On the scalar potential models from the isospectral potential class

In a previous paper the absorption of γ-rays in the K-X-ray levels of the atom in which they are emitted was calculated according to the Quantum Mechanics, supposing the γ-rays to be emitted from a doublet of moment f ( t ) at the centre of the atom. The non-relativity wave equation derived from the relativity wave equation for an electron of charge — ε moving in an electro-magnetic field of vector potential K and scalar potential V is h 2 ∇ 2 ϕ + 2μ ( ih ∂/∂ t + εV + ih ε/μ c (K. grad)) ϕ = 0. (1) Suppose, however, that K involves the space co-ordinates. Then, (K. grad) ϕ ≠ (grad . K) ϕ , and the expression (K . grad) ϕ is not Hermitic. Equation (1) cannot therefore be the correct non-relativity wave equation for a single electron in an electron agnetic field, and we must substitute h 2 ∇ 2 ϕ + 2μ ( ih ∂/∂ t + εV) ϕ + ih ε/ c ((K. grad) ϕ + (grad. K) ϕ ) = 0. (2)

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Systematics of type IIA moduli stabilisation

Journal of High Energy Physics ◽

10.1007/jhep11(2020)113 ◽

2020 ◽

Vol 2020 (11) ◽

Author(s):

Fernando Marchesano ◽

David Prieto ◽

Joan Quirant ◽

Pramod Shukla

Keyword(s):

Scalar Potential ◽

Systematic Search ◽

Stability Criteria ◽

De Sitter ◽

Large Subset

Abstract We analyse the flux-induced scalar potential for type IIA orientifolds in the presence of p-form, geometric and non-geometric fluxes. Just like in the Calabi-Yau case, the potential presents a bilinear structure, with a factorised dependence on axions and saxions. This feature allows one to perform a systematic search for vacua, which we implement for the case of geometric backgrounds. Guided by stability criteria, we consider configurations with a particular on-shell F-term pattern, and show that no de Sitter extrema are allowed for them. We classify branches of supersymmetric and non-supersymmetric vacua, and argue that the latter are perturbatively stable for a large subset of them. Our solutions reproduce and generalise previous results in the literature, obtained either from the 4d or 10d viewpoint.

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ChemInform Abstract: BINUCLEAR CRYPTATES. BINUCLEAR COPPER(I) AND COPPER(II) INCLUSION COMPLEXES OF POLYTHIA CYLINDRICAL MACROTRICYCLIC LIGANDS. POTENTIAL MODELS FOR BINUCLEA METALLOPROTEINS

Chemischer Informationsdienst ◽

10.1002/chin.197813296 ◽

1978 ◽

Vol 9 (13) ◽

Author(s):

A. H. ALBERTS ◽

R. ANNUNZIATA ◽

J.-M. LEHN

Keyword(s):

Inclusion Complexes ◽

Binuclear Copper ◽

Potential Models

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Harmonic hybrid inflation

Journal of High Energy Physics ◽

10.1007/jhep12(2020)161 ◽

2020 ◽

Vol 2020 (12) ◽

Author(s):

Federico Carta ◽

Nicole Righi ◽

Yvette Welling ◽

Alexander Westphal

Keyword(s):

Domain Wall ◽

Symmetry Breaking ◽

Initial Conditions ◽

Scalar Potential ◽

Field Range ◽

Slow Roll ◽

Minimal Form ◽

Wide Range ◽

Hybrid Inflation ◽

Type Iib String Theory

Abstract We present a mechanism for realizing hybrid inflation using two axion fields with a purely non-perturbatively generated scalar potential. The structure of the scalar potential is highly constrained by the discrete shift symmetries of the axions. We show that harmonic hybrid inflation generates observationally viable slow-roll inflation for a wide range of initial conditions. This is possible while accommodating certain UV arguments favoring constraints f ≲ MP and ∆ϕ60 ≲ MP on the axion periodicity and slow-roll field range, respectively. We discuss controlled ℤ2-symmetry breaking of the adjacent axion vacua as a means of avoiding cosmological domain wall problems. Including a minimal form of ℤ2-symmetry breaking into the minimally tuned setup leads to a prediction of primordial tensor modes with the tensor-to-scalar ratio in the range 10−4 ≲ r ≲ 0.01, directly accessible to upcoming CMB observations. Finally, we outline several avenues towards realizing harmonic hybrid inflation in type IIB string theory.

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