Heat-kernels and functional determinants on the generalized cone

We consider zeta functions and heat-kernel expansions on the bounded, generalized cone in arbitrary dimensions using an improved calculational technique. The specific case of a global monopole is analysed in detail and some restrictions thereby placed on the $A_{5/2}$ coefficient. The computation of functional determinants is also addressed. General formulas are given and known results are incidentally, and rapidly, reproduced.Comment: 26p,LaTeX.(Cosmetic changes and eqns (9.8),(11.2) corrected.

The super-LHC

We review here the prospects of a long-term upgrade programme for the Large Hadron Collider (LHC), CERN laboratory's new proton-proton collider. The super-LHC, which is currently under evaluation and design, is expected to deliver of the order of ten times the statistics of the LHC. In addition to a non-technical summary of the principal physics arguments for the upgrade, I present a pedagogical introduction to the technological challenges on the accelerator and experimental fronts, and a review of the current status of the planning.Comment: To appear in Contemporary Physic

Detecting chaos in particle accelerators through the frequency map analysis method

The motion of beams in particle accelerators is dominated by a plethora of non-linear effects which can enhance chaotic motion and limit their performance. The application of advanced non-linear dynamics methods for detecting and correcting these effects and thereby increasing the region of beam stability plays an essential role during the accelerator design phase but also their operation. After describing the nature of non-linear effects and their impact on performance parameters of different particle accelerator categories, the theory of non-linear particle motion is outlined. The recent developments on the methods employed for the analysis of chaotic beam motion are detailed. In particular, the ability of the frequency map analysis method to detect chaotic motion and guide the correction of non-linear effects is demonstrated in particle tracking simulations but also experimental data.Comment: Submitted for publication in Chaos, Focus Issue: Chaos Detection Methods and Predictabilit

Relativistic Quantum Information in Detectors-Field Interactions

We review Unruh-DeWitt detectors and other models of detector-field interaction in a relativistic quantum field theory setting as a tool for extracting detector-detector, field-field and detector-field correlation functions of interest in quantum information science, from entanglement dynamics to quantum teleportation. We in particular highlight the contrast between the results obtained from linear perturbation theory which can be justified provided switching effects are properly accounted for, and the nonperturbative effects from available analytic expressions which incorporate the backreaction effects of the quantum field on the detector behaviour.Comment: 21 pages, 3 figures. Prepared for the special focus issue on RQ

Frequency dependent specific heat of viscous silica

We apply the Mori-Zwanzig projection operator formalism to obtain an expression for the frequency dependent specific heat c(z) of a liquid. By using an exact transformation formula due to Lebowitz et al., we derive a relation between c(z) and K(t), the autocorrelation function of temperature fluctuations in the microcanonical ensemble. This connection thus allows to determine c(z) from computer simulations in equilibrium, i.e. without an external perturbation. By considering the generalization of K(t) to finite wave-vectors, we derive an expression to determine the thermal conductivity \lambda from such simulations. We present the results of extensive computer simulations in which we use the derived relations to determine c(z) over eight decades in frequency, as well as \lambda. The system investigated is a simple but realistic model for amorphous silica. We find that at high frequencies the real part of c(z) has the value of an ideal gas. c'(\omega) increases quickly at those frequencies which correspond to the vibrational excitations of the system. At low temperatures c'(\omega) shows a second step. The frequency at which this step is observed is comparable to the one at which the \alpha-relaxation peak is observed in the intermediate scattering function. Also the temperature dependence of the location of this second step is the same as the one of the $\alpha-$peak, thus showing that these quantities are intimately connected to each other. From c'(\omega) we estimate the temperature dependence of the vibrational and configurational part of the specific heat. We find that the static value of c(z) as well as \lambda are in good agreement with experimental data.Comment: 27 pages of Latex, 8 figure

Challenges in QCD matter physics --The scientific programme of the Compressed Baryonic Matter experiment at FAIR

Substantial experimental and theoretical efforts worldwide are devoted to explore the phase diagram of strongly interacting matter. At LHC and top RHIC energies, QCD matter is studied at very high temperatures and nearly vanishing net-baryon densities. There is evidence that a Quark-Gluon-Plasma (QGP) was created at experiments at RHIC and LHC. The transition from the QGP back to the hadron gas is found to be a smooth cross over. For larger net-baryon densities and lower temperatures, it is expected that the QCD phase diagram exhibits a rich structure, such as a first-order phase transition between hadronic and partonic matter which terminates in a critical point, or exotic phases like quarkyonic matter. The discovery of these landmarks would be a breakthrough in our understanding of the strong interaction and is therefore in the focus of various high-energy heavy-ion research programs. The Compressed Baryonic Matter (CBM) experiment at FAIR will play a unique role in the exploration of the QCD phase diagram in the region of high net-baryon densities, because it is designed to run at unprecedented interaction rates. High-rate operation is the key prerequisite for high-precision measurements of multi-differential observables and of rare diagnostic probes which are sensitive to the dense phase of the nuclear fireball. The goal of the CBM experiment at SIS100 (sNN= 2.7--4.9 GeV) is to discover fundamental properties of QCD matter: the phase structure at large baryon-chemical potentials (μB> 500 MeV), effects of chiral symmetry, and the equation of state at high density as it is expected to occur in the core of neutron stars. In this article, we review the motivation for and the physics programme of CBM, including activities before the start of data taking in 2024, in the context of the worldwide efforts to explore high-density QCD matter

Twisted convolution and Moyal star product of generalized functions

We consider nuclear function spaces on which the Weyl-Heisenberg group acts continuously and study the basic properties of the twisted convolution product of the functions with the dual space elements. The final theorem characterizes the corresponding algebra of convolution multipliers and shows that it contains all sufficiently rapidly decreasing functionals in the dual space. Consequently, we obtain a general description of the Moyal multiplier algebra of the Fourier-transformed space. The results extend the Weyl symbol calculus beyond the traditional framework of tempered distributions.Comment: LaTeX, 16 pages, no figure

Chiral Modulations in Curved Space II: Conifold Geometries

In this paper, we extend our previous analysis concerning the formation of inhomogeneous condensates in strongly-coupled fermion effective field theories on curved spaces and include the case of conifold geometries that represent the simplest tractable case of manifolds with curvature singularities. In the set-up considered here, by keeping the genuine thermodynamical temperature constant, we may single out the role that curvature effects play on the breaking/restoration of chiral symmetry and on the appearance of inhomogeneous phases. The first goal of this paper is to construct a general expression of the finite temperature effective action for inhomogeneous condensates in the case of four-fermion effective field theories on conifold geometries with generic Riemannian smooth base (generalised cones). The other goal is to implement numerically the above formal results and construct self-consistent solutions for the condensate. We explicitly show that the condensate assumes a kink-like profile, vanishing at the singularity that is surrounded by a bubble of restored chiral symmetry phase.Comment: 14 pages; 4 figure