Papers

2025

1. J. Stat. Mech.

   

   The Hamiltonian mechanics of exotic particles

   Andrea Amoretti, Daniel K. Brattan, and Luca Martinoia

   Journal of Statistical Mechanics, Dec 2025

   Abs DOI arXiv Bib HTML PDF

   

   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.

   @article{Amoretti:2025jlw,
     author = {Amoretti, Andrea and Brattan, Daniel K. and Martinoia, Luca},
     title = {{The Hamiltonian mechanics of exotic particles}},
     eprint = {2506.13848},
     archiveprefix = {arXiv},
     journal = {Journal of Statistical Mechanics},
     primaryclass = {cond-mat.stat-mech},
     doi = {https://doi.org/10.1088/1742-5468/ae1572},
     month = dec,
     pages = {50},
     year = {2025},
   }

2. Acta Phys.Polon.B

   

   A note on the canonical approach to hydrodynamics and linear response theory

   Luca Martinoia and Rajeev Singh

   Acta Physica Polonica B, Feb 2025

   Abs DOI arXiv Bib HTML PDF

   

   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.

   @article{Martinoia:2024hip,
     author = {Martinoia, Luca and Singh, Rajeev},
     title = {{A note on the canonical approach to hydrodynamics and linear response theory}},
     eprint = {2408.10698},
     archiveprefix = {arXiv},
     primaryclass = {hep-th},
     journal = {Acta Physica Polonica B},
     doi = {10.5506/APhysPolB.56.1-A4},
     month = feb,
     volume = {56},
     pages = {44},
     year = {2025},
   }

2024

1. JHEP

   

   Dissipative electrically driven fluids

   Andrea Amoretti, Daniel K. Brattan, Luca Martinoia, and Jonas Rongen

   JHEP, Dec 2024

   Abs DOI arXiv Bib HTML PDF

   

   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 = {10.1007/JHEP12(2024)114},
     year = {2024},
     volume = {12},
     pages = {114},
   }

2. Phys.Rev.E

   

   Thermodynamic constraints and exact scaling exponents of flocking matter

   Andrea Amoretti, Daniel K. Brattan, and Luca Martinoia

   Phys. Rev. E, Nov 2024

   Abs DOI arXiv Bib HTML PDF

   

   We use advances in the formalism of boost agnostic passive fluids to constrain transport in polar active fluids, which are subsequently described by the Toner-Tu equations. Acknowledging that the system fundamentally breaks boost symmetry, we compel what were previously entirely phenomenological parameters in the Toner-Tu model to satisfy precise relationships among themselves. Consequently, we propose a thermodynamic argument to determine the scalings of the transport coefficients under dynamical renormalization group flow given that the scaling of the noise correlator is exact, as has been supported numerically. These scalings perfectly agree with the results of recent state-of-the-art numerical simulation and experiments.

   @article{Amoretti:2024obt,
     author = {Amoretti, Andrea and Brattan, Daniel K. and Martinoia, Luca},
     title = {{Thermodynamic constraints and exact scaling exponents of flocking matter}},
     eprint = {2405.02283},
     archiveprefix = {arXiv},
     primaryclass = {cond-mat.stat-mech},
     doi = {10.1103/PhysRevE.110.054108},
     journal = {Phys. Rev. E},
     publisher = {American Physical Society,},
     volume = {110},
     number = {5},
     pages = {054108},
     month = nov,
     year = {2024},
   }

3. JHEP

   

   Relaxation terms for anomalous hydrodynamic transport in Weyl semimetals from kinetic theory

   Andrea Amoretti, Daniel K. Brattan, Luca Martinoia, Ioannis Matthaiakakis, and Jonas Rongen

   JHEP, Feb 2024

   Abs DOI arXiv Bib HTML PDF

   

   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},
   }

2023

1. Phys.Rev.D

   

   Restoring time-reversal covariance in relaxed hydrodynamics

   Andrea Amoretti, Daniel K. Brattan, Luca Martinoia, and Ioannis Matthaiakakis

   Phys. Rev. D, Sep 2023

   Abs DOI arXiv Bib HTML PDF

   

   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},
     preview2 = {PRD.jpg},
   }

2. Phys.Rev.D

   

   Leading order magnetic field dependence of conductivities in anomalous hydrodynamics

   Andrea Amoretti, Daniel K. Brattan, Luca Martinoia, and Ioannis Matthaiakakis

   Phys. Rev. D, Jul 2023

   Abs DOI arXiv Bib HTML PDF

   

   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.

