We are concerned with singular elliptic equations of the form −∆u = p(x)(g(u) + f (u) + |∇u| a) in R N (N ≥ 3), where p is a positive weight and 0 < a < 1. Under the hypothesis that f is a nondecreasing function with sublinear growth and g is decreasing and unbounded around the origin, we establish the existence of a ground state solution vanishing at infinity. Our arguments rely essentially on...

Results of large-basis shell-model calculations for nuclei with A = 7 − 11 are presented. The effective interactions used in the study were derived microscopically from the Reid93 potential and take into account the Coulomb potential as well as the charge dependence of T = 1 partial waves. For A = 7, a 6h̄Ω model space was used, while for the rest of the studied nuclides, the calculations were p...

We consider the positive solutions u of −∆u+u−u = 0 in [0, 2π]× RN−1, which are 2π-periodic in x1 and tend uniformly to 0 in the other variables. There exists a constant C such that any solution u verifies u(x1, x ′) ≤ Cw0(x) where w0 is the ground state solution of −∆v + v − v = 0 in RN−1. We prove that exactly the same estimate is true when the period is 2π/ε, even when ε tends to 0. We have ...

The ground state of the four-chain Heisenberg ladder model is numerically investigated. Hiddenorder correlations suitable for the system are introduced and calculated with an emphasis on the spatially isotropic point, where a corresponding material exists. The existence of a long-range hidden correlation indicates formation of a short-range RVB state in the case of the antiferromagnetic inter-c...

We examine the M-theory version of SQCD which is known as MQCD. In the IIA limit, this theory appears to have a supersymmetry-breaking brane configuration which corresponds to the meta-stable state of N = 1 SU(Nc) SQCD. However, the behavior at infinity of this non-supersymmetric brane construction differs from that of the supersymmetric ground state of MQCD. We interpret this to mean that it i...

In this paper we report our systematic calculations of angular momentum I ground state probabilities (P (I)) of boson systems with spin l in the presence of random two-body interactions. It is found that the P (0) dominance is usually not true for a system with an odd number of bosons, while it is valid for an even number of bosons, which indicates that the P (0) dominance is partly connected t...

The time evolution of even and odd squeezed states, as well as that of squeezed number states, has been given in simple, analytic form. This follows experimental work on trapped ions which has demonstrated even and odd coherent states, number states, and squeezed (but not displaced) ground states. We review this situation and consider the extension to even and odd squeezed number states. Questi...

The observed electromagnetic (EM) properties of a nucleon at high energy are studied to search for a possible metastable color superconducting phase, called a virtual phase, that has an energy density close to the true ground state of the vacuum. The discussion is based on a mechanism of spontaneous partial breaking of the EM U(1) gauge symmetry inside a color superconductor. Favorable evidence...

We consider solutions u(t) to the 3d focusing NLS equation i∂tu+∆u+ |u|2u = 0 such that ‖xu(t)‖L2 = ∞ and u(t) is nonradial. Denoting by M [u] and E[u], the mass and energy, respectively, of a solution u, and byQ(x) the ground state solution to −Q+∆Q+ |Q|2Q = 0, we prove the following: if M [u]E[u] < M [Q]E[Q] and ‖u0‖L2‖∇u0‖L2 > ‖Q‖L2‖∇Q‖L2 , then either u(t) blows-up in finite positive time o...