Symmetry breaking in two-dimensional square grids: persistence and failure of the dimensional crossover
From MaRDI portal
Publication:2668974
DOI10.1016/j.matpur.2021.12.010zbMath1486.35007arXiv2104.13842OpenAlexW3159417356MaRDI QIDQ2668974
Lorenzo Tentarelli, Simone Dovetta
Publication date: 9 March 2022
Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2104.13842
nonlinear Schrödinger equationSobolev inequalitydefectmetric graphsdimensional crossovertwo-dimensional grid
Variational inequalities (49J40) NLS equations (nonlinear Schrödinger equations) (35Q55) PDEs in connection with quantum mechanics (35Q40) Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals (35A23) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35) PDEs on graphs and networks (ramified or polygonal spaces) (35R02)
Related Items
Standing waves on quantum graphs, On the notion of ground state for nonlinear Schrödinger equations on metric graphs
Uses Software
Cites Work
- NLS ground states on graphs
- NLS ground states on metric graphs with localized nonlinearities
- Bifurcations of standing localized waves on periodic graphs
- Eigenvalue estimates for Schrödinger operators on metric trees
- Spectral analysis on graph-like spaces
- Compressions and isoperimetric inequalities
- Coupled-mode equations and gap solitons in a two-dimensional nonlinear elliptic problem with a separable periodic potential
- Bounds on the tight-binding approximation for the Gross-Pitaevskii equation with a periodic potential
- Justification of the nonlinear Schrödinger equation in spatially periodic media
- On the spectra of carbon nano-structures
- A note on percolation on \(\mathbb Z^d\): isoperimetric profile via exponential cluster repulsion
- Edge-isoperimetric inequalities in the grid
- On the structure of band edges of \(2\)-dimensional periodic elliptic operators
- Multiple positive bound states for the subcritical NLS equation on metric graphs
- Spectral estimates for infinite quantum graphs
- Nonlinear Schrödinger equations on periodic metric graphs
- A stability result for the cube edge isoperimetric inequality
- Isoperimetry and heat kernel decay on percolation clusters.
- Standing waves of the quintic NLS equation on the tadpole graph
- Uniqueness and non-uniqueness of prescribed mass NLS ground states on metric graphs
- Supercritical percolation on nonamenable graphs: isoperimetry, analyticity, and exponential decay of the cluster size distribution
- Edge-localized states on quantum graphs in the limit of large mass
- On the nonlinear Dirac equation on noncompact metric graphs
- Degenerate band edges in periodic quantum graphs
- Quantum graphs and dimensional crossover: the honeycomb
- Limits of quantum graph operators with shrinking edges
- Mass-constrained ground states of the stationary NLSE on periodic metric graphs
- Dimensional crossover with a continuum of critical exponents for NLS on doubly periodic metric graphs
- \(L^2\)-critical NLS on noncompact metric graphs with localized nonlinearity: topological and metric features
- Semigroup methods for evolution equations on networks
- Normal and integral currents
- An overview of periodic elliptic operators
- Nonlinear Schrödinger equation on graphs: recent results and open problems
- A Relation Between Pointwise Convergence of Functions and Convergence of Functionals
- Growth and isoperimetric profile of planar graphs
- NLS ground states on metric trees: existence results and open questions
- Discrete Isoperimetric Problems
- The isoperimetric inequality
- Kirchhoff's rule for quantum wires
- Some connections between isoperimetric and Sobolev-type inequalities
- Sobolev met Poincaré
- Nonlinear dynamics on branched structures and networks
- Periodic quantum graphs from the Bethe–Sommerfeld perspective
- Nonlinear Dirac Equation on Graphs with Localized Nonlinearities: Bound States and Nonrelativistic Limit
- Isoperimetry in integer lattices
- On Tight‐Binding Approximations in Optical Lattices
- Local minimizers in absence of ground states for the critical NLS energy on metric graphs
- Linear hyperbolic systems on networks: well-posedness and qualitative properties
- Strong Isoperimetric Inequality for Tessellating Quantum Graphs
- Surgery principles for the spectral analysis of quantum graphs
- One-dimensional versions of three-dimensional system: Ground states for the NLS on the spatial grid
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
