A Dynamic Model of Final Service Competition in fixed Electronic Communications under a Capacity Interconnection Regime

Recientemente el regulador español ha implementado un nuevo modelo de interconexión en redes fijas de telecomunicaciones basado en la compra de capacidad que podrá ser utilizado en combinación con el modelo habitual de interconexión por tiempo. Se propone un modelo dinámico de competencia en duopolio en el cual el entrante puede comprar ex ante un cierto nivel de capacidad al incumbente paraluego ambos operadores competir en precios. Se introduce la posibilidad de que el entrante pueda asignar eficientemente el tráfico entre distintas franjas horarias. Los resultados muestran que el uso simultáneo de ambos modelos genera una competencia más agresiva en precios y puede llegar a producir significativas ganancias de eficiencia (asignativa y otras internas a la firma). De cualquier forma, el entrante necesita alcanzar una masa crítica antes de que el nuevo modelo pueda representar una alternativa para él. Además, una vez alcanzado este nivel, su conveniencia para el entrante dependerá de determinadas condiciones.The Spanish regulatory authority recently implemented a new interconnection regime based on capacity (and not per time) payments in fixed telecommunications. We propose a dynamic duopolistic model of final service competition in which the entrant first acquires a certain capacity at the local loop (at a fixed payment) from the incumbent and then both operators compete in prices for the final services. We introduce the entrant’s possibility to assign efficiently the traffic he offer between different hours along the day as well as the possibility for him to use the capacity based model as well as the per-unit-oftime interconnection regime vis à vis the incumbent. The results show that, the simultaneous use of both interconnection models (instead of only the one based on time) leads always to tougher competition (more aggressive pricing) in the final service market and efficiency (internal to the firm and allocative) gains. Nevertheless, the entrant needs a minimum scale before this new model can be a viable alternative. In addition, once reached this scale, its convenience for the entrant will depend on certain conditions.Interconnection per time, Interconnection by capacity, Dynamics of the competition, Regulation, Network dimension.

Entropy bounds in terms of the w parameter

In a pair of recent articles [PRL 105 (2010) 041302 - arXiv:1005.1132; JHEP 1103 (2011) 056 - arXiv:1012.2867] two of the current authors have developed an entropy bound for equilibrium uncollapsed matter using only classical general relativity, basic thermodynamics, and the Unruh effect. An odd feature of that bound, S <= A/2, was that the proportionality constant, 1/2, was weaker than that expected from black hole thermodynamics, 1/4. In the current article we strengthen the previous results by obtaining a bound involving the (suitably averaged) w parameter. Simple causality arguments restrict this averaged parameter to be <= 1. When equality holds, the entropy bound saturates at the value expected based on black hole thermodynamics. We also add some clarifying comments regarding the (net) positivity of the chemical potential. Overall, we find that even in the absence of any black hole region, we can nevertheless get arbitrarily close to the Bekenstein entropy.Comment: V1: 14 pages. V2: One reference added. V3: This version accepted for publication in JHE

Hawking-like radiation does not require a trapped region

We discuss the issue of quasi-particle production by ``analogue black holes'' with particular attention to the possibility of reproducing Hawking radiation in a laboratory. By constructing simple geometric acoustic models, we obtain a somewhat unexpected result: We show that in order to obtain a stationary and Planckian emission of quasi-particles, it is not necessary to create a trapped region in the acoustic spacetime (corresponding to a supersonic regime in the fluid flow). It is sufficient to set up a dynamically changing flow asymptotically approaching a sonic regime with sufficient rapidity in laboratory time.Comment: revtex4, 4 pages, 1 figur

Stability analysis of sonic horizons in Bose-Einstein condensates

We examine the linear stability of various configurations in Bose-Einstein condensates with sonic horizons. These configurations are chosen in analogy with gravitational systems with a black hole horizon, a white hole horizon and a combination of both. We discuss the role of different boundary conditions in this stability analysis, paying special attention to their meaning in gravitational terms. We highlight that the stability of a given configuration, not only depends on its specific geometry, but especially on these boundary conditions. Under boundary conditions directly extrapolated from those in standard General Relativity, black hole configurations, white hole configurations and the combination of both into a black hole--white hole configuration are shown to be stable. However, we show that under other (less stringent) boundary conditions, configurations with a single black hole horizon remain stable, whereas white hole and black hole--white hole configurations develop instabilities associated to the presence of the sonic horizons.Comment: 14 pages, 7 figures (reduced resolution

