Exceptional Points in a Microwave Billiard with Time-Reversal Invariance Violation

We report on the experimental study of an exceptional point (EP) in a dissipative microwave billiard with induced time-reversal invariance (T) violation. The associated two-state Hamiltonian is non-Hermitian and non-symmetric. It is determined experimentally on a narrow grid in a parameter plane around the EP. At the EP the size of T violation is given by the relative phase of the eigenvector components. The eigenvectors are adiabatically transported around the EP, whereupon they gather geometric phases and in addition geometric amplitudes different from unity

Boundary bound states and boundary bootstrap in the sine-Gordon model with Dirichlet boundary conditions.

We present a complete study of boundary bound states and related boundary S-matrices for the sine-Gordon model with Dirichlet boundary conditions. Our approach is based partly on the bootstrap procedure, and partly on the explicit solution of the inhomogeneous XXZ model with boundary magnetic field and of the boundary Thirring model. We identify boundary bound states with new ``boundary strings'' in the Bethe ansatz. The boundary energy is also computed.Comment: 25 pages, harvmac macros Report USC-95-001

Realization of compact Lie algebras in K\"ahler manifolds

The Berezin quantization on a simply connected homogeneous K\"{a}hler manifold, which is considered as a phase space for a dynamical system, enables a description of the quantal system in a (finite-dimensional) Hilbert space of holomorphic functions corresponding to generalized coherent states. The Lie algebra associated with the manifold symmetry group is given in terms of first-order differential operators. In the classical theory, the Lie algebra is represented by the momentum maps which are functions on the manifold, and the Lie product is the Poisson bracket given by the K\"{a}hler structure. The K\"{a}hler potentials are constructed for the manifolds related to all compact semi-simple Lie groups. The complex coordinates are introduced by means of the Borel method. The K\"{a}hler structure is obtained explicitly for any unitary group representation. The cocycle functions for the Lie algebra and the Killing vector fields on the manifold are also obtained

Dispersion relations and speeds of sound in special sectors for the integrable chain with alternating spins

Based on our previous analysis \cite{doerfel3} of the anisotropic integrable chain consisting of spins $s=1/2$ and $s=1$ we compare the dispersion relations for the sectors with infinite Fermi zones. Further we calculate the speeds of sound for regions close to sector borders, where the Fermi radii either vanish or diverge, and compare the results.Comment: 11 pages, LaTeX2e, uses iopart.cls,graphicx.sty and psfrag.sty, 2 figure

Free field representation for the O(3) nonlinear sigma model and bootstrap fusion

The possibility of the application of the free field representation developed by Lukyanov for massive integrable models is investigated in the context of the O(3) sigma model. We use the bootstrap fusion procedure to construct a free field representation for the O(3) Zamolodchikov- Faddeev algebra and to write down a representation for the solutions of the form-factor equations which is similar to the ones obtained previously for the sine-Gordon and SU(2) Thirring models. We discuss also the possibility of developing further this representation for the O(3) model and comment on the extension to other integrable field theories.Comment: 14 pages, latex, revtex v3.0 macro package, no figures Accepted for publication in Phys. Rev.

Deuteron tensor polarization component T_20(Q^2) as a crucial test for deuteron wave functions

The deuteron tensor polarization component T_20(Q^2) is calculated by relativistic Hamiltonian dynamics approach. It is shown that in the range of momentum transfers available in to-day experiments, relativistic effects, meson exchange currents and the choice of nucleon electromagnetic form factors almost do not influence the value of T_20(Q^2). At the same time, this value depends strongly on the actual form of the deuteron wave function, that is on the model of NN-interaction in deuteron. So the existing data for T_20(Q^2) provide a crucial test for deuteron wave functions.Comment: 11 pages, 3 figure

Integrals of motion of the Haldane Shastry Model

In this letter we develop a method to construct all the integrals of motion of the $SU(p)$ Haldane-Shastry model of spins, equally spaced around a circle, interacting through a $1/r^2$ exchange interaction. These integrals of motion respect the Yangian symmetry algebra of the Hamiltonian.Comment: 13 pages, REVTEX v3.

Form-factors of the sausage model obtained with bootstrap fusion from sine-Gordon theory

We continue the investigation of massive integrable models by means of the bootstrap fusion procedure, started in our previous work on O(3) nonlinear sigma model. Using the analogy with SU(2) Thirring model and the O(3) nonlinear sigma model we prove a similar relation between sine-Gordon theory and a one-parameter deformation of the O(3) sigma model, the sausage model. This allows us to write down a free field representation for the Zamolodchikov-Faddeev algebra of the sausage model and to construct an integral representation for the generating functions of form-factors in this theory. We also clear up the origin of the singularities in the bootstrap construction and the reason for the problem with the kinematical poles.Comment: 16 pages, revtex; references added, some typos corrected. Accepted for publication in Physical Review

Correlation functions of disorder fields and parafermionic currents in Z(N) Ising models

We study correlation functions of parafermionic currents and disorder fields in the Z(N) symmetric conformal field theory perturbed by the first thermal operator. Following the ideas of Al. Zamolodchikov, we develop for the correlation functions the conformal perturbation theory at small scales and the form factors spectral decomposition at large ones. For all N there is an agreement between the data at the intermediate distances. We consider the problems arising in the description of the space of scaling fields in perturbed models, such as null vector relations, equations of motion and a consistent treatment of fields related by a resonance condition.Comment: 41 pp. v2: some typos and references are corrected

Braid Structure and Raising-Lowering Operator Formalism in Sutherland Model

We algebraically construct the Fock space of the Sutherland model in terms of the eigenstates of the pseudomomenta as basis vectors. For this purpose, we derive the raising and lowering operators which increase and decrease eigenvalues of pseudomomenta. The operators exchanging eigenvalues of two pseudomomenta have been known. All the eigenstates are systematically produced by starting from the ground state and multiplying these operators to it.Comment: 11 pages, Latex, no figure