Gautam Mandal

We consider quantum quench from a gapped to a gapless system in 1+1 dimensions. We 

provide a rigorous proof of the thermalization of the reduced density matrix, hence that of

an arbitrary string of local operators in an interval. In case the system is integrable, the "thermalization" leads to a generalized Gibbs ensemble (GGE). We model the critical quench in terms of an initial state in terms of a conformal boundary state deformed by exponential cutoffs involving hamiltonian and other charges. We justify this choice of the initial state by explicitly

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We discuss collective coordinate quantization of the half-BPS geometries of Lin, Lunin and Maldacena (hep-th/0409174). The LLM geometries are parameterized by a single function u on a plane. We treat this function as a collective coordinate. We arrive at the collective coordinate action as well as path integral measure by considering D3 branes in an arbitrary LLM geometry. The resulting functional integral is shown, using known methods (hep-th/9309028), to be the classical limit of a functional integral for free fermions in a harmonic oscillator.