6,078 research outputs found
Higher-order supersymmetric quantum mechanics
We review the higher-order supersymmetric quantum mechanics (H-SUSY QM),
which involves differential intertwining operators of order greater than one.
The iterations of first-order SUSY transformations are used to derive in a
simple way the higher-order case. The second order technique is addressed
directly, and through this approach unexpected possibilities for designing
spectra are uncovered. The formalism is applied to the harmonic oscillator: the
corresponding H-SUSY partner Hamiltonians are ruled by polynomial Heisenberg
algebras which allow a straight construction of the coherent states.Comment: 42 pages, 12 eps figure
Unraveling the origin of black holes from effective spin measurements with LIGO-Virgo
We investigate how to use information on the effective spin parameter of
binary black hole mergers from the LIGO-Virgo gravitational wave detections to
discriminate the origin of the merging black holes. We calculate the expected
probability distribution function for the effective spin parameter for
primordial black holes. Using LIGO-Virgo observations, we then calculate odds
ratios for different models for the distribution of black holes' spin magnitude
and alignment. We evaluate the posterior probability density for a possible
mixture of astrophysical and primordial black holes as emerging from current
data, and calculate the number of future merger events needed to discriminate
different spin and alignment models at a given level of statistical
significance.Comment: 22 pages, 10 figure
Comment on "keV Neutrino Dark Matter in a Fast Expanding Universe" by Biswas et al
Biswas et al. found that the thermal relic density of a dark matter particle
freezing out while the universe's energy density is dominated by a non-standard
extra component , whose energy density redshifts faster than radiation,
can be greatly suppressed. Here we show that this result, which contradicts
extensive previous literature, is incorrect: the mistake lies with the
assumption that the (decoupled) extra component contributes to the
entropic degrees of freedom relevant for dark matter freeze out. If this were
the case, a completely different approach would be needed to calculate the dark
matter relic abundance, with dramatically different results
Discrete second order constrained Lagrangian systems: first results
We briefly review the notion of second order constrained (continuous) system
(SOCS) and then propose a discrete time counterpart of it, which we naturally
call discrete second order constrained system (DSOCS). To illustrate and test
numerically our model, we construct certain integrators that simulate the
evolution of two mechanical systems: a particle moving in the plane with
prescribed signed curvature, and the inertia wheel pendulum with a Lyapunov
constraint. In addition, we prove a local existence and uniqueness result for
trajectories of DSOCSs. As a first comparison of the underlying geometric
structures, we study the symplectic behavior of both SOCSs and DSOCSs.Comment: 17 pages, 6 figure
When the Universe Expands Too Fast: Relentless Dark Matter
We consider a modification to the standard cosmological history consisting of
introducing a new species whose energy density red-shifts with the scale
factor like . For , such a red-shift is
faster than radiation, hence the new species dominates the energy budget of the
universe at early times while it is completely negligible at late times. If
equality with the radiation energy density is achieved at low enough
temperatures, dark matter can be produced as a thermal relic during the new
cosmological phase. Dark matter freeze-out then occurs at higher temperatures
compared to the standard case, implying that reproducing the observed abundance
requires significantly larger annihilation rates. Here, we point out a
completely new phenomenon, which we refer to as dark
matter: for large enough , unlike the standard case where annihilation ends
shortly after the departure from thermal equilibrium, dark matter particles
keep annihilating long after leaving chemical equilibrium, with a significant
depletion of the final relic abundance. Relentless annihilation occurs for and for s-wave and p-wave annihilation, respectively, and it
thus occurs in well motivated scenarios such as a quintessence with a kination
phase. We discuss a few microscopic realizations for the new cosmological
component and highlight the phenomenological consequences of our calculations
for dark matter searches.Comment: 14 pages, 9 figure
On the Sobolev trace Theorem for variable exponent spaces in the critical range
In this paper we study the Sobolev Trace Theorem for variable exponent spaces
with critical exponents. We find conditions on the best constant in order to
guaranty the existence of extremals. Then we give local conditions on the
exponents and on the domain (in the spirit of Adimurthy and Yadava) in order to
satisfy such conditions, and therefore to ensure the existence of extremals.Comment: 21 pages, submitte
- âŠ