Sensitivity of Hawking radiation to superluminal dispersion relations

We analyze the Hawking radiation process due to collapsing configurations in the presence of superluminal modifications of the dispersion relation. With such superluminal dispersion relations, the horizon effectively becomes a frequency-dependent concept. In particular, at every moment of the collapse, there is a critical frequency above which no horizon is experienced. We show that, as a consequence, the late-time radiation suffers strong modifications, both quantitative and qualitative, compared to the standard Hawking picture. Concretely, we show that the radiation spectrum becomes dependent on the measuring time, on the surface gravities associated with different frequencies, and on the critical frequency. Even if the critical frequency is well above the Planck scale, important modifications still show up.Comment: 14 pages, 7 figures. Extensive paragraph added in conclusions to clarify obtained result

Quasi-particle creation by analogue black holes

We discuss the issue of quasi-particle production by ``analogue black holes'' with particular attention to the possibility of reproducing Hawking radiation in a laboratory. By constructing simple geometric acoustic models, we obtain a somewhat unexpected result: We show that in order to obtain a stationary and Planckian emission of quasi-particles, it is not necessary to create an ergoregion in the acoustic spacetime (corresponding to a supersonic regime in the flow). It is sufficient to set up a dynamically changing flow either eventually generating an arbitrarily small sonic region v=c, but without any ergoregion, or even just asymptotically, in laboratory time, approaching a sonic regime with sufficient rapidity.Comment: 30 pages, 16 figure

A dynamic model of final service competition in fixed electronic communications under a capacity interconnection regime

The Spanish regulatory authority recently implemented a new interconnection regime based on capacity (and not per time) payments in fixed telecommunications. We propose a dynamic duopolistic model of final service competition in which the entrant first acquires a certain capacity at the local loop (at a fixed payment) from the incumbent and then both operators compete in prices for the final services. We introduce the entrant’s possibility to assign efficiently the traffic he offer between different hours along the day as well as the possibility for him to use the capacity based model as well as the per-unit-oftime interconnection regime vis à vis the incumbent. The results show that, the simultaneous use of both interconnection models (instead of only the one based on time) leads always to tougher competition (more aggressive pricing) in the final service market and efficiency (internal to the firm and allocative) gains. Nevertheless, the entrant needs a minimum scale before this new model can be a viable alternative. In addition, once reached this scale, its convenience for the entrant will depend on certain conditions. Recientemente el regulador español ha implementado un nuevo modelo de interconexión en redes fijas de telecomunicaciones basado en la compra de capacidad que podrá ser utilizado en combinación con el modelo habitual de interconexión por tiempo. Se propone un modelo dinámico de competencia en duopolio en el cual el entrante puede comprar ex ante un cierto nivel de capacidad al incumbente para luego ambos operadores competir en precios. Se introduce la posibilidad de que el entrante pueda asignar eficientemente el tráfico entre distintas franjas horarias. Los resultados muestran que el uso simultáneo de ambos modelos genera una competencia más agresiva en precios y puede llegar a producir significativas ganancias de eficiencia (asignativa y otras internas a la firma). De cualquier forma, el entrante necesita alcanzar una masa crítica antes de que el nuevo modelo pueda representar una alternativa para él. Además, una vez alcanzado este nivel, su conveniencia para el entrante dependerá de determinadas condiciones

On thermodynamic and quantum fluctuations of cosmological constant

We discuss from the condensed-matter point of view the recent idea that the Poisson fluctuations of cosmological constant about zero could be a source of the observed dark energy. We argue that the thermodynamic fluctuations of Lambda are much bigger. Since the amplitude of fluctuations is proportional to V^{-1/2}, where V is the volume of the Universe, the present constraint on the cosmological constant provides the lower limit for V, which is much bigger than the volume within the cosmological horizon.Comment: 4 pages, version submitted to JETP Letter

Hawking radiation from "phase horizons" in laser filaments?

Belgiorno et al have reported on experiments aiming at the detection of (the analogue of) Hawking radiation using laser filaments [F. Belgiorno et al, Phys. Rev. Lett. 105, 203901 (2010)]. They sent intense focused Bessel pulses into a non-linear dielectric medium in order to change its refractive index via the Kerr effect and saw creation of photons orthogonal to the direction of travel of the pluses. Since the refractive index change in the pulse generated a "phase horizon" (where the phase velocity of these photons equals the pulse speed), they concluded that they observed the analogue of Hawking radiation. We study this scenario in a model with a phase horizon and a phase velocity very similar to that of their experiment and find that the effective metric does not quite correspond to a black hole. The photons created in this model are not due to the analogue of black hole evaporation but have more similarities to cosmological particle creation. Nevertheless, even this effect cannot explain the observations -- unless the pulse has significant small scale structure in both the longitudinal and transverse dimensions.Comment: 13 pages RevTeX, 2 figure