Spectral determinants for Schroedinger equation and Q-operators of Conformal Field Theory

Relation between the vacuum eigenvalues of CFT Q-operators and spectral determinants of one-dimensional Schroedinger operator with homogeneous potential, recently conjectured by Dorey and Tateo for special value of Virasoro vacuum parameter p, is proven to hold, with suitable modification of the Schroedinger operator, for all values of p.Comment: 9 pages, harvmac.tex, typos correcte

Integrable Structure of Conformal Field Theory II. Q-operator and DDV equation

This paper is a direct continuation of\ \BLZ\ where we begun the study of the integrable structures in Conformal Field Theory. We show here how to construct the operators ${\bf Q}_{\pm}(\lambda)$ which act in highest weight Virasoro module and commute for different values of the parameter $\lambda$. These operators appear to be the CFT analogs of the $Q$ - matrix of Baxter\ \Baxn, in particular they satisfy famous Baxter's ${\bf T}-{\bf Q}$ equation. We also show that under natural assumptions about analytic properties of the operators ${\bf Q}(\lambda)$ as the functions of $\lambda$ the Baxter's relation allows one to derive the nonlinear integral equations of Destri-de Vega (DDV)\ \dVega\ for the eigenvalues of the ${\bf Q}$-operators. We then use the DDV equation to obtain the asymptotic expansions of the ${\bf Q}$ - operators at large $\lambda$; it is remarkable that unlike the expansions of the ${\bf T}$ operators of \ \BLZ, the asymptotic series for ${\bf Q}(\lambda)$ contains the ``dual'' nonlocal Integrals of Motion along with the local ones. We also discuss an intriguing relation between the vacuum eigenvalues of the ${\bf Q}$ - operators and the stationary transport properties in boundary sine-Gordon model. On this basis we propose a number of new exact results about finite voltage charge transport through the point contact in quantum Hall system.Comment: Revised version, 43 pages, harvmac.tex. Minor changes, references adde

High-Energy Approach for Heavy-Ion Scattering with Excitations of Nuclear Collective States

A phenomenological optical potential is generalized to include the Coulomb and nuclear interactions caused by the dynamical deformation of its surface. In the high-energy approach analytical expressions for elastic and inelastic scattering amplitudes are obtained where all the orders in the deformation parameters are included. The multistep effect of the 2$^+$ rotational state excitation on elastic scattering is analyzed. Calculations of inelastic cross sections for the $^{17}$O ions scattered on different nuclei at about hundred Mev/nucleon are compared with experimental data, and important role of the Coulomb excitation is established.Comment: 9 pages; 3 figures. Submitted to the Physics of Atomic Nucle

Giant neutron halo in nuclei beyond beta-stability line

The radii of nucleon distribution and neutron skin in nuclei beyond the \beta-stability line are studied within the extended Thomas-Fermi approximation. We show that the growth of neutron skin in unstable nuclei does not obey the saturation condition because of the neutron coat. The neutron coat indicates the possibility of giant neutron halo which is growing with moving away from the beta stability line. We demonstrate the presence of strong shell oscillations in the charge radius R_C and the relation of R_C to the isospin shift of neutron-proton chemical potentials \Delta\lambda =\lambda_n-\lambda_p for nuclei beyond the beta-stability line at fixed value of mass number A.Comment: 10 pages, 6 figures; few sentences and one reference added; published in Nucl. Phys. At. Energ. V.11, N4, 335 (2010

Bukhvostov-Lipatov model and quantum-classical duality

The Bukhvostov-Lipatov model is an exactly soluble model of two interacting Dirac fermions in 1+1 dimensions. The model describes weakly interacting instantons and anti-instantons in the $O(3)$ non-linear sigma model. In our previous work [arXiv:1607.04839] we have proposed an exact formula for the vacuum energy of the Bukhvostov-Lipatov model in terms of special solutions of the classical sinh-Gordon equation, which can be viewed as an example of a remarkable duality between integrable quantum field theories and integrable classical field theories in two dimensions. Here we present a complete derivation of this duality based on the classical inverse scattering transform method, traditional Bethe ansatz techniques and analytic theory of ordinary differential equations. In particular, we show that the Bethe ansatz equations defining the vacuum state of the quantum theory also define connection coefficients of an auxiliary linear problem for the classical sinh-Gordon equation. Moreover, we also present details of the derivation of the non-linear integral equations determining the vacuum energy and other spectral characteristics of the model in the case when the vacuum state is filled by 2-string solutions of the Bethe ansatz equations.Comment: 49 pages, 8 figure