Integrable models with unstable particles

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-Gordon model in terms of infinite products of q-deformed gamma functions. When relaxing the usual restriction on the coupling constants, the model contains additional bound states which admit an interpretation as breathers. For that situation we compute the complete S-matrix of all sectors. We carry out various reductions of the model, one of them leading to a new type of theory, namely an elliptic version of the minimal SO(n)-affine Toda field theory

Finite temperature correlation functions from form factors

We investigate proposals of how the form factor approach to compute correlation functions at zero temperature can be extended to finite temperature. For the two-point correlation function we conclude that the suggestion to use the usual form factor expansion with the modification of introducing dressing functions of various kinds is only suitable for free theories. Dynamically interacting theories require a more severe change of the form factor program

Bi-partite Entanglement Entropy in Massive QFT with a Boundary: the Ising 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 entanglement entropy and of the two-point function of twist fields in the bulk theory, to a great degree of precision by including up to 500 form factor contributions

Decoupling the SU(N)2-homogeneous sine-Gordon model

We provide a systematic construction for all n-particle form factors of the SU(N)2/U(1)N-1-homogeneous sine-Gordon model in terms of general determinant formulas for a large class of local operators. The ultraviolet limit is carried out and the corresponding Virasoro central charge, together with the conformal dimensions of various operators, are identified. The renormalization-group flow is studied and we find a precise rule, depending on the relative order of magnitude of the resonance parameters, according to which the theory decouples into new cosets along the flow

Unstable particles versus resonances in impurity systems, conductance in quantum wires

We compute the DC conductance for a homogeneous sine-Gordon model and an impurity system of Luttinger liquid type by means of the thermodynamic Bethe ansatz and standard potential scattering theory. We demonstrate that unstable particles and resonances in impurity systems lead to a sharp increase of the conductance as a function of the temperature, which is characterized by the Breit-Wigner formula.Comment: 5 pages Latex, 1 figure replaced, version to appear in J. Phys.

Quantum dynamics of a spin-1/2 charged particle in the presence of magnetic field with scalar and vector couplings

The quantum dynamics of a spin-1/2 charged particle in the presence of magnetic field is analyzed for the general case where scalar and vector couplings are considered. The energy spectra are explicitly computed for different physical situations, as well as their dependencies on the magnetic field strength, spin projection parameter and vector and scalar coupling constants.Comment: arXiv admin note: text overlap with arXiv:1403.411

Lithium abundances in exoplanet host stars as test of planetary formation scenarii

Following the observations of Israelian et al. 2004, we compare different evolutionary models in order to study the lithium destruction processes and the planetary formation scenarii.Comment: 4 pages, 5 figures, proceeding of the meeting "Element Stratification in stars : 40 years of atomic diffusion", Mons 6-11 Juin 200

The mobility and diffusion of a particle coupled to a Luttinger liquid

We study the mobility of a particle coupled to a one dimensional interacting fermionic system, a Luttinger liquid. We bosonize the Luttinger liquid and find the effective interaction between the particle and the bosonic system. We show that the dynamics of this system is completely equivalent to the acoustic polaron problem where the interaction has purely electronic origin. This problem has a zero mode excitation, or soliton, in the strong coupling limit which corresponds to the formation of a polarization cloud due to the fermion-fermion interaction around the particle. We obtain that, due to the scattering of the residual bosonic modes, the soliton has a finite mobility and diffusion coefficient at finite temperatures which depend on the fermion-fermion interaction. We show that at low temperatures the mobility and the diffusion coefficient are proportional to $T^{-4}$ and $T^5$ respectively and at high temperatures the mobility vanishes as $T^{-1}$ while the diffusion increases as $T$.Comment: 9 pages, Revtex, UIUC preprin