Executive Summary : | In the present proposal, we lay out the possibilities for gravitational probes into nonrelativistic quantum many body dynamics near its quantum criticality. The key idea is based the so called ``holographic principle" which relates strongly correlated quantum many body dynamics to classical theories of gravity living in one higher dimension. The symmetries of the gravitational counterpart is driven by the nonrelativistic symmetries of the quantum mechanical system under consideration. Based on the underlying symmetries, these geometries are broadly classified as Non-Lorentzian manifolds those preserve the Galilean invariance as a global part of the nonrelativistic diffeomorphism invariance. Given these Non-Lorentzian backgrounds, it is natural to conjecture that the degrees of freedom (for example nonrelativistic strings, D branes etc.) propagating over these backgrounds precisely capture the strongly correlated physics near its quantum criticality. Taking these Non-Lorentzian backgrounds as the backbone, we would like to probe various exotic quantum phenomena for example the Quantum Hall Transitions near the quantum criticality and in particular to study their near equilibrium dynamics. Our analysis might lead to several other spinoffs like unveiling the underlying universality class associated to these quantum critical points and so on. Understanding a minor fraction of which might lead to a significant progress in our present day understanding of the nonrelativistic quantum many body physics near its equilibrium. |