Abstract:
Some aspects of lasing at vibronic transitions in impurity crystals are theoretically studied. The threshold conditions for a vibronic laser are shown to be dependent on the strength of interaction of optical centers with a local vibration, which forms the vibronic spectrum, and the crystal lattice temperature. The theory can be easily generalized to the spectrum containing a structureless phonon sideband and well agrees with the experimental temperature dependence of the output power of a Mg2SiO4:Cr4+ forsterite laser.

Abstract:
The paper examines superradiance in impurity crystals in the field of a coherent phonon wave excited by two ultrashort laser pulses via Raman scattering processes at the moment of preparation of the initial state of an ensemble of emitters. It is shown that by varying the power of the excitation pulses and their mutual direction of propagation, one can control the superradiance parameters and extract data on the electron-phonon coupling constant and its anisotropy.

Abstract:
A mean field theory for Raman superradiance (SR) with recoil is presented, where the typical SR signatures are recovered, such as quadratic dependence of the intensity on the number of atoms and inverse proportionality of the time scale to the number of atoms. A comparison with recent experiments and theories on Rayleigh SR and collective atomic recoil lasing (CARL) are included. The role of recoil is shown to be in the decay of atomic coherence and breaking of the symmetry of the SR end-fire modes.

Abstract:
We discuss semiempirical approaches and parametric methods developed for modeling molecular vibronic spectra. These methods, together with databases of molecular fragments, have proved efficient and flexible for solving various problems ranging from detailed interpretation of conventional vibronic spectra and calculation of radiative transition probabilities to direct simulations of dynamical (time-resolved) spectra and spectrochemical analysis of individual substances and mixtures. A number of specific examples and applications presented here show the potential of the semiempirical approach for predictive calculations of spectra and solution of inverse spectral problems. It is noteworthy that these advances provide computational insights into developing theories of photoinduced isomer transformations and nonradiative transitions in polyatomic molecules and molecular ensembles, theory of new methods for standardless quantitative spectral analysis.

Abstract:
Superradiance is a radiation enhancement process that involves dissipative systems. With a 60 year-old history, superradiance has played a prominent role in optics, quantum mechanics and especially in relativity and astrophysics. In General Relativity, black-hole superradiance is permitted by dissipation at the event horizon, that allows for energy, charge and angular momentum extraction from the vacuum, even at the classical level. Black-hole superradiance is intimately connected to the black-hole area theorem, Penrose process, tidal forces and even Hawking radiation, which can be interpreted as a quantum version of black-hole superradiance. Various mechanisms (as diverse as massive fields, magnetic fields, anti-de Sitter boundaries, nonlinear interactions, etc...) can confine the amplified radiation and give rise to strong instabilities. These "black-hole bombs" have applications in searches of dark matter and of physics beyond the Standard Model, are associated to the threshold of formation of new black hole solutions that evade the no-hair theorems, can be studied in the laboratory by devising analog models of gravity, and might even provide a holographic description of spontaneous symmetry breaking and superfluidity through the gauge-gravity duality. This work is meant to provide a unified picture of this multifaceted subject, which was missing in the literature. We focus on the recent developments in the field, and work out a number of novel examples and applications, ranging from fundamental physics to astrophysics.

Abstract:
We review the basic theoretical background for working out a variational band solution for vibronic polarons in crystals. It is based on the Lee-Low-Pines proposal as extended by Thomas et al. for describing Jahn-Teller polarons along a linear chain of atoms. The variational properties of antiadiabatic itinerant polarons are also discussed.

Abstract:
Vibronic coupling constants in the monoanionic, trianionic, and excited states of picene are evaluated from the total energy gradients using the density functional theory. Employing the calculated vibronic coupling constants in the excited state of the neutral molecule, electron energy loss spectrum (EELS) is simulated to be compared with the experimental spectrum. The calculated vibronic coupling constants are analyzed in terms of the vibronic coupling density which enables us to analyze vibronic couplings based on the relation between the electronic and vibrational structures. The vibronic coupling constants reported by Kato et al. [J. Chem. Phys. 116, 3420 (2002) and Phys. Rev. Lett. 107, 077001 (2011)] are critically discussed based on the vibronic coupling density analysis.

Abstract:
We review basic theoretical concepts and developments regarding the local and itinerant properties of off-center vibronic polarons in crystals. These include the electron self-trapping and the local rotation of the species on a square planar lattice. Phase transitions within the gas of vibronic small polarons are also discussed.

Abstract:
Filamentary high-temperature superconductivity (HTSC) theory differs fundamentally from continuous HTSC theories because it emphasizes self-organized, discrete dopant networks and does not make the effective medium approximation (EMA). Analysis of neutron and infrared (especially with c-axis polarization) vibrational spectra, primarily for YBa2Cu3O(6+x), within the filamentary framework, shows that the observed vibronic anomalies near 400 cm-1 (50 meV) are associated with curvilinear filamentary paths. these paths pass through cuprate chains and planes, as well as resonant tunneling centers in the BaO layers. The analysis and the data confirm earlier filamentary structural models containing ferroelastic domains of 3-4 nm in the CuO2 planes; it is these nanodomains that are responsible for the discrete glassy nature of both electronic and vibronic properties. Chemical trends in vibronic energies and oscillator strengths, both for neutron and photon scattering, that were anomalous in continuum models, are readily explained by the filamentary model.

Abstract:
A comparative analysis is given of spin superradiance and atomic superradiance. Their similarities and distinctions are emphasized. It is shown that, despite a close analogy, these phenomena are fundamentally different. In atomic systems, superradiance is a self-organized process, in which both the initial cause, being spontaneous emission, as well as the collectivizing mechanism of their interactions through the common radiation field, are of the same physical nature. Contrary to this, in actual spin systems with dipole interactions, the latter are the major reason for spin motion. Electromagnetic spin interactions through radiation are negligible and can never produce collective effects. The possibility of realizing superradiance in molecular magnets by coupling them to a resonant circuit is discussed.