Dr. Aranya Bhattacharya

I, along with my collaborators, have worked on the idea of entanglement and computational complexity in situations where the Page curve is reproduced using the concept of entanglement islands. In [1] (single authored paper in PRD), I studied a multiboundary wormhole model while in [2] and [3], we looked at the evolution of the holographic subregion complexity for evaporating and eternal AdS black holes respectively.

In this program ([4] and [5]), we have developed the notion of operator growth and Krylov complexity for various open quantum systems. Krylov complexity quantifies how an initial state or operator spreads in the corresponding Hilbert space along Hamiltonian time evolution in the Schrödinger or Heisenberg picture respectively. It is related to the spectrum of the Hamiltonian or Liouvillean, and hence acts as a simple but elegant probe of quantum chaos as this spread of operator is known to be fastest for chaotic evolution. One can also figure out different timescales (Scrambling time, Heisenberg time etc.) where this process of spreading of operator goes through major and noticeable changes affecting the overall scaling of the Krylov complexity. We investigate how the notion of chaos changes in the presence of interaction with the environment where the information leaks out to the environment causing a decay of probability in the system degrees of freedom and affecting the notion of chaos. 

In this work [6], I, along with a masters student from IISc Bangalore, figured out a way how to quantify chaotic nature of scattering amplitudes. We study the statistics of the poles of several scattering amplitudes with respect to some probe input variable (momenta or scattering angle) and treat them as eigenvalues of a Hamiltonian, which evolves one copy of a thermofield double state non-trivially. Through this method, we study the complexity of several scattering amplitudes and find that the amplitudes for highly excited string states scattering to multiple tachyons show chaotic behaviour typical to the Gaussian Unitary Ensemble (GUE) universality class among the well-known Random matrix universality class. This also indicates the fact that black hole scattering is chaotic since the highly excited string states are conjectured to be dual to black hole microstates due to the string/black hole correspondence by Susskind-Horowitz-Polchinski.