Über den Zusammenhang des Abschlusses der Elektronengruppen im Atom mit der Komplexstruktur der Spektren

Pauli, Wolfgang

doi:10.1007/bf02980631

Cited by 815 publications

(375 citation statements)

References 6 publications

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“…After electrons were argued to possess the additional degree of freedom [3] (later called spin [4]) and obey the Pauli exclusion principle [5], the Fermi-Dirac statistics was found [6,7] and the general notion of fermion particles emerged. The antisymmetric nature of fermionic wavefunction [7] has provoked development of the canonical anticommutation relation [8] and the general theory of second quantization [9], which deals with systems with a varying number of particles.…”

Section: Introductionmentioning

confidence: 99%

Spectral properties of reduced fermionic density operators and parity superselection rule

Amosov

Filippov

2016

Quantum Inf Process

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We consider pure fermionic states with a varying number of quasiparticles and analyze two types of reduced density operators: one is obtained via tracing out modes, the other is obtained via tracing out particles. We demonstrate that spectra of mode-reduced states are not identical in general and fully characterize pure states with equispectral mode-reduced states. Such states are related via local unitary operations with states satisfying the parity superselection rule. Thus, valid purifications for fermionic density operators are found. To get particle-reduced operators for a general system, we introduce the operation Φ(̺) = i ai̺a † i . We conjecture that spectra of Φ p (̺) and conventional p-particle reduced density matrix ̺p coincide. Nontrivial generalized Pauli constraints are derived for states satisfying the parity superselection rule.

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Section: Introductionmentioning

confidence: 99%

Spectral properties of reduced fermionic density operators and parity superselection rule

Amosov

Filippov

2016

Quantum Inf Process

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“…This extra "nonclassical two-valuedness" ("klassisch nicht beschreibbare Zweideutigkeit", Pauli's [10] description of electron spin) is a previously unrecognized essential ingredient in any attempt to construct a quantum hamiltonian with eigenvalues corresponding to the imaginary parts of the nontrivial Riemann zeros. Next, consider the "completed" zeta function Λ(s) := Γ ∞ (s)ζ(s), where Γ ∞ (s) := π −s/2 Γ(s/2) and Γ(z) is the Euler gamma function.…”

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confidence: 99%

Nonclassical Degrees of Freedom in the Riemann Hamiltonian

Srednicki

2011

Phys. Rev. Lett.

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The Hilbert-Polya conjecture states that the imaginary parts of the zeros of the Riemann zeta function are eigenvalues of a quantum hamiltonian. If so, conjectures by Katz and Sarnak put this hamiltonian in Altland and Zirnbauer's universality class C. This implies that the system must have a nonclassical two-valued degree of freedom. In such a system, the dominant primitive periodic orbits contribute to the density of states with a phase factor of -1. This resolves a previously mysterious sign problem with the oscillatory contributions to the density of the Riemann zeros.Comment: 4 pages, no figures; v3-6 have minor corrections to v2, v2 has a more complete solution of the sign problem than v

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“…(ii) The HF wf is taken to be the Slater determinant [2,3], hereafter noted D0, in order to obey the antisymmetry principle characterizing the fermions [4][5][6] or the Pauli exclusion principle [7,8] for the electrons: The monoelectronic functions j k (c i ) are called spinorbitals. The spinorbitals are expressed as simple products of a spatial continuous function and a spin discrete function: j i ðcÞ5 f i ðð rÞsðsÞ.…”

Section: Introductionmentioning

confidence: 99%

The Hartree–Fock triplet instability: influence of conformation and substitution

Geron

Dive

Dehareng

2006

Journal of Molecular Structure: THEOCHEM

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The triplet Hartree-Fock (HF) instability is investigated through the examples of substituted ethylenes and the small linear conjugated systems butadiene, hexatriene, octatetraene. A statistical analysis is performed for several conformations of the latters. The second eigenvalue of the instability matrix appears to be able to discriminate the groups of unsaturated compounds. The HF instability is largely influenced by conjugation and mesomeric effects and thus by the geometry. The number of p electrons is also an important factor. The electronic correlation related to the HF instability is not quantified by the energy difference between the post-HF and HF levels. q

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Über den Zusammenhang des Abschlusses der Elektronengruppen im Atom mit der Komplexstruktur der Spektren

Cited by 815 publications

References 6 publications

Spectral properties of reduced fermionic density operators and parity superselection rule

Spectral properties of reduced fermionic density operators and parity superselection rule

Nonclassical Degrees of Freedom in the Riemann Hamiltonian

The Hartree–Fock triplet instability: influence of conformation and substitution

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