arXiv subjects

H. J. Shin

Publications and source records attributed to H. J. Shin.

28 records · Page 2Linked to original sources

arXiv1996

Effective Field Theory for Coherent Optical Pulse Propagation

Hidden nonabelian symmetries in nonlinear interactions of radiation with matter are clarified. In terms of a nonabelian potential variable, we construct an effective field theory of self-induced transparency, a phenomenon of lossless coherent pulse propagation, in association with Hermitian symmetric spaces $G/H$. Various new properties of self-induced transparency, e.g. soliton numbers, effective potential energy, gauge symmetry and discrete symmetries, modified pulse area, conserved $U(1)$-charge etc. are addressed and elaborated in the nondegenerate two-level case where $G/H = SU(2)/U(1)$. Using the $U(1)$-charge conservation, a new type of analysis on pulse stability is given which agrees with earlier numerical results.

hep-th↗

arXiv1995

Lagrangian Formulation of Symmetric Space sine-Gordon Models

The symmetric space sine-Gordon models arise by conformal reduction of ordinary 2-dim $σ$-models, and they are integrable exhibiting a black-hole type metric in target space. We provide a Lagrangian formulation of these systems by considering a triplet of Lie groups $F \supset G \supset H$. We show that for every symmetric space $F/G$, the generalized sine-Gordon models can be derived from the $G/H$ WZW action, plus a potential term that is algebraically specified. Thus, the symmetric space sine-Gordon models describe certain integrable perturbations of coset conformal field theories at the classical level. We also briefly discuss their vacuum structure, Backlund transformations, and soliton solutions.

hep-th↗

arXiv1995

Complex sine-Gordon Theory for Coherent Optical Pulse Propagation

It is shown that the McCall-Hahn theory of self-induced transparency in coherent optical pulse propagation can be identified with the complex sine-Gordon theory in the sharp line limit. We reformulate the theory in terms of the deformed gauged Wess-Zumino-Witten sigma model and address various new aspects of self-induced transparency.

hep-th↗

arXiv1995

Duality in Complex sine-Gordon Theory

New aspects of the complex sine-Gordon theory are addressed through the reformulation of the theory in terms of the gauged Wess-Zumino-Witten action. A dual transformation between the theory for the coupling constant $\b > 0$ and the theory for $\b < 0$ is given which agrees with the Krammers-Wannier duality in the context of perturbed conformal field theory. The Bäcklund transform and the nonlinear superposition rule for the complex sine-Gordon theory are presented and from which, exact solutions, solitons and breathers with U(1) charge, are derived. We clarify topological and nontopological nature of neutral and charged solitons respectively, and discuss about the duality between the vector and the axial U(1) charges.

hep-th↗

arXiv1995

Classical Matrix sine-Gordon Theory

The matrix sine-Gordon theory, a matrix generalization of the well-known sine-Gordon theory, is studied. In particular, the $A_{3}$-generalization where fields take value in $SU(2)$ describes integrable deformations of conformal field theory corresponding to the coset $SU(2) \times SU(2) /SU(2)$. Various classical aspects of the matrix sine-Gordon theory are addressed. We find exact solutions, solitons and breathers which generalize those of the sine-Gordon theory with internal degrees of freedom, by applying the Zakharov-Shabat dressing method and explain their physical properties. Infinite current conservation laws and the Bäcklund transformation of the theory are obtained from the zero curvature formalism of the equation of motion. From the Bäcklund transformation, we also derive exact solutions as well as a nonlinear superposition principle by making use of the Bianchi's permutability theorem.

hep-th↗

arXiv1994

An Effective Action for Quasi-elastic Scatterings in QCD

A new effective action for the high energy quark-quark scatterings is obtained by applying a scaling approximation to the QCD action. The propagators are shown to factorize into the transverse and the longitudinal parts so that the scattering amplitudes are given in terms of the products of two dimensional $S$-matrices. we show that our action provides a natural effective field theory for the Lipatov's theory of quark scatterings with quasi-elastic unitarity. The amplitude with quasi-elastic unitarity obtained from this action shows `Regge' behavior and is eikonalized.

hep-th↗

arXiv1994

Deformed Minimal Models and Generalized Toda Theory

We introduce a generalization of $A_{r}$-type Toda theory based on a non-abelian group G, which we call the $(A_{r},G)$-Toda theory, and its affine extensions in terms of gauged Wess-Zumino-Witten actions with deformation terms. In particular, the affine $(A_{1},SU(2))$-Toda theory describes the integrable deformation of the minimal conformal theory for the critical Ising model by the operator $Φ_{(2,1)}$. We derive infinite conserved charges and soliton solutions from the Lax pair of the affine $(A_{1}, SU(2))$-Toda theory. Another type of integrable deformation which accounts for the $Φ_{(3,1)}$-deformation of the minimal model is also found in the gauged Wess-Zumino-Witten context and its infinite conserved charges are given.

hep-th↗

arXiv1993

Possible Tests of Conformal Turbulence through Boundaries

We investigate various boundary conditions in two dimensional turbulence systematically in the context of conformal field theory. Keeping the conformal invariance, we can either change the shape of boundaries through finite conformal transformations, or insert boundary operators so as to handle more general cases. Effects of such operations will be reflected in physically measurable quantities such as the energy power spectrum $E(k)$ or the average velocity profiles. We propose that these effects can be used as a possible test of conformal turbulence in an experimental setting. We also study the periodic boundary conditions, i.e. turbulence on a torus geometry. The dependence of moduli parameter $q$ appears explictly in the one point functions in the theory, which can also be tested.

hep-th↗

arXiv1993

Solutions of Conformal Turbulence on a Half Plane

Exact solutions of conformal turbulence restricted on a upper half plane are obtained. We show that the inertial range of homogeneous and isotropic turbulence with constant enstrophy flux develops in a distant region from the boundary. Thus in the presence of an anisotropic boundary, these exact solutions of turbulence generalize Kolmogorov's solution consistently and differ from the Polyakov's bulk case which requires a fine tunning of coefficients. The simplest solution in our case is given by the minimal model of $p=2, q=33$ and moreover we find a fixed point of solutions when $p,q$ become large.

hep-th↗

arXiv1993

Conformal Turbulence with Boundary

Based upon the formalism of conformal field theory with a boundary, we give a description of the boundary effect on fully developed two dimensional turbulence. Exact one and two point velocity correlation functions and energy power spectrum confined in the upper half plane are obtained using the image method. This result enables us to address the infrared problem of the theory of conformal turbulence.

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