Quantum interfaces
We review recent results on interface states in quantum statistical mechanics.
Quantum relativistic Toda chain.
Quantum relativistic Toda chain at root of unity: isospectrality, modified -operator, and functional Bethe ansatz.
Quantum waveguides with corners
The simplest modeling of planar quantum waveguides is the Dirichlet eigenproblem for the Laplace operator in unbounded open sets which are uniformly thin in one direction. Here we consider V-shaped guides. Their spectral properties depend essentially on a sole parameter, the opening of the V. The free energy band is a semi-infinite interval bounded from below. As soon as the V is not flat, there are bound states below the free energy band. There are a finite number of them, depending on the opening....
Quantum-dot-based photon emission and media conversion for quantum information applications.
Quasicrystallographic groups on Minkowski spaces.
Quasilinear hyperbolic equations with hysteresis
Quasi-neutral limit for a viscous capillary model of plasma
Quasi-periodic solutions of nonlinear random Schrödinger equations
Quasi-polynomial mixing of the 2D stochastic Ising model with “plus” boundary up to criticality
We considerably improve upon the recent result of [37] on the mixing time of Glauber dynamics for the 2D Ising model in a box of side at low temperature and with random boundary conditions whose distribution stochastically dominates the extremal plus phase. An important special case is when is concentrated on the homogeneous all-plus configuration, where the mixing time is conjectured to be polynomial in . In [37] it was shown that for a large enough inverse-temperature and any there...
Quelques applications de la positivité en théorie du transport
Quelques résultats d’hypocoercitivité en théorie cinétique collisionnelle
Nous présentons une introduction à un nouveau champ de recherche, l’hypocoercitivité. Nous énonçons quelques résultats obtenus récemment avec différents co-auteurs (Lukas Neumann, Jean Dolbeault, Christian Schmeiser) dans le cas des équations cinétiques collisionnelles, en particulier pour les équations de type Boltzmann. Puis nous présentons quelques perspectives de recherche à plus long terme, dans le but de dégager une théorie unifiée de l’hypocoercitivité en théorie cinétique collisionnelle.
Quenched law of large numbers for branching brownian motion in a random medium
We study a spatial branching model, where the underlying motion is d-dimensional (d≥1) brownian motion and the branching rate is affected by a random collection of reproduction suppressing sets dubbed mild obstacles. The main result of this paper is the quenched law of large numbers for the population for all d≥1. We also show that the branching brownian motion with mild obstacles spreads less quickly than ordinary branching brownian motion by giving an upper estimate on its speed. When the underlying...
Quenched limits for transient, ballistic, sub-gaussian one-dimensional random walk in random environment
We consider a nearest-neighbor, one-dimensional random walk {Xn}n≥0 in a random i.i.d. environment, in the regime where the walk is transient with speed vP>0 and there exists an s∈(1, 2) such that the annealed law of n−1/s(Xn−nvP) converges to a stable law of parameter s. Under the quenched law (i.e., conditioned on the environment), we show that no limit laws are possible. In particular we show that there exist sequences {tk} and {tk'} depending on the environment only, such that a quenched...
Quenched non-equilibrium central limit theorem for a tagged particle in the exclusion process with bond disorder
For a sequence of i.i.d. random variables {ξx: x∈ℤ} bounded above and below by strictly positive finite constants, consider the nearest-neighbor one-dimensional simple exclusion process in which a particle at x (resp. x+1) jumps to x+1 (resp. x) at rate ξx. We examine a quenched non-equilibrium central limit theorem for the position of a tagged particle in the exclusion process with bond disorder {ξx: x∈ℤ}. We prove that the position of the tagged particle converges under diffusive scaling to a...
Radial symmetric solutions of the Cahn-Hilliard equation with degenerate mobility.
Radially symmetric solutions of the Poisson-Boltzmann equation with a given energy
We consider the following problem: where Φ: Ω ⊂ → ℝ is an unknown function, Θ is an unknown constant and M, E are given parameters.
Random hysteresis loops
Dynamical hysteresis is a phenomenon which arises in ferromagnetic systems below the critical temperature as a response to adiabatic variations of the external magnetic field. We study the problem in the context of the mean-field Ising model with Glauber dynamics, proving that for frequencies of the magnetic field oscillations of order , the size of the system, the “critical” hysteresis loop becomes random.
Random matrices and permutations, matrix integrals and integrable systems
Random matrices, non-colliding processes and queues