Abstract. We introduce unitary quantum phase operators for material particles. We carry out a model study on quantum phases of interacting bosons in a symmetric double-well potential in terms of unitary and commonly-used non-unitary phase operators and compare the results for different number of bosons. We find that the results for unitary quantum phase operators are significantly different from those for non-unitary ones especially in the case of low number of bosons. We introduce unitary operators corresponding to the quantum phase-difference between two single-particle states of fermions. As an application of fermionic phase operators, we study a simple model of a pair of interacting two-component fermions in a symmetric double-well potential. We also investigate quantum phase and number fluctuations to ascertain number-phase uncertainty in terms of unitary phase operators.

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We have observed Markarian 501 in Very High Energy (VHE) gamma-ray wavelength band for 70.6 hours from 15 April to 30 May, 2012 using TACTIC telescope. Detailed analysis of ∼66.3 hours of clean data revealed the presence of a TeV γ-ray signal (686±77 γ-ray events) from the source direction with a statistical significance of 8.89σ above 850 GeV. Further, a total of 375 ± 47 γ-ray like events were detected in 25.2 hours of observation from 22 -27 May, 2012 with a statistical significance of 8.05σ indicating that the source has possibly switched over to a relatively high gamma-ray emission state. We have derived time-averaged differential energy spectrum of the state in the energy range 850 GeV -17.24 TeV which fits well with a power law function of the form dF/dE = f 0 E −Γ with f 0 = (2.27 ± 0.38) × 10photons cm −2 s −1 TeV −1 and Γ = 2.57 ± 0.15. In order to investigate the source state, we have also used almost simultaneous multiwavelength observations viz: high energy data collected by Fermi-LAT, X-ray data collected by Swift-XRT and MAXI, optical and UV data collected by Swift-UVOT, and radio data collected by OVRO, and reconstructed broad-band Spectral Email address: chandrap@barc.gov.in (P Chandra) Preprint submitted to New AstronomyJanuary 26, 2017 Energy Distribution (SED). The obtained SED supports leptonic model (homogeneous single zone) for VHE gamma-ray emission involving synchrotron and synchrotron self Compton (SSC) processes.

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