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H. Saleur

Publications and source records attributed to H. Saleur.

At least 73 records · Page 4Linked to original sources
arXiv1997

Tunneling in quantum wires I: Exact solution of the spin isotropic case

We show that the problem of impurity tunneling in a Luttinger liquid of electrons with spin is solvable in the spin isotropic case ($g_σ=2$, $g_ρ$ arbitrary). The resulting integrable model is similar to a two channel anisotropic Kondo model, but with the impurity spin in a "cyclic representation" of the quantum algebra $su(2)_q$ associated with the anisotropy. Using exact, non-perturbative techniques we study the RG flow, and compute the DC conductance. As expected from the analysis of Kane and Fisher we find that the IR fixed point corresponds to two separate leads. We also prove an exact duality between the UV and IR expansions of the current at vanishing temperature.

cond-mat.str-el↗
arXiv1997

The Maxwell-Bloch Theory in Quantum Optics and the Kondo Model

In this letter, the problem of radiation in a fiber geometry interacting with a two level atom is mapped onto the anisotropic Kondo model. Thermodynamical and dynamical properties are then computed exploiting the integrability of this latter system. We compute some correlation functions, decay rates and Lamb shifts. In turn this leads to an analysis of the classical limit of the anisotropic Kondo model.

hep-th↗
arXiv1996

Precursors, aftershocks, criticality and self-organized criticality

We present a simple model of earthquakes on a pre-existing hierarchical fault network. The system self-organizes on long time scales in a stationary state with a power law Gutenberg-Richter distribution of earthquake sizes. The largest fault carries irregular great earthquakes preceded by precursors developing over long time scales and followed by aftershocks obeying an Omori's law. The cumulative energy released by precursors follows a time-to-failure power law with log-periodic structures, qualifying a large event as an effective dynamical (depinning) critical point. Down the hierarchy, smaller earthquakes exhibit the same phenomenology, albeit with increasing irregularities.

cond-mat↗
arXiv1996

Correlations in one dimensional quantum impurity problems with an external field or a temperature

We discuss in more details the theory of low energy excitations in quantum impurity problems with an external field at vanishing temperature, giving further support to results of the previous paper. We then extend these results to the next order at low frequency, obtaining in particular the exact expression, as a function of the bias, of the first two derivatives of the response function $χ''(ω)$ at $ω=0$ in the double well problem of dissipative quantum mechanics. We also extend our approach to the case of non vanishing temperature and no external field. Fendley et al. had obtained in that case an expression for the Hall conductance with a single impurity using a Landauer-Büttiker type approach. We recover their result in the framework of linear response theory using renormalized form-factors. We also obtain, as a function of the temperature, the first derivative of the response function $χ''(ω)$ at $ω=0$ in the double well problem of dissipative quantum mechanics.

cond-mat↗
arXiv1996

Correlations in one dimensional quantum impurity problems with an external field

We study response functions of integrable quantum impurity problems with an external field at $T=0$ using non perturbative techniques derived from the Bethe ansatz. We develop the first steps of the theory of excitations over the new, field dependent ground state, leading to renormalized (or ``dressed'') form-factors. We obtain exactly the low frequency behaviour of the dynamical susceptibility $χ''(ω)$ in the double well problem of dissipative quantum mechanics (or equivalently the anisotropic Kondo problem),and the low frequency behaviour of the AC noise $S_t(ω)$ for tunneling between edges in fractional quantum Hall devices. We also obtain exactly the structure of singularities in $χ''(ω)$ and $S_t(ω)$. Our results differ significantly from previous perturbative approaches.

cond-mat↗
arXiv1996

Finite temperature correlations in the one-dimensional quantum Ising model

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 \Korbook, 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 spacetime derivatives, of which three are equivalent to the equations obtained earlier in \mccoy,\perk. 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.

cond-mat↗
arXiv1996

Exact Friedel oscillations in the g=1/2 Luttinger liquid

A single impurity in the 1D Luttinger model creates a local modification of the charge density analogous to the Friedel oscillations. In this paper, we present an exact solution of the case $g={1\over 2}$ (the equivalent of the Toulouse point) at any temperature $T$ and impurity coupling, expressing the charge density in terms of a hypergeometric function. We find in particular that at $T=0$, the oscillatory part of the density goes as $\ln x$ at small distance and $x^{-1/2}$ at large distance.

cond-mat↗
arXiv1996

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

We show how to compute analytically time and space dependent correlations in one dimensional quantum integrable systems with an impurity. Our approach is based on a description of these systems in terms of massless scattering of quasiparticles. Correlators follow then from matrix elements of local operators between multiparticle states, the ``massless form factors''. Although an infinite sum of these form factors has to be considered in principle, we find that for current, spin, and energy operators, only a few (typically two or three) are necessary to obtain an accuracy of more than $1\%$, for {\bf arbitrary coupling strength}, that is all the way from short to large distances. As examples we compute, at zero temperature, the frequency dependent conductance in a Luttinger liquid with impurity, the spectral function in the double well problem of dissipative quantum mechanics and part of the space dependent succeptibility in the Kondo model .

