The quantum-classical correspondence principle for work distributions

For closed quantum systems driven away from equilibrium, work is often defined in terms of projective measurements of initial and final energies. This definition leads to statistical distributions of work that satisfy nonequilibrium work and fluctuation relations. While this two-point measurement definition of quantum work can be justified heuristically by appeal to the first law of thermodynamics, its relationship to the classical definition of work has not been carefully examined. In this paper we employ semiclassical methods, combined with numerical simulations of a driven quartic oscillator, to study the correspondence between classical and quantal definitions of work in systems with one degree of freedom. We find that a semiclassical work distribution, built from classical trajectories that connect the initial and final energies, provides an excellent approximation to the quantum work distribution when the trajectories are assigned suitable phases and are allowed to interfere. Neglecting the interferences between trajectories reduces the distribution to that of the corresponding classical process. Hence, in the semiclassical limit, the quantum work distribution converges to the classical distribution, decorated by a quantum interference pattern. We also derive the form of the quantum work distribution at the boundary between classically allowed and forbidden regions, where this distribution tunnels into the forbidden region. Our results clarify how the correspondence principle applies in the context of quantum and classical work distributions, and contribute to the understanding of work and nonequilibrium work relations in the quantum regime.Comment: 22 pages, 9 figure

Structure in the Epislon Eridani dusty disk caused by mean motion resonances with a 0.3 eccentricity planet at periastron

The morphology of the epsilon Eridani dust ring is reproduced by a numerical simulation of dust particles captured into the 5:3 and 3:2 exterior mean-motion resonances with a 0.3 eccentricity 10^-4 solar mass planet at periastron at a semi-major axis of 40 AU. The morphology will differ when the planet is at aphelion, in about 140 years. Moderate eccentricity planets in outer extra-solar systems will cause observable variations in the morphology of associated dusty rings.Comment: accepted to ApJ

Gauge and Lorentz transformation placed on the same foundation

In this note we show that a "dynamical" interaction for arbitrary spin can be constructed in a straightforward way if gauge and Lorentz transformations are placed on the same foundation. As Lorentz transformations act on space-time coordinates, gauge transformations are applied to the gauge field. Placing these two transformations on the same ground means that all quantized field like spin-1/2 and spin-3/2 spinors are functions not only of the coordinates but also of the gauge field components. This change of perspective solves a couple of problems occuring for higher spin fields like the loss of causality, bad high-energy properties and the deviation of the gyromagnetic ratio from its constant value g=2 for any spin, as caused by applying the minimal coupling. Starting with a "dynamical" interaction, a non-minimal coupling can be derived which is consistent with causality, the expectation for the gyromagnetic ratio, and well-behaved for high energies. As a consequence, on this stage the (elektromagnetic) gauge field has to be considered as classical field. Therefore, standard quantum field theory cannot be applied. Despite this inconvenience, such a common ground is consistent with an old dream of physicists almost a century ago. Our approach, therefore, indicates a straightforward way to realize this dream.Comment: 12 pages, no figures, published version. arXiv admin note: substantial text overlap with arXiv:0908.376

Steps toward a high precision solar rotation profile: Results from SDO/AIA coronal bright point data

Coronal bright points (CBP) are ubiquitous small brightenings in the solar corona associated with small magnetic bipoles. We derive the solar differential rotation profile by tracing the motions of CBPs detected by the Atmospheric Imaging Assembly (AIA) instrument aboard the Solar Dynamics Observatory (SDO). We also investigate problems related to detection of coronal bright points resulting from instrument and detection algorithm limitations. To determine the positions and identification of coronal bright points we used a segmentation algorithm. A linear fit of their central meridian distance and latitude versus time was utilised to derive velocities. We obtained 906 velocity measurements in a time interval of only 2 days. The differential rotation profile can be expressed as $\omega_{rot} = (14.47\pm 0.10 + (0.6\pm 1.0)\sin^{2}(b) + (-4.7\pm 1.7)\sin^{4}(b))$\degr day$^{-1}$. Our result is in agreement with other work and it comes with reasonable errors in spite of the very short time interval used. This was made possible by the higher sensitivity and resolution of the AIA instrument compared to similar equipment as well as high cadence. The segmentation algorithm also played a crucial role by detecting so many CBPs, which reduced the errors to a reasonable level. Data and methods presented in this paper show a great potential to obtain very accurate velocity profiles, both for rotation and meridional motion and, consequently, Reynolds stresses. The amount of coronal bright point data that could be obtained from this instrument should also provide a great opportunity to study changes of velocity patterns with a temporal resolution of only a few months. Other possibilities are studies of evolution of CBPs and proper motions of magnetic elements on the Sun

Interactions of the magnetospheres of stars and close-in giant planets

Since the first discovery of an extrasolar planetary system more than a decade ago, hundreds more have been discovered. Surprisingly, many of these systems harbor Jupiter-class gas giants located close to the central star, at distances of 0.1 AU or less. Observations of chromospheric 'hot spots' that rotate in phase with the planetary orbit, and elevated stellar X-ray luminosities,suggest that these close-in planets significantly affect the structure of the outer atmosphere of the star through interactions between the stellar magnetic field and the planetary magnetosphere. Here we carry out the first detailed three-dimensional MagnetoHydroHynamics (MHD) simulation containing the two magnetic bodies and explore the consequences of such interactions on the steady-state coronal structure. The simulations reproduce the observable features of 1) increase in the total X-ray luminosity, 2) appearance of coronal hot spots, and 3) phase shift of these spots with respect to the direction of the planet. The proximate cause of these is an increase in the density of coronal plasma in the direction of the planet, which prevents the corona from expanding and leaking away this plasma via a stellar wind. The simulations produce significant low temperature heating. By including dynamical effects, such as the planetary orbital motion, the simulation should better reproduce the observed coronal heating