Publications

1. 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).
   
   

2. Thermodynamic constraints and exact scaling exponents of flocking matter
   Amoretti, Andrea; Brattan, Daniel K.; Martinoia, Luca
   
   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.
   
   Physical Review E, Volume 110, Issue 5, id.054108, 11 pp (November 2024).
   
   

3. Relaxed hydrodynamic theory of electrically driven nonequilibrium steady states
   Brattan, Daniel K.;  Matsumoto, Masataka; Baggioli, Matteo; Amoretti, Andrea
   
   The capability of hydrodynamics to accurately describe slow and long-wavelength fluctuations around nonequilibrium steady states (NESS), characterized by a stationary flow of energy or matter in the presence of a driving force, remains an open question. In this study, we explicitly construct a hydrodynamic description of electrically driven nonequilibrium charged steady states in the limit in which the relaxation of the first nonhydrodynamic excitation is parametrically slow. Our approach involves introducing gapped modes and extending the effective description into a relaxed hydrodynamic theory (RHT). Leveraging the gauge-gravity duality as a tool for controlled computations within nonequilibrium systems, we establish an ultraviolet complete model for these NESS that confirms the validity of our RHT. In summary, our findings provide a concrete realization of the validity of hydrodynamics beyond thermal equilibrium, offering valuable insights into the dynamics of nonequilibrium systems.
   
   Physical Review Research, Volume 6, Issue 4, id.043097, 14 pp (November 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. On the hydrodynamics of (2 + 1)-dimensional strongly coupled relativistic theories in an external magnetic field
   Amoretti, Andrea; Brattan, Daniel K.
   
   In this paper, we review recent progress on relativistic hydrodynamics in (2 + 1) dimensions with an external magnetic field. We discuss the formalism allowing for momentum loss due to the explicit and spontaneous breaking of translation invariance by scalar operators. We also compare to some results from the gauge/gravity correspondence.
   
   Mod. Phys. Lett. A 37 21, 2230010 (September 2022).
   
   

9. Hydrodynamic magneto-transport in holographic charge density wave states
   Amoretti, Andrea; Areán, Daniel; Brattan, Daniel K.; Martinoia, Luca
   
   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.
   
   JHEP 11 011 (November 2021).
   
   

10. 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).
    
    

11. 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).
    
    

12. Hydrodynamical description for magneto-transport in the strange metal phase of Bi-2201
    Amoretti, Andrea; Meinero, Martina; Brattan, Daniel K.; Caglieris, Federico; Giannini, Enrico; Affronte, Marco; Hess, Christian; Buechner, Bernd; Magnoli, Nicodemo;  Putti, Marina
    
    High-temperature superconductors are strongly coupled systems which present a complicated phase diagram with many coexisting phases. This makes it difficult to understand the mechanism which generates their singular transport properties. Hydrodynamics, which mostly relies on the symmetries of the system without referring to any specific microscopic mechanism, constitutes a promising framework to analyze these materials. In this paper we show that, in the strange metal phase of the cuprates, a whole set of transport coefficients are described by a universal hydrodynamic framework once one accounts for the effects of quantum critical charge-density waves. We corroborate our theoretical prediction by measuring the DC transport properties of Bi-2201 close to optimal doping, proving the validity of our approach. Our argument can be used as a consistency check to understand the universality class governing the behavior of high-temperature cuprate superconductors.
    
    Phys. Rev. Research 2, 023387 (June 2020).

13. How to construct a holographic EFT for phonons
    Amoretti, Andrea
    
    These notes are based on a series of lectures given at the XV Modave Summer School in September, 2019. The course was organized in five lectures on Holographic techniques applied to condensed matter physics. In order to be self consistent, in the first three lectures I introduced the basic concepts of the so called holographic dictionary. Since AdS/CFT is by now a very well established framework to analyze strongly coupled quantum field theories, and many good reviews have been written on the topic I decided to refer to the existing literature for the basic derivation of the holographic dictionary. What illustrated in here consists instead in the analysis of a holographic model which breaks translation spontaneously or pseudo-spontaneously, the holographic realization of a charge density wave. Part of the computations outlined in this manuscript, and in particular the derivation of the Ward Identities, have never appeared in the literature so far. The paper constitute a small exercise which a reader interested in learning more advanced techniques to analyze bottom-up holographic models can use as a warm up to eventually tackle more difficult tasks.
    
    Proceedings of Science, Volume 384 - XV Modave Summer School in Mathematical Physics (April 2020).

