operator frequently appear in quantum mechanics. We prove that physically reasonable minimum-uncertainty solutions to such relations have quantized expectation values of the conjugate momentum. This implies, for example, that the mean angular momentum is quantized for any minimum-uncertainty state obtained from any uncertainty relation involving the angular-momentum operator and a conjugate coordinate. Experiments specifically seeking to create minimum-uncertainty states localized in angular coordinates therefore must produce packets with integer angular momentum.Comment: accepted for publication in Physical Review

Probing Lorentz and CPT violation with space-based experiments

Space-based experiments offer sensitivity to numerous unmeasured effects involving Lorentz and CPT violation. We provide a classification of clock sensitivities and present explicit expressions for time variations arising in such experiments from nonzero coefficients in the Lorentz- and CPT-violating Standard-Model Extension.Comment: 15 page