相关论文: NLS ground states on graphs
The reduced BCS model that is commonly used for ultrasmall superconducting grains has an exact solution worked out long ago by Richardson in the context of nuclear physics. We use it to check the quality of previous treatments of this…
We provide a phenomenological theory for topological transitions in restructuring networks. In this statistical mechanical approach energy is assigned to the different network topologies and temperature is used as a quantity referring to…
The effects of topology and electron-electron interactions on the phase diagram of ABC stacked trilayer graphene (TLG) at the neutrality point are investigated within a weak coupling renormalization group approach. We find that the leading…
Topological phase transitions can be remarkably induced purely by manipulating gain and loss mechanisms, offering a novel approach to engineering topological properties. Recent theoretical studies have revealed gain-loss-induced topological…
In this article we study the notion of capacity of a vertex for infinite graphs over non-Archimedean fields. In contrast to graphs over the real field monotone limits do not need to exist. Thus, in our situation next to positive and null…
Traditional optimization-based techniques for time-synchronized state estimation (SE) often suffer from high online computational burden, limited phasor measurement unit (PMU) coverage, and presence of non-Gaussian measurement noise.…
In this work, the ground states of the Hubbard model on complete graph are studied, for a finite lattice size $L$ and arbitrary on-site energy $U$. We construct explicitly the ground states of the system when the number of the electrons…
Understanding the topology of the state space has proven to be extremely efficient for dynamical systems with a continuous state space. On the other hand, for particle systems on finite simple graphs, it has not yet been subject to deep…
We study the nature of the Nonlinear Schr\"odinger equation ground states on the product spaces $\R^n\times M^k$, where $M^k$ is a compact Riemannian manifold. We prove that for small $L^2$ masses the ground states coincide with the…
This paper introduces new variational methods centered on the direct application of a profile decomposition theorem for bounded sequences in Sobolev spaces. We employ these methods to prove the existence of ground state solutions for a…
Graph-based approximation methods are of growing interest in many areas, including transportation, biological and chemical networks, financial models, image processing, network flows, and more. In these applications, often a basis for the…
We provide information on a non trivial structure of phase space of the cubic NLS on a three-edge star graph. We prove that, contrarily to the case of the standard NLS on the line, the energy associated to the cubic focusing Schr\"odinger…
We discuss the stability of a class of normal forms of the completely resonant non--linear Schr\"odinger equation on a torus described in a previous paper. The discussion is essentially combinatorial and algebraic in nature. Thus this paper…
We apply optimization algorithms to the problem of finding ground states for crystalline surfaces and flux lines arrays in presence of disorder. The algorithms provide ground states in polynomial time, which provides for a more precise…
Motivated by recent interests in fracton topological phases, we explore the interplay between gapped 2D $\mathbb{Z}_N$ topological phases which admit fractional excitations with restricted mobility and geometry of the lattice on which such…
On the grounds of a Feynman-Kac--type formula for Hamiltonian lattice systems we derive analytical expressions for the matrix elements of the evolution operator. These expressions are valid at long times when a central limit theorem…
We consider manifestations of topological order in time-reversal-symmetric fractional topological liquids (TRS-FTLs), defined on planar surfaces with holes. We derive a formula for the topological ground state degeneracy of such a TRS-FTL,…
Knowledge of the topology of the electronic ground state of materials has led to deep insights to novel phenomena such as the integer quantum Hall effect and fermion-number fractionalization, as well as other properties of matter. Joining…
We consider the problem whether graph states can be ground states of local interaction Hamiltonians. For Hamiltonians acting on n qubits that involve at most two-body interactions, we show that no n-qubit graph state can be the exact,…
It is well known that the Hubbard model on a line graph has a flat band and ferromagnetic ground states in a certain density range. We show that for a Hubbard model on a line graph of a planar bipartite graph the ferromagnetic ground state…