Related papers: Existence and uniqueness of ground states for $p$ …
In this paper we prove the existence of a solution to a nonlinear Schr{\"o}dinger--Poisson eigenvalue problem in dimension less than $3$. Our proof is based on a global approach to the determination of eigenvalues and eigenfunctions which…
We study existence and properties of ground states for the nonlinear Schr\"odinger equation with combined power nonlinearities \[ -\Delta u= \lambda u + \mu |u|^{q-2} u + |u|^{p-2} u \qquad \text{in $\mathbb{R}^N$, $N \ge 1$,} \] having…
We analyse Hamiltonian-type systems of second-order elliptic PDE invariant under a non-compact group and, consequently, involve a lack of compactness of the Sobolev embedding. We show that the loss of compactness can be compensated by using…
We prove existence and qualitative properties of ground state solutions to a generalized nonlocal 3rd-4th order Gross-Pitaevskii equation. Using a mountain pass argument on spheres and constructing appropriately localized Palais-Smale…
Stabilizer states, which are also known as the Clifford states, have been commonly utilized in quantum information, quantum error correction, and quantum circuit simulation due to their simple mathematical structure. In this work, we apply…
In this paper, we study the existence of ground state standing waves and orbital stability, of prescribed mass, for the nonlinear critical Choquard equation \begin{equation*} \left\{\begin{array}{l} i \partial_t u+\Delta u…
In this paper, we study the following fractional Choquard system \begin{align*} \begin{split} \left\{ \begin{array}{ll} (-\Delta)^{1/2}u=\lambda_1 u+(I_\mu*F(u,v))F_u (u,v), \quad\mbox{in}\ \ \mathbb{R}, (-\Delta)^{1/2}v=\lambda_2…
We study the behavior of a probability measure near the bottom of its support in terms of time averaged quotients of its Laplace transform. We discuss how our results are connected to both rank-one perturbation theory as well as renewal…
The characterization of ground states among all quantum states is an important problem in quantum many-body physics. For example, the celebrated entanglement area law for gapped Hamiltonians has allowed for efficient simulation of 1d and…
Some mixed states composed of only GHZ states can be expressed in terms of only W-states. This fact implies that such states have vanishing three-tangle. One of such rank-3 states, $\Pi_{GHZ}$, is explicitly presented in this paper. These…
A space-periodic ground state is shown to exist for lattices of smeared ions in $\R^3$ coupled to the Schr\"odinger and scalar fields. The elementary cell is necessarily neutral. The 1D, 2D and 3D lattices in $\R^3$ are considered, and a…
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…
This paper concerns the normalized ground states for the nonlinear Schr\"{o}dinger equation in the Bopp-Podolsky electrodynamics. This equation has a nonlocal nonlinearity and a mass supercritical power nonlinearity, both of which have deep…
In this article, we investigate normalized solutions for nonlinear problems involving variable exponents. To the best of our knowledge, normalized solutions have not been previously studied in this setting, and our results appear to be new.…
We investigate the existence and the singular limit of normalized ground states for focusing doubly nonlinear Schr\"odinger equations with both standard and concentrated nonlinearities on two-dimensional square grids. First, we provide…
This paper is concerned with the ground states of a coupled pseudo-relativistic Hartree system in $\mathbb{R} ^{3} $ with trapping potentials, where the intraspecies and the interspecies interaction are both attractive. By investigating an…
We investigate the existence and the properties of normalized ground states of a nonlinear Schr\"odinger equation on a quantum hybrid formed by two planes connected at a point. The nonlinearities are of power type and $L^2$-subcritical,…
We consider here solutions of the nonlinear fractional Schr\"odinger equation $$\epsilon^{2s}(-\Delta)^s u+V(x)u=u^p.$$ We show that concentration points must be critical points for $V$. We also prove that, if the potential $V$ is coercive…
In this work we examine the existence and uniqueness of the groundstate of a SU(N)x G2 octonionic matrix model on a bounded domain of R^N. The existence and uniqueness argument of the groundstate wavefunction follows from the Lax-Milgram…
A set of new exact ground states of the generalized Hubbard models in arbitrary dimensions with explicitly given parameter regions is presented. This is based on a simple method for constructing exact ground states for homogeneous quantum…