Q-Deformed Bosons at Quasi-classical Limit of SO（3）

When a boson interacts with another to form a composite system with SO（3） dynamic symmetry, it is shown that there exists the q-deformed 5osonic excitation satisfying the q-deformed Heisenberg commutation relation in the quasi-classical limit that the angular momentum j for SO（3） is large, but not infinite. In second quantization this quasi-excitation is associated with the boson realization of SO（3） Lie algebra. Physically, the phenomena of q-deformed excitation can happen in many models of quantum dynamics, such as super emission from a system of many identical two-level atoms, the spin wave in Heisenberg chain, the high spin precession and the coherent output of Bose-Einstein atoms in a trap. Especially, in these models, the deformation parameter q is well defined intrinsically by a conservative quantity, such as the total atomic number and the angular momentum.

Q-Deformed Bosons at Quasi-classical Limit of SO(3)

When a boson interacts with another to form a composite system withSO(3) dynamic symmetry, it is shown that there exists theq-deformed bosonic excitation satisfying the q-deformedHeisenberg commutation relation in the quasi-classical limit thatthe angular momentum j for SO(3) is large, but not infinite. Insecond quantization this quasi-excitation is associated with theboson realization of SO(3) Lie algebra. Physically, the phenomenaof q-deformed excitation can happen in many models of quantumdynamics, such as super emission from a system of many identicaltwo-level atoms, the spin wave in Heisenberg chain, the high spinprecession and the coherent output of Bose-Einstein atoms in a trap.Especially, in these models, the deformation parameter q is welldefined intrinsically by a conservative quantity, such as the totalatomic number and the angular momentum.