Instability of coherent states of a real scalar field
Abstract
We investigate stability of both localized timeperiodic coherent states (pulsons) and uniformly distributed coherent states (oscillating condensate) of a real scalar field satisfying the KleinGordon equation with a logarithmic nonlinearity. The linear analysis of timedependent parts of perturbations leads to the Hill equation with a singular coefficient. To evaluate the characteristic exponent we extend the LindemannStieltjes method, usually applied to the Mathieu and Lame equations, to the case that the periodic coefficient in the general Hill equation is an unbounded function of time. As a result, we derive the formula for the characteristic exponent and calculate the stabilityinstability chart. Then we analyze the spatial structure of the perturbations. Using these results we show that the pulsons of any amplitudes, remaining welllocalized objects, lose their coherence with time. This means that, strictly speaking, all pulsons of the model considered are unstable. Nevertheless, for the nodeless pulsons the rate of the coherence breaking in narrow ranges of amplitudes is found to be very small, so that such pulsons can be longlived. Further, we use the obtained stabilityinstability chart to examine the AffleckDinetype condensate. We conclude the oscillating condensate can decay into an ensemble of the nodeless pulsons.
 Authors:
 Pushkov Institute of Terrestrial Magnetism, Ionosphere and Radiowave Propagation of the Russian Academy of Sciences (IZMIRAN), Troitsk, Moscow Region, 142190 (Russian Federation)
 Publication Date:
 OSTI Identifier:
 20768725
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Mathematical Physics; Journal Volume: 47; Journal Issue: 2; Other Information: DOI: 10.1063/1.2167918; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; AMPLITUDES; ANNIHILATION OPERATORS; EIGENSTATES; HILL EQUATION; INSTABILITY; KLEINGORDON EQUATION; NONLINEAR PROBLEMS; PERIODICITY; PERTURBATION THEORY; SCALAR FIELDS; SOLITONS; STABILITY; TIME DEPENDENCE
Citation Formats
Koutvitsky, Vladimir A., and Maslov, Eugene M. Instability of coherent states of a real scalar field. United States: N. p., 2006.
Web. doi:10.1063/1.2167918.
Koutvitsky, Vladimir A., & Maslov, Eugene M. Instability of coherent states of a real scalar field. United States. doi:10.1063/1.2167918.
Koutvitsky, Vladimir A., and Maslov, Eugene M. Wed .
"Instability of coherent states of a real scalar field". United States.
doi:10.1063/1.2167918.
@article{osti_20768725,
title = {Instability of coherent states of a real scalar field},
author = {Koutvitsky, Vladimir A. and Maslov, Eugene M.},
abstractNote = {We investigate stability of both localized timeperiodic coherent states (pulsons) and uniformly distributed coherent states (oscillating condensate) of a real scalar field satisfying the KleinGordon equation with a logarithmic nonlinearity. The linear analysis of timedependent parts of perturbations leads to the Hill equation with a singular coefficient. To evaluate the characteristic exponent we extend the LindemannStieltjes method, usually applied to the Mathieu and Lame equations, to the case that the periodic coefficient in the general Hill equation is an unbounded function of time. As a result, we derive the formula for the characteristic exponent and calculate the stabilityinstability chart. Then we analyze the spatial structure of the perturbations. Using these results we show that the pulsons of any amplitudes, remaining welllocalized objects, lose their coherence with time. This means that, strictly speaking, all pulsons of the model considered are unstable. Nevertheless, for the nodeless pulsons the rate of the coherence breaking in narrow ranges of amplitudes is found to be very small, so that such pulsons can be longlived. Further, we use the obtained stabilityinstability chart to examine the AffleckDinetype condensate. We conclude the oscillating condensate can decay into an ensemble of the nodeless pulsons.},
doi = {10.1063/1.2167918},
journal = {Journal of Mathematical Physics},
number = 2,
volume = 47,
place = {United States},
year = {Wed Feb 15 00:00:00 EST 2006},
month = {Wed Feb 15 00:00:00 EST 2006}
}

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