Related papers: Uniqueness of normalized ground states for NLS mod…
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 discuss the problem of establishing the existence of the Ground States for the subcritical focusing Nonlinear Schr\"odinger energy on a domain made of a line and a plane intersecting at a point. The problem is physically motivated by the…
In this article, we study the Schr\"{o}dinger-Newton equation \begin{equation} -\Delta u+\lambda u=\frac{1}{4\pi}\left(\frac{1}{|x|}\star u^{2}\right)u+|u|^{q-2}u \quad \text{in}~\mathbb{R}^3, \end{equation} where $\lambda\in\mathbb{R}_+$,…
Using a cone-theoretical method, we prove the uniqueness of the ground state for two Bose Hubbard models. The first model is the usual Bose Hubbard model with real hopping coefficients and attractive interactions. The second model is a…
In the present paper, we study the existence of normalized solutions for a Choquard type equation involving mixed diffusion type operators. We also provide regularity results of these solutions. Next, the equivalence between existence of…
We study the $p$-Choquard equation in 3-dimensional case and establish existence and uniqueness of ground states for the corresponding Weinstein functional. For proving the uniqueness of ground states, we use the radial symmetry to…
We develop a new framework to prove the existence of two positive solutions with prescribed mass on star-shaped bounded domains: one is the normalized ground state and another is of M-P type. We merely address the Sobolev critical cases…
We study uniqueness and nondegeneracy of ground states for nonlinear scalar field equations in two dimensions with a point interaction at the origin. It is known that the all ground states are radial, positive, and decreasing functions. In…
We prove the existence, uniqueness, and strict positivity of ground states of the possibly massless renormalized Nelson operator under an infrared regularity condition and for Kato decomposable electrostatic potentials fulfilling a binding…
In recent years, a variety of normalization methods have been proposed to help train neural networks, such as batch normalization (BN), layer normalization (LN), weight normalization (WN), group normalization (GN), etc. However,…
We consider a nonlinear Schr\"odinger equation (NLS) posed on a graph or network composed of a generic compact part to which a finite number of half-lines are attached. We call this structure a starlike graph. At the vertices of the graph…
We investigate the existence of ground states for functionals with nonhomogenous principal part. Roughly speaking, we show that the Nehari manifold method requires no homogeinity on the principal part of a functional. This result is…
We prove an existence and uniqueness result for ground states of one-dimensional Schr\"{o}dinger-Newton equations.
In this work, we investigate the use of normalizing flows to model conditional distributions. In particular, we use our proposed method to analyze inverse problems with invertible neural networks by maximizing the posterior likelihood. Our…
We prove an existence and uniqueness result for ground states and for purely angular excitations of two-dimensional Schr\"{o}dinger-Newton equations. From the minimization problem for ground states we obtain a sharp version of a logarithmic…
We propose a second renormalization group method to handle the tensor-network states or models. This method reduces dramatically the truncation error of the tensor renormalization group. It allows physical quantities of classical…
We study a set of exactly soluble net spin models. There exist two kinds of ground state, one is a complete dimerized state, and the other one is the ground state of corresponding spin-1 model. For the excitation gap, various phases were…
An important but little-studied property of spin glasses is the stability of their ground states to changes in one or a finite number of couplings. It was shown in earlier work that, if multiple ground states are assumed to exist, then…
Standard methods of the theory of permanent state reduction are shown to offer an alternative realization of Omn\`es' project. Our proposal, as simple as Omn\`es' one, possesses closed master equation for the ensemble density operator,…
Normalization techniques are essential for accelerating the training and improving the generalization of deep neural networks (DNNs), and have successfully been used in various applications. This paper reviews and comments on the past,…