Instability of coherent states of a real scalar field

Abstract

We investigate stability of both localized time-periodic coherent states (pulsons) and uniformly distributed coherent states (oscillating condensate) of a real scalar field satisfying the Klein-Gordon equation with a logarithmic nonlinearity. The linear analysis of time-dependent parts of perturbations leads to the Hill equation with a singular coefficient. To evaluate the characteristic exponent we extend the Lindemann-Stieltjes 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 stability-instability chart. Then we analyze the spatial structure of the perturbations. Using these results we show that the pulsons of any amplitudes, remaining well-localized 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 long-lived. Further, we use the obtaned stability-instability chart to examine the Affleck-Dine type condensate. We conclude the oscillating condensate can decay into an ensemble of the nodeless pulsons.Comment: 11 pages, 8 figures, submitted to Physical Review

Gravitational geons in asymptotically anti-de Sitter spacetimes

“…In asymptotically flat spacetimes, breathers represent the exception to the rule "anything that can radiate, does radiate", and they exist only in rather special circumstances (e.g. sine-Gordon theory in 1+1 dimension, scalar theories with V-shaped [30,31] or logarithmic potentials [32]). On the other hand, families of long-lived, closely time-periodic oscillons exist in a number of field theories containing massive scalars in Minkowski or asymptotically flat spacetimes [33][34][35].…”

Gravipulsons

“…[21]. For discrete E ¼ 4n the above functions acquire the subscript n, so we shall write ' n ðÞ, X AE n ðÞ, n ða 2 max Þ.…”

“…Subsequent investigations have shown that pulsons exist in various models and spatial dimensions, and that they evolve from the diversity of initial conditions [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] (see [23] for a review). It turns out that pulsons can arise from both uniform and nonuniform field distributions.…”

“…It turns out that pulsons can arise from both uniform and nonuniform field distributions. Thus pulsons can emerge in scalar condensates due to the parametric instability of the spatially uniform background oscillating near a vacuum value [14,18,19,21]. In this case the energy of the background oscillations is transferred to an incipient pulson via the resonance mechanism.…”

On localized long-lived three-dimensional solutions of the nonlinear Klein-Gordon equation with a fractional power potential

“…Furthermore, the existence of three dimensional periodic solutions that do not decay in time altogether is of interest itself. In the numerical experiments with spatially three dimensional equations, logarithmic potentials were considered (see, e.g., [18,23]). How ever, the authors of those works did not consider a fractional power potential, as in cosmological models.…”