Laser phase fluctuations in a four-level atomic system in N-configuration

We discuss here the effect of laser phase fluctuations on coherent spectroscopy of four-level N-system interacting with a trichromatic radiation field of frequencies Ω _i , (i = 1?3). The laser phase variables are described by the Wiener-Levy diffusion process to specify the bandwidths (Γ _i ) and cross-correlations (Γ _ij ) that may exist between pairs of laser fields. A general formalism based on the master equation and theory of multiplicative stochastic processes is developed and used to study three-photon and (2+1)-photon absorptive resonances in model N-system of ⁴⁰Ca⁺ ion. It is observed that the resonances are suppressed or broadened by all Γ _i ,(i = 1?3), while their revival is dependent only on Γ ₁₂ and Γ ₂₃, and yet the revival is only partial even when the relevant fields are critically correlated. In contrast Γ ₁₃ is observed to deteriorate the absorptive resonances. The distinctive features of the steady state and time dependent behavior of the system under three-photon and (2 + 1)-photon resonance conditions and for fluctuating fields are discussed.     

A skew ray tracing-based approach to the error analysis of optical elements with flat boundary surfaces

This study applies skew ray tracing based on a 4×4 homogeneous coordinate transformation matrix and Snell's law to develop a detailed methodology for analyzing the errors of a ray's light path as it passes through optical elements with flat boundary surfaces. The error analysis methodology considers two fundamental sources of light path error, namely (1) the translational errors (ΔX_i, ΔY_i and ΔZ_i) and rotational errors (ΔΓ_i, ΔΨ_i and ΔΦ_i) which determine the deviation of the light path at each boundary surface in terms of the coordinate frame attached to that surface, and (2) the differential changes induced in the incident point and unit directional vector of the refracted/reflected ray by differential changes in the position and unit directional vector of the light source. The validity of the proposed methodology is verified using a solid glass corner-cube.     

Raman scattering under pressure in ZnGa2Se4

The Raman scattering spectra of ZnGa₂Se₄ under pressure were investigated at 300 K up to 18.9 GPa. Two stages were observed in the pressure dependences of Raman bands. Such behavior in accordance with the experimental findings existing in literature and was attributed as arising due to the order–disorder phase transition in the cation sublattice.Using the Harrison–Keating's model of the lattice dynamics modified for the crystals with the tetragonal structure, the bulk modulus B and the mode-Grüneisen parameters Γ_i were determined for the first time. It is shown that a better agreement between the experimental and calculated values of Γ_i is observed, if one takes into consideration different frequency-pressure behavior for the bond-bending and the bond-stretching parameters, which determine the low- (lower than 140 cm⁻¹) and high- (higher than 140 cm⁻¹) frequency phonons, respectively.     

A skew ray tracing approach for the error analysis of optical elements with paraboloidal boundary surfaces

Using the error analysis methodology developed by the current author in previous studies for optical systems comprising elements with flat boundary surfaces, this study examines the errors induced in a light ray's path as it is reflected or refracted at a paraboloidal boundary surface. In analyzing the light path, two principal sources of error are considered, namely (1) translational errors (Δx_i, Δy_i and Δz_i) and rotational errors (ΔΓ_i, ΔΨ_i and ΔΦ_i), which collectively determine the deviation of the light path at each boundary surface, and (2) the differential changes induced in the incident point position and unit directional vector of the refracted/reflected ray as a result of differential changes in the position and unit directional vector of the light source. The validity of the proposed approach is verified using a generic parabaloidal boundary surface for illustration purposes. Overall, the results show that the proposed error analysis methodology provides a straightforward means of analyzing the performance of optical systems characterized by paraboloidal boundary surfaces such as headlight reflectors, optical telescope mirrors, flashlights and so forth.     

Geometrical string and dual spin systems

We are able to perform the duality transformation of the spin system which was found before as a lattice realization of the string with linear action. In four and higher dimensions this spin system can be described in terms of a two-plaquette gauge hamiltonian. The duality transformation is constructed in geometrical and algebraic language. The dual hamiltonian represents a new type of spin system with local gauge invariance. At each vertex ξ there are d (d − 1) /2 Ising spins ∧_{μ, η} = ∧_{η,μ N}. ≠ P = 1, … , d and one Ising spin Γ on every linkξ ξ + e,). For the frozen spin Γ  1 the dual hamiltonian factorizes into d (d − 1) /2 two-dimensional Ising ferromagnets and into antiferromagnets in the case Γ  −1. For fluctuating F it is a sort of spin-glass system with local gauge invariance. The generalization to p-membranes is given.     

