469 research outputs found
Instability of coherent states of a real scalar field
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
Testing Lorentz invariance of dark matter
We study the possibility to constrain deviations from Lorentz invariance in
dark matter (DM) with cosmological observations. Breaking of Lorentz invariance
generically introduces new light gravitational degrees of freedom, which we
represent through a dynamical timelike vector field. If DM does not obey
Lorentz invariance, it couples to this vector field. We find that this coupling
affects the inertial mass of small DM halos which no longer satisfy the
equivalence principle. For large enough lumps of DM we identify a (chameleon)
mechanism that restores the inertial mass to its standard value. As a
consequence, the dynamics of gravitational clustering are modified. Two
prominent effects are a scale dependent enhancement in the growth of large
scale structure and a scale dependent bias between DM and baryon density
perturbations. The comparison with the measured linear matter power spectrum in
principle allows to bound the departure from Lorentz invariance of DM at the
per cent level.Comment: 42 pages, 9 figure
Information-Entropic for Travelling Solitons in Lorentz and CPT Breaking Systems
In this work we group three research topics apparently disconnected, namely
solitons, Lorentz symmetry breaking and entropy. Following a recent work [Phys.
Lett. B 713 (2012) 304], we show that it is possible to construct in the
context of travelling wave solutions a configurational entropy measure in
functional space, from the field configurations. Thus, we investigate the
existence and properties of travelling solitons in Lorentz and CPT breaking
scenarios for a class of models with two interacting scalar fields. Here, we
obtain a complete set of exact solutions for the model studied which display
both double and single-kink configurations. In fact, such models are very
important in applications that include Bloch branes, Skyrmions, Yang-Mills,
Q-balls, oscillons and various superstring-motivated theories. We find that the
so-called Configurational Entropy (CE) for travelling solitons, which we name
as travelling Configurational Entropy (TCE), shows that the best value of
parameter responsible to break the Lorentz symmetry is one where the energy
density is distributed equally around the origin. In this way, the
information-theoretical measure of travelling solitons in Lorentz symmetry
violation scenarios opens a new window to probe situations where the parameters
responsible for breaking the symmetries are random. In this case, the TCE
selects the best value
Booms, Recessions and Financial Turmoil: A Fresh Look at Investment Decisions under Cyclical Uncertainty
The paper studies the interaction between cyclical uncertainty and investment in a stochastic real option framework where demand shifts stochastically between three different states, each with different rates of drift and volatility. In our setting the shifts are governed by a three-state Markov switching model with constant transition probabilities. The magnitude of the link between cyclical uncertainty and investment is quantified using simulations of the model. The chief implication of the model is that recessions and financial turmoil are important catalysts for waiting. In other words, our model shows that macroeconomic risk acts as an important deterrent to investments.business cycles, real options, investment, Markov switching, Tobin’s q, uncertainty
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