Constraints on transmission, dispersion, and density of states in dielectric multilayers and stepwise potential barriers with arbitrary layer arrangement

Normal-incidence transmission and dispersion properties of optical multilayers and one-dimensional stepwise potential barriers in the non-tunneling regime are analytically investigated. The optical paths of every constituent layer in a multilayer structure, as well as the parameters of every step of the stepwise potential barrier, are constrained by a generalized quarter-wave condition. No other restrictions on the structure geometry is imposed, i.e., the layers are arranged arbitrarily. We show that the density of states (DOS) spectra of the multilayer or barrier in question are subject to integral conservation rules similar to the Barnett-Loudon sum rule but ocurring within a finite frequency or energy interval. In the optical case, these frequency intervals are regular. For the potential barriers, only non-periodic energy intervals can be present in the spectrum of any given structure, and only if the parameters of constituent potential steps are properly chosen. Abstract The integral conservation relations derived analytically have also been verified numerically. The relations can be used in dispersion-engineered multilayer-based devices, e.g., ultrashort pulse compressors or ultracompact optical delay lines, as well as to design multiple-quantum-well electronic heterostructures with engineered DOS.Comment: 10 pages, 5 figures, to be submitted to PR

Gravitational catalysis of chiral and color symmetry breaking of quark matter in hyperbolic space

We study the dynamical breaking of chiral and color symmetries of dense quark matter in the ultrastatic hyperbolic spacetime $R\otimes H^3$ in the framework of an extended Nambu--Jona-Lasinio model. On the basis of analytical expressions for chiral and color condensates as functions of curvature and temperature, the phenomenon of dimensional reduction and gravitational catalysis of symmetry breaking in strong gravitational field is demonstrated in the regime of weak coupling constants. In the case of strong couplings it is shown that curvature leads to small corrections to the flat-space values of condensate and thus enhances the symmetry breaking effects. Finally, using numerical calculations phase transitions under the influence of chemical potential and negative curvature are considered and the phase portrait of the system is constructed.Comment: 14 pages, 5 figure

Chiral dynamics in QED and QCD in a magnetic background and nonlocal noncommutative field theories

We study the connection of the chiral dynamics in QED and QCD in a strong magnetic field with noncommutative field theories (NCFT). It is shown that these dynamics determine complicated nonlocal NCFT. In particular, although the interaction vertices for electrically neutral composites in these gauge models can be represented in the space with noncommutative spatial coordinates, there is no field transformation that could put the vertices in the conventional form considered in the literature. It is unlike the Nambu-Jona-Lasinio (NJL) model in a magnetic field where such a field transformation can be found, with a cost of introducing an exponentially damping form factor in field propagators. The crucial distinction between these two types of models is in the characters of their interactions, being short-range in the NJL-like models and long-range in gauge theories. The relevance of the NCFT connected with the gauge models for the description of the quantum Hall effect in condensed matter systems with long-range interactions is briefly discussed.Comment: 19 pages, REVTeX4, v2: clarifications added, v3: to match PRD versio

Inhomogeneous charged pion condensation phenomenon in the NJL2_2 model with quark number and isospin chemical potentials

The properties of two-flavored massive Nambu--Jona-Lasinio model in (1+1)-dimensional spacetime are investigated in the presence of isospin and quark number chemical potentials. The consideration is performed in the large-$N_c$ limit, where $N_c$ is the number of colored quarks. It is shown in the framework of this model that charged pion condensation phenomenon of dense quark/hadron isotopically asymmetric matter is rather a spatially inhomogeneous than a homogeneous one.Comment: 11 pages, 8 figures; version accepted for publication in PRD. arXiv admin note: text overlap with arXiv:1106.2928, arXiv:1102.407

ВИКОРИСТАННЯ ПРОГРАМИ «ВИХОВАННЯ ХАРАКТЕРУ» В СУЧАСНІЙ АМЕРИКАНСЬКІЙ ШКОЛІ. (Using the Program "Character Educations" in modern American schools.)

У статті проаналізовано поняття, мету, зміст, методи та засоби реалізації програми «Виховання характеру» в сучасній американській школі. Розкрито актуальність її використання та географію поширення в школах США. (In this article the concept, purpose, contents, methods and means of the program «Character education» in modern American schools are analyzed. The importance and geography of its use in the schools of the USA is revealed.

Color superconductivity in the static Einstein Universe

We study the behavior of quark and diquark condensates in dense quark matter under the influence of a gravitational field adopting as a simple model the static $D-$dimensional Einstein Universe. Calculations are performed in the framework of the extended Nambu--Jona-Lasinio model at finite temperature and quark density on the basis of the thermodynamic potential and the gap equations. Quark and diquark condensates as functions of the chemical potential and temperature at different values of the curvature have been studied. Phase portraits of the system have been constructed

Chiral phase transitions in strong chromomagnetic fields at finite temperature and dimensional reduction

Dynamical fermion mass generation in external chromomagnetic fields is considered at non--zero temperature. The general features of dynamical chiral symmetry breaking ($D\chi SB$) are investigated for several field configurations in relation to their symmetry properties and the form of the quark spectrum. According to the fields, there arises dimensional reduction by one or two units. In all cases there exists $D\chi SB$ even at weak quark attraction, confirming the idea about the dimensional insensitivity of this mechanism in a chromomagnetic field.Comment: LATEX file, 12 pages, no figure

Switchable lasing in coupled multimode microcavities

We propose the new concept of a switchable multimode microlaser. As a generic, realistic model of a multimode microresonator a system of two coupled defects in a two-dimensional photonic crystal is considered. We demonstrate theoretically that lasing of the cavity into one selected resonator mode can be caused by injecting an appropriate optical pulse at the onset of laser action (injection seeding). Temporal mode-to-mode switching by re-seeding the cavity after a short cool-down period is demonstrated by direct numerical solution. A qualitative analytical explanation of the mode switching in terms of the laser bistability is presented.Comment: Accepted for publication in Physical Review Letters. Published, somewhat shortened versio

Chiral density waves in the NJL2_2 model with quark number and isospin chemical potentials

We investigate the phase portrait of the (1+1)-dimensional massless two-flavored NJL$_2$ model containing a quark number chemical potential $\mu$ and an isospin chemical potential $\mu_I$ in the limit of a large number of colors $N_c\to\infty$. Particular attention is paid to the question to what extent the inclusion of an isospin asymmetry affects chiral condensates to have a spatial inhomogeneity in the form of the so-called chiral density waves (CDW) (chiral spirals). It is shown that at zero temperature and comparatively small values of $\mu$, i.e. at $\mu<\mu_c\approx 0.68M_0$ ($M_0$ is the dynamical quark mass in the vacuum) only the homogeneous charged pion condensation phase is realized for arbitrary nonzero values of $\mu_I$. Contrary to this, for large values of $\mu>\mu_c$, two CDW phases appear in the $(\mu_I,\mu)$-phase diagram of the model. In the first phase, CDWs are clockwise twisted chiral spirals and in the second phase they are counterclockwise. The influence of nonzero temperature on the formation of the CDW phases is also investigated.Comment: 14 pages, 9 figures; typos corrected; one reference adde