The universal R-matrix and its associated quantum algebra as functionals of the classical r-matrix: the sl2sl_{2} case

Using a geometrical approach to the quantum Yang-Baxter equation, the quantum algebra ${\cal U}_{\hbar}(sl_{2})$ and its universal quantum $R$-matrix are explicitely constructed as functionals of the associated classical $r$-matrix. In this framework, the quantum algebra ${\cal U}_{\hbar}(sl_{2})$ is naturally imbedded in the universal envelopping algebra of the $sl_{2}$ current algebra

On the thermodynamic limit of form factors in the massless XXZ Heisenberg chain

We consider the problem of computing form factors of the massless XXZ Heisenberg spin-1/2 chain in a magnetic field in the (thermodynamic) limit where the size M of the chain becomes large. For that purpose, we take the particular example of the matrix element of the third component of spin between the ground state and an excited state with one particle and one hole located at the opposite ends of the Fermi interval (umklapp-type term). We exhibit its power-law decrease in terms of the size of the chain M, and compute the corresponding exponent and amplitude. As a consequence, we show that this form factor is directly related to the amplitude of the leading oscillating term in the long-distance asymptotic expansion of the two-point correlation function of the third component of spin.Comment: 28 page

Two-dimensional hydrodynamic lattice-gas simulations of binary immiscible and ternary amphiphilic fluid flow through porous media

The behaviour of two dimensional binary and ternary amphiphilic fluids under flow conditions is investigated using a hydrodynamic lattice gas model. After the validation of the model in simple cases (Poiseuille flow, Darcy's law for single component fluids), attention is focussed on the properties of binary immiscible fluids in porous media. An extension of Darcy's law which explicitly admits a viscous coupling between the fluids is verified, and evidence of capillary effects are described. The influence of a third component, namely surfactant, is studied in the same context. Invasion simulations have also been performed. The effect of the applied force on the invasion process is reported. As the forcing level increases, the invasion process becomes faster and the residual oil saturation decreases. The introduction of surfactant in the invading phase during imbibition produces new phenomena, including emulsification and micellisation. At very low fluid forcing levels, this leads to the production of a low-resistance gel, which then slows down the progress of the invading fluid. At long times (beyond the water percolation threshold), the concentration of remaining oil within the porous medium is lowered by the action of surfactant, thus enhancing oil recovery. On the other hand, the introduction of surfactant in the invading phase during drainage simulations slows down the invasion process -- the invading fluid takes a more tortuous path to invade the porous medium -- and reduces the oil recovery (the residual oil saturation increases).Comment: 48 pages, 26 figures. Phys. Rev. E (in press

Measuring frequency fluctuations in nonlinear nanomechanical resonators

Advances in nanomechanics within recent years have demonstrated an always expanding range of devices, from top-down structures to appealing bottom-up MoS$_2$ and graphene membranes, used for both sensing and component-oriented applications. One of the main concerns in all of these devices is frequency noise, which ultimately limits their applicability. This issue has attracted a lot of attention recently, and the origin of this noise remains elusive up to date. In this Letter we present a very simple technique to measure frequency noise in nonlinear mechanical devices, based on the presence of bistability. It is illustrated on silicon-nitride high-stress doubly-clamped beams, in a cryogenic environment. We report on the same $T/f$ dependence of the frequency noise power spectra as reported in the literature. But we also find unexpected {\it damping fluctuations}, amplified in the vicinity of the bifurcation points; this effect is clearly distinct from already reported nonlinear dephasing, and poses a fundamental limit on the measurement of bifurcation frequencies. The technique is further applied to the measurement of frequency noise as a function of mode number, within the same device. The relative frequency noise for the fundamental flexure $\delta f/f_0$ lies in the range $0.5 - 0.01~$ppm (consistent with literature for cryogenic MHz devices), and decreases with mode number in the range studied. The technique can be applied to {\it any types} of nano-mechanical structures, enabling progresses towards the understanding of intrinsic sources of noise in these devices.Comment: Published 7 may 201

On classical q-deformations of integrable sigma-models

JHEP is an open-access journal funded by SCOAP3 and licensed under CC BY 4.0A procedure is developed for constructing deformations of integrable σ-models which are themselves classically integrable. When applied to the principal chiral model on any compact Lie group F, one recovers the Yang-Baxter σ-model introduced a few years ago by C. Klimčík. In the case of the symmetric space σ-model on F/G we obtain a new one-parameter family of integrable σ-models. The actions of these models correspond to a deformation of the target space geometry and include a torsion term. An interesting feature of the construction is the q-deformation of the symmetry corresponding to left multiplication in the original models, which becomes replaced by a classical q-deformed Poisson-Hopf algebra. Another noteworthy aspect of the deformation in the coset σ-model case is that it interpolates between a compact and a non-compact symmetric space. This is exemplified in the case of the SU(2)/U(1) coset σ-model which interpolates all the way to the SU(1, 1)/U(1) coset σ-modelPeer reviewedFinal Published versio

A reduced model for shock and detonation waves. II. The reactive case

We present a mesoscopic model for reactive shock waves, which extends a previous model proposed in [G. Stoltz, Europhys. Lett. 76 (2006), 849]. A complex molecule (or a group of molecules) is replaced by a single mesoparticle, evolving according to some Dissipative Particle Dynamics. Chemical reactions can be handled in a mean way by considering an additional variable per particle describing a rate of reaction. The evolution of this rate is governed by the kinetics of a reversible exothermic reaction. Numerical results give profiles in qualitative agreement with all-atom studies

Alleviating the non-ultralocality of coset sigma models through a generalized Faddeev-Reshetikhin procedure

The Faddeev-Reshetikhin procedure corresponds to a removal of the non-ultralocality of the classical SU(2) principal chiral model. It is realized by defining another field theory, which has the same Lax pair and equations of motion but a different Poisson structure and Hamiltonian. Following earlier work of M. Semenov-Tian-Shansky and A. Sevostyanov, we show how it is possible to alleviate in a similar way the non-ultralocality of symmetric space sigma models. The equivalence of the equations of motion holds only at the level of the Pohlmeyer reduction of these models, which corresponds to symmetric space sine-Gordon models. This work therefore shows indirectly that symmetric space sine-Gordon models, defined by a gauged Wess-Zumino-Witten action with an integrable potential, have a mild non-ultralocality. The first step needed to construct an integrable discretization of these models is performed by determining the discrete analogue of the Poisson algebra of their Lax matrices.Comment: 31 pages; v2: minor change

Drinfeld Twists and Symmetric Bethe Vectors of Supersymmetric Fermion Models

We construct the Drinfeld twists (factorizing $F$-matrices) of the $gl(m|n)$-invariant fermion model. Completely symmetric representation of the pseudo-particle creation operators of the model are obtained in the basis provided by the $F$-matrix (the $F$-basis). We resolve the hierarchy of the nested Bethe vectors in the $F$-basis for the $gl(m|n)$ supersymmetric model.Comment: Latex File, 24 pages, no figure, some misprints are correcte

Current Algebra of Super WZNW Models

We derive the current algebra of supersymmetric principal chiral models with a Wess-Zumino term. At the critical point one obtains two commuting super Kac-Moody algebra as expected, but in general there are intertwining fields connecting both right and left sectors, analogously to the bosonic case. Moreover, in the present supersymmetric extension we have a quadratic algebra, rather than an affine Lie algebra, due to the mixing between bosonic and fermionic fields since the purely fermionic sector displays a Lie algebra as well.Comment: 13 page