Collective and Single-Particle Coordinates in Nuclear Physics

Zickendraht, W.

doi:10.1063/1.1665789

Cited by 109 publications

(48 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Then £ 2 (R 3A ) = £ 2 (G7(3,R),<fm(#)) ® C 2 (M), and GCM(3) acts irreducibly on the first component of this tensor product. [17][18][19] However, this irreducible representation is not unitary, since the measure is drn(g) = (detg) A du(g). To attain unitary equiva lence with the irreducible representations constructed by geometric quantization, the invariant measure dv(g) of Eq.…”

Section: Geometric Quantization Of Gcm(3)mentioning

confidence: 98%

Geometric Quantization of Riemann Rotors

Rosensteel

Ihrig

1993

Quantization and Coherent States Methods

View full text Add to dashboard Cite

Geometric quantization enables the unification of the classical and quantum the ories of rotating fluids. The Riemann hydrodynamic equations of motion form a Hamiltonian dynamical system on co-adjoint orbits of a Lie subgroup GCM(3) of the noncompact Lie group Sp(3,R). The general collective motion group GCM(3) is a 15-dimensional semidirect product of a six-dimensional abelian normal subgroup R 6 with the motion group G1(3,R). The Lie algebra of R 6 is spanned by the in ertia tensor. The quantum theory of rotating fluids is constructed from irreducible unitary representations of GCM(3). The Kelvin circulation of the fluid is quantized to nonnegative integer multiples of h. Riemann's ModelRotating systems of particles are a ubiquitous form of collectivity that is found in nature on a continuum scale spanning 35 orders of magnitude from galaxies (period T~ 200 million years ~ 10 15 s), stars (T~ 10 6 s), and fluid droplets (T~ Is) to atomic nuclei (T~ lO" 2^) . 1 ' 2 A rotating system may be either classical (L>> h) or quantum mechanical (L~ h) depending upon the value of its angular momentum L compared to h. The moment of inertia may attain the limiting cases of rigid rotation or irrotational flow or it may fall at some intermediate value.Amidst this dynamical complexity, there is one simplifying common denominator. The shape of a rotating system is usually ellipsoidal. The size, deformation, and orientation of an ellipsoid is characterized completely by the inertia tensor, Q% ="£m a X ai X aj ,a where m^ is the mass of particle a located at the position vector X a with respect to an inertial center of mass frame. For a continuous fluid, the sum is replaced by an integral over the mass density distribution. With respect to the body-fixed principal axis frame, the inertia tensor is, by definition, diagonal,n 0 Quantization and Coherent States Methods Downloaded from www.worldscientific.com by UNIVERSITY OF BIRMINGHAM on 08/20/15. For personal use only.

show abstract

Section: Geometric Quantization Of Gcm(3)mentioning

confidence: 98%

Geometric Quantization of Riemann Rotors

Rosensteel

Ihrig

1993

Quantization and Coherent States Methods

View full text Add to dashboard Cite

show abstract

“…Our partitions come from the separation of degrees of freedom induced by the symmetric hyperspherical coordinate representation. 3,5,[33][34][35][36]38,39,43 Such a separation is expected to be more physically motivated, in distinguishing different kinds of motions, than the usual separation of molecular vibrations and rotations, when dynamics is considered for clusters or reactions.…”

Section: Partitions Of the Kinetic Energymentioning

confidence: 99%

Phase-space invariants for aggregates of particles: Hyperangular momenta and partitions of the classical kinetic energy

Aquilanti

Lombardi

Sevryuk

2004

The Journal of Chemical Physics

View full text Add to dashboard Cite

Rigorous definitions are presented for the kinematic angular momentum K of a system of classical particles (a concept dual to the conventional angular momentum J), the angular momentum L(xi) associated with the moments of inertia, and the contributions to the total kinetic energy of the system from various modes of the motion of the particles. Some key properties of these quantities are described-in particular, their invariance under any orthogonal coordinate transformation and the inequalities they are subject to. The main mathematical tool exploited is the singular value decomposition of rectangular matrices and its differentiation with respect to a parameter. The quantities introduced employ as ingredients particle coordinates and momenta, commonly available in classical trajectory studies of chemical reactions and in molecular dynamics simulations, and thus are of prospective use as sensitive and immediately calculated indicators of phase transitions, isomerizations, onsets of chaotic behavior, and other dynamical critical phenomena in classical microaggregates, such as nanoscale clusters.

show abstract

“…On the other hand it is clear that if one observes this system with such a large wavelength one is likely to observe the dynamics of all nucleons together. In this case it looks as if the resonance state |R is obtained by a scaling transformation |0 is proportional to the low-q (long wavelength) limit of M. The transformation in the previous equation acts scaling the positions r i of all particles into αr i , and therefore also of the hyperradius, namely one of the six collective coordinates defined by the group GL + (3, R) [11,12] (breathing). In order to further prove that this is the case one could evaluate m −1 (connected to the compressibility) in terms of the moment m 3 , in a similar case as it was done in Ref.…”

Section: Epj Web Of Conferencesmentioning

confidence: 99%