New series of 3D lattice integrable models

In this paper we present a new series of 3-dimensional integrable lattice models with $N$ colors. The case $N=2$ generalizes the elliptic model of our previous paper. The weight functions of the models satisfy modified tetrahedron equations with $N$ states and give a commuting family of two-layer transfer-matrices. The dependence on the spectral parameters corresponds to the static limit of the modified tetrahedron equations and weights are parameterized in terms of elliptic functions. The models contain two free parameters: elliptic modulus and additional parameter $\eta$. Also we briefly discuss symmetry properties of weight functions of the models.Comment: 17 pages, IHEP-93-126, Late

New solution of vertex type tetrahedron equations

In this paper we formulate a new N-state spin integrable model on a three-dimensional lattice with spins interacting round each elementary cube of the lattice. This model can be also reformulated as a vertex type model. Weight functions of the model satisfy tetrahedron equations.Comment: 12 pages, LaTeX, IHEP-94-10

PsiPsi - Vectors for Three Dimensional Models

In this paper we apply the method of psi-vectors to three dimensional statistical models. This method gives the correspondence between the Bazhanov -- Baxter model and its vertex formulation. Considering psi-vectors for the Planar model, we obtain its self-duality.Comment: 11 pages, LaTeX, no figure

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

Effects of Electron-Electron and Electron-Phonon Interactions in Weakly Disordered Conductors and Heterostuctures

We investigate quantum corrections to the conductivity due to the interference of electron-electron (electron-phonon) scattering and elastic electron scattering in weakly disordered conductors. The electron-electron interaction results in a negative $T^2 \ln T$-correction in a 3D conductor. In a quasi-two-dimensional conductor, $d < v_F/T$ ($d$ is the thickness, $v_F$ is the Fermi velocity), with 3D electron spectrum this correction is linear in temperature and differs from that for 2D electrons (G. Zala et. al., Phys. Rev.B {\bf 64}, 214204 (2001)) by a numerical factor. In a quasi-one-dimensional conductor, temperature-dependent correction is proportional to $T^2$. The electron interaction via exchange of virtual phonons also gives $T^2$-correction. The contribution of thermal phonons interacting with electrons via the screened deformation potential results in $T^4$-term and via unscreened deformation potential results in $T^2$-term. The interference contributions dominate over pure electron-phonon scattering in a wide temperature range, which extends with increasing disorder.Comment: 6 pages, 2figure