Work and energy in inertial and non inertial reference frames

It is usual in introductory courses of mechanics to develop the work and energy formalism from Newton's laws. On the other hand, literature analyzes the way in which forces transform under a change of reference frame. Notwithstanding, no analogous study is done for the way in which work and energy transform under those changes of reference frames. We analyze the behavior of energy and work under such transformations and show explicitly the expected invariance of the formalism under Galilean transformations for one particle and a system of particles. The case of non inertial systems is also analyzed and the fictitious works are characterized. In particular, we show that the total fictitious work in the center of mass system vanishes even if the center of mass defines a non inertial frame. Finally, some subtleties that arise from the formalism are illustrated by examples.Comment: 4 pages, 2 figures. LaTeX2e. Part of the approach has been changed but results are unaltered. Version to appear im American Journal of Physic

Recurrences Associated with a Classical Orbit in the Node of a Quantum Wave Function

Absorption spectra of atoms in magnetic fields reveal recurrences: manifestations of classical orbits (or quantum wave packets) that go out from the atom and later return. A formula from closed-orbit theory asserts that if the orbit lies on a node of the outgoing wave function, then the strength of the recurrence is zero. New quantum calculations, however, show that the recurrence strength is nonzero, though small. We derive a semiclassical formula for the recurrence strength associated with a classical orbit at a node of the quantum wave function. This formula is compared to the quantum mechanical calculation. Compared to other orbits, the recurrence is about 100 times weaker, and obeys a different classical scaling law

Simple Pendulum Revisited

We describe a 8085 microprocessor interface developed to make reliable time period measurements. The time period of each oscillation of a simple pendulum was measured using this interface. The variation of the time period with increasing oscillation was studied for the simple harmonic motion (SHM) and for large angle initial displacements (non-SHM). The results underlines the importance of the precautions which the students are asked to take while performing the pendulum experiment.Comment: 17 pages with 10 figure

Moments of inertia for solids of revolution and variational methods

We present some formulae for the moments of inertia of homogeneous solids of revolution in terms of the functions that generate the solids. The development of these expressions exploits the cylindrical symmetry of these objects, and avoids the explicit use of multiple integration, providing an easy and pedagogical approach. The explicit use of the functions that generate the solid gives the possibility of writing the moment of inertia as a functional, which in turn allows us to utilize the calculus of variations to obtain a new insight into some properties of this fundamental quantity. In particular, minimization of moments of inertia under certain restrictions is possible by using variational methods.Comment: 6 pages, 6 figures, LaTeX2e. Two paragraphs added. Minor typos corrected. Version to appear in European Journal of Physic

Work and energy in rotating systems

Literature analyzes the way in which Newton's second law can be used when non-inertial rotating systems are used. However, the treatment of the work and energy theorem in rotating systems is not considered in textbooks. In this paper, we show that the work and energy theorem can still be applied to a closed system of particles in a rotating system, as long as the work of fictitious forces is properly included in the formalism. The coriolis force does not contribute to the work coming from fictitious forces. It worths remarking that real forces that do not do work in an inertial reference frame can do work in the rotating reference frame and viceversa. The combined effects of acceleration of the origin and rotation of the non-inertial system are also studied.Comment: 6 pages, 3 figures, LaTeX2

Atomic Resonance and Scattering

Contains reports on eleven research projects.U.S. Air Force - Office of Scientific Research (Grant AFOSR-81-0067

Crossover from weak to strong coupling regime in dispersive circuit QED

We study the decoherence of a superconducting qubit due to the dispersive coupling to a damped harmonic oscillator. We go beyond the weak qubit-oscillator coupling, which we associate with a phase Purcell effect, and enter into a strong coupling regime, with qualitatively different behavior of the dephasing rate. We identify and give a physicaly intuitive discussion of both decoherence mechanisms. Our results can be applied, with small adaptations, to a large variety of other physical systems, e. g. trapped ions and cavity QED, boosting theoretical and experimental decoherence studies.Comment: Published versio

Statistics of Oscillator Strengths in Chaotic Systems

The statistical description of oscillator strengths for systems like hydrogen in a magnetic field is developed by using the supermatrix nonlinear $\sigma$-model. The correlator of oscillator strengths is found to have a universal parametric and frequency dependence, and its analytical expression is given. This universal expression applies to quantum chaotic systems with the same generality as Wigner-Dyson statistics.Comment: 11 pages, REVTeX3+epsf, two EPS figures. Replaced by the published version. Minor changes

Testing Lorentz and CPT symmetry with hydrogen masers

We present details from a recent test of Lorentz and CPT symmetry using hydrogen masers. We have placed a new limit on Lorentz and CPT violation of the proton in terms of a recent standard model extension by placing a bound on sidereal variation of the F = 1 Zeeman frequency in hydrogen. Here, the theoretical standard model extension is reviewed. The operating principles of the maser and the double resonance technique used to measure the Zeeman frequency are discussed. The characterization of systematic effects is described, and the method of data analysis is presented. We compare our result to other recent experiments, and discuss potential steps to improve our measurement.Comment: 26 pages, 16 figure

Characterizing the spin state of an atomic ensemble using the magneto-optical resonance method

Quantum information protocols utilizing atomic ensembles require preparation of a coherent spin state (CSS) of the ensemble as an important starting point. We investigate the magneto-optical resonance method for characterizing a spin state of cesium atoms in a paraffin coated vapor cell. Atoms in a constant magnetic field are subject to an off-resonant laser beam and an RF magnetic field. The spectrum of the Zeeman sub-levels, in particular the weak quadratic Zeeman effect, enables us to measure the spin orientation, the number of atoms, and the transverse spin coherence time. Notably the use of 894nm pumping light on the D1-line, ensuring the state F=4, m_F=4 to be a dark state, helps us to achieve spin orientation of better than 98%. Hence we can establish a CSS with high accuracy which is critical for the analysis of the entangled states of atoms.Comment: 12 pages ReVTeX, 6 figures, in v2 added ref. and corrected typo