Renormalization constants in asymptotically free field theories

Renormalization constants Z_i for asymptotically free field theories can be computed via renormalization group techniques from perturbation theory. We show that there exists a subclass of these theories in which, by virtue of a new eigenvalue condition on the gauge parameter, the Z_i are asymptotically gauge independent, and hence can vanish in all gauges.     

Paraphotons and axions: Similarities in stellar emission and detection

The massless gauge boson of an extra U(1) symmetry - the paraphoton - could have low-energy effective couplings to ordinary matter. The coupling to electrons would behave much like the invisible axion-electron coupling at keV energies. We find astrophysical bounds on the paraphoton-electron coupling strength: α_Γee<1.5 × 10⁻²² (sun), and α_Γee≲10⁻²⁶ (while dwarfs). We also show that planned solar axion detectors would not distinguish axions and paraphotons.     

On the energy-momentum tensor in gauge field theories

The energy-momentum tensor in spontaneously broken non-Abelian gauge field theories is studied. The motivation is to show that recent results on the finiteness and gauge independence of S-matrix elements in gauge theories extends to observable amplitudes for transitions in a gravitational field. Path integral methods and dimensional regularization are used throughout. Green's functions Γ_μν^(j)(q; p₁,…,p_j) involving the energy-momentum tensor and j particle fields are proved finite to all orders in perturbation theory to zero and first order in q, and finite to one loop order for general q. Amputated Green's functions of the energy momentum tensor are proved to be gauge independent on mass shell.     

Topological vortices in chiral gauge theory of graphene

Generation mechanism of energy gaps between conductance and valence bands is at the centre of the study of graphene material. Recently, Chamon, Jackiw et al. proposed a mechanism of using a Kekulé distortion background field φ and its induced gauge potential A_i to generate energy gaps. In this paper, various vortex structures inhering in this model are studied. Regarding φ as a generic background field rather than a fixed Nielson-Oleson type distribution, we have found two new types of vortices on the graphene surface—the velocity field vortices and the monopole-motion induced vortices—from the inner structure of the potential A_i. These vortex structures naturally arise from the motion of the Dirac fermions instead of from the background distortion field.     

The two confining phases of lattice gauge theories

I suggest that the roughening transition of lattice gauge theories is the boundary between two different confining phases: In the hot phase the short-distance interquark potential is exponentially decreasing, while in the cool confining phase it is proportional to $\text{1}\text{R}$, independently of space dimensionality d. As d increases, the cool confining phase shrinks to zero and the system undergoes a first-order deconfining transition.     

A quasi-temporal gauge

We prove that a complete fixing of the temporal gauge,A _o =0, in which one imposesa subsidiary gauge condition, such as, for instance ?_i A _i (x,t ₀) = 0 leads to consistent formulation of the theory with simple Feynman rulesand a well defined gluon propagator. The correct exponentiation of the time dependence of the Wilson loop has been checked to occur up to order g⁴.     

Factorizations for self-dual gauge fields

For a particular class of patching matrices onP ₃(?), including those for the complex instanton bundles with structure group Sp(k,?) orO(2k,?), we show that the associated Riemann-Hilbert problemG(x, λ)=G?(x, λ)·G ₊ ^?1 (x, λ) can be generically solved in the factored formG _?=φ ₁ φ ₂.....φ _n . IfГ=Г _n is the potential generated in the usual way fromG _?, and we setψ _i =φ ₁.....,φ _i withψ _n =G _?, then eachψ _i also generates a selfdual gauge potentialΓ _i . The potentials are connected via the “dressing transformations” $$\Gamma _\iota = \phi _i^{ - 1} \cdot \Gamma _{\iota - 1} \cdot \phi _i + \phi _i ^{ - 1} D\phi _i$$ of Zakharov-Shabat. The factorization is not unique; it depends on the (arbitrary) ordering of the poles of the patching matrix.     

