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Non-linearity, complexity, and quantization concepts in biology. [PDF]
Front Hum NeurosciTheise ND, Tuszynski JA.
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Frustration-Induced Many-Body Degeneracy in Spin -1/2 Molecular Quantum Rings. [PDF]
J Am Chem SocLi D +10 more
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Magnons from time-dependent density-functional perturbation theory and nonempirical Hubbard functionals. [PDF]
NPJ Comput MaterBinci L, Marzari N, Timrov I.
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Bertrand mate of null biharmonic curves in the Lorentzian Heisenberg group Heis.
, 2010 Talat Körpınar, Essin Turhan
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ON THE QUADRATIC HEISENBERG GROUP
Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2010In this paper we introduce the quadratic Weyl operators canonically associated to the one mode renormalized square of white noise (RSWN) algebra as unitary operator acting on the one mode interacting Fock space {Γ, {ωn, n ∈ ℕ}, Φ} where {ωn, n ∈ ℕ} is the principal Jacobi sequence of the nonstandard (i.e. neither Gaussian nor Poisson) Meixner classes.
ACCARDI, LUIGI, Ouerdiane, H, Rebei, H.
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Geodesics in Heisenberg Groups
Geometriae Dedicata, 1997For the Heisenberg group \(H^{2n+1}\) the author defines a left-invariant metric and computes the Levi-Civita connection and the curvature tensor. He also determines the isotropy subgroup \( \text{Iso}_0(H^{2n+1}) \). Then, equations for geodesics in \(H^{2n+1}\) are given which simplify considerably for ``horizontal'' lines.
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1997
Abstract The Heisenberg group is a nilpotent Lie group ‒ or rather a family of Lie groups, one for each odd dimension ≥ 3 ‒ which have many features in common with Euclidean spaces.
Guy David, Stephen Semmes
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Abstract The Heisenberg group is a nilpotent Lie group ‒ or rather a family of Lie groups, one for each odd dimension ≥ 3 ‒ which have many features in common with Euclidean spaces.
Guy David, Stephen Semmes
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2015
This chapter is meant to give a brief and by no means complete description of the Heisenberg group \(\mathbb {H}\), that will be the setting of this work. Customarily this group is presented as a particular group on \(\mathbb {R}^3\). This is not restrictive and to explain why we recall some definitions and basic properties of Carnot groups in order to
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This chapter is meant to give a brief and by no means complete description of the Heisenberg group \(\mathbb {H}\), that will be the setting of this work. Customarily this group is presented as a particular group on \(\mathbb {R}^3\). This is not restrictive and to explain why we recall some definitions and basic properties of Carnot groups in order to
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Journal of Physics A: Mathematical and General, 1993
Summary: The Heisenberg algebra \(h(3)\) is the Lie algebra of the Lie group \(H(3)\) of \(3\times 3\) upper triangular matrices with the 1's on the diagonal. This group is quantized. The dual algebra \(h(3)^*\) is also quantized, resulting in a quantum coadjoint representation of the quantum group \(H(3)_{a,b,c, d,m,n}\).
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Summary: The Heisenberg algebra \(h(3)\) is the Lie algebra of the Lie group \(H(3)\) of \(3\times 3\) upper triangular matrices with the 1's on the diagonal. This group is quantized. The dual algebra \(h(3)^*\) is also quantized, resulting in a quantum coadjoint representation of the quantum group \(H(3)_{a,b,c, d,m,n}\).
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