arXiv subjects

Frédéric Combes

Publications and source records attributed to Frédéric Combes.

4 recordsLinked to original sources

arXiv2017

Statistical mechanics approach to the electric polarization and dielectric constant of band insulators

We develop a theory for the analytic computation of the free energy of band insulators in the presence of a uniform and constant electric field. The two key ingredients are a perturbation-like expression of the Wannier-Stark energy spectrum of electrons and a modified statistical mechanics approach involving a local chemical potential in order to deal with the unbounded spectrum and impose the physically relevant electronic filling. At first order in the field, we recover the result of King-Smith, Vanderbilt and Resta for the electric polarization in terms of a Zak phase - albeit at finite temperature - and, at second order, deduce a general formula for the electric susceptibility, or equivalently for the dielectric constant. Advantages of our method are the validity of the formalism both at zero and finite temperature and the easy computation of higher order derivatives of the free energy. We verify our findings on two different one-dimensional tight-binding models.

cond-mat.str-el↗

arXiv2016

Competition between Spin Echo and Spin Self-Rephasing in a Trapped Atom Interferometer

We perform Ramsey interferometry on an ultracold 87Rb ensemble confined in an optical dipoletrap. We use a π-pulse set at the middle of the interferometer to restore the coherence of the spinensemble by canceling out phase inhomogeneities and creating a spin echo in the contrast. However,for high atomic densities, we observe the opposite behavior: the π-pulse accelerates the dephasingof the spin ensemble leading to a faster contrast decay of the interferometer. We understand thisphenomenon as a competition between the spin-echo technique and an exchange-interaction drivenspin self-rephasing mechanism based on the identical spin rotation effect. Our experimental data iswell reproduced by a numerical model.

physics.atom-ph↗

arXiv2014

Tensor models from the viewpoint of matrix models: the case of loop models on random surfaces

We study a connection between random tensors and random matrices through $U(τ)$ matrix models which generate fully packed, oriented loops on random surfaces. The latter are found to be in bijection with a set of regular edge-colored graphs typically found in tensor models. It is shown that the expansion in the number of loops is organized like the 1/N expansion of rank-three tensor models. Recent results on tensor models are reviewed and applied in this context. For example, configurations which maximize the number of loops are precisely the melonic graphs of tensor models and a scaling limit which projects onto the melonic sector is found. We also reinterpret the double scaling limit of tensor models from the point of view of loops on random surfaces. This approach is eventually generalized to higher-rank tensor models, which generate loops with fugacity $τ$ on triangulations in dimension $d-1$.

hep-th↗

arXiv2014

Tensor models from the viewpoint of matrix models: the case of the Gaussian distribution

Observables in random tensor theory are polynomials in the entries of a tensor of rank $d$ which are invariant under $U(N)^d$. It is notoriously difficult to evaluate the expectations of such polynomials, even in the Gaussian distribution. In this article, we introduce singular value decompositions to evaluate the expectations of polynomial observables of Gaussian random tensors. Performing the matrix integrals over the unitary group leads to a notion of effective observables which expand onto regular, matrix trace invariants. Examples are given to illustrate that both asymptotic and exact new calculations of expectations can be performed this way.

math-ph↗