Asymptotics of Quantum Relative Entropy From Representation Theoretical Viewpoint

In this paper it was proved that the quantum relative entropy $D(\sigma \| \rho)$ can be asymptotically attained by Kullback Leibler divergences of probabilities given by a certain sequence of POVMs. The sequence of POVMs depends on $\rho$, but is independent of the choice of $\sigma$.Comment: LaTeX2e. 8 pages. The title was changed from "Asymptotic Attainment for Quantum Relative Entropy

Kinematic approach to the mixed state geometric phase in nonunitary evolution

A kinematic approach to the geometric phase for mixed quantal states in nonunitary evolution is proposed. This phase is manifestly gauge invariant and can be experimentally tested in interferometry. It leads to well-known results when the evolution is unitary.Comment: Minor changes; journal reference adde

Quantum thermodynamics with missing reference frames: Decompositions of free energy into non-increasing components

If an absolute reference frame with respect to time, position, or orientation is missing one can only implement quantum operations which are covariant with respect to the corresponding unitary symmetry group G. Extending observations of Vaccaro et al., I argue that the free energy of a quantum system with G-invariant Hamiltonian then splits up into the Holevo information of the orbit of the state under the action of G and the free energy of its orbit average. These two kinds of free energy cannot be converted into each other. The first component is subadditive and the second superadditive; in the limit of infinitely many copies only the usual free energy matters. Refined splittings of free energy into more than two independent (non-increasing) terms can be defined by averaging over probability measures on G that differ from the Haar measure. Even in the presence of a reference frame, these results provide lower bounds on the amount of free energy that is lost after applying a covariant channel. If the channel properly decreases one of these quantities, it decreases the free energy necessarily at least by the same amount, since it is unable to convert the different forms of free energies into each other.Comment: 17 pages, latex, 1 figur

The Potential-Density Phase Shift Method for Determining the Corotation Radii in Spiral and Barred Galaxies

We have developed a new method for determining the corotation radii of density waves in disk galaxies, which makes use of the radial distribution of an azimuthal phase shift between the potential and density wave patterns. The approach originated from improved theoretical understandings of the relation between the morphology and kinematics of galaxies, and on the dynamical interaction between density waves and the basic-state disk stars which results in the secular evolution of disk galaxies. In this paper, we present the rationales behind the method, and the first application of it to several representative barred and grand-design spiral galaxies, using near-infrared images to trace the mass distributions, as well as to calculate the potential distributions used in the phase shift calculations. We compare our results with those from other existing methods for locating the corotations, and show that the new method both confirms the previously-established trends of bar-length dependence on galaxy morphological types, as well as provides new insights into the possible extent of bars in disk galaxies. Application of the method to a larger sample and the preliminary analysis of which show that the phase shift method is likely to be a generally-applicable, accurate, and essentially model-independent method for determining the pattern speeds and corotation radii of single or nested density wave patterns in galaxies. Other implications of this work are: most of the nearby bright disk galaxies appear to possess quasi-stationary spiral modes; that these density wave modes and the associated basic state of the galactic disk slowly transform over time; and that self-consistent N-particle systems contain physics not revealed by the passive orbit analysis approaches.Comment: 48 pages, 16 figures. Accepted for publication in the Astronomical Journa

Geometric phase distributions for open quantum systems

In an open system, the geometric phase should be described by a distribution. We show that a geometric phase distribution for open system dynamics is in general ambiguous, but the imposition of reasonable physical constraints on the environment and its coupling with the system yields a unique geometric phase distribution that applies even for mixed states, non-unitary dynamics, and non-cyclic evolutions.Comment: Some minor revisions, references update

Magnetic fields in barred galaxies. II. Dynamo models

We study the generation and maintenance of large-scale magnetic fields in barred galaxies. We take a velocity field (with strong noncircular components) from a published gas dynamical simulation of Athanassoula (1992), and use this as input to a galactic dynamo calculation. Our work is largely motivated by recent high quality VLA radio observations of the barred galaxy NGC 1097, and we compare our results in detail with the regular magnetic fields deduced from these observations. We are able to reproduce most of the conspicuous large-scale features of the observed regular field, including the field structure in the central regions, by using a simple mean-field dynamo model in which the intensity of interstellar turbulence (more precisely, the turbulent diffusivity) is enhanced by a factor of 2-6 in the dust lanes and near the circumnuclear ring. We argue that magnetic fields can be dynamically important, and therefore should be included in models of gas flow in barred galaxies.Comment: 16 pages, 13 figures, submitted to Astronomy and Astrophysics. Revised version (changes shown in bold face

Quantum ratchets in dissipative chaotic systems

Using the method of quantum trajectories we study a quantum chaotic dissipative ratchet appearing for particles in a pulsed asymmetric potential in the presence of a dissipative environment. The system is characterized by directed transport emerging from a quantum strange attractor. This model exhibits, in the limit of small effective Planck constant, a transition from quantum to classical behavior, in agreement with the correspondence principle. We also discuss parameter values suitable for implementation of the quantum ratchet effect with cold atoms in optical lattices.Comment: Significant changes: Several text improvements and new results. Figure 2 modified. Figure 4 adde

A formula for the Bloch vector of some Lindblad quantum systems

Using the Bloch representation of an N-dimensional quantum system and immediate results from quantum stochastic calculus, we establish a closed formula for the Bloch vector, hence also for the density operator, of a quantum system following a Lindblad evolution with selfadjoint Lindblad operators.Comment: Accepted in Phys. Lett. A (shorter version than original

A Dust-Penetrated Classification Scheme for Bars as Inferred from their Gravitational Force Fields

The division of galaxies into ``barred'' (SB) and ``normal'' (S) spirals is a fundamental aspect of the Hubble galaxy classification system. This ``tuning fork'' view was revised by de Vaucouleurs, whose classification volume recognized apparent ``bar strength'' (SA, SAB, SB) as a continuous property of galaxies called the ``family''. However, the SA, SAB, and SB families are purely visual judgments that can have little bearing on the actual bar strength in a given galaxy. Until very recently, published bar judgments were based exclusively on blue light images, where internal extinction or star formation can either mask a bar completely or give the false impression of a bar in a nonbarred galaxy. Near-infrared camera arrays, which principally trace the old stellar populations in both normal and barred galaxies, now facilitate a quantification of bar strength in terms of their gravitational potentials and force fields. In this paper, we show that the maximum value, Qb, of the ratio of the tangential force to the mean radial force is a quantitative measure of the strength of a bar. Qb does not measure bar ellipticity or bar shape, but rather depends on the actual forcing due to the bar embedded in its disk. We show that a wide range of true bar strengths characterizes the category ``SB'', while de Vaucouleurs category ``SAB'' corresponds to a much narrower range of bar strengths. We present Qb values for 36 galaxies, and we incorporate our bar classes into a dust-penetrated classification system for spiral galaxies.Comment: Accepted for publication in the Astrophysical Journal (LaTex, 30 pages + 3 figures); Figs. 1 and 3 are in color and are also available at http://bama.ua.edu/~rbuta/bars