   @article{Amoretti:2022vxq,
     author = {Amoretti, Andrea and Brattan, Daniel K. and Martinoia, Luca and Matthaiakakis, Ioannis},
     title = {{Leading order magnetic field dependence of conductivities in anomalous hydrodynamics}},
     eprint = {2212.09761},
     archiveprefix = {arXiv},
     primaryclass = {hep-th},
     reportnumber = {CPHT-RR064.122022},
     doi = {10.1103/PhysRevD.108.016003},
     journal = {Phys. Rev. D},
     publisher = {American Physical Society,},
     volume = {108},
     number = {1},
     pages = {016003},
     month = jul,
     year = {2023},
     preview2 = {PRD.jpg},
   }

3. JHEP

   

   Non-dissipative electrically driven fluids

   Andrea Amoretti, Daniel K. Brattan, Luca Martinoia, and Ioannis Matthaiakakis

   JHEP, May 2023

   Abs DOI arXiv Bib HTML PDF

   

   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},
     preview2 = {JHEP.jpg},
   }

2022

1. Phys.Rev.Research

   

   Destroying superconductivity in thin films with an electric field

   Andrea Amoretti, Daniel K. Brattan, Nicodemo Magnoli, Luca Martinoia, Ioannis Matthaiakakis, and Paolo Solinas

   Phys. Rev. Res., Sep 2022

   Abs DOI arXiv Bib HTML PDF

   

   In this paper, we use a Ginzburg-Landau approach to show that a suitably strong electric field can drive a phase transition from a superconductor to a normal metal. The transition is induced by taking into account corrections to the permittivity due to the superconductive gap and persists even when screening effects are considered. We test the model against recent experimental observations in which a strong electric field has been observed to control the supercurrent in superconducting thin films. We find excellent agreement with the experimental data and are able to explain several observed features. We additionally suggest a way to test our theoretical proposal via superconductor-superconductor electron tunneling.

   @article{Amoretti:2022smp,
     author = {Amoretti, Andrea and Brattan, Daniel K. and Magnoli, Nicodemo and Martinoia, Luca and Matthaiakakis, Ioannis and Solinas, Paolo},
     title = {{Destroying superconductivity in thin films with an electric field}},
     eprint = {2202.00687},
     archiveprefix = {arXiv},
     primaryclass = {cond-mat.supr-con},
     doi = {10.1103/PhysRevResearch.4.033211},
     journal = {Phys. Rev. Res.},
     publisher = {American Physical Society,},
     volume = {4},
     number = {3},
     pages = {033211},
     month = sep,
     year = {2022},
     preview2 = {PRR.png},
   }

2021

1. JHEP

   

   Hydrodynamic magneto-transport in holographic charge density wave states

   Andrea Amoretti, Daniel Arean, Daniel K. Brattan, and Luca Martinoia

   JHEP, Nov 2021

   Abs DOI arXiv Bib HTML PDF

   

   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},
     preview2 = {JHEP.jpg},
   }

Thesis

2024

1. PhD thesis

   

   Developments in quasihydrodynamics

   Luca Martinoia

   University of Genoa, Mar 2024

   Abs DOI arXiv Bib PDF

   

   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},
   }

2020

1. Master thesis

   

   Anomalous hydrodynamic description of thermoelectric transport in a Weyl semimetal

   Luca Martinoia

   University of Genoa, Sep 2020

   Bib PDF

   @mastersthesis{Martinoia:2021,
     author = {Martinoia, Luca},
     title = {{Anomalous hydrodynamic description of thermoelectric transport in a Weyl semimetal}},
     school = {University of Genoa},
     month = sep,
     year = {2020},
   }