arXiv subjects

Nicola Pinamonti

Publications and source records attributed to Nicola Pinamonti.

48 records · Page 3Linked to original sources

arXiv2013

Return currents and energy transport in the solar flaring atmosphere

According to a standard ohmic perspective, the injection of accelerated electrons into the flaring region violates local charge equilibrium and therefore, in response, return currents are driven by an electric field to equilibrate such charge violation. In this framework, the energy loss rate associated to these local currents has an ohmic nature and significantly shortens the acceleration electron path. In the present paper we adopt a different viewpoint and, specifically, we study the impact of the background drift velocity on the energy loss rate of accelerated electrons in solar flares. We first utilize the Rutherford cross-section to derive the formula of the energy loss rate when the collisional target has a finite temperature and the background instantaneously and coherently moves up to equilibrate the electron injection. We then use the continuity equation for electrons and imaging spectroscopy data provided by RHESSI to validate this model. Specifically, we show that this new formula for the energy loss rate provides a better fit of the experimental data with respect to the model based on the effects of standard ohmic return currents.

astro-ph.SR↗

arXiv2012

Rigorous construction and Hadamard property of the Unruh state in Schwarzschild spacetime

The discovery of the radiation properties of black holes prompted the search for a natural candidate quantum ground state for a massless scalar field theory on Schwarzschild spacetime, here considered in the Eddington-Finkelstein representation. Among the several available proposals in the literature, an important physical role is played by the so-called Unruh state which is supposed to be appropriate to capture the physics of a black hole formed by spherically symmetric collapsing matter. Within this respect, we shall consider a massless Klein-Gordon field and we shall rigorously and globally construct such state, that is on the algebra of Weyl observables localised in the union of the static external region, the future event horizon and the non-static black hole region. Eventually, out of a careful use of microlocal techniques, we prove that the built state fulfils, where defined, the so-called Hadamard condition; hence, it is perturbatively stable, in other words realizing the natural candidate with which one could study purely quantum phenomena such as the role of the back reaction of Hawking's radiation. From a geometrical point of view, we shall make a profitable use of a bulk-to-boundary reconstruction technique which carefully exploits the Killing horizon structure as well as the conformal asymptotic behaviour of the underlying background. From an analytical point of view, our tools will range from Hormander's theorem on propagation of singularities, results on the role of passive states, and a detailed use of the recently discovered peeling behaviour of the solutions of the wave equation in Schwarzschild spacetime.

gr-qc↗

arXiv2011

State independence for tunneling processes through black hole horizons and Hawking radiation

Tunneling processes through black hole horizons have recently been investigated in the framework of WKB theory discovering interesting interplay with the Hawking radiation. In this paper we instead adopt the point of view proper of QFT in curved spacetime, namely, we use a suitable scaling limit technique to obtain the leading order of the correlation function related with some tunneling process through a Killing horizon. The computation is done for certain large class of reference quantum states for scalar fields. In the limit of sharp localization either on the external side or on opposite sides of the horizon, the quantum correlation functions appear to have thermal nature, where in both cases the characteristic temperature is the Hawking one. Our approach is valid for every stationary charged rotating non extremal black hole, however, since the computation is completely local, it covers the case of a Killing horizon which just temporarily exists in some finite region too. These results give a strong support to the idea that the Hawking radiation, which is detected at future infinity and needs some global structures to be defined, is actually related to a local phenomenon taking place even for local geometric structures (local Killing horizons) existing just for a while.

gr-qc↗

arXiv2011

Local causal structures, Hadamard states and the principle of local covariance in quantum field theory

In the framework of the algebraic formulation, we discuss and analyse some new features of the local structure of a real scalar quantum field theory in a strongly causal spacetime. In particular we use the properties of the exponential map to set up a local version of a bulk-to-boundary correspondence. The bulk is a suitable subset of a geodesic neighbourhood of any but fixed point p of the underlying background, while the boundary is a part of the future light cone having p as its own tip. In this regime, we provide a novel notion for the extended *-algebra of Wick polynomials on the said cone and, on the one hand, we prove that it contains the information of the bulk counterpart via an injective *-homomorphism while, on the other hand, we associate to it a distinguished state whose pull-back in the bulk is of Hadamard form. The main advantage of this point of view arises if one uses the universal properties of the exponential map and of the light cone in order to show that, for any two given backgrounds M and M' and for any two subsets of geodesic neighbourhoods of two arbitrary points, it is possible to engineer the above procedure such that the boundary extended algebras are related via a restriction homomorphism. This allows for the pull-back of boundary states in both spacetimes and, thus, to set up a machinery which permits the comparison of expectation values of local field observables in M and M'.

hep-th↗

arXiv2010

Approximate KMS states for scalar and spinor fields in Friedmann-Robertson-Walker spacetimes

We construct and discuss Hadamard states for both scalar and Dirac spinor fields in a large class of spatially flat Friedmann-Robertson-Walker spacetimes characterised by an initial phase either of exponential or of power-law expansion. The states we obtain can be interpreted as being in thermal equilibrium at the time when the scale factor a has a specific value a=a_0. In the case a_0=0, these states fulfil a strict KMS condition on the boundary of the spacetime, which is either a cosmological horizon, or a Big Bang hypersurface. Furthermore, in the conformally invariant case, they are conformal KMS states on the full spacetime. However, they provide a natural notion of an approximate KMS state also in the remaining cases, especially for massive fields. On the technical side, our results are based on a bulk-to-boundary reconstruction technique already successfully applied in the scalar case and here proven to be suitable also for spinor fields. The potential applications of the states we find range over a broad spectrum, but they appear to be suited to discuss in particular thermal phenomena such as the cosmic neutrino background or the quantum state of dark matter.

