Thermodynamics is one of the founding scientific pillars that has helped us better understand heat engines, biology, ecosystems, and even black holes. While it fundamentally describes large systems... Show moreThermodynamics is one of the founding scientific pillars that has helped us better understand heat engines, biology, ecosystems, and even black holes. While it fundamentally describes large systems by examining the bulk behavior of their constituents, it is anchored in the statistical equivalence of equilibrium configurations of a formally infinite number of microscopic constituents. A question of its validity arises when one scales down to small quantum systems. Here, we have derived dynamic non-equilibrium relations that surprisingly resemble the classical thermodynamics laws, with a mix of quantum features that encode the dynamics of quantum information. Understanding the relation between the out-of-equilibrium dynamics of finite-size quantum systems and their initial thermodynamic state might have been a purely academic exercise fifteen years ago. But now, thanks to ultra-cold atomic quantum simulators and progress in quantum computers, the thermodynamics of finite-size quantum systems has practical implications too. The findings of this thesis contribute to understanding quantum many-body systems, particularly in the context of entanglement, non-equilibrium dynamics, thermalization, and charge transport. Show less
High-Tc cuprate strange metals are characterized by a DC resistivity that scales linearly with T from the onset of superconductivity to the crystal melting temperature, characterized by a current... Show moreHigh-Tc cuprate strange metals are characterized by a DC resistivity that scales linearly with T from the onset of superconductivity to the crystal melting temperature, characterized by a current life time τℏ≃ℏ/(kBT), the “Planckian dissipation”. At the same time, the optical conductivity ceases to be of the Drude form at high temperatures, suggesting a change of the underlying dynamics that surprisingly leaves the T-linear DC resistivity unaffected. We use the AdS/CFT correspondence that describes strongly coupled, densely many-body entangled metallic states of matter to study the DC thermoelectrical transport properties and the optical conductivities of the local quantum critical Gubser-Rocha holographic strange metal in 2+1 dimensions in the presence of a lattice potential, a prime candidate to compare with experiment. We find that the electrical DC resistivity is linear in T at low temperatures for a large range of potential strengths and wave vectors, even as it transitions between different dissipative regimes. At weak lattice potential the optical conductivity evolves as a function of increasing temperature from a Drude form to a “bad metal” characterized by a mid-IR resonance without changing the DC transport, similar to that seen in cuprate strange metals. This mid-IR peak and notably its temperature evolution can be fully understood as a consequence of umklapp hydrodynamics: i.e., hydrodynamic perturbations are Bloch modes in the presence of a lattice. At strong lattice potential an “incoherent metal” is realized instead where momentum conservation no longer plays a role in the transport. We confirm that in this regime the thermal diffusivity appears to be insensitive to the breaking of translations and can be explained by Planckian dissipation originating in universal microscopic chaos. A similar behavior has been found for holographic metals with strong homogeneous momentum relaxation. The charge diffusivity does not submit to this chaos explanation, even though the continuing linear-in-T DC resistivity saturates to an apparent universal slope, numerically equal to a Planckian rate. Show less
