Quantenmechanik

Cohen‐Tannoudji, Claude; Diu, Bernard; Laloë, Franck

doi:10.1515/9783110924176

Cited by 1,251 publications

(2,184 citation statements)

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“…Likewise, the state in momentum space is also entangled. In addition, this state meets the symmetry postulate for bosons stipulating that the sign should not change when any two dimer sites, say j, k, l, and j ′′ , k ′′ , l ′′ , or any two sites within dimers, are interchanged [29].…”

Section: Macroscopic Statessupporting

confidence: 51%

Evidence of macroscopically entangled protons in a mixed isotope crystal of KH_pD_1−pCO₃

Cousson¹,

Gutmann²

2010

J. Phys.: Condens. Matter

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Abstract. We examine whether protons and deuterons in the crystal of KH 0.76 D 0.24 CO 3 at 300 K are particles or matter waves. The neutron scattering function measured over a broad range of reciprocal space reveals the enhanced diffraction pattern anticipated for antisymmetrized macroscopic states for protons (fermions). These features exclude a statistical distribution of protons and deuterons. Raman spectra are consistent with a mixture of KHCO 3 and KDCO 3 sublattices whose isomorphous structures are independent of the isotope content. We propose a theoretical framework for decoherence-free proton and deuteron states.

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Section: Macroscopic Statessupporting

confidence: 51%

Evidence of macroscopically entangled protons in a mixed isotope crystal of KH_pD_1−pCO₃

Cousson¹,

Gutmann²

2010

J. Phys.: Condens. Matter

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“…The radial wave functions of the corresponding p-states are shown in the lower panel. The oscillator length b determines the position of the maximum and the dispersion of the wave function [27]. The deeper the potential, the smaller the oscillator length, and the wave functions become more localised.…”

mentioning

confidence: 99%

How atomic nuclei cluster

Ebran

Khan

Nikšić

et al. 2012

Nature

167

244

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Nucleonic matter displays a quantum liquid structure, but in some cases finite nuclei behave like molecules composed of clusters of protons and neutrons. Clustering is a recurrent feature in light nuclei, from beryllium to nickel. For instance, in 12 C the Hoyle state, crucial for stellar nucleosynthesis, can be described as a nuclear molecule consisting of three alpha-particles. The mechanism of cluster formation, however, has not yet been fully understood. We show that the origin of clustering can be traced back to the depth of the confining nuclear potential. By employing the theoretical framework of energy density functionals that encompasses both cluster and quantum liquid-drop aspects of nuclei, it is shown that the depth of the potential determines the energy spacings between single-nucleon orbitals, the localization of the corresponding wave functions and, therefore, the degree of nucleonic density clustering. Relativistic functionals, in particular, are characterized by deep single-nucleon potentials. When compared to non-relativistic functionals that yield similar ground-state properties (binding energy, deformation, radii), they predict the occurrence of much more pronounced cluster structures. More generally, clustering is considered as a transitional phenomenon between crystalline and quantum liquid phases of fermionic systems.The occurrence of molecular states in atomic nuclei and the formation of clusters of nucleons were already predicted in the 30's by von Weizsäcker and Wheeler [1,2]. Even though the description of nuclear dynamics became predominantly based on the concept of independent nucleons in a mean-field potential, a renewed interest in clustering phenomena in the 60's led to the development of dedicated theoretical methods [3]. Numerous experimental studies have revealed a wealth of data on clustering phenomena in light nuclei [4], and modern theoretical approaches use microscopic models that fully take into account single-nucleon degrees of freedom [5][6][7]. Clustering gives rise to nuclear molecules. For instance, in 12 C the second 0 + state the Hoyle state that plays a critical role in stellar nucleosynthesis, is predicted to display a three-α structure [8,9]. The binding energy of the α-particle, formed from two protons and two neutrons, is much larger than in other light nuclei. Cluster radioactivity [10], discovered in the 80's, is another manifestation of clustering in atomic nuclei. Experimental signatures of clustering are usually indirect. Quasi-molecular resonances are probed by scattering one cluster on another, such as in the 12 C+ 12 C system [4,11], and cluster structures are also discernible in the breakup of nuclei. Evidence has been reported for the formation of clusters in ground and excited states of a number of α-conjugate nuclei [4], that is nuclei with an equal even number of protons and neutrons, from 8 Be to 56 Ni.The mechanism of cluster formation in nuclei has not yet been fully understood. Deformation plays an important role because it removes the degenera...

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“…Therefore, as many physical problems, it can be solved approximately. We propose a perturbation method inspired by quantum physics methods for non degenerate states [12]. The solutions that we obtain have analytical expressions.…”

Section: Principe Of the Perturbation Methodsmentioning

confidence: 99%

“…In a first paper [11] we have combined the theory of perturbation with the method of curvilinear coordinates. However, this work was inspired by text book [12] widely used in quantum mechanics. In that field, the perturbation method has been established from Hamiltonian operator which is a hermitian operator of which the eigenvalues (energy levels) are real and the eigenvectors form an orthonormal basis in the case of non-degenerate states.…”

Section: Introductionmentioning

confidence: 99%

Propagative and Evanescent Waves Diffracted by Periodic Surfaces: Perturbation Method

Gavaix¹,

Chandezon²,

Granet³

2011

PIER B

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Abstract-The propagation equation, written in a curvilinear coordinate system, is solved by using a perturbation method inspired from quantum physics and extended to imaginary eigenvalues and evanescent waves. The parameter of perturbation is the groove depth which is small compared to the period. The method is expanded up to second order for the non-degenerate problem. In this way the solutions have analytical form compared to a numerical method. They present the advantage to put in evidence the evolution of the energy distribution for different diffraction orders as a function of the magnitude of the perturbation. The efficiencies which are deduced from these analytical solutions are compared of those obtained by the curvilinear coordinate method. The good agreement between the two methods occurs for a groove depth with respect to the wavelength less than or equal to 0.16. Thus, this new approach opens a new range of applications for inverse problems.

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Quantenmechanik

Cited by 1,251 publications

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Evidence of macroscopically entangled protons in a mixed isotope crystal of KH_pD_1−pCO₃

Evidence of macroscopically entangled protons in a mixed isotope crystal of KH_pD_1−pCO₃

How atomic nuclei cluster

Propagative and Evanescent Waves Diffracted by Periodic Surfaces: Perturbation Method

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Quantenmechanik

Cited by 1,251 publications

References 0 publications

Evidence of macroscopically entangled protons in a mixed isotope crystal of KHpD1−pCO3

Evidence of macroscopically entangled protons in a mixed isotope crystal of KHpD1−pCO3

How atomic nuclei cluster

Propagative and Evanescent Waves Diffracted by Periodic Surfaces: Perturbation Method

Contact Info

Product

Resources

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Evidence of macroscopically entangled protons in a mixed isotope crystal of KH_pD_1−pCO₃

Evidence of macroscopically entangled protons in a mixed isotope crystal of KH_pD_1−pCO₃