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Manifestly non-Hermitian quantum graphs with real spectra are introduced and shown tractable as a new class of phenomenological models with several appealing descriptive properties. For illustrative purposes, just equilateral star-graphs…
We apply the envelope function approach to abrupt heterostructures starting with the least action principle for the microscopic wave function. The interface is treated nonperturbatively, and our approach is applicable to mismatched…
We investigate both experimentally and theoretically the traffic of particles flowing in microfluidic obstacle networks. We show that the traffic dynamics is a non-linear process: the particle current does not scale with the particle…
We study the original $\alpha$-Fermi-Pasta-Ulam (FPU) system with $N=16,32$ and $64$ masses connected by a nonlinear quadratic spring. Our approach is based on resonant wave-wave interaction theory, i.e. we assume that, in the weakly…
Realizing systems that support robust, controlled interactions between individual photons is an exciting frontier of nonlinear optics. To this end, one approach that has emerged recently is to leverage atomic interactions to create strong…
We present a general theoretical approach for the quantitative description of parametric excitation of spin-wave modes in confined micromagnetic systems. This type of problem belongs to a broader class of nonlinear modal dynamics that arise…
We demonstrate via numerical simulation that in the \textit{strongly} nonlinear limit, the $\beta$-FPU system in thermal equilibrium behaves surprisingly like weakly nonlinear waves in properly renormalized normal variables. This arises…
We consider a non-relativistic quantum particle interacting with a singular potential supported by two parallel straight lines in the plane. We locate the essential spectrum under the hypothesis that the interaction asymptotically…
We study the existence and uniqueness of wavefronts to the scalar reaction-diffusion equations $u_{t}(t,x) = \Delta u(t,x) - u(t,x) + g(u(t-h,x)),$ with monotone delayed reaction term $g: \R_+ \to \R_+$ and $h >0$. We are mostly interested…
We show that any interacting integrable model possesses a class of initial states for which the leading corrections to ballistic transport are subdiffusive rather than diffusive. These initial states are natural to realize experimentally…
In recent years, there has been growing interest in non-Hermitian phenomena in low-symmetry conductors, particularly optical gain driven by electro-optic effects. Conventional semiclassical treatments typically attribute these effects to…
We study a system of $N$ interacting particles on $\bf{Z}$. The stochastic dynamics consists of two components: a free motion of each particle (independent random walks) and a pair-wise interaction between particles. The interaction belongs…
For the interaction energy with repulsive-attractive potentials, we give generic conditions which guarantee the radial symmetry of the local minimizers in the infinite Wasserstein distance. As a consequence, we obtain the uniqueness of…
We consider hamiltonian models representing an arbitrary number of spin $1/2$ fermion quantum fields interacting through arbitrary processes of creation or annihilation of particles. The fields may be massive or massless. The interaction…
We establish the existence of two weak coupling regime effective dynamics for an open quantum system of repeated interactions (vanishing strength and individual interaction duration, respectively). This generalizes known results in that the…
With the appropriate choice of parameters and sufficient cooling, charged particles in a circular accelerator are believed to undergo a transition to a highly-ordered crystalline state. The simplest possible crystalline configuration is a…
We consider a mathematical model of the Fermi theory of weak interactions as patterned according to the well-known current-current coupling of quantum electrodynamics. We focuss on the example of the decay of the muons into electrons,…
We study optomechanical interactions in non-Hermitian photonic molecules that support two photonic states and one acoustic mode. The nonlinear steady-state solutions and their linear stability landscapes are investigated as a function of…
We report on the deterministic preparation of antiferromagnetic Heisenberg spin chains consisting of up to four fermionic atoms in a one-dimensional trap. These chains are stabilized by strong repulsive interactions between the two spin…
We are interested in the existence of depolarization waves in the human brain. These waves propagate in the grey matter and are absorbed in the white matter. We consider a two-dimensional model $u_t=\Delta u + f(u) \1_{|y|\leq R} - \alpha u…