WKB approximation

Abstract: A new formulation of an approximate conservation relation of wave-activity pseudomomentum is derived, which is applicable for either stationary or migratory quasigeostrophic (QG) eddies on a zonally varying basic flow. The authors utilize a combination of a quantity A that is proportional to wave enstrophy and another quantity E that is proportional to wave energy. Both A and E are approximately related to the wave-activity pseudomomentum. It is shown for QG eddies on a slowly varying, unforced nonzonal flow that a particular linear combination of A and E, namely, M ≡ (A + E)/2, is independent of the wave phase, even if unaveraged, in the limit of a small-amplitude plane wave. In the same limit, a flux of M is also free from an oscillatory component on a scale of one-half wavelength even without any averaging. It is shown that M is conserved under steady, unforced, and nondissipative conditions and the flux of M is parallel to the local three-dimensional group velocity in the WKB limit. The autho...

Abstract: Global 1 83 18 climatologies of the first baroclinic gravity-wave phase speed c1 and the Rossby radius of deformation l1 are computed from climatological average temperature and salinity profiles. These new atlases are compared with previously published 5 83 58 coarse resolution maps of l1 for the Northern Hemisphere and the South Atlantic and with a 1 83 18 fine-resolution map of c1 for the tropical Pacific. It is concluded that the methods used in these earlier estimates yield values that are biased systematically low by 5%‐15% owing to seemingly minor computational errors. Geographical variations in the new high-resolution maps of c1 and l1 are discussed in terms of a WKB approximation that elucidates the effects of earth rotation, stratification, and water depth on these quantities. It is shown that the effects of temporal variations of the stratification can be neglected in the estimation of c1 and l1 at any particular location in the World Ocean. This is rationalized from consideration of the WKB approximation.

Abstract: What is Quantum Optics? Ante The Wigner Function Quantum States in Phase Space Waves a la WKB WKB Wave Functions and Berry's Phase Interference in Phase Space Applications of Interference in Phase Space Wave Packet Dynamics Quantization of the Radiation Field Quantum States of the Radiation Field Phase Space Functions Optical Interferometry Atom-Field Interaction Dynamics of Jaynes-Cummings-Paul Model State Preparation and Entanglement The Paul Trap Damping and Amplification Atom Optics in Quantized Light Fields Wigner Functions in Atom Optics Appendix Time Dependent Operators - Derivation of Equations Determining the Moyal Function - Energy Wave Functions of Harmonic Oscillator - Method of Stationary Phase - Radial Equation - Airy Function - Asymptotic Expansion of the Poisson Distribution - Area of Overlap - P-Distributions - Homodyne Detection Kernel - Effective Hamiltonian - Spontaneous Emission - A Model for the Square Root of a Delta Function - Bessel Functions

Abstract: We consider BPS states in a large class of d=4, N=2 field theories, obtained by reducing six-dimensional (2,0) superconformal field theories on Riemann surfaces, with defect operators inserted at points of the Riemann surface. Further dimensional reduction on S^1 yields sigma models, whose target spaces are moduli spaces of Higgs bundles on Riemann surfaces with ramification. In the case where the Higgs bundles have rank 2, we construct canonical Darboux coordinate systems on their moduli spaces. These coordinate systems are related to one another by Poisson transformations associated to BPS states, and have well-controlled asymptotic behavior, obtained from the WKB approximation. The existence of these coordinates implies the Kontsevich-Soibelman wall-crossing formula for the BPS spectrum. This construction provides a concrete realization of a general physical explanation of the wall-crossing formula which was proposed in 0807.4723. It also yields a new method for computing the spectrum using the combinatorics of triangulations of the Riemann surface.