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Nicholas Sirica Quantum Field Theory II May 6, 2013

The Theory of Photoemission: From the Many-Body Propagator to the Breakdown of the Sudden Approximation. Nicholas Sirica Quantum Field Theory II May 6, 2013. The Propagator. Why so important?.

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Nicholas Sirica Quantum Field Theory II May 6, 2013

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  1. The Theory of Photoemission: From the Many-Body Propagator to the Breakdown of the Sudden Approximation Nicholas Sirica Quantum Field Theory II May 6, 2013

  2. The Propagator Why so important? Defines the probability amplitude that a particle created in state k1 at time t1 will be scattered into state k2 at some later time t2

  3. Photoemission as a Gedankenexperiment Spectral Representation

  4. Many-Body effects Expressing the spectral function as

  5. Quasi-Particles Expanding the pole about the Fermi level Gives an approximate free-particle state With a lifetime Additionally QP renormalization factor defines discontinuity in T=0 momentum distribution function

  6. Finite Temperature For perturbative expansion to hold, take ensemble average of imaginary time propagator where In going to the frequency domain By making use of the anti-periodic nature Find frequency to take on discrete values

  7. Keldysh Formalism In the interaction picture Where Gell-mann and Low say For non-equilibrium processes Have to define a Keldysh contour such that

  8. Three Current Diagram Expansion of the photocurrent Yields lowest order diagram which is quadratic in response Physical interpretation: 1) creation of an electron-hole pair 2) uncorrelated propagation of pair 3) ejection of electron and filling of hole

  9. Higher order contributions: renormalized propagators and dressed vertices. Propagation of electron and hole no longer uncorrelated! Represents a breakdown of the sudden approximation! Experimentally observed by examining the intensity ratio of unscreened versus total screened and unscreened for Nitrogen 1s. Find that as threshold is approached the transition from sudden to adiabatic occurs abrubtly

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