Measurement of the strong-interaction shift and broadening of the ground state of the pp̄ atom

The K_α X-rays from pp̄ atoms formed in H₂ gas at normal temperature and pressure are unambiguously identified by coincidences with L X-rays populating the 2P level. Background due to inner bremsstrahlung is suppressed by selecting events annihilating into neutral final states only. The K_α line is observed with a significance of more than 25 standard deviations at an energy of 8.67 (15) keV. From fits to the K_α line we obtain a strong-interaction shift and width of the 1S level, averaged over the unresolved spin singlet and triplet contributions, of ΔE + iΓ/2 = [−0.70(15) + i0.80(20)] keV.     

Confining string formed by P vortices in the indirect Z(2) projection of SU(2) lattice gauge theory

We study the distribution of P vortices near the confining string in the indirect _Z(2) projection of SU(2) lattice gauge theory. We find that the density of vortices approaches the vacuum value at large distances and is strongly suppressed near the line connecting the test quark-antiquark pair. This implies that the condensate of P vortices is broken inside the confining string. The width of the _P-vortex density distribution increases with increasing distance between the quark and antiquark. Our best fit indicates the logarithmic dependence of this width on q q? separation.     

Effect of intrinsic degrees of freedom on the quantum tunneling of a collective variable

The effect of intrinsic degrees of freedom on tunneling through a potential barrier is discussed using a BKW-like approximation. In the present work intrinsic degrees of freedom are represented by a single harmonic oscillator. The theory leads to a formula for the effect of the coupling on the decay width Γ of a metastable state. When the frequency ω of the intrinsic degree of freedom is large, then Γ → Γ_ad where Γ_ad is the decay width calculated with the adiabatic barrier. An inequality Γ ≤ Γ_ad is proved for any form of the coupling hamitonian. Corrections are discussed and are shown to be of order $\text{1}\text{M}$ where M is the mass of the tunneling coordinate. An application to fission is considered. The generalization of our formula for Γ to the case of many intrinsic degrees of freedom is given explicitly.     

Attraction to large gauge orbits

SU(N) gauge systems are attracted to large orbits of the global gauge group by an invariant and calculable potential. In models the wave function becomes increasingly localized near the maximal orbit as N → ∞, which explains the success of semiclassical methods. Picturing the links U_i of the lattice as particles on an SU(N) group manifold, the effect favors large moments of inertia about U = 1. It thus opposes the magnetic interaction, and tends to destabilize the perturbative vacuum.     

Supercompositeness from superstrings

String Unified Models based on the k = 1 level of the Kac-Moody Algebra, predict the existence of “exotic” new states which carry fractional electric charges. We analyse the possibility of considering these “exotics” as preonic matter which can be used to form the families and the gauge group breaking higgs scalars. It is proposed that such a formation may occur provided that these states transform non-trivially under a non-Abelian gauge group with a relatively large rank in order to confine them at a sufficiently large scale. Such a situation is natural in string derived unified models, since the role of the confining group can be played by (part of) the Hidden symmetry. As an example, we present a string derived toy model based on the SU(4) × SU(2) _L × SU(2) _R Pati-Salam gauge group.     

Radiative transitions and the P wave levels in charmonium

A value of $\text{1}\text{2}$ or less for the ratio $\text{[E(2}{}^{\mathrm{++}}\text{) ? E(1}{}^{\mathrm{++}}\text{)]}\text{[E(1}{}^{\mathrm{++}}\text{) ? E(0}{}^{\mathrm{++}}\text{)]}$ of the P level splittings in approximate agreement with the assignment of the states at 3.41, 3.50 and 3.55 to the 0⁺⁺,and 2⁺⁺ P-wave levels, is obtained with a short-range Coulomb (Lorentz vector) potential together with a long-range linear (Lorentz scalar) confining potential. The radiative transition widths Γ(ψ′ → 3.41 + γ), Γ(ψ′ → 3.50 + γ), Γ(χ′ → 3.55 + γ) are significantly smaller than those obtained in previous (one-channel) charmonium calculations. The best results were obtained by allowing the Coulomb coupling constant α_s to have a momentum dependence suggested by asymptotic freedom formulae.