Supplement of the translation of Kogelnik's "Introduction to Integrated Optics"

Семенов, А С; Smirnov, V. L.

doi:10.1070/pu1977v020n04abeh005386

Cited by 3 publications

(4 citation statements)

References 97 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This will enable us to calculate the elastic energy of the copolymer domains. The elastic energy scales as h 2 / Na 2 ∼ N 1/3 since the strong-stretching domain period is known to scale with aN 2/3 . Thus for long chains a large pressure must exist to stretch the chains out over the height of the brush, which leads us to look for asymptotic solutions to equation III.5.…”

Section: Elastic Energymentioning

confidence: 99%

See 1 more Smart Citation

Corrections to Strong-Stretching Theories

1997

View full text Add to dashboard Cite

We derive the strong-stretching approximation from the full partition function for diblock copolymer melts. Using a perturbation expansion for the free energy, with ( N) -1/3 as the expansion parameter, we calculate the leading corrections to the asymptotic N f ∞ limit for the domain period and the free energy. The leading corrections to the free energy scale as log N. They arise from the entropy gain due to the wandering of chain ends over the domains and the entropy loss to localize the joints in the interfacial region.

show abstract

Section: Elastic Energymentioning

confidence: 99%

“…The domain period scales as aN 2/3 (where a is the Kuhn length for a monomer), implying that the chains must be highly distorted from the Gaussian coil state. Analytical theories exist that postulate that the copolymer chains are strongly stretched perpendicular to the interface, , providing insight into the physics in this limit.…”

Section: Introductionmentioning

confidence: 99%

Corrections to Strong-Stretching Theories

1997

View full text Add to dashboard Cite

show abstract

“…Let us consider a nucleus A that is strongly clusterized as a core A − 1 plus a weekly-bound valence nucleon N . It is well-known [13] that the spatial HHs for A nucleons can be written as a product of a spatial HHs for A − 1 nucleons, the spherical function Y lm ( ξA−1 ) and a function ϕ n (θ) which is an eigenfunction of the angular part of Laplacian in variable θ defined as θ = arctan ξ A−1 /ρ c . Here ρ c is the hyperradius for the A − 1 core,…”

Section: Hyperspherical Cluster Harmonicsmentioning

confidence: 99%

Long-range behavior of valence nucleons in a hyperspherical formalism

Timofeyuk¹

2007

Phys. Rev. C

View full text Add to dashboard Cite

It is shown that hyperspherical harmonics can be represented in a form typical of traditional microscopic cluster models. This allows those hyperharmonics that are responsible for long-range behavior of valence nucleons in loosely bound nuclei to be selected. The hyperspherical cluster model based on such hyperharmonics is tested for 5 He in a "toy model" that uses a simplified description of the 4 He core. The comparison of the hyperspherical expansion to a microscopic cluster model calculation confirms the feasibility of the hyperspherical treatment of long-range behavior by basis convergence only.

show abstract

“…(15) involve at most six particle coordinates. By appropriate choices [15] of Jacobi systems these can be expressed in terms of the five vectors η N −1 , . .…”

mentioning

confidence: 99%

Two-body correlations in Bose-Einstein condensates

et al. 2002

View full text Add to dashboard Cite

We formulate a method to study two-body correlations in a condensate of N identical bosons. We use the adiabatic hyperspheric approach and assume a Faddeev like decomposition of the wave function. We derive for a fixed hyperradius an integro-differential equation for the angular eigenvalue and wave function. We discuss properties of the solutions and illustrate with numerical results. The interaction energy is for N ≈ 20 five times smaller than that of the Gross-Pitaevskii equation. PACS number(s): 03.75.Fi, 05.30.Jp Introduction. Few-body correlations often express the distinguishing characteristic features of an N -body system [1]. Two-body correlations are not only the simplest but in most cases also the most important. Higher order correlations have a tendency to either strongly confine spatially or correlate into clusters of particles effectively reducing the correlations to lower order. Exceptions are the three-body correlations decisive for the stability of Borromean systems known for dripline nuclei [2].Non-correlated mean-field computations of nuclei with the free two-body nucleon-nucleon interaction produce disastrously wrong results. Two-body correlations compensating for the short range hard core repulsion are absolutely necessary [3]. For atoms the effective interaction is also strongly repulsive at shorter distances. Furthermore for an atomic Bose condensate a short-range twobody attraction produces diatomic recombination and thereby the atoms decay out of the condensate [4]. For both nuclei and molecules correlations are decisive. For nuclei various methods have been designed to deal with this problem, i.e. Jastrow theory, Bruckner theory, effective interactions in model spaces [5].For Bose condensates the Gross-Pitaevskii (noncorrelated) mean-field equation has been the starting point since the first observation of the condensate in 1995 [6]. The wave function does not include any correlations and the assumed repulsive δ-interaction has the immediate consequence that the short range behavior cannot be described even qualitatively correct. Repulsive zero range potentials are not physically meaningful [7] although sometimes useful in selected Hilbert spaces. Attractive δ-interactions in three dimensions lead to divergencies demanding renormalization [8,9] or a change of boundary conditions [10]. When two-body bound states appear even dimer condensates may be possible [11].To include correlations we must necessarily go beyond the mean-field Hartree-Fock-Boguliubov approximation. Then finite range potentials with realistic features can as well be used as the starting point in the theoretical formulation. The other crucial ingredient is the degrees of freedom or, equivalently, the Hilbert space. An interesting formulation was recently introduced in terms of generalized hyperspherical coordinates and an adiabatic expansion with the hyperradius as the adiabatic

show abstract

Supplement of the translation of Kogelnik's "Introduction to Integrated Optics"

Cited by 3 publications

References 97 publications

Corrections to Strong-Stretching Theories

Corrections to Strong-Stretching Theories

Long-range behavior of valence nucleons in a hyperspherical formalism

Two-body correlations in Bose-Einstein condensates

Contact Info

Product

Resources

About