A theoretical look at the direct detection of giant planets outside the Solar System

Astronomy is at times a science of unexpected discovery. When it is, and if we are lucky, new intellectual territories emerge to challenge our views of the cosmos. The recent indirect detections using high-precision Doppler spectroscopy of now more than one hundred giant planets orbiting more than one hundred nearby stars is an example of such rare serendipity. What has been learned has shaken our preconceptions, for none of the planetary systems discovered to date is like our own. However, the key to unlocking a planet's chemical, structural, and evolutionary secrets is the direct detection of the planet's light. I review the embryonic theory of the spectra, atmospheres, and light curves of irradiated giant planets and put this theory into the context of the many proposed astronomical campaigns to image them.Comment: pre-editorial, non-copyrighted version of Review Article just published in Nature. 5 figures, one in JPEG forma

Euclidean resonance in a magnetic field

An analogy between Wigner resonant tunneling and tunneling across a static potential barrier in a static magnetic field is found. Whereas in the process of Wigner tunneling an electron encounters a classically allowed regions, where a discrete energy level coincides with its energy, in the magnetic field a potential barrier is a constant in the direction of tunneling. Along the tunneling path the certain regions are formed, where, in the classical language, the kinetic energy of the motion perpendicular to tunneling is negative. These regions play a role of potential wells, where a discrete energy level can coincide with the electron energy. Such phenomenon, which occurs at the certain magnetic field, is called Euclidean resonance and substantially depends on a shape of potential forces in the direction perpendicular to tunneling. Under conditions of Euclidean resonance a long distance underbarrier motion is possible.Comment: 7 pages, 4 figure

Chiral tunneling in single and bilayer graphene

We review chiral (Klein) tunneling in single-layer and bilayer graphene and present its semiclassical theory, including the Berry phase and the Maslov index. Peculiarities of the chiral tunneling are naturally explained in terms of classical phase space. In a one-dimensional geometry we reduced the original Dirac equation, describing the dynamics of charge carriers in the single layer graphene, to an effective Schr\"odinger equation with a complex potential. This allowed us to study tunneling in details and obtain analytic formulas. Our predictions are compared with numerical results. We have also demonstrated that, for the case of asymmetric n-p-n junction in single layer graphene, there is total transmission for normal incidence only, side resonances are suppressed.Comment: submitted to Proceedings of Nobel Symposium on graphene, May 201

Low-energy fusion caused by an interference

Fusion of two deuterons of room temperature energy is studied. The nuclei are in vacuum with no connection to any external source (electric or magnetic field, illumination, surrounding matter, traps, etc.) which may accelerate them. The energy of the two nuclei is conserved and remains small during the motion through the Coulomb barrier. The penetration through this barrier, which is the main obstacle for low-energy fusion, strongly depends on a form of the incident flux on the Coulomb center at large distances from it. In contrast to the usual scattering, the incident wave is not a single plane wave but the certain superposition of plane waves of the same energy and various directions, for example, a convergent conical wave. As a result of interference, the wave function close to the Coulomb center is determined by a cusp caustic which is probed by de Broglie waves. The particle flux gets away from the cusp and moves to the Coulomb center providing a not small probability of fusion (cusp driven tunneling). Getting away from a caustic cusp also occurs in optics and acoustics

Landau-Zener problem for energies close to potential crossing points

We examine one overlooked in previous investigations aspect of well - known Landau - Zener (LZ) problem, namely, the behavior in the intermediate, i.e. close to a crossing point, energy region, when all four LZ states are coupled and should be taken into account. We calculate the 4 x 4 connection matrix in this intermediate energy region, possessing the same block structure as the known connection matrices for the tunneling and in the over-barrier regions of the energy, and continously matching those in the corresponding energy regions.Comment: 5 pages, 1 figur

Conductivity and quasinormal modes in holographic theories

We show that in field theories with a holographic dual the retarded Green's function of a conserved current can be represented as a convergent sum over the quasinormal modes. We find that the zero-frequency conductivity is related to the sum over quasinormal modes and their high-frequency asymptotics via a sum rule. We derive the asymptotics of the quasinormal mode frequencies and their residues using the phase-integral (WKB) approach and provide analytic insight into the existing numerical observations concerning the asymptotic behavior of the spectral densities.Comment: 24 pages, 3 figure

Vacuum decay in quantum field theory

We study the contribution to vacuum decay in field theory due to the interaction between the long and short-wavelength modes of the field. The field model considered consists of a scalar field of mass $M$ with a cubic term in the potential. The dynamics of the long-wavelength modes becomes diffusive in this interaction. The diffusive behaviour is described by the reduced Wigner function that characterizes the state of the long-wavelength modes. This function is obtained from the whole Wigner function by integration of the degrees of freedom of the short-wavelength modes. The dynamical equation for the reduced Wigner function becomes a kind of Fokker-Planck equation which is solved with suitable boundary conditions enforcing an initial metastable vacuum state trapped in the potential well. As a result a finite activation rate is found, even at zero temperature, for the formation of true vacuum bubbles of size $M^{-1}$. This effect makes a substantial contribution to the total decay rate.Comment: 27 pages, RevTeX, 1 figure (uses epsf.sty

Moyal star product approach to the Bohr-Sommerfeld approximation

The Bohr-Sommerfeld approximation to the eigenvalues of a one-dimensional quantum Hamiltonian is derived through order $\hbar^2$ (i.e., including the first correction term beyond the usual result) by means of the Moyal star product. The Hamiltonian need only have a Weyl transform (or symbol) that is a power series in $\hbar$, starting with $\hbar^0$, with a generic fixed point in phase space. The Hamiltonian is not restricted to the kinetic-plus-potential form. The method involves transforming the Hamiltonian to a normal form, in which it becomes a function of the harmonic oscillator Hamiltonian. Diagrammatic and other techniques with potential applications to other normal form problems are presented for manipulating higher order terms in the Moyal series.Comment: 27 pages, no figure

Vacuum decay in quantum field theory

We study the contribution to vacuum decay in field theory due to the interaction between the long and short-wavelength modes of the field. The field model considered consists of a scalar field of mass $M$ with a cubic term in the potential. The dynamics of the long-wavelength modes becomes diffusive in this interaction. The diffusive behaviour is described by the reduced Wigner function that characterizes the state of the long-wavelength modes. This function is obtained from the whole Wigner function by integration of the degrees of freedom of the short-wavelength modes. The dynamical equation for the reduced Wigner function becomes a kind of Fokker-Planck equation which is solved with suitable boundary conditions enforcing an initial metastable vacuum state trapped in the potential well. As a result a finite activation rate is found, even at zero temperature, for the formation of true vacuum bubbles of size $M^{-1}$. This effect makes a substantial contribution to the total decay rate.Comment: 27 pages, RevTeX, 1 figure (uses epsf.sty