su(N,N) algebra and constants of motion for bosonic mean-field exciton equations

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Abstract

The ultrafast (picosecond) coherent dynamics of exciton systems in semiconductors can be approximately described by bosonic mean-field equations. These equations are nonlinear and therefore difficult to solve analytically. It is thus important to study the general dynamical properties of these equations, such as the underlying symmetry and corresponding conservation laws. It is shown in this paper that, for an N-species exciton system (e.g., heavy-hole and light-hole excitons), a mean-field Hamiltonian (including the coupling to external fields and fermionic corrections) can be formulated which is a member of the su(N,N) algebra. As a consequence, the equations of motion for the center-of-mass momentum dependent exciton distribution and the coherent biexciton amplitude can be cast into a form similar to that of the optical Bloch vector in two-level atoms that belong to the algebra su(2) [or, more generally, N-level atoms with algebra su(N)]. It is shown that the analog to the Bloch sphere in N-level atoms is an unbounded hypersurface (generalized hyperboloid) that constrains the motion of the exciton distribution and coherent biexciton amplitude. Further constants of motions that constrain the motion on the hypersurface are found from an su(N,N) generalization to the Hioe-Eberly method in su(N) systems (N-level atoms).

Original languageEnglish (US)
Article number195319
Pages (from-to)1-11
Number of pages11
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume70
Issue number19
DOIs
StatePublished - Nov 2004

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Excitons
Algebra
algebra
excitons
Atoms
atoms
Hamiltonians
conservation laws
Nonlinear equations
nonlinear equations
Equations of motion
center of mass
casts
Conservation
Momentum
equations of motion
LDS 751
analogs
Semiconductor materials
momentum

ASJC Scopus subject areas

  • Condensed Matter Physics

Cite this

su(N,N) algebra and constants of motion for bosonic mean-field exciton equations. / Yang, Z. S.; Kwong, Nai-Hang; Binder, Rudolf.

In: Physical Review B - Condensed Matter and Materials Physics, Vol. 70, No. 19, 195319, 11.2004, p. 1-11.

Research output: Contribution to journalArticle

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