The Bargmann representation for the quantum mechanics on a sphere

The Bargmann representation is constructed corresponding to the coherent states for a particle on a sphere introduced in: K. Kowalski and J. Rembielinski, J. Phys. A: Math. Gen. 33, 6035 (2000). The connection is discussed between the introduced formalism and the standard approach based on the Hilbert space of square integrable functions on a sphere S^2.Comment: LaTe

Parameterizations of Chromospheric Condensations in dG and dMe Model Flare Atmospheres

The origin of the near-ultraviolet and optical continuum radiation in flares is critical for understanding particle acceleration and impulsive heating in stellar atmospheres. Radiative-hydrodynamic simulations in 1D have shown that high energy deposition rates from electron beams produce two flaring layers at T~10^4 K that develop in the chromosphere: a cooling condensation (downflowing compression) and heated non-moving (stationary) flare layers just below the condensation. These atmospheres reproduce several observed phenomena in flare spectra, such as the red wing asymmetry of the emission lines in solar flares and a small Balmer jump ratio in M dwarf flares. The high beam flux simulations are computationally expensive in 1D, and the (human) timescales for completing NLTE models with adaptive grids in 3D will likely be unwieldy for a time to come. We have developed a prescription for predicting the approximate evolved states, continuum optical depth, and the emergent continuum flux spectra of radiative-hydrodynamic model flare atmospheres. These approximate prescriptions are based on an important atmospheric parameter: the column mass (m_ref) at which hydrogen becomes nearly completely ionized at the depths that are approximately in steady state with the electron beam heating. Using this new modeling approach, we find that high energy flux density (>F11) electron beams are needed to reproduce the brightest observed continuum intensity in IRIS data of the 2014-Mar-29 X1 solar flare and that variation in m_ref from 0.001 to 0.02 g/cm2 reproduces most of the observed range of the optical continuum flux ratios at the peaks of M dwarf flares.Comment: 29 pages, 9 figures, accepted for publication in the Astrophysical Journa

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 uncertainty relations and squeezed states for the quantum mechanics on a circle

The uncertainty relations for the position and momentum of a quantum particle on a circle are identified minimized by the corresponding coherent states. The sqeezed states in the case of the circular motion are introduced and discussed in the context of the uncertainty relations.Comment: 4 figure

Bubble statistics and positioning in superhelically stressed DNA

We present a general framework to study the thermodynamic denaturation of double-stranded DNA under superhelical stress. We report calculations of position- and size-dependent opening probabilities for bubbles along the sequence. Our results are obtained from transfer-matrix solutions of the Zimm-Bragg model for unconstrained DNA and of a self-consistent linearization of the Benham model for superhelical DNA. The numerical efficiency of our method allows for the analysis of entire genomes and of random sequences of corresponding length ($10^6-10^9$ base pairs). We show that, at physiological conditions, opening in superhelical DNA is strongly cooperative with average bubble sizes of $10^2-10^3$ base pairs (bp), and orders of magnitude higher than in unconstrained DNA. In heterogeneous sequences, the average degree of base-pair opening is self-averaging, while bubble localization and statistics are dominated by sequence disorder. Compared to random sequences with identical GC-content, genomic DNA has a significantly increased probability to open large bubbles under superhelical stress. These bubbles are frequently located directly upstream of transcription start sites.Comment: to be appeared in Physical Review

A Unified Computational Model for Solar and Stellar Flares

We present a unified computational framework which can be used to describe impulsive flares on the Sun and on dMe stars. The models assume that the flare impulsive phase is caused by a beam of charged particles that is accelerated in the corona and propagates downward depositing energy and momentum along the way. This rapidly heats the lower stellar atmosphere causing it to explosively expand and dramatically brighten. Our models consist of flux tubes that extend from the sub-photosphere into the corona. We simulate how flare-accelerated charged particles propagate down one-dimensional flux tubes and heat the stellar atmosphere using the Fokker-Planck kinetic theory. Detailed radiative transfer is included so that model predictions can be directly compared with observations. The flux of flare-accelerated particles drives return currents which additionally heat the stellar atmosphere. These effects are also included in our models. We examine the impact of the flare-accelerated particle beams on model solar and dMe stellar atmospheres and perform parameter studies varying the injected particle energy spectra. We find the atmospheric response is strongly dependent on the accelerated particle cutoff energy and spectral index.Comment: Accepted for publication by the Astrophysical Journa

Causal sets and conservation laws in tests of Lorentz symmetry

Many of the most important astrophysical tests of Lorentz symmetry also assume that energy-momentum of the observed particles is exactly conserved. In the causal set approach to quantum gravity a particular kind of Lorentz symmetry holds but energy-momentum conservation may be violated. We show that incorrectly assuming exact conservation can give rise to a spurious signal of Lorentz symmetry violation for a causal set. However, the size of this spurious signal is much smaller than can be currently detected and hence astrophysical Lorentz symmetry tests as currently performed are safe from causal set induced violations of energy-momentum conservation.Comment: 8 pages, matches version published in PR

Coherent states for a particle on a sphere

The coherent states for a particle on a sphere are introduced. These states are labelled by points of the classical phase space, that is the position on the sphere and the angular momentum of a particle. As with the coherent states for a particle on a circle discussed in Kowalski K {\em et al} 1996 {\em J. Phys. A} {\bf 29} 4149, we deal with a deformation of the classical phase space related with quantum fluctuations. The expectation values of the position and the angular momentum in the coherent states are regarded as the best possible approximation of the classical phase space. The correctness of the introduced coherent states is illustrated by an example of the rotator.Comment: LaTeX, 16 pages, 2 figure