13 research outputs found
Light Nuclei as Quantized Skyrmions
We consider the rigid body quantization of Skyrmions with topological charges
1 to 8, as approximated by the rational map ansatz. Novel, general expressions
for the elements of the inertia tensors, in terms of the approximating rational
map, are presented and are used to determine the kinetic energy contribution to
the total energy of the ground and excited states of the quantized Skyrmions.
Our results are compared to the experimentally determined energy levels of the
corresponding nuclei, and the energies and spins of a few as yet unobserved
states are predicted.Comment: 33 pages, 16 figures, Section 13 replace
Angularly localized Skyrmions
Quantized Skyrmions with baryon numbers and 4 are considered and
angularly localized wavefunctions for them are found. By combining a few low
angular momentum states, one can construct a quantum state whose spatial
density is close to that of the classical Skyrmion, and has the same
symmetries. For the B=1 case we find the best localized wavefunction among
linear combinations of and angular momentum states. For B=2, we
find that the ground state has toroidal symmetry and a somewhat reduced
localization compared to the classical solution. For B=4, where the classical
Skyrmion has cubic symmetry, we construct cubically symmetric quantum states by
combining the ground state with the lowest rotationally excited
state. We use the rational map approximation to compare the classical and
quantum baryon densities in the B=2 and B=4 cases.Comment: 22 page
Star products, duality and double Lie algebras
Quantization of classical systems using the star-product of symbols of
observables is discussed. In the star-product scheme an analysis of dual
structures is performed and a physical interpretation is proposed. At the Lie
algebra level duality is shown to be connected to double Lie algebras. The
analysis is specified to quantum tomography. The classical tomographic Poisson
bracket is found.Comment: 22 pages, no figure
Underlying Event measurements in pp collisions at and 7 TeV with the ALICE experiment at the LHC
Probability representation of quantum states
The review of new formulation of conventional quantum mechanics where the quantum states are identified with probability distributions is presented. The invertible map of density operators and wave functions onto the probability distributions describing the quantum states in quantum mechanics is constructed both for systems with continuous variables and systems with discrete variables by using the Born’s rule and recently suggested method of dequantizer–quantizer operators. Examples of discussed probability representations of qubits (spin-1/2, two-level atoms), harmonic oscillator and free particle are studied in detail. Schrödinger and von Neumann equations, as well as equations for the evolution of open systems, are written in the form of linear classical–like equations for the probability distributions determining the quantum system states. Relations to phase–space representation of quantum states (Wigner functions) with quantum tomography and classical mechanics are elucidated
Gross-Pitaevskii equation for the density matrix in the position representation
We consider the generalized pure-state density matrix, which depends on different time moments, and obtain the evolution equation for this density matrix for the case where the density matrix corresponds to solutions of the Gross–Pitaevskii equation
Gross-Pitaevskii equation for the density matrix in the position representation
We consider the generalized pure-state density matrix, which depends on different time moments, and obtain the evolution equation for this density matrix for the case where the density matrix corresponds to solutions of the Gross–Pitaevskii equation