Anish Kulkarni

Symmetry of non-Hermitian matrices underpins many physical phenomena. In particular, chaotic open quantum systems exhibit universal bulk spectral correlations classified on the basis of time-reversal symmetry † (TRS † ), coinciding with those of non-Hermitian random matrices in the same symmetry class. Here, we analytically study the spectral correlations of non-Hermitian random matrices in the presence of TRS † with signs +1 and −1, corresponding to symmetry classes AI † and AII † , respectively. Using the fermionic replica non-linear sigma model approach, we derive n-fold integral expressions for the nth moment of the one-point and two-point characteristic polynomials, valid for any matrix dimension. We also study, in the limit of large matrix dimensions, the replica limit n → 0 to derive the density of states and level–level correlations of non-Hermitian random matrices with TRS † . We compare our analytical findings with numerical results.

Drawing from the Chandra archive and using a carefully selected set of nearby dwarf galaxies, we present a calibrated high-mass X-ray binary (HMXB) luminosity function in the low-mass galaxy regime and search for an already hinted at dependence on metallicity. Our study introduces a new sample of local dwarf galaxies (D < 12.5 Mpc and M _* < 5 × 10⁹ M _⊙), expanding the specific star formation rates (sSFR) and gas-phase metallicities probed in previous investigations. Our analysis of the observed X-ray luminosity function indicates a shallower power-law slope for the dwarf galaxy HMXB population. In our study, we focus on dwarf galaxies that are more representative in terms of sSFR compared to prior work. In this regime, the HMXB luminosity function exhibits significant stochastic sampling at high luminosities. This likely accounts for the pronounced scatter observed in the galaxy-integrated HMXB population’s L _X/SFR versus metallicity for our galaxy sample. Our calibration is necessary to understand the active galactic nuclei content of low-mass galaxies identified in current and future X-ray survey fields and has implications for binary population synthesis models, as well as X-ray-driven cosmic heating in the early Universe.

We study the open quantum dynamics of the Sachdev-Ye-Kitaev (SYK) model described by the Lindblad master equation, where the SYK model is coupled to Markovian reservoirs with jump operators that are either linear or quadratic in the Majorana fermion operators. Of particular interest for us is the time evolution of the dissipative form factor, which quantifies the average overlap between the initial and time-evolved density matrices as an open quantum generalization of the Loschmidt echo. We find that the dissipative form factor exhibits dynamical quantum phase transitions. We analytically demonstrate a discontinuous dynamical phase transition in the limit of a large number of fermion flavors, which is formally akin to the thermal phase transition in the two-coupled SYK model between the black-hole and wormhole phases. We also find continuous dynamical phase transitions that do not have counterparts in the two-coupled SYK model. While the phase transitions are sharp in the limit of a large number of fermion flavors, their qualitative signatures are present even for a finite number of fermion flavors, as we show numerically.