In this paper, a new kind of multigrid method is proposed for the ground state solution Bose–Einstein condensates based on Newton iteration scheme. Instead treating eigenvalue $$\lambda $$ and eigenvector u separately, we regard eigenpair $$(\lambda , u)$$ as one element in composite space $${\mathbb {R}} \times H_0^1(\varOmega )$$ then step adopted nonlinear problem. Thus scheme, main computat...

We prove development of type I singularities for a suitable concept of weak evolution in the context of the quintic focussing NLW on R3`1, for data near and “above” the ground state static solution.

A closed form expression for the ground-state energy density of the general extensive many-body problem is given in terms of the Lanczos tridiagonal form of the Hamiltonian. Given the general expressions of the diagonal and off-diagonal elements of the Hamiltonian Lanczos matrix, an(N) and bn(N), asymptotic forms a(z) and b(z) can be defined in terms of a parameter z[n/N (n is the Lanczos itera...

In this paper, we prove the energy diminishing of a normalized gradient flow which provides a mathematical justification of the imaginary time method used in physical literatures to compute the ground state solution of Bose-Einstein condensates (BEC). We also investigate the energy diminishing property for the discretization of the normalized gradient flow. Two numerical methods are proposed fo...

For a large class of finite-range quantum spin models with half-integer spins, we prove that uniqueness of the ground state implies the existence of a low-lying excited state. For systems of linear size L, of arbitrary finite dimension, we obtain an upper bound on the excitation energy (i.e., the gap above the ground state) of the form (C logL)/L. This result can be regarded as a multi-dimensio...

We obtain the exact Green function for excited-state geminate reversible dissociation with two different lifetimes and quenching in one dimension, in the absence of a potential of interaction. We consider the ground-state and irreversible reactions as special limits, and investigate the long time asymptotic behavior in comparison with that observed in three dimensions. © 1999 American Institute...

For a large class of finite-range quantum spin models with half-integer spins, we prove that uniqueness of the ground state implies the existence of a low-lying excited state. For systems of linear size L, of arbitrary finite dimension, we obtain an upper bound on the excitation energy (i.e., the gap above the ground state) of the form (C log L)/L. This result can be regarded as a multi-dimensi...

We present results for the ground state and first excited state static potentials in the confinement " phase " of the SU(2) Higgs model. String breaking and the crossing of the energy levels are clearly visible. We address the question of the cutoff effects in our results and observe a remarkable scaling of the static potentials.

The quantum state distributions of the C, radical from the UV multiphoton dissociation of allene and propyne in a pulsed molecular beam have been measured. The observed distributions for both molecules are identical and are much colder than a phase space model would predict, implying that direct dissociation is occurring in one step and isomerization in another. It is concluded that both allene...

Angular distrihutions of the ‘rC(d, 6Li)8Be reaction at i& = 78.0 MeVand the 1’B(3He, ‘Li)*Be reaction at E,,, = 71.8 MeV were measured. Transitions leading to ‘Be in the ground state and the 3.04, 16.63, 16.92, 17.64 and 18.15 MeV excited states were observed. A DWBA analysis was performed regarding the (d, 6Li) and (3He, 6Li) reactions as direct LY particle or triton transfers, respectively. ...