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pro vyhledávání: '"harmonic potential"'
Creating macroscopic spatial superposition states is crucial for investigating matter-wave interferometry and advancing quantum sensor technology. Currently, two potential methods exist to achieve this objective. The first involves using inverted har
Externí odkaz:
http://arxiv.org/abs/2408.11909
Autor:
Gou, Tianxiang, Radulescu, Vicentiu D.
In this paper, we establish the uniqueness of positive solutions to the following fractional nonlinear elliptic equation with harmonic potential \begin{align*} (-\Delta)^s u+ \left(\omega+|x|^2\right) u=|u|^{p-2}u \quad \mbox{in}\,\, \R^n, \end{align
Externí odkaz:
http://arxiv.org/abs/2407.10126
We provide the first and rigorous confirmations of the hypotheses by Ludwig Boltzmann in his seminal paper \cite{Boltzmann} within the context of the Landau equation in the presence of a harmonic potential. We prove that (i) Each {\it entropy-invaria
Externí odkaz:
http://arxiv.org/abs/2407.07659
We consider a "symmetric" quantum droplet in two spatial dimensions, which rotates in a harmonic potential, focusing mostly on the limit of "rapid" rotation. We examine this problem using a purely numerical approach, as well as a semi-analytic Wigner
Externí odkaz:
http://arxiv.org/abs/2407.02221
Autor:
Schmicker, Detlef
We construct a three dimensional toy systems with two types of fermions forming a composite boson. They are hold in a harmonic potential. The basis functions are constructed from an internal and an external Gauss function. All integrals have analytic
Externí odkaz:
http://arxiv.org/abs/2404.14430
Autor:
Bichelmaier, Sebastian, Carrete, Jesús, Wanzenböck, Ralf, Buchner, Florian, Madsen, Georg K. H.
Phonon-based approaches and molecular dynamics are widely established methods for gaining access to a temperature-dependent description of material properties. However, when a compound's phase space is vast, density-functional-theory-backed studies q
Externí odkaz:
http://arxiv.org/abs/2406.10542
Publikováno v:
Opuscula Mathematica, Vol 44, Iss 5, Pp 749-765 (2024)
In this article we consider the following fractional semilinear elliptic equation \[(-\Delta)^su+|x|^2u =\omega u+|u|^{2\sigma}u \quad \text{ in } \mathbb{R}^N,\] where \(s\in (0,1)\), \(N\gt 2s\), \(\sigma\in (0,\frac{2s}{N-2s})\) and \(\omega\in (0
Externí odkaz:
https://doaj.org/article/b01bc7e49b3f4d1d871c3e6471d3fcd6
Publikováno v:
Phys. Rev. E 108, 034205 (2023)
The classical dynamics of the isotropic two-dimensional harmonic oscillator confined by an elliptic hard wall is discussed. The interplay between the harmonic potential with circular symmetry and the boundary with elliptical symmetry does not spoil t
Externí odkaz:
http://arxiv.org/abs/2403.08523
Ground state of the Gross–Pitaevskii equation with a harmonic potential in the energy-critical case.
Autor:
Pelinovsky, Dmitry E.1 (AUTHOR) dmpeli@math.mcmaster.ca, Sobieszek, Szymon1 (AUTHOR) sobieszs@mcmaster.ca
Publikováno v:
Asymptotic Analysis. 2024, Vol. 139 Issue 1/2, p1-29. 29p.
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