相关论文: NLS ground states on graphs

In the Matrix approach to graph transformation we represent simple digraphs and rules with Boolean matrices and vectors, and the rewriting is expressed using Boolean operators only. In previous works, we developed analysis techniques…

We investigate the existence of ground states for the focusing Nonlinear Schr\"odinger Equation on the infinite three-dimensional cubic grid. We extend the result found for the analogous two-dimensional grid by proving an appropriate…

Recent experiments [L. Ju et al., Nature, 2015, 520, 650] confirm the existence of gapless states at domain walls created in gated bilayer graphene, when the sublattice stacking is changed from AB to BA. These states are significant because…

We propose a functional description of rewriting systems on topological vector spaces. We introduce the topological confluence property as an approximation of the confluence property. Using a representation of linear topological rewriting…

We study continuity, and lack thereof, of thermodynamical properties for one-dimensional dynamical systems. Under quite general hypotheses, the free energy is shown to be almost upper-semicontinuous: some normalised component of a limit…

Recently, there has been a major emphasis on developing data-driven approaches involving machine learning (ML) for high-speed static state estimation (SE) in power systems. The emphasis stems from the ability of ML to overcome difficulties…

This paper addresses the following verification task: Given a graph transformation system and a class of initial graphs, can we guarantee (non-)reachability of a given other class of graphs that characterizes bad or erroneous states? Both…

We investigate the ground state of a system of interacting particles in small nonlinear lattices with M > 2 sites, using as a prototypical example the discrete nonlinear Schroedinger equation that has been recently used extensively in the…

Graph states and hypergraph states can be constructed from products of basic operations that appear in SU(N)1. The level-rank dual of a theorem of Salton, Swingle, and Walter implies that these operations can be prepared topologically in…

Weconsider Burgers equation on metric graphs for simplest topologies such as star, loops, and tree graphs. Exact traveling wave solutions are obtained for the vertex boundary conditions providing mass conservation and continuity of the…

We provide explicit lower bounds for the ground-state energy of the renormalized Nelson model in terms of the coupling constant $\alpha$ and the number of particles $N$, uniform in the meson mass and valid even in the massless case. In…

The excited states of a charged particle interacting with the quantized electromagnetic field and an external potential all decay, but such a particle should have a true ground state--one that minimizes the energy and satisfies the…

Normalized ground state solutions (NGSS) of Schrodinger equations (SE) have attracted the attention of many research groups during the last decades. This is essentially due to their relevance in many fields in physics and engineering, where…

We consider the existence of bound and ground states for a family of nonlinear elliptic systems in $\mathbb{R}^N$, which involves equations with critical power nonlinearities and Hardy-type singular potentials. The equations are coupled by…

This work develops a flexible and mathematically sound framework for the design and analysis of graph scattering networks with variable branching ratios and generic functional calculus filters. Spectrally-agnostic stability guarantees for…

Graph neural networks are experiencing a surge of popularity within the machine learning community due to their ability to adapt to non-Euclidean domains and instil inductive biases. Despite this, their stability, i.e., their robustness to…

The energy super-critical Gross--Pitaevskii equation with a harmonic potential is revisited in the particular case of cubic focusing nonlinearity and dimension d > 4. In order to prove the existence of a ground state (a positive, radially…

Complications arising from the non-compact nature of the phase space of N-body systems prevent any asymptotic characterization of chaotic behaviour (since no equilibrium final states can exist). This leads us to revisit some of the old…

We show that the ground state in the Fisher--KPP model on a compact metric graph with Dirichlet conditions on boundary vertices is either trivial (zero) or nontrivial and strictly positive. For positive initial data, we prove that the…

In this work, we explore the state-space formulation of network processes to recover the underlying structure of the network (local connections). To do so, we employ subspace techniques borrowed from system identification literature and…