scholarly journals Double Logarithmic Stability in the Identification of a Scalar Potential by a Partial Elliptic Dirichlet-to-Neumann Map

2015 ◽  
Vol 8 (3) ◽  
pp. 78-94 ◽  
Author(s):  
M. Choulli ◽  
◽  
Y. Kian ◽  
E. Soccorsi ◽  
◽  
...  
Keyword(s):  
Scalar Potential ◽  
Dirichlet To Neumann Map ◽  
Logarithmic Stability

Stability estimate for an inverse problem of the convection-diffusion equation

2020 ◽  
Vol 28 (1) ◽  
pp. 71-92
Author(s):  
Mourad Bellassoued ◽  
Imen Rassas
Keyword(s):  
Inverse Problem ◽  
Diffusion Equation ◽  
Scalar Potential ◽  
Stability Estimate ◽  
Inverse Boundary ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
First Order ◽  
Order Coefficient ◽  
Dirichlet To Neumann Map

AbstractWe consider the inverse boundary value problem for the dynamical steady-state convection-diffusion equation. We prove that the first-order coefficient and the scalar potential are uniquely determined by the Dirichlet-to-Neumann map. More precisely, we show in dimension {n\geq 3} a log-type stability estimate for the inverse problem under consideration. The method is based on reducing our problem to an auxiliary inverse problem and the construction of complex geometrical optics solutions of this problem.

scholarly journals A Hölder-logarithmic stability estimate for an inverse problem in two dimensions

2015 ◽  
Vol 23 (1) ◽  
Author(s):  
Matteo Santacesaria
Keyword(s):  
Inverse Problem ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Stability Estimate ◽  
Two Dimensions ◽  
Positive Energy ◽  
Two Dimensional ◽  
Ill Posed ◽  
Dirichlet To Neumann Map ◽  
Logarithmic Stability

AbstractThe problem of the recovery of a real-valued potential in the two-dimensional Schrödinger equation at positive energy from the Dirichlet-to-Neumann map is considered. It is know that this problem is severely ill-posed and the reconstruction of the potential is only logarithmic stable in general. In this paper a new stability estimate is proved, which is explicitly dependent on the regularity of the potentials and on the energy. Its main feature is an efficient

scholarly journals The internal conversion of gamma-rays.—Part II

1928 ◽  
Vol 121 (787) ◽  
pp. 447-456
Keyword(s):  
Magnetic Field ◽  
Quantum Mechanics ◽  
Wave Equation ◽  
Gamma Rays ◽  
Internal Conversion ◽  
Scalar Potential ◽  
X Ray ◽  
Electro Magnetic Field ◽  
Γ Rays ◽  
Electro Magnetic

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)

scholarly journals Systematics of type IIA moduli stabilisation

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.

scholarly journals Harmonic hybrid inflation

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.

scholarly journals Neutrino masses, vacuum stability and quantum gravity prediction for the mass of the top quark

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Guillem Domènech ◽  
Mark Goodsell ◽  
Christof Wetterich
Keyword(s):  
Quantum Gravity ◽  
Top Quark ◽  
Quark Mass ◽  
Scalar Potential ◽  
Planck Scale ◽  
Neutrino Masses ◽  
Top Quark Mass ◽  
Vacuum Stability ◽  
Intermediate Scale ◽  
Yukawa Couplings

Abstract A general prediction from asymptotically safe quantum gravity is the approximate vanishing of all quartic scalar couplings at the UV fixed point beyond the Planck scale. A vanishing Higgs doublet quartic coupling near the Planck scale translates into a prediction for the ratio between the mass of the Higgs boson MH and the top quark Mt. If only the standard model particles contribute to the running of couplings below the Planck mass, the observed MH∼ 125 GeV results in the prediction for the top quark mass Mt∼ 171 GeV, in agreement with recent measurements. In this work, we study how the asymptotic safety prediction for the top quark mass is affected by possible physics at an intermediate scale. We investigate the effect of an SU(2) triplet scalar and right-handed neutrinos, needed to explain the tiny mass of left-handed neutrinos. For pure seesaw II, with no or very heavy right handed neutrinos, the top mass can increase to Mt ∼ 172.5 GeV for a triplet mass of M∆ ∼ 108GeV. Right handed neutrino masses at an intermediate scale increase the uncertainty of the predictions of Mt due to unknown Yukawa couplings of the right-handed neutrinos and a cubic interaction in the scalar potential. For an appropriate range of Yukawa couplings there is no longer an issue of vacuum stability.

