Intrinsic Ultracontractivity and Ground State Estimates of Non-local Dirichlet forms on Unbounded Open Sets

2019 ◽  
Vol 366 (1) ◽  
pp. 67-117
Author(s):  
Xin Chen ◽  
Panki Kim ◽  
Jian Wang
Keyword(s):  
Ground State ◽  
Dirichlet Forms ◽  
Intrinsic Ultracontractivity ◽  
Non Local

scholarly journals Lower estimates of heat kernels for non-local Dirichlet forms on metric measure spaces

2017 ◽  
Vol 272 (8) ◽  
pp. 3311-3346 ◽  
Author(s):  
Alexander Grigor'yan ◽  
Eryan Hu ◽  
Jiaxin Hu
Keyword(s):  
Dirichlet Forms ◽  
Heat Kernels ◽  
Metric Measure Spaces ◽  
Measure Spaces ◽  
Non Local

scholarly journals Non-local to local transition for ground states of fractional Schrödinger equations on $$\mathbb {R}^N$$

2020 ◽  
Vol 22 (3) ◽  
Author(s):  
Bartosz Bieganowski ◽  
Simone Secchi
Keyword(s):  
Ground State ◽  
Ground States ◽  
Ground State Solution ◽  
State Solution ◽  
Local Problem ◽  
Schrödinger Equations ◽  
Ground State Solutions ◽  
Fractional Schrödinger Equations ◽  
Non Local ◽  
Local Transition

Abstract We consider the nonlinear fractional problem $$\begin{aligned} (-\Delta )^{s} u + V(x) u = f(x,u)&\quad \hbox {in } \mathbb {R}^N \end{aligned}$$ ( - Δ ) s u + V ( x ) u = f ( x , u ) in R N We show that ground state solutions converge (along a subsequence) in $$L^2_{\mathrm {loc}} (\mathbb {R}^N)$$ L loc 2 ( R N ) , under suitable conditions on f and V, to a ground state solution of the local problem as $$s \rightarrow 1^-$$ s → 1 - .

scholarly journals Intrinsic metrics for non-local symmetric Dirichlet forms and applications to spectral theory

2014 ◽  
Vol 266 (8) ◽  
pp. 4765-4808 ◽  
Author(s):  
Rupert L. Frank ◽  
Daniel Lenz ◽  
Daniel Wingert
Keyword(s):  
Spectral Theory ◽  
Dirichlet Forms ◽  
Intrinsic Metrics ◽  
Non Local

On ground state of some non local Schrödinger operators

2016 ◽  
Vol 96 (8) ◽  
pp. 1390-1400 ◽  
Author(s):  
Yuri Kondratiev ◽  
Stanislav Molchanov ◽  
Sergey Pirogov ◽  
Elena Zhizhina
Keyword(s):  
Ground State ◽  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Non Local

Ground state of liquid helium-3: off-shell effects due to non-local potentials

Pramana ◽  
1976 ◽  
Vol 6 (6) ◽  
pp. 373-382
Author(s):  
Y S T Rao ◽  
I Rama Rao
Keyword(s):  
Liquid Helium ◽  
Ground State ◽  
Shell Effects ◽  
Non Local ◽  
Local Potentials ◽  
Helium 3

scholarly journals A Three-Dimensional Non-Local Quantum Vacuum as the Origin of Photons

2020 ◽  
Vol 65 (2) ◽  
pp. 106
Author(s):  
D. Fiscaletti ◽  
A. Sorli
Keyword(s):  
Ground State ◽  
Three Dimensional ◽  
Black Body ◽  
Physical Reality ◽  
Density Fluctuations ◽  
Quantum Vacuum ◽  
Local Quantum ◽  
Non Local ◽  
Planck’S Law ◽  
Quantization Volume

A model of a three-dimensional quantum vacuum defined by the processes of creation/annihilation of quanta corresponding to elementary energy density fluctuations is proposed. In it, a photon is not a primary physical reality but emerges itself as a special state of the three-dimensional quantum vacuum. In this model, the three-dimensional quantum vacuum has a ground state which acts as a “cosmic reservoir” of photons, which emits and absorbs photons and Planck’s law of the spectral distribution of the energy radiated by a black body derives from the fundamental processes in the three-dimensional quantum vacuum, in particular, in the context of a quantization volume responsible for the appearance of photons. Finally, the idea of the Lamb shift of hydrogenoid atoms as a phenomenon determined by the ground state of the quantum vacuum which acts as a reservoir of photons is explored.

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