On the Formation of Boxy and Disky Elliptical Galaxies

The origin of boxy and disky elliptical galaxies is investigated. The results of two collisionless N-body simulations of spiral-spiral mergers with mass ratios of 1:1 and 3:1 are discussed and the projected properties of the merger remnants are investigated. It is shown that the equal-mass merger leads to an anisotropic, slowly rotating system with preferentially boxy isophotes and significant minor axis rotation. The unequal-mass merger results in the formation of a rotationally supported elliptical with disky isophotes and small minor axis rotation. The observed scatter in the kinematical and isophotal properties of both classes of elliptical galaxies can be explained by projection effects.Comment: 12 pages, incl. 5 figures, accepted by ApJ Letter

Extending PT symmetry from Heisenberg algebra to E2 algebra

The E2 algebra has three elements, J, u, and v, which satisfy the commutation relations [u,J]=iv, [v,J]=-iu, [u,v]=0. We can construct the Hamiltonian H=J^2+gu, where g is a real parameter, from these elements. This Hamiltonian is Hermitian and consequently it has real eigenvalues. However, we can also construct the PT-symmetric and non-Hermitian Hamiltonian H=J^2+igu, where again g is real. As in the case of PT-symmetric Hamiltonians constructed from the elements x and p of the Heisenberg algebra, there are two regions in parameter space for this PT-symmetric Hamiltonian, a region of unbroken PT symmetry in which all the eigenvalues are real and a region of broken PT symmetry in which some of the eigenvalues are complex. The two regions are separated by a critical value of g.Comment: 8 pages, 7 figure

Harmonic oscillator well with a screened Coulombic core is quasi-exactly solvable

In the quantization scheme which weakens the hermiticity of a Hamiltonian to its mere PT invariance the superposition V(x) = x^2+ Ze^2/x of the harmonic and Coulomb potentials is defined at the purely imaginary effective charges (Ze^2=if) and regularized by a purely imaginary shift of x. This model is quasi-exactly solvable: We show that at each excited, (N+1)-st harmonic-oscillator energy E=2N+3 there exists not only the well known harmonic oscillator bound state (at the vanishing charge f=0) but also a normalizable (N+1)-plet of the further elementary Sturmian eigenstates \psi_n(x) at eigencharges f=f_n > 0, n = 0, 1, ..., N. Beyond the first few smallest multiplicities N we recommend their perturbative construction.Comment: 13 pages, Latex file, to appear in J. Phys. A: Math. Ge

Vector Casimir effect for a D-dimensional sphere

The Casimir energy or stress due to modes in a D-dimensional volume subject to TM (mixed) boundary conditions on a bounding spherical surface is calculated. Both interior and exterior modes are included. Together with earlier results found for scalar modes (TE modes), this gives the Casimir effect for fluctuating ``electromagnetic'' (vector) fields inside and outside a spherical shell. Known results for three dimensions, first found by Boyer, are reproduced. Qualitatively, the results for TM modes are similar to those for scalar modes: Poles occur in the stress at positive even dimensions, and cusps (logarithmic singularities) occur for integer dimensions $D\le1$. Particular attention is given the interesting case of D=2.Comment: 20 pages, 1 figure, REVTe

The Isophotal Structure of Early-Type Galaxies in the SDSS: Dependence on AGN Activity and Environment

We study the dependence of the isophotal shape of early-type galaxies on their absolute B-band magnitude, their dynamical mass, and their nuclear activity and environment, using an unprecedented large sample of 847 early-type galaxies identified in the SDSS by Hao et al (2006). We find that the fraction of disky galaxies smoothly decreases with increasing luminosity. The large sample allows us to describe these trends accurately with tight linear relations that are statistically robust against the uncertainty in the isophotal shape measurements. There is also a host of significant correlations between the disky fraction and indicators of nuclear activity (both in the optical and in the radio) and environment (soft X-rays, group mass, group hierarchy). Our analysis shows however that these correlations can be accurately matched by assuming that the disky fraction depends only on galaxy luminosity or mass. We therefore conclude that neither the level of activity, nor group mass or group hierarchy help in better predicting the isophotal shape of early-type galaxies.Comment: 31 pages, 10 figures, accepted for publication in Ap

Homogeneity of Stellar Populations in Early-Type Galaxies with Different X-ray Properties

We have found the stellar populations of early-type galaxies are homogeneous with no significant difference in color or Mg2 index, despite the dichotomy between X-ray extended early-type galaxies and X-ray compact ones. Since the X-ray properties reflect the potential gravitational structure and hence the process of galaxy formation, the homogeneity of the stellar populations implies that the formation of stars in early-type galaxies predat es the epoch when the dichotomy of the potential structure was established.Comment: 6 pages, 5 figures, accepted for publication in Ap

Chaotic systems in complex phase space

This paper examines numerically the complex classical trajectories of the kicked rotor and the double pendulum. Both of these systems exhibit a transition to chaos, and this feature is studied in complex phase space. Additionally, it is shown that the short-time and long-time behaviors of these two PT-symmetric dynamical models in complex phase space exhibit strong qualitative similarities.Comment: 22 page, 16 figure

Spin switching via quantum dot spin valves

We develop a theory for spin transport and magnetization dynamics in a quantum-dot spin valve, i.e., two magnetic reservoirs coupled to a quantum dot. Our theory is able to take into account effects of strong correlations. We demonstrate that, as a result of these strong correlations, the dot gate voltage enables control over the current-induced torques on the magnets, and, in particular, enables voltage-controlled magnetic switching. The electrical resistance of the structure can be used to read out the magnetic state. Our model may be realized by a number of experimental systems, including magnetic scanning-tunneling microscope tips and artificial quantum dot systems