Mathematical Physics
We construct quantum Turing patterns in Lindblad lattice dynamics and establish a rigorous theory of their nonlinear order and quantum fluctuations. For an explicit completely positive family with finite-range couplings, the first-moment…
We introduce the multispecies version of the harmonic process on a one-dimensional chain in contact with boundary reservoirs. This process is a continuous-time Markov chain where each site can host an unbounded number of colored particles.…
In electromagnetic heating and other applications, we need to compute the volume enclosed by an isosurface of the 3D temperature distribution that is numerically represented on a rectangular grid. This situation arises naturally when the…
In classical statistical physics, the Mori-Zwanzig projection operator technique is used to derive generalized Langevin equations for a random variable (observable). Standard derivations implicitly assume the existence of solutions to the…
The problem of finding lower and upper bounds on multivariate homogeneous polynomials is both difficult and important given its applications to questions ranging from dynamical stability in complex potential landscapes to data analysis.…
We reconsider the analysis of the Classical Painlev\'e Problem developed by F. G\'enot and B. Brogliato ([1] New results on Painlev\'e paradoxes. - European Journal of Mechanics-A/Solids, 18(4):653{677, 1999), focusing on the consistency of…
This paper studies finite-time blow-up of pseudospherical metrics induced by solutions of the Cauchy problem for the Degasperis--Procesi equation. For initial momentum profiles satisfying suitable left--right sign conditions, we use the…
Upon fixing the adiabatic index, the spherically symmetric liquid Lane-Emden stars governed by the Euler-Poisson system with a "stiffened gas" equation of state $p=\rho^\gamma-1$ form a one-parameter family, naturally parametrised by the…
We study the partition function of Abelian $BF$ theory with an axial gauge fixing condition given by a Morse--Smale vector field, and we show that it recovers the Milnor metric on the determinant line on the twisted cohomology of the…
We consider one-frequency quasiperiodic Schr\"odinger operators \[ (H_{v,\alpha,\theta}u)(n) = u(n+1)+u(n-1) + v(\theta+n\alpha)u(n) \] acting on $\ell^2(\mathbb Z)$, where $\alpha\notin\mathbb Q$ and $v\in C^2(\mathbb T,\mathbb R)$ is an…
We study the variance of a local Weyl law over a fixed smooth energy window, when averaged over large Weil--Petersson hyperbolic surfaces. Our results are consistent with the predictions of Berry's random wave model. Our approach allows to…
The hard sphere model is a classical model from statistical physics in which particles are represented by equal-sized spheres. Longstanding predictions from the physics literature indicate that in $\mathbb{R}^2$ and $\mathbb{R}^3$ the…
We consider a collection of pairwise commuting quantum observables in the setting of Berezin--Toeplitz quantization of a closed K\"{a}hler manifold and assume that the Arnold--Liouville theorem applies to their principal symbols. We use…
The $N$-th order rational rogue wave of the nonlinear Schr\"odinger equation (NLS), which depends on $2 N-2$ real parameters, has been shown to be impossible to generate by the nonlinear superposition formula. We here generate this sequence…
We derive the $\mathcal{P}(\Phi)_2$ measure on the two-dimensional unit torus as the rigorous limit of many-body quantum Gibbs states. In particular, the quantum model corresponding to the $\Phi^{2p}_2$ measure is formulated in the…
We study the high-temperature mean-field limit of grand-canonical bosonic Gibbs states on the torus with renormalized nonlocal three-body interactions. In dimensions two and three, we construct the limiting nonlinear classical Gibbs measure…
A semi-bounded operator that is bounded below by one is essentially self-adjoint if the kernel of the adjoint is trivial. This is the case if the kernel of the adjoint belongs to the form domain of the Friedrichs extension. We describe a…
Multiphoton light-matter interactions, in which a bosonic mode exchanges $k$ excitations at a time with a quantum system, are a source of genuine nonlinearity in quantum optics and are increasingly accessible experimentally. Here we study…
We define the lift of a partial cohomological field theory with respect to a Frobenius algebra and the corresponding lift of local polyvector fields, extending the lift procedure proposed by Della Vedova, Lorenzoni, and Savoldi. This allows…
In this paper, we classify all six-dimensional real nilpotent Lie bialgebras of symplectic type. The Poisson structures on all of the related six-dimensional Poisson-Lie groups are obtained. Some new integrable Hamiltonian systems for which…