We examine in detail the relationship between smooth fast quantum quenches, characterized by a time scale δt, and instantaneous quenches, within the framework of exactly solvable mass quenches in free scalar field theory. Our earlier studies [1, 2] highlighted that the two protocols remain distinct in the limit δt → 0 because of the relation of the quench rate to the UV cut-off, i.e., 1/δt ≪ Λ always holds in the fast smooth quenches while 1/δt ∼ Λ for instantaneous quenches. Here we study UV finite quantities like correlators at finite spatial distances and the excess energy produced above the final ground state energy. We show that at late times and large distances (compared to the quench time scale) the smooth quench correlator approaches that for the instantaneous quench. At early times, we find that for small spatial separation and small δt, the correlator scales universally with δt, exactly as in the scaling of renormalized one point functions found in earlier work. At larger separation, the dependence on δt drops out. The excess energy density is finite (for finite mδt) and scales in a universal fashion for all d. However, the scaling behaviour produces a divergent result in the limit mδt → 0 for d ≥ 4, just as in an instantaneous quench, where it is UV divergent for d ≥ 4. We argue that similar results hold for arbitrary interacting theories: the excess energy density produced is expected to diverge for scaling dimensions Δ > d/2.
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Article funded by SCOAP3.
S.R.D. would like to thank the Galileo Galilei Institute for Theoretical Physics for the hospitality and the INFN for partial support during the completion of this work. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research & Innovation. RCM and DAG are also supported by an NSERC Discovery grant. RCM is also supported by research funding from the Canadian Institute for Advanced Research. The work of SRD is partially supported by the National Science Foundation grant NSF-PHY-1214341. DAG also thanks the Kavli Institute for Theoretical Physics for hospitality during the last stages of this project. Research at KITP is supported, in part, by the National Science Foundation under Grant No. NSF PHY11-25915.
Das, Sumit R.; Galante, Damián A.; and Myers, Robert C., "Smooth and Fast Versus Instantaneous Quenches in Quantum Field Theory" (2015). Physics and Astronomy Faculty Publications. 359.