The Decay of Unstable Noncommutative Solitons
arXiv:hep-th/0301119 · doi:10.1007/s00220-003-0863-z
Abstract
We study the classical decay of unstable scalar solitons in noncommutative field theory in 2+1 dimensions. This can, but does not have to, be viewed as a toy model for the decay of D-branes in string theory. In the limit that the noncommutativity parameter θis infinite, the gradient term is absent, there are no propagating modes and the soliton does not decay at all. If θis large, but finite, the rotationally symmetric decay channel can be described as a highly excited nonlinear oscillator weakly coupled to a continuum of linear modes. This system is closely akin to those studied in the context of discrete breathers. We here diagonalize the linear problem and compute the decay rate to first order using a version of Fermi's Golden Rule, leaving a more rigorous treatment for future work.
36 pages, 7 figures, dedicated to Rudolf Haag. v2: uniform estimate for Weyl criterion provided, refs added
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- Jacobi Polynomials, Bernstein-type Inequalities and Dispersion Estimates for the Discrete Laguerre Operator
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- Structure of Noncommutative Solitons: Existence and Spectral Theory
- Dynamics of Noncommutative Solitons I: Spectral Theory and Dispersive Estimates
- Dispersion Estimates for the Discrete Laguerre Operator
- Heat kernels of the discrete Laguerre operators
- Trace formulas and inverse spectral theory for generalized indefinite strings
- Dynamics of Noncommutative Solitons II: Spectral Theory, Dispersive Estimates and Stability
- Dissolving D0-brane into D2-brane with background B-field
- Polar Coordinates and Noncommutative Phase Space