Transport Theories for Strongly-Interacting Systems

Robin Steinigeweg

The decay of current autocorrelation functions is investigated for quantum systems featuring strong interactions. Here the term "interaction" refers to that part of the Hamiltonian causing the (major) decay of the current. On the time scale before the (first) zero crossing of the current, its relaxation is shown to be well described by a suitable perturbation theory in the lowest orders of the interaction strength, particularly if interactions are strong. In this description the relaxation is found to be rather close to a Gaussian decay and the resulting diffusion coefficient approximately scales with the inverse interaction strength. These findings are confirmed by numerical results from exact diagonalization for several one-dimensional transport models including spin transport in the Heisenberg chain with respect to different spin quantum numbers, anisotropy, next-nearest-neighbor interaction, or alternating magnetic field; energy transport in the Ising chain with tilted magnetic field; and transport of excitations in a randomly coupled modular quantum system. The impact of these results for weak interactions is discussed.

Assa Auerbach, Sauri Bhattacharyya

Antti‐Pekka Jauho

Van Vliet, M Carolyn

Equilibrium Statistical Mechanics: General Principles of Many-Particle Systems Classical and Quantum Formalisms. The Boltzmann Gas, the Perfect Bose Gas and Fermi Gas Quantum Systems with Strong Interactions Non-Equilibrium Statistical Mechanics: Classical Transport Theory Linear Response Theory and Quantum Transport Stochastic Phenomena Appendices: The Schrodinger, Heisenberg and Interaction Pictures Spin and Statistics.

Eric Nilsson

Modern quantum materials host a wide range of electronic phases in which transport properties are governed by strong interactions and collective effects. This thesis investigates charge, heat, and momentum transport in interacting electronic systems across different theoretical frameworks, ranging from Fermi liquid theory to strongly coupled strange metals.The first part of the thesis focuses on two-dimensional Fermi liquids at finite temperature, where rapid electron-electron scattering can give rise to hydrodynamic behavior. A kinetic-theory framework allowing an exact treatment of quasiparticle distribution functions beyond the asymptotic low-temperature regime is used to compute the full spectrum of collective modes, providing a detailed characterization of long-lived odd-parity excitations and the intermediate transport regime between ballistic and hydrodynamic flow. The same framework is employed to determine the shear viscosity of interacting electron liquids beyond conventional perturbative limits.The second part of the thesis concerns strongly interacting quantum systems where the quasiparticle picture breaks down.Holographic duality is used to study transport and thermoelectric response in quantum critical systems subject to periodic potentials, providing a controlled framework for momentum relaxation and magnetotransport in non-Fermi liquids. The thesis further develops holographic models of collective charge dynamics in systems with dynamical electromagnetism, including bulk plasmons and surface plasmon polaritons, and explores connections between Fermi surface physics and holographic gauge-field dynamics.

Leonardo Lauck, Aurea Rosas Vasconcellos, Roberto Luzzi