Quantum transfer-matrices for the sausage model

In this work we revisit the problem of the quantization of the two-dimensional O(3) non-linear sigma model and its one-parameter integrable deformation -- the sausage model. Our consideration is based on the so-called ODE/IQFT correspondence, a variant of the Quantum Inverse Scattering Method.The approach allowed us to explore the integrable structures underlying the quantum O(3)/sausage model. Among the obtained results is a system of non-linear integral equations for the computation of the vacuum eigenvalues of the quantum transfer-matrices.Comment: 89 pages, 10 figures, v2: misprints corrected, some comments added, v3, v4: minor corrections, references adde

Winding vacuum energies in a deformed O(4) sigma model

We consider the problem of calculating the Casimir energies in the winding sectors of Fateev's SS-model, which is an integrable two-parameter deformation of the O(4) non-linear sigma model in two dimensions. This problem lies beyond the scope of all traditional methods of integrable quantum field theory including the thermodynamic Bethe ansatz and non-linear integral equations. Here we propose a solution based on a remarkable correspondence between classical and quantum integrable systems and express the winding energies in terms of certain solutions of the classical sinh-Gordon equation.Comment: 10 pages, 4 figure

Crack Under Shear Loading in a Plate of Finite Thickness

Application of the plane theory of elasticity to planar crack geometries leads to the concept of stress singularity and stress intensity factor, which are the cornerstone of contemporary fracture mechanics. However, the stress state near an actual crack tip is always three-dimensional, and the meaning of the results obtained with the plane theory of elasticity and their relation to the actual 3D problems is still not fully understood. In particular, it is not clear whether the stress field found from the 2D solutions of the theory of elasticity do describe the corresponding stress components in an actual plate made of a sufficiently brittle material and subjected to in-plane loading, and what effect the plate thickness has. In the present study, first order plate theory is adopted in attempt to answer these questions. New features of the elastic solutions obtained within this theory are discussed and compared with 2D results as well as with 3D numerical and experimental studies

ODE/IQFT correspondence for the generalized affine sl(2)\mathfrak{ sl}(2) Gaudin model

An integrable system is introduced, which is a generalization of the $\mathfrak{sl}(2)$ quantum affine Gaudin model. Among other things, the Hamiltonians are constructed and their spectrum is calculated within the ODE/IQFT approach. The model fits within the framework of Yang-Baxter integrability. This opens a way for the systematic quantization of a large class of integrable non-linear sigma models. There may also be some interest in terms of Condensed Matter applications, as the theory can be thought of as a multiparametric generalization of the Kondo model.Comment: v2: 75 pages, 2 tables, 6 figures, minor typos corrected, published versio

Bethe state norms for the Heisenberg spin chain in the scaling limit

In this paper we discuss the norms of the Bethe states for the spin one-half Heisenberg chain in the critical regime. Our analysis is based on the ODE/IQFT correspondence. Together with numerical work, this has lead us to formulate a set of conjectures concerning the scaling behavior of the norms. Also, we clarify the role of the different Hermitian structures associated with the integrable structure studied in the series of works of Bazhanov, Lukyanov and Zamolodchikov in the mid nineties.Comment: 31 pages, 5 figures, v2: minor changes, refs adde

A model-based method for damage detection with guided waves

Abstract not availablePouria Aryan, Andrei Kotousov, Ching-Tai Ng and Benjamin Cazzolat

A baseline-free and non-contact method for detection and imaging of structural damage using 3D laser vibrometry

Abstract not availableP. Aryan, A. Kotousov, C. T. Ng and B. S. Cazzolat

Equilibrium density matrices for the 2D black hole sigma models from an integrable spin chain

This work concerns the quantum Lorentzian and Euclidean black hole non-linear sigma models. For the Euclidean black hole sigma model an equilibrium density matrix is proposed, which reproduces the modular invariant partition function from the 2001 paper of Maldacena, Ooguri and Son. For the Lorentzian black hole sigma model, using its formulation as a gauged ${\rm SL}(2,\mathbb{R})$ WZW model, we describe the linear and Hermitian structure of its space of states and also propose an expression for the equilibrium density matrix. Our analysis is guided by the results of the study of a certain critical, integrable spin chain. In the scaling limit, the latter exhibits the key features of the Lorentzian black hole sigma model including the same global symmetries, the same algebra of extended conformal symmetry and a continuous spectrum of conformal dimensions.Comment: 43 pages, 2 figures, 2 tables; published version, minor misprints correcte