Conserved charges cannot be destroyed locally, hence they relax slowly.
The main focus of my research is the theory of hydrodynamics. The two main applications I am interested in are condensed matter phenomenology and holography.
Hydrodynamics is a low-enegy many-body effective theory of universal transport that describes systems near thermal equilibrium in the long-timescale, long-wavelength regime. The relevant degrees of freedom are the (almost-)conserved charges, usually energy, momentum and internal-symmetry charges (e.g., a \( U(1) \) electric current). Hydrodynamic applies when the scattering time between the microscopic constituent of the fluid (e.g., electrons in condensed matters) is the shortest timescale of the system (electron-impurity scatterings are rare), therefore strongly-coupled phases have an enchanced hydrodynamic regime (Martinoia, 2024).
One interesting application is the fluid/gravity duality, grounded in holography. It allows us to study strongly-coupled quantum systems using a theory of classical gravity, in particular a Black Hole solution in the bulk of AdS space is dual to a thermal CFT that lives on the boundary. It is then possible to study the transport properties of the quantum system using the duality, which gives a relationship between the gravitational and hydrodynamic descriptions (Amoretti et al., 2021).
Examples of hydrodynamic electron flow. Left: simulation of vortices. Right: ballistic and hydrodynamic regimes.
In hydrodynamics charges are exactly conserved. However, in real materials this is rarely true, since electrons can lose momentum and energy to impurities and phonons. Therefore the theory of hydrodynamics must be expanded to what is known as quasihydrodynamics, a theory in which charges are not exactly conserved, but are allowed to slowly relax to equilibrium (Amoretti et al., 2024).
On this regard, the research questions I am working on are: is it possible to develop a formally well-defined theory of quasihydrodynamics (Amoretti et al., 2023; Amoretti et al., 2024)? How are the equations modified with respect to standard fluid dynamics? Are there constraints coming from symmetries and entropy production (Amoretti et al., 2023)? And how should we interpret these physically?
At its core, hydrodynamics is a many-body low-energy effective theory for the long-wavelength, long-timescale dynamics of conserved charges in systems close to thermodynamic equilibrium. It has a wide range of applications spanning from nuclear physics, astrophysics, cosmology, and more recently strongly-interacting electronic phases of matter. In solid-state systems, however, symmetries are often only approximate, and softly broken by the presence of the lattice, impurities, and defects, or because the symmetry is accidental. Therefore, the hydrodynamic regime must be expanded to include weak non-conservation effects, which lead to a theory known as quasihydrodynamics. In this thesis we make progress in understanding the theory of (quasi) hydrodynamics, with a specific focus on applications to condensed matter systems and their holographic description.
@phdthesis{Martinoia:2024cbw,author={Martinoia, Luca},title={{Developments in quasihydrodynamics}},eprint={2403.14254},archiveprefix={arXiv},primaryclass={hep-th},doi={10.15167/martinoia-luca_phd2024-03-01},school={University of Genoa},month=mar,year={2024},}
JHEP
Relaxation terms for anomalous hydrodynamic transport in Weyl semimetals from kinetic theory
We consider as a model of Weyl semimetal thermoelectric transport a \((3+1)\)-dimensional charged, relativistic and relaxed fluid with a \(U(1)_V\times U(1)_ A\) chiral anomaly. We take into account all possible mixed energy, momentum, electric and chiral charge relaxations, and discover which are compatible with electric charge conservation, Onsager reciprocity and a finite DC conductivity. We find that all relaxations respecting these constraints necessarily render the system open and violate the second law of thermodynamics. We then demonstrate how the relaxations we have found arise from kinetic theory and a modified relaxation time approximation. Our results lead to DC conductivities that differ from those found in the literature opening the path to experimental verification.
@article{Amoretti:2023hpb,author={Amoretti, Andrea and Brattan, Daniel K. and Martinoia, Luca and Matthaiakakis, Ioannis and Rongen, Jonas},title={{Relaxation terms for anomalous hydrodynamic transport in Weyl semimetals from kinetic theory}},eprint={2309.05692},archiveprefix={arXiv},primaryclass={hep-th},reportnumber={CPHT-RR060.092023},doi={10.1007/JHEP02(2024)071},journal={JHEP},publisher={Springer},volume={02},pages={071},month=feb,year={2024},}
We consider entropy generating flows for fluids that achieve a steady state in the presence of a driving electric field. Having chosen one among the space of stationarity constraints that define such flows we show how energy and momentum relaxation are related in the presence of dissipation. Furthermore, we find that if such a fluid obeys Onsager reciprocity then the incoherent conductivity must be identically zero and consequently makes no contribution to the observable AC or DC charge conductivities.