gr-qc↗

arXiv2010

Dark Energy from Quantum Matter

We study the backreaction of free quantum fields on a flat Robertson-Walker spacetime. Apart from renormalization freedom, the vacuum energy receives contributions from both the trace anomaly and the thermal nature of the quantum state. The former represents a dynamical realisation of dark energy, while the latter mimics an effective dark matter component. The semiclassical dynamics yield two classes of asymptotically stable solutions. The first reproduces the concordance model in a suitable regime. The second lacks a classical counterpart, but is in excellent agreement with recent observations.

astro-ph.CO↗

arXiv2010

On the initial conditions and solutions of the semiclassical Einstein equations in a cosmological scenario

In this paper we shall discuss the backreaction of a massive quantum scalar field on the curvature, the latter treated as a classical field. Furthermore, we shall deal with this problem in the realm of cosmological spacetimes by analyzing the Einstein equations in a semiclassical fashion. More precisely, we shall show that, at least on small intervals of time, solutions for this interacting system exist. This result will be achieved providing an iteration scheme and showing that the series, obtained starting from the massless solution, converges in the appropriate Banach space. The quantum states with good ultraviolet behavior (Hadamard property), used in order to obtain the backreaction, will be completely determined by their form on the initial surface if chosen to be lightlike. Furthermore, on small intervals of time, they do not influence the behavior of the exact solution. On large intervals of time the situation is more complicated but, if the spacetime is expanding, we shall show that the end-point of the evolution does not depend strongly on the quantum state, because, in this limit, the expectation values of the matter fields responsible for the backreaction do not depend on the particular homogeneous Hadamard state at all. Finally, we shall comment on the interpretation of the semiclassical Einstein equations for this kind of problems. Although the fluctuations of the expectation values of pointlike fields diverge, if the spacetime and the quantum state have a large spatial symmetry and if we consider the smeared fields on regions of large spatial volume, they tend to vanish. Assuming this point of view the semiclassical Einstein equations become more reliable.

gr-qc↗

arXiv2009

The extended algebra of observables for Dirac fields and the trace anomaly of their stress-energy tensor

We discuss from scratch the classical structure of Dirac spinors on an arbitrary globally hyperbolic, Lorentzian spacetime, their formulation as a locally covariant quantum field theory, and the associated notion of a Hadamard state. Eventually, we develop the notion of Wick polynomials for spinor fields, and we employ the latter to construct a covariantly conserved stress-energy tensor suited for back-reaction computations. We shall explicitly calculate its trace anomaly in particular.

math-ph↗

arXiv2009

Conformal generally covariant quantum field theory: The scalar field and its Wick products

In this paper we generalize the construction of generally covariant quantum theories given in the work of Brunetti, Fredenhagen and Verch to encompass the conformal covariant case. After introducing the abstract framework, we discuss the massless conformally coupled Klein Gordon field theory, showing that its quantization corresponds to a functor between two certain categories. At the abstract level, the ordinary fields, could be thought as natural transformations in the sense of category theory. We show that, the Wick monomials without derivatives (Wick powers), can be interpreted as fields in this generalized sense, provided a non trivial choice of the renormalization constants is given. A careful analysis shows that the transformation law of Wick powers is characterized by a weight, and it turns out that the sum of fields with different weights breaks the conformal covariance. At this point there is a difference between the previously given picture due to the presence of a bigger group of covariance. It is furthermore shown that the construction does not depend upon the scale mu appearing in the Hadamard parametrix, used to regularize the fields. Finally, we briefly discuss some further examples of more involved fields.

math-ph↗

arXiv2008

Distinguished quantum states in a class of cosmological spacetimes and their Hadamard property

In a recent paper, we proved that a large class of spacetimes, not necessarily homogeneous or isotropous and relevant at a cosmological level, possesses a preferred codimension one submanifold, i.e., the past cosmological horizon, on which it is possible to encode the information of a scalar field theory living in the bulk. Such bulk-to-boundary reconstruction procedure entails the identification of a preferred quasifree algebraic state for the bulk theory, enjoying remarkable properties concerning invariance under isometries (if any) of the bulk and energy positivity, and reducing to well-known vacua in standard situations. In this paper, specialising to open FRW models, we extend previously obtained results and we prove that the preferred state is of Hadamard form, hence the backreaction on the metric is finite and the state can be used as a starting point for renormalisation procedures. That state could play a distinguished role in the discussion of the evolution of scalar fluctuations of the metric, an analysis often performed in the development of any model describing the dynamic of an early Universe which undergoes an inflationary phase of rapid expansion in the past.

gr-qc↗

arXiv2008

Stable cosmological models driven by a free quantum scalar field

In the mathematically rigorous analysis of semiclassical Einstein's equations, the renormalisation of the stress-energy tensor plays a crucial role. We address such a topic in the case of a scalar field with both arbitrary mass and coupling with gravity in the hypothesis that the underlying algebraic quantum state is of Hadamard type. Particularly, if we focus on highly symmetric solutions of the semiclassical Einstein's equations, the envisaged method displays a de Sitter type behaviour even without an a priori introduced cosmological constant. As a further novel result we shall show that these solutions turn out to be stable.

gr-qc↗

arXiv2007

On localization and position operators in Moebius-covariant theories

Some years ago it was shown that, in some cases, a notion of locality can arise from the group of symmetry enjoyed by the theory, thus in an intrinsic way. In particular, when Moebius covariance is present, it is possible to associate some particular transformations to the Tomita Takesaki modular operator and conjugation of a specific interval of an abstract circle. In this context we propose a way to define an operator representing the coordinate conjugated with the modular transformations. Remarkably this coordinate turns out to be compatible with the abstract notion of locality. Finally a concrete example concerning a quantum particle on a line is also given.

math-ph↗