We show that the particles in the Calogero-Sutherland Model obey fractional exclusion statistics as defined by Haldane. We construct anyon number densities and derive the energy distribution function. We show that the partition function factorizes in the form characteristic of an ideal gas. The virial expansion is exactly computable and interestingly it is only the second virial coefficient that encodes the statistics information.

The upcoming 50 kt magnetized iron calorimeter (ICAL) detector at the India-based Neutrino Observatory (INO) is designed to study the atmospheric neutrinos and antineutrinos separately over a wide range of energies and path lengths. The primary focus of this experiment is to explore the Earth matter effects by observing the energy and zenith angle dependence of the atmospheric neutrinos in the multi-GeV range. This study will be crucial to address some of the outstanding issues in neutrino oscillation physics, including the fundamental issue of neutrino mass hierarchy. In this document, we present the physics potential of the detector as obtained from realistic detector simulations. We describe the simulation framework, the neutrino interactions in the detector, and the expected response of the detector to particles traversing it. The ICAL detector can determine the energy and direction of the muons to a high precision, and in addition, its sensitivity to multi-GeV hadrons increases its physics reach substantially. Its charge identification capability, and hence its ability to distinguish neutrinos from antineutrinos, makes it an efficient detector for determining the neutrino mass hierarchy. In this report, we outline the analyses carried out for the determination of neutrino mass hierarchy and precision measurements of atmospheric neutrino mixing parameters at ICAL, and give the expected physics reach of the detector with 10 years of runtime. We also explore the potential of ICAL for probing new physics scenarios like CPT violation and the presence of magnetic monopoles. v Physics Potential of ICAL at INO vi PrefaceThe past two decades in neutrino physics have been very eventful, and have established this field as one of the flourishing areas of high energy physics. Starting from the confirmation of neutrino oscillations that resolved the decades-old problems of the solar and atmospheric neutrinos, we have now been able to show that neutrinos have nonzero masses, and different flavors of neutrinos mix among themselves. Our understanding of neutrino properties has increased by leaps and bounds. Many experiments have been constructed and envisaged to explore different facets of neutrinos, in particular their masses and mixing.The Iron Calorimeter (ICAL) experiment at the India-based Neutrino Observatory (INO) [1] is one of the major detectors that is expected to see the light of the day soon. It will have unique features like the ability to distinguish muon neutrinos from antineutrinos at GeV energies, and measure the energies of hadrons in the same energy range. It is therefore well suited for the identification of neutrino mass hierarchy, the measurement of neutrino mixing parameters, and many probes of new physics. The site for the INO has been identified, and the construction is expected to start soon. In the meanwhile, the R&D for the ICAL detector, including the design of its modules, the magnet coils, the active detector elements and the associated electronics, has been underway over the past deca...

It is by now established that neutrinos mix, have (different) non-zero masses, and therefore oscillate. The oscillation parameters themselves, however, are not all well-known. An open problem is that of the neutrino mass hierarchy. We study the possibility of determining the neutrino mass hierarchy with atmospheric neutrinos using an iron calorimeter detector capable of charge identification such as the proposed monolith and ical/ino detectors. We find that such detectors are sensitive to the sign of the mass-squared difference, δ 32 = m 2 3 − m 2 2 , provided the as-yet unknown mixing angle between the first and third generations, θ 13 , is greater than 6 • (sin 2 2θ 13 > 0.04). A result with a significance greater than 90% CL requires large exposures (more than 500 kton-years) as well as good energy and angular resolution of the detected muons (better than 15%), especially for small θ 13 . Hence obtaining definitive results with such a detector is difficult, unless θ 13 turns out to be large. In contrast, such detectors can establish a clear oscillation pattern in atmospheric neutrinos in about 150 kton-years, therefore determining the absolute value of δ 32 and sin 2 2θ 23 to within 10%.

We investigate the particle and kinetic energy densities of harmonically trapped fermion gases at zero temperature in arbitrary dimensions. We derive analytically a differential equation connecting these densities, which so far have been proven only in one or two dimensions, and give other interesting relations involving several densities or the particle density alone. We show that in the asymptotic limit of large particle numbers, the densities go over into the semi-classical Thomas-Fermi (TF) densities. Hereby the Fermi energy to be used in the TF densities is identified uniquely. We derive an analytical expansion for the remaining oscillating parts and obtain very simple closed forms for the leading-order oscillating densities. Finally, we show that the simple TF functional relation τ T F [ρ] between kinetic and particle density is fulfilled also for the asymptotic quantum densities τ (r) and ρ(r) including their leading-order oscillating terms.