Spontaneous symmetry emergence as a source of new class of phase transitions

Spontaneous symmetry breaking in systems with symmetry is core-stone phenomenon accompanying second-order phase transitions. Here, we predict an opposite phenomenon, namely, spontaneous symmetry emergence in a system without symmetry. On the example of two coupled oscillators interacting non-symmetrically with a set of oscillators whose frequencies uniformly fill a finite frequency range, we demonstrate that the system state can acquire symmetry, which is not inherent to the system Hamiltonian. The symmetry emergence manifests in the change of the system dynamics, which can be interpreted as a new class of phase transitions

BLR kinematics and Black Hole Mass in Markarian 6

We present results of the optical spectral and photometric observations of the nucleus of Markarian 6 made with the 2.6-m Shajn telescope at the Crimean Astrophysical Observatory. The continuum and emission Balmer line intensities varied more than by a factor of two during 1992-2008. The lag between the continuum and Hbeta emission line flux variations is 21.1+-1.9 days. For the Halpha line the lag is about 27 days but its uncertainty is much larger. We use Monte-Carlo simulation of the random time series to check the effect of our data sampling on the lag uncertainties and we compare our simulation results with those obtained by random subset selection (RSS) method of Peterson et al. (1998). The lag in the high-velocity wings are shorter than in the line core in accordance with the virial motions. However, the lag is slightly larger in the blue wing than in the red wing. This is a signature of the infall gas motion. Probably the BLR kinematic in the Mrk 6 nucleus is a combination of the Keplerian and infall motions. The velocity-delay dependence is similar for individual observational seasons. The measurements of the Hbeta line width in combination with the reverberation lag permits us to determine the black hole mass, M_BH=(1.8+-0.2)x10^8 M_sun. This result is consistent with the AGN scaling relationships between the BLR radius and the optical continuum luminosity (R_BLR is proportional to L^0.5) as well as with the black-hole mass-luminosity relationship (M_BH-L) under the Eddington luminosity ratio for Mrk 6 to be L_bol/L_Edd ~ 0.01.Comment: 17 pages, 10 figures, accepted for publication in MNRA

Phase transition at exceptional point in Hermitian systems

Exceptional point (EP) is a spectral singularity in non-Hermitian systems. The passing over the EP leads to a phase transition which endows the system with unconventional features that find a wide range of applications. However, the need of using the dissipation and amplification limits the possible applications of systems with the EP. In this work, the concept of phase transitions at the EP is expanded to Hermitian systems which are free from dissipation and amplification. It is considered a composite Hermitian system including both two coupled subsystems and their environment consisting only of several tens degrees of freedom such that the energy can return from the environment to the subsystems. It is shown that the dynamics of such a Hermitian system demonstrates a clear phase transition. It occurs at the critical coupling strength between subsystems corresponding to the EP in the non-Hermitian system. This phase transition manifests itself even in the non-Markovian regime of the system dynamics in which collapses and revivals of the energy occur. A photonic circuit is proposed for observing the EP phase transition in systems free from dissipation and amplification. The obtained results extend the range of practical applications of the EP phenomena to Hermitian systems.Comment: 16 pages, 8 figure

Self-consistent description of relaxation processes in systems with ultra- and deep-strong coupling

An ultra-strong coupling regime takes place in a compound system when a coupling strength between the subsystems exceeds one tenth of the system eigenfrequency. It transforms into a deep-strong coupling regime when the coupling strength exceeds the system eigenfrequency. In these regimes, there are difficulties with description of relaxation processes without explicit considering of environment degrees of freedom. To correctly evaluate the relaxation rates, it is necessary to consider the interaction of the system with its environment taking into account the counter-rotating wave and diamagnetic terms. We develop a self-consistent theory for calculation of the relaxation rates in the systems, in which the coupling strength is of the order of the system eigenfrequency. We demonstrate that the increase in the coupling strength can lead to a significant decrease in the relaxation rates. In particular, we show that for frequency-independent density of states of the environment, the relaxation rates decrease exponentially with the increase in the coupling strength. This fact can be used to suppress losses by tuning the strength coupling and the environment states

Functional Tetrahedron Equation

We describe a scheme of constructing classical integrable models in 2+1-dimensional discrete space-time, based on the functional tetrahedron equation - equation that makes manifest the symmetries of a model in local form. We construct a very general "block-matrix model" together with its algebro-geometric solutions, study its various particular cases, and also present a remarkably simple scheme of quantization for one of those cases.Comment: LaTeX, 16 page

Variability of Fe II Emission Features in the Seyfert 1 Galaxy NGC 5548

We study the low-contrast Fe II emission blends in the ultraviolet (1250--2200A) and optical (4000--6000A) spectra of the Seyfert 1 galaxy NGC 5548 and show that these features vary in flux and that these variations are correlated with those of the optical continuum. The amplitude of variability of the optical Fe II emission is 50% - 75% that of Hbeta and the ultraviolet Fe II emission varies with an even larger amplitude than Hbeta. However, accurate measurement of the flux in these blends proves to be very difficult even using excellent Fe II templates to fit the spectra. We are able to constrain only weakly the optical Fe II emission-line response timescale to a value less than several weeks; this upper limit exceeds all the reliably measured emission-line lags in this source so it is not particularly meaningful. Nevertheless, the fact that the optical Fe II and continuum flux variations are correlated indicates that line fluorescence in a photoionized plasma, rather than collisional excitation, is responsible for the Fe II emission. The iron emission templates are available upon request.Comment: 34 pages including 12 figures and 2 tables. Accepted for publication by ApJ (tentatively in vol. 626 June 10, 2005

Higher order glass-transition singularities in colloidal systems with attractive interactions

The transition from a liquid to a glass in colloidal suspensions of particles interacting through a hard core plus an attractive square-well potential is studied within the mode-coupling-theory framework. When the width of the attractive potential is much shorter than the hard-core diameter, a reentrant behavior of the liquid-glass line, and a glass-glass-transition line are found in the temperature-density plane of the model. For small well-width values, the glass-glass-transition line terminates in a third order bifurcation point, i.e. in a A_3 (cusp) singularity. On increasing the square-well width, the glass-glass line disappears, giving rise to a fourth order A_4 (swallow-tail) singularity at a critical well width. Close to the A_3 and A_4 singularities the decay of the density correlators shows stretching of huge dynamical windows, in particular logarithmic time dependence.Comment: 19 pages, 12 figures, Phys. Rev. E, in prin

Reverberation Mapping Results from MDM Observatory

We present results from a multi-month reverberation mapping campaign undertaken primarily at MDM Observatory with supporting observations from around the world. We measure broad line region (BLR) radii and black hole masses for six objects. A velocity-resolved analysis of the H_beta response shows the presence of diverse kinematic signatures in the BLR.Comment: To appear in the Proceedings of the IAU Symposium No. 267: Co-Evolution of Central Black Holes and Galaxies, Rio de Janeiro, 200