Publications

1. The Hamiltonian mechanics of exotic particles
   Amoretti, Andrea; Brattan, Daniel K.; Martinoia, Luca
   
   We develop Hamiltonian mechanics on Aristotelian manifolds, which lack local boost symmetry and admit absolute time and space structures. We construct invariant phase space dynamics, define free Hamiltonians, and establish a generalized Liouville theorem. Conserved quantities are identified via lifted Killing vectors. Extending to kinetic theory, we show that the charge current and stress tensor reproduce ideal hydrodynamics at leading order, with the ideal gas law emerging universally. Our framework provides a geometric and dynamical foundation for systems where boost invariance is absent, with applications including but not limited to: condensed matter, active matter and optimization dynamics.
   
   arXiv 2506.13848 (June 2025).
   
   

2. A note on the canonical approach to hydrodynamics and linear response theory
   Martinoia, Luca; Singh, Rajeev
   
   This note provides a comprehensive examination of the various approaches to formulating relativistic hydrodynamics, with a particular emphasis on the canonical approach. Relativistic hydrodynamics plays a crucial role in understanding the behavior of fluids in high-energy astrophysical phenomena and heavy-ion collisions. The canonical approach is explored in detail, highlighting its foundational principles, mathematical formulations, and practical implications in modeling relativistic fluid dynamics. Following this, we delve into the linear response theory, elucidating its relevance in the context of hydrodynamics. We analyze the response of relativistic fluids to external perturbations, discussing the theoretical framework and key results. This dual focus aims to bridge the gap between theoretical foundations and practical applications, offering a robust perspective on the dynamic interplay between relativistic hydrodynamics and linear response theory.
   
   Acta Phys. Pol. B 56, 1-A4 (February 2025).
   
   

3. Dissipative electrically driven fluids
   Amoretti, Andrea; Brattan, Daniel K.; Martinoia, Luca; Rongen, Jonas 
   
   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.
   
   JHEP 12 114 (December 2024).
   
   

4. Relaxation terms for anomalous hydrodynamic transport in Weyl semimetals from kinetic theory
   Amoretti, Andrea; Brattan, Daniel K.; Martinoia, Luca; Matthaiakakis, Ioannis; Rongen, Jonas
   
   We consider as a model of Weyl semimetal thermoelectric transport a (3 + 1)-dimensional charged, relativistic and relaxed fluid with a U(1)_V × 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.
   
   JHEP 02 071 (February 2024).
   
   

5. Restoring time-reversal covariance in relaxed hydrodynamics
   Amoretti, Andrea; Brattan, Daniel K.; Martinoia, Luca; Matthaiakakis, Ioannis
   
   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).
   
   Phys. Rev. D 108 5, 5 (September 2023).
   
   

6. Leading order magnetic field dependence of conductivities in anomalous hydrodynamics
   Amoretti, Andrea; Brattan, Daniel K.; Martinoia, Luca; Matthaiakakis, Ioannis
   
   We show that literature results claimed for the magnetic field dependence of the longitudinal conductivity in anomalous first-order hydrodynamics are frame dependent at this derivative order. In particular, we focus on (3+1)-dimensional hydrodynamics in the presence of a constant O(∂) magnetic field with a  U(1) chiral anomaly and demonstrate that, for constitutive relations up to and including order one in derivatives, the anomaly drops out of the longitudinal conductivity. In particular, magnetic field dependent terms that were previously found in the literature only enter the nonzero frequency thermoelectric conductivities through explicitly frame dependent pieces indicating that they are not physical. This issue can be avoided entirely by incorporating the magnetic field into the fluid’s equilibrium state.
   
   Phys. Rev. D 108 1, 1 (July 2023).
   
   

7. Non-dissipative electrically driven fluids
   Amoretti, Andrea; Brattan, Daniel K.; Martinoia, Luca; Matthaiakakis, Ioannis
   
   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.
   
   JHEP 05 218 (May 2023).
   
   

8. Hydrodynamic magneto-transport in charge density wave states
   Amoretti, Andrea; Areán, Daniel; Brattan, Daniel K.; Magnoli, Nicodemo
   
   In this paper we study the dynamical properties of charged systems immersed in an external magnetic field and perturbed by a set of scalar operators breaking translations either spontaneously or pseudo-spontaneously. By combining hydrodynamic and quantum field theory arguments we provide analytic expressions for all the hydrodynamic transport coefficients relevant for the diffusive regime in terms of thermodynamic quantities and DC thermo-electric conductivities. This includes the momentum dissipation rate. We shed light on the role of the momentum dissipation rate in the transition between the pseudo-spontaneous and the purely explicit regimes in this class of systems. Finally, we clarify several relations between the hydrodynamic transport coefficients which have been observed in the holographic literature of charge density wave models.
   
   Journal of High Energy Physics, Volume 2021, Issue 05, article id. 27 (May 2021).
   
   

9. Magneto-thermal transport implies an incoherent Hall conductivity
   Amoretti, Andrea; Brattan, Daniel K.; Magnoli, Nicodemo; Scanavino, Marcello
   
   We consider magnetohydrodynamics with an external magnetic field. We find that in general one must allow for a non-zero incoherent Hall conductivity to correctly describe the DC longitudinal and Hall thermal conductivities beyond order zero in the magnetic field expansion. We apply our result to the dyonic black hole, determining the incoherent Hall conductivity in that case, and additionally prove that the existence of this transport coefficient leads to a significantly better match between the hydrodynamic and AC thermo-electric correlators.
   
   JHEP 08 097 (August 2020).