F. Lesage

Dynamical correlation functions in the Calogero-Sutherland model

Abstract We compute the dynamical Green function and density-density correlation in the Calogero-Sutherland model for all integer values of the coupling constant. An interpretation of the intermediate states in terms of quasi-particles is found.

BOUNDARY FLOWS IN MINIMAL MODELS

Abstract We discuss in this paper the behaviour of minimal models of conformal theory perturbed by the operator Φ13 at the boundary. Using the RSOS restriction of the sine-Gordon model, adapted to the boundary problem, a series of boundary flows between different set of conformally invariant boundary conditions are described. Generalizing the “staircase” phenomenon discovered by Al. Zamolodchikov, we find that an analytic continuation of the boundary sinh-Gordon model provides a flow interpolating not only between all minimal models in the bulk, but also between their possible conformal boundary conditions. In the particular case where the bulk sinh-Gordon coupling is turned to zero, we obtain a boundary roaming trajectory in the c=1 theory, that interpolates between all the possible spin s Kondo models.

FINITE TEMPERATURE CORRELATIONS IN THE ONE-DIMENSIONAL QUANTUM ISING MODEL

Abstract We extend the form-factors approach to the quantum Ising model at finite temperature. The two-point function of the energy is obtained in closed form, while the two-point function of the spin is written as a Fredholm determinant. Using the approach of Korepin et al., we obtain, starting directly from the continuum formulation, a set of six differential equations satisfied by this two-point function. Four of these equations involve only space-time derivatives, of which three are equivalent to the equations obtained earlier. In addition, we obtain two new equations involving a temperature derivative. Some of these results are generalized to the Ising model on the half line with a magnetic field at the origin.

A Unified Framework for the Kondo Problem and for an Impurity in a Luttinger Liquid

We develop a unified theoretical framework for the anisotropic Kondo model and the boundary sine-Gordon model. They are both boundary integrable quantum field theories with a quantum-group spin at the boundary which takes values, respectively, in standard or cyclic representations of the quantum groupSU(2)q. This unification is powerful, and allows us to find new results for both models. For the anisotropic Kondo problem, we find exact expressions (in the presence of a magnetic field) for all the coefficients in the Anderson-Yuval perturbative expansion. Our expressions hold initially in the very anisotropic regime, but we show how to continue them beyond the Toulouse point all the way to the isotropic point using an analog of dimensional regularization. The analytic structure is transparent, involving only simple poles which we determine exactly, together with their residues. For the boundary sine-Gordon model, which describes an impurity in a Luttinger liquid, we find the nonequilibrium conductance for all values of the Luttinger coupling. This is an intricate computation because the voltage operator and the boundary scattering do not commute with each other.

Solving 1D Plasmas and 2D Boundary Problems Using Jack Polynomials and Functional Relations

The general one-dimensional “log-sine” gas is defined by restricting the positive and negative charges of a two-dimensional Coulomb gas to live on a circle. Depending on charge constrannts, this problem is equivalent to different boundary field theories.We study the electrically neutral case, which is equivalent to a two-dimensional free boson with an impurity cosine potential. We use two different methods: a perturbative one based on Jack symmetric functions, and a nonperturbative one based on the thermodynamic Bethe ansatz and functional relations. The first method allows us to find an explicit series expression for all coefficients in the virial expansion of the free energy and the experimentally measurable conductance. Some results for correlation functions are also presented. The second method gives an expression for the full free energy, which yields a surprising fluctuation-dissipation relation between the conductance and the free energy.

BOUNDARY INTERACTION CHANGING OPERATORS AND DYNAMICAL CORRELATIONS IN QUANTUM IMPURITY PROBLEMS

Recent developments have made possible the computation of equilibrium dynamical correlators in quantum impurity problems. In many situations however, one is rather interested in correlators subject to a non equilibrium initial preparation; this is the case for instance for the occupation probability

Form factors approach to current correlations in one-dimensional systems with impurities

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The Maxwell-Bloch theory in quantum optics and the Kondo model

in the double well problem of dissipative quantum mechanics (DQM). We show in this paper how to handle this situation in the framework of integrable quantum field theories by introducing ``boundary interactions changing operators. We determine the properties of these operators by using an axiomatic approach similar in spirit to what is done for form-factors. This allows us to obtain new exact results for

Time correlations in 1D quantum impurity problems

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Correlations in one-dimensional quantum impurity problems with an external field

; for instance, we find that that at large times (or small