Electron Phonon Collisions, Fermi Dirac Distribution and Bloch's T5T^5 law

In this paper, we model exchange of energy between electrons in solids and the phonon bath as electron-phonon collisions. Phonons are modelled as packets which create a lattice deformation potential of which electrons scatter. We show how these collisions exchange energy between electrons and phonons, leading to Fermi-Dirac distribution for electrons. Using these collisions, we derive the temperature dependence of resistivity of metals and the Bloch's $T$ and $T^5$ law for high and low temperature regime respectively. Unlike standard derivations of $T$ dependence of high temperature resistivity, our derivation rests fundamentally on the temperature dependence of the scattering angle.Comment: 14 pages, 10 Figures. arXiv admin note: text overlap with arXiv:1710.0348

Boundary of Quantum Evolution under Decoherence

Relaxation effects impose fundamental limitations on our ability to coherently control quantum mechanical phenomena. In this letter, we establish physical limits on how closely can a quantum mechanical system be steered to a desired target state in the presence of relaxation. In particular, we explicitly compute the maximum coherence or polarization that can be transferred between coupled nuclear spins in the presence of very general decoherence mechanisms that include cross-correlated relaxation. We give analytical expressions for the control laws (pulse sequences) which achieve these physical limits and provide supporting experimental evidence. Exploitation of cross-correlation effects has recently led to the development of powerful methods in NMR spectroscopy to study very large biomolecules in solution. We demonstrate with experiments that the optimal pulse sequences provide significant gains over these state of the art methods, opening new avenues for spectroscopy of much larger proteins. Surprisingly, in spite of very large relaxation rates, optimal control can transfer coherence without any loss when cross-correlated relaxation rates are tuned to auto-correlated relaxation rates