@article{Amoretti:2024jig,author={Amoretti, Andrea and Brattan, Daniel K. and Martinoia, Luca and Rongen, Jonas},title={{Dissipative electrically driven fluids}},eprint={2407.18856},archiveprefix={arXiv},primaryclass={cond-mat.stat-mech},journal={JHEP},publisher={Springer},month=dec,doi={https://doi.org/10.1007/JHEP12(2024)114},year={2024},volume={12},pages={114},google_scholar_id={_FxGoFyzp5QC}}
Existing hydrodynamic models of charged fluids consider any external electric field acting on the fluid as either first order in the hydrodynamic derivative expansion and completely arbitrary or zeroth order but constrained by the fluid’s chemical potential. This is in tension with experiments on charged fluids, where the electric field is both zeroth order and completely arbitrary. In this work, we take the first step at resolving this conundrum by introducing a new class of hydrodynamic stationary states, including an arbitrary zeroth order electric field, upon which hydrodynamics can be built. We achieve this by first writing down the hydrostatic constitutive relations for a boost-agnostic charged fluid up to first order in derivatives. Then we introduce suitable energy and momentum relaxation terms to balance the influence of the electric field on the fluid. This analysis leads to a new hydrostatic constraint on the spatial fluid velocity, which can be used to define our class of states. This constraint generalizes to the realm of hydrodynamics a similar constraint on the velocity found in the Drude model of electronic transport. Our class of states exhibits non-trivial thermo-electric transport even at ideal order, since it hosts non-zero DC electric and heat currents. We derive the explicit form of the corresponding conductivities and show they depend non-linearly on the electric field.
@article{Amoretti:2022ovc,author={Amoretti, Andrea and Brattan, Daniel K. and Martinoia, Luca and Matthaiakakis, Ioannis},title={{Non-dissipative electrically driven fluids}},eprint={2211.05791},archiveprefix={arXiv},primaryclass={hep-th},doi={10.1007/JHEP05(2023)218},journal={JHEP},publisher={Springer},volume={05},pages={218},month=may,year={2023},}
Phys.Rev.D
Restoring time-reversal covariance in relaxed hydrodynamics
In hydrodynamics, for generic relaxations, the stress tensor and \(U(1)\) charge current two-point functions are not time-reversal covariant. This remains true even if the Martin-Kadanoff procedure happens to yield Onsager reciprocal correlators. We consider linearized relativistic hydrodynamics on Minkowski space in the presence of energy, \(U(1)\) charge, and momentum relaxation. We then show how one can find the minimal relaxed hydrodynamic framework that does yield two-point functions consistent with time-reversal covariance. We claim the same approach naturally applies to boost agnostic hydrodynamics and its limits (e.g., Carrollian, Galilean, and Lifshitz fluids).
@article{Amoretti:2023vhe,author={Amoretti, Andrea and Brattan, Daniel K. and Martinoia, Luca and Matthaiakakis, Ioannis},title={{Restoring time-reversal covariance in relaxed hydrodynamics}},eprint={2304.01248},archiveprefix={arXiv},primaryclass={hep-th},reportnumber={CPHT-RR015.042023},doi={10.1103/PhysRevD.108.056003},journal={Phys. Rev. D},publisher={American Physical Society,},volume={108},number={5},pages={056003},month=sep,year={2023},}
2021
JHEP
Hydrodynamic magneto-transport in holographic charge density wave states
We employ hydrodynamics and gauge/gravity to study magneto-transport in phases of matter where translations are broken (pseudo-)spontaneously. First we provide a hydrodynamic description of systems where translations are broken homogeneously at nonzero lattice pressure and magnetic field. This allows us to determine analytic expressions for all the relevant transport coefficients. Next we construct holographic models of those phases and determine all the DC conductivities in terms of the dual black hole geometry. Combining the hydrodynamic and holographic descriptions we obtain analytic expression for the AC thermo-electric correlators. These are fixed in terms of the black hole geometry and a pinning frequency we determine numerically. We find an excellent agreement between our hydrodynamic and holographic descriptions and show that the holographic models are good avatars for the study of magneto-phonons.
@article{Amoretti:2021lll,author={Amoretti, Andrea and Arean, Daniel and Brattan, Daniel K. and Martinoia, Luca},title={{Hydrodynamic magneto-transport in holographic charge density wave states}},eprint={2107.00519},archiveprefix={arXiv},primaryclass={hep-th},doi={10.1007/JHEP11(2021)011},journal={JHEP},volume={11},pages={011},month=nov,year={2021},}
