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Smooth and fast versus instantaneous quenches in quantum field theory

By U.S.A. 40506 KY Lexington 505 Rose St University of Kentucky SumitDepartment of Physics and Astronomy Das, Canada) N6A 5B7 ON London 1151 Richmond Street University of Western Ontario Damián(Department of Applied Mathematics Galante and Canada) N2L 2Y5 ON Waterloo 55 Caroline St N Robert(Perimeter Institute for Theoretical Physics Myers


We examine in detail the relationship between smooth fast quantum quenches, characterized by a time scale δ t , 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 δ t → 0 because of the relation of the quench rate to the UV cut-off, i.e., 1 / δ t ≪ Λ always holds in the fast smooth quenches while 1 / δ t ∼ 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 δ t , the correlator scales universally with δ t , exactly as in the scaling of renormalized one point functions found in earlier work. At larger separation, the dependence on δ t drops out. The excess energy density is finite (for finite m δ t ) and scales in a universal fashion for all d . However, the scaling behaviour produces a divergent result in the limit m δ t → 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

Year: 2015
DOI identifier: 10.1007/JHEP08(2015)073
OAI identifier:

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