cond-mat↗
arXiv1996

Non-equilibrium DC noise in a Luttinger liquid with impurity

We compute exactly the non-equilibrium DC noise in a Luttinger liquid with an impurity and an applied voltage. By generalizing Landauer transport theory for Fermi liquids to interacting, integrable systems, we relate this noise to the density fluctuations of quasiparticles. We then show how to compute these fluctuations using the Bethe ansatz. The non-trivial density correlations from the interactions result in a substantial part of the non-equilibrium noise. The final result for the noise is a scaling function of the voltage, temperature and impurity coupling. It may eventually be observable in tunneling between edges of a fractional quantum Hall effect device.

cond-mat↗
arXiv1995

Time correlations in 1D quantum impurity problems

We develop in this letter an analytical approach using form- factors to compute time dependent correlations in integrable quantum impurity problems. As an example, we obtain for the first time the frequency dependent conductivity $G(ω)$ for the tunneling between the edges in the $ν=1/3$ fractional quantum Hall effect, and the spectrum $S(w)$ of the spin-spin correlation in the anisotropic Kondo model and equivalently in the double well system of dissipative quantum mechanics, both at vanishing temperature.

cond-mat↗
arXiv1995

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 group $SU(2)_q$. 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. For the boundary sine-Gordon model, which describes an impurity in a Luttinger liquid, we find the non-equilibrium conductance for all values of the Luttinger coupling.

cond-mat↗
arXiv1995

Exact non-equilibrium transport through point contacts in quantum wires and fractional quantum Hall devices

We have recently calculated exact non-equilibrium quantum transport properties through a point contact in a Luttinger liquid. Using a particular quasiparticle basis of the Hilbert space dictated by integrability, we here compute explicitly the exact $I(V)$ characteristic and conductance out of equilibrium as a function of driving voltage $V$ and temperature $T$. These are described by universal scaling functions of two variables, the scaled point-contact interaction strength, and $V/T$. The differential-conductance curve as a function of the interaction strength broadens significantly as $V/T$ is increased, and develops a pronounced maximum at a (universal) critical value $(e V/k_B T)=7.18868...$. In addition, we derive an exact duality between strong and weak backscattering. The theory presented here has recently been realized experimentally in resonant tunneling-transport experiments between edge states in fractional quantum Hall effect devices. In this context the exact duality is between electron tunneling and Laughlin-quasiparticle tunneling.

cond-mat↗
arXiv1995

Exact perturbative solution of the Kondo problem

We explicitly evaluate the infinite series of integrals that appears in the "Anderson-Yuval" reformulation of the anisotropic Kondo problem in terms of a one-dimensional Coulomb gas. We do this by developing a general approach relating the anisotropic Kondo problem of arbitrary spin with the boundary sine-Gordon model, which describes impurity tunneling in a Luttinger liquid and in the fractional quantum Hall effect. The Kondo solution then follows from the exact perturbative solution of the latter model in terms of Jack polynomials.

cond-mat↗
arXiv1995

Exact non-equilibrium DC shot noise in Luttinger liquids and fractional quantum Hall devices

A point contact in a Luttinger liquid couples the left- and right-moving channels, producing shot noise. We calculate exactly the DC shot noise at zero temperature in the out-of-equilibrium steady state where current is flowing. Integrability of the interaction ensures the existence of a quasiparticle basis where quasiparticles scatter ``one by one'' off the point contact. This enables us to apply a direct generalization of the Landauer approach to shot noise to this interacting model. We find a simple relation of the noise to the current and the differential conductance. Our results should be experimentally-testable in a fractional quantum Hall effect device, providing a clear signal of the fractional charge of the Laughlin quasiparticles.

cond-mat↗
arXiv1995

Boundary energy and boundary states in integrable quantum field theories

We study the ground state energy of integrable $1+1$ quantum field theories with boundaries (the genuine Casimir effect). In the scalar case, this is done by introducing a new, ``R-channel TBA'', where the boundary is represented by a boundary state, and the thermodynamics involves evaluating scalar products of boundary states with all the states of the theory. In the non-scalar, sine-Gordon case, this is done by generalizing the method of Destri and De Vega. The two approaches are compared. Miscellaneous other results are obtained, in particular formulas for the overall normalization and scalar products of boundary states, exact partition functions for the critical Ising model in a boundary magnetic field, and also results for the energy, excited states and boundary S-matrix of $O(n)$ and minimal models.

hep-th↗
arXiv1995

Boundary bound states and boundary bootstrap in the sine-Gordon model with Dirichlet boundary conditions.

We present a complete study of boundary bound states and related boundary S-matrices for the sine-Gordon model with Dirichlet boundary conditions. Our approach is based partly on the bootstrap procedure, and partly on the explicit solution of the inhomogeneous XXZ model with boundary magnetic field and of the boundary Thirring model. We identify boundary bound states with new ``boundary strings'' in the Bethe ansatz. The boundary energy is also computed.

hep-th↗
arXiv1994

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 constraints, 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 non-perturbative one based on the thermodynamic Bethe ansatz and functional relations. The first method allows us to compute explicitly 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 provides in particular a surprising fluctuation-dissipation relation between the free energy and the conductance.

hep-th↗