The Fröhlich Hamiltonian: mathematical results. I. Hamiltonian with cut-off

1976 ◽  
Vol 54 (15) ◽  
pp. 1613-1620 ◽  
Author(s):  
Bernard M. de Dormale ◽  
Georges Bader
Keyword(s):  
Lower Bound ◽  
Coulomb Interaction ◽  
Fock Space ◽  
Perturbation Series ◽  
Operator Norm

We study the Fröhlich Hamiltonian with cut-off. We show that this Hamiltonian is self-adjoint in the Fock space and semibounded when the number of electrons is kept constant. The lower bound we give generalizes the bound obtained for one electron by Lee and Pines to the case of several electrons. We also give a domain where the perturbation series for the resolvent of the Hamiltonian does converge in the operator norm. Finally, we study the influence of the Coulomb interaction.

scholarly journals Operator norm and lower bound of four-dimensional matrices

2017 ◽  
Vol 28 (6) ◽  
pp. 1134-1143 ◽  
Author(s):  
Gholamreza Talebi
Keyword(s):  
Lower Bound ◽  
Operator Norm

BEST CONSTANTS IN NORMS OF WICK PRODUCTS

2006 ◽  
Vol 09 (02) ◽  
pp. 169-185 ◽  
Author(s):  
AUREL I. STAN
Keyword(s):  
Lower Bound ◽  
Fock Space ◽  
Best Constants ◽  
Negative Integer ◽  
Wick Product ◽  
Bilinear Operator ◽  
Wick Products

Let [Formula: see text] be a Fock space and, for any non-negative integer k, let [Formula: see text] be the sum of all homogeneous chaos spaces of order at most k. For all non-negative integers m and n, the Wick product is a bounded bilinear operator from Γ (Hc)m × Γ (Hc)n into Γ (Hc)m +n with norm greater than or equal to [Formula: see text]. In the monograph1 S. Janson conjectured that this lower bound is exact. In this paper we prove this conjecture. In addition, we prove that a pair of nonzero vectors (ϕ, ψ)∈ Γ (Hc)m × Γ (Hc)n achieve this bound if and only if both vectors are multiples of the homogeneous products, i.e. ϕ =αu⊗m, ψ =βu⊗n, with u, v∈ Hc and α, β ∈ ℂ.

Coulomb interaction of composite particles

1983 ◽  
Vol 141 (11) ◽  
pp. 552
Author(s):  
D.A. Kirzhnits ◽  
F.M. Pen'kov
Keyword(s):  
Coulomb Interaction ◽  
Composite Particles

Excitonic quasimolecules containing of two quantum dots

2016 ◽  
pp. 4024-4028 ◽  
Author(s):  
Sergey I. Pokutnyi ◽  
Wlodzimierz Salejda
Keyword(s):  
Quantum Dots ◽  
Binding Energy ◽  
Exchange Interaction ◽  
Coulomb Interaction ◽  
Silicate Glass ◽  
Glass Matrix ◽  
Silicate Glass Matrix

The possibility of occurrence of the excitonic  quasimolecule formed of spatially separated electrons and holes in a nanosystem that consists  of  CuO quantum dots synthesized in a silicate glass matrix. It is shown that the major contribution to the excitonic quasimolecule binding energy is made by the energy of the exchange interaction of electrons with holes and this contribution is much more substantial than the contribution of the energy of Coulomb interaction between the electrons and holes.

The least distance between extremums and minimal period of solutions to autonomous vector differential equations

2019 ◽  
Vol 485 (2) ◽  
pp. 142-144
Author(s):  
A. A. Zevin
Keyword(s):  
Lower Bound ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Lipschitz Constant ◽  
Minimal Period ◽  
Arbitrary Vector ◽  
Vector Norm ◽  
Sharp Lower Bound

Solutions x(t) of the Lipschitz equation x = f(x) with an arbitrary vector norm are considered. It is proved that the sharp lower bound for the distances between successive extremums of xk(t) equals π/L where L is the Lipschitz constant. For non-constant periodic solutions, the lower bound for the periods is 2π/L. These estimates are achieved for norms that are invariant with respect to permutation of the indices.

Sign in / Sign up

Export Citation Format

Share Document