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This work investigates the edge-buckling experienced by a sectorial plate in a uniform bi-axial state of stress and subject to in-plane bending. Since the governing differential equations have variable coefficients, it turns out that the neutrally stable eigenfunctions can be qualitatively quite different as the mode number varies. Our interactive boundary-layer analysis succeeds in capturing the most dangerous mode associated with the global minimum of the marginal stability curve, while a complementary WKB route supplies an explanation for the morphological transitions experienced by the eigenmodes. The validity of our analysis is confirmed by direct numerical simulations of the full fourth-order buckling equation, which are in excellent agreement with the theoretical considerations.
We review some recent results concerning integrable quantum field theories in 1+1 space-time dimensions which contain unstable particles in their spectrum. Recalling first the main features of analytic scattering theories associated to integrable models, we subsequently propose a new bootstrap principle which allows for the construction of particle spectra involving unstable as well as stable particles. We describe the general Lie algebraic structure which underlies theories with unstable particles and formulate a decoupling rule, which predicts the renormalization group flow in dependence of the relative ordering of the resonance parameters. We extend these ideas to theories with an infinite spectrum of unstable particles. We provide new expressions for the scattering amplitudes in the soliton-antisoliton sector of the elliptic sine-G...
The renormalization group flow of an integrable two dimensional quantum field theory which contains unstable particles is investigated. The analysis is carried out for the Virasoro central charge and the conformal dimensions as a function of the renormalization group flow parameter. This allows to identify the corresponding conformal field theories together with their operator content when the unstable particles vanish from the particle spectrum. The specific model considered is the $SU(3)_{2}$-homogeneous Sine-Gordon model.
In this paper we give an exact infinite-series expression for the bi-partite entanglement entropy of the quantum Ising model in the ordered regime, both with a boundary magnetic field and in infinite volume. This generalizes and extends previous results involving the present authors for the bi-partite entanglement entropy of integrable quantum field theories, which exploited the generalization of the form factor program to branch-point twist fields. In the boundary case, we isolate in a universal way the part of the entanglement entropy which is related to the boundary entropy introduced by Affleck and Ludwig, and explain how this relation should hold in more general QFT models. We provide several consistency checks for the validity of our form factor results, notably, the identification of the leading ultraviolet behaviour both of the...
We present determinant formulae for the form factors of spin operators of general integrable XXX Heisenberg spin chains for arbitrary (finite-dimensional) spin representations. The results apply to any 'mixed' spin chains, such as alternating spin chains, or to spin chains with magnetic impurities.
On the basis of various examples we provide evidence that noncommutative spacetime involving position-dependent structure constants will give rise to deformed oscillator algebras. In turn, starting from some q-deformations of these algebras in a two-dimensional space for which the entire deformed Fock space can be constructed explicitly, we derive the commutation relations for the dynamical variables in noncommutative spacetime. We compute minimal areas resulting from these relations, i.e. finitely extended regions for which it is impossible to resolve any substructure in form of measurable knowledge. The size of the regions we find is determined by the noncommutative constant and the deformation parameter q. Any object in this type of spacetime structure has to be of membrane type or in certain limits of string type.
We briefly explain some simple arguments based on pseudo Hermiticity, supersymmetry and PT-symmetry which explain the reality of the spectrum of some non-Hermitian Hamiltonians. Subsequently we employ PT-symmetry as a guiding principle to construct deformations of some integrable systems, the Calogero-Moser-Sutherland model and the Korteweg deVries equation. Some properties of these models are discussed.
We address the question of whether integrable models allow for -symmetric deformations which preserve their integrability. For this purpose we carry out the Painlevé test for -symmetric deformations of Burgers and the Korteweg–De Vries equations. We find that the former equation allows for infinitely many deformations which pass the Painlevé test. For a specific deformation we prove the convergence of the Painlevé expansion and thus establish the Painlevé property for these models, which are therefore thought to be integrable. The Korteweg–De Vries equation does not allow for deformations which pass the Painlevé test in complete generality, but we are able to construct a defective Painlevé expansion.
In this paper, we generalize the main result of a recent work by J L Cardy and the present authors concerning the bi-partite entanglement entropy between a connected region and its complement. There the expression of the leading-order correction to saturation in the large distance regime was obtained for integrable quantum field theories possessing diagonal scattering matrices. It was observed to depend only on the mass spectrum of the model and not on the specific structure of the diagonal scattering matrix. Here we extend that result to integrable models with backscattering (i.e. with non-diagonal scattering matrices). We use again the replica method, which connects the entanglement entropy to partition functions on Riemann surfaces with two branch points. Our main conclusion is that the mentioned infrared correction takes exactly th...
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