scholarly journals Effective Scalar Potential in Asymptotically Safe Quantum Gravity

Universe ◽  
2021 ◽  
Vol 7 (2) ◽  
pp. 45
Author(s):  
Christof Wetterich
Keyword(s):  
Quantum Gravity ◽  
Top Quark ◽  
Particle Physics ◽  
Scalar Potential ◽  
Scalar Fields ◽  
The Standard Model ◽  
Scaling Potential ◽  
Realistic Description ◽  
The Masses ◽  
Dynamical Dark Energy

We compute the effective potential for scalar fields in asymptotically safe quantum gravity. A scaling potential and other scaling functions generalize the fixed point values of renormalizable couplings. The scaling potential takes a non-polynomial form, approaching typically a constant for large values of scalar fields. Spontaneous symmetry breaking may be induced by non-vanishing gauge couplings. We strengthen the arguments for a prediction of the ratio between the masses of the top quark and the Higgs boson. Higgs inflation in the standard model is unlikely to be compatible with asymptotic safety. Scaling solutions with vanishing relevant parameters can be sufficient for a realistic description of particle physics and cosmology, leading to an asymptotically vanishing “cosmological constant” or dynamical dark energy.

scholarly journals Solving puzzles in deformed JT gravity: phase transitions and non-perturbative effects

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Clifford V. Johnson ◽  
Felipe Rosso
Keyword(s):  
Phase Structure ◽  
Scalar Potential ◽  
String Equation ◽  
Two Dimensional ◽  
Leading Order ◽  
Classical Analysis ◽  
First Order ◽  
First Order Phase Transition ◽  
Definition Of ◽  
First Order Phase

Abstract Recent work has shown that certain deformations of the scalar potential in Jackiw-Teitelboim gravity can be written as double-scaled matrix models. However, some of the deformations exhibit an apparent breakdown of unitarity in the form of a negative spectral density at disc order. We show here that the source of the problem is the presence of a multi-valued solution of the leading order matrix model string equation. While for a class of deformations we fix the problem by identifying a first order phase transition, for others we show that the theory is both perturbatively and non-perturbatively inconsistent. Aspects of the phase structure of the deformations are mapped out, using methods known to supply a non-perturbative definition of undeformed JT gravity. Some features are in qualitative agreement with a semi-classical analysis of the phase structure of two-dimensional black holes in these deformed theories.

scholarly journals An inverse problem of radiative potentials and initial temperatures in parabolic equations with dynamic boundary conditions

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
El Mustapha Ait Ben Hassi ◽  
Salah-Eddine Chorfi ◽  
Lahcen Maniar
Keyword(s):  
Inverse Problem ◽  
Boundary Conditions ◽  
Parabolic Equations ◽  
Stability Result ◽  
Stability Estimate ◽  
Lipschitz Stability ◽  
Dynamic Boundary Conditions ◽  
Logarithmic Convexity ◽  
Dynamic Boundary ◽  
Logarithmic Stability

Abstract We study an inverse problem involving the restoration of two radiative potentials, not necessarily smooth, simultaneously with initial temperatures in parabolic equations with dynamic boundary conditions. We prove a Lipschitz stability estimate for the relevant potentials using a recent Carleman estimate, and a logarithmic stability result for the initial temperatures by a logarithmic convexity method, based on observations in an arbitrary subdomain.

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