14. Gapless and gapped holographic phonons
    Amoretti, Andrea; Areán, Daniel; Goutéraux, Blaise; Musso, Daniele
    
    We study a holographic model where translations are both spontaneously and explicitly broken, leading to the presence of (pseudo)-phonons in the spectrum. The weak explicit breaking is due to two independent mechanisms: a small source for the condensate itself and additional linearly space-dependent marginal operators. The low energy dynamics of the model is described by Wigner crystal hydrodynamics. In absence of a source for the condensate, the phonons remain gapless, but momentum is relaxed. Turning on a source for the condensate damps and pins the phonons. Finally, we verify that the universal relation between the phonon damping rate, mass and diffusivity reported in [1] continues to hold in this model for weak enough explicit breaking.
    
    JHEP 01 058 (January 2020).
    
    

15. Universal relaxation in a holographic metallic density wave phase
    Amoretti, Andrea; Areán, Daniel; Goutéraux, Blaise; Musso, Daniele
    
    In this Letter, we uncover a universal relaxation mechanism of pinned density waves, combining gauge-gravity duality and effective field theory techniques. Upon breaking translations spontaneously, new gapless collective modes emerge, the Nambu-Goldstone bosons of broken translations. When translations are also weakly broken (e.g., by disorder or lattice effects), these phonons are pinned with a mass 𝑚 and damped at a rate Ω, which we explicitly compute. This contribution to Ω is distinct from that of topological defects. We show that Ω ≃𝐺⁡𝑚2⁢Ξ, where 𝐺 is the shear modulus and Ξ is related to a diffusivity of the purely spontaneous state. This result follows from the smallness of the bulk and shear moduli, as would be the case in a phase with fluctuating translational order. At low temperatures, the collective modes relax quickly into the heat current, so that late time transport is dominated by the thermal diffusivity. In this regime, the resistivity in our model is linear in temperature and the ac conductivity displays a significant rearranging of the degrees of freedom, as spectral weight is shifted from an off-axis, pinning peak to a Drude-like peak. These results could shed light on transport properties in cuprate high 𝑇𝑐 superconductors, where quantum critical behavior and translational order occur over large parts of the phase diagram and transport shows qualitatively similar features.
    
    Phys. Rev. Lett. 123, 211602 November 2019).
    
    

16. Diffusion and universal relaxation of holographic phonons
    Amoretti, Andrea; Areán, Daniel; Goutéraux, Blaise; Musso, Daniele
    
    In phases where translations are spontaneously broken, new gapless degrees of freedom appear in the low energy spectrum (the phonons). At long wavelengths, they couple to small fluctuations of the conserved densities of the system. This mixing is captured by new diffusive transport coefficients, as well as qualitatively different collective modes, such as shear sound modes. We use Gauge/Gravity duality to model such phases and analytically compute the corresponding diffusivities in terms of data of the dual background black hole solution. In holographic quantum critical low temperature phases, we show that these diffusivities are governed by universal relaxation of the phonons into the heat current when the dynamical critical exponent z > 2. Finally, we compute the spectrum of transverse collective modes and show that their dispersion relation matches the dispersion relation of the shear sound modes of the hydrodynamic theory of crystalline solids.
    
    JHEP 10 068 (October 2019).
    
    

17. Effective holographic theory of charge density waves
    Amoretti, Andrea; Areán, Daniel; Goutéraux, Blaise; Musso, Daniele
    
    We use gauge/gravity duality to write down an effective low energy holographic theory of charge density waves. We consider a simple gravity model which breaks translations spontaneously in the dual field theory in a homogeneous manner, capturing the low energy dynamics of phonons coupled to conserved currents. We first focus on the leading two-derivative action, which leads to excited states with nonzero strain. We show that including subleading quartic derivative terms leads to dynamical instabilities of  translation invariant states and to stable phases breaking translations spontaneously. We compute analytically the real part of the electric conductivity. The model allows to construct Lifshitz-like hyperscaling violating quantum critical ground states breaking translations spontaneously. At these critical points, the real part of the dc conductivity can be metallic or insulating.
    
    Phys. Rev. D 97, 086017 (April 2018).
    
    

18. DC resistivity of quantum critical, charge density wave states from gauge-gravity duality
    Amoretti, Andrea; Areán, Daniel; Goutéraux, Blaise; Musso, Daniele
    
    In contrast to metals with weak disorder, the resistivity of weakly pinned charge density waves (CDWs) is not controlled by irrelevant processes relaxing momentum. Instead, the leading contribution is governed by incoherent, diffusive processes which do not drag momentum and can be evaluated in the clean limit. We compute analytically the dc resistivity for a family of holographic charge density wave quantum critical phases and discuss its temperature scaling. Depending on the critical exponents, the ground state can be conducting or insulating. We connect our results to dc electrical transport in underdoped cuprate high  superconductors. We conclude by speculating on the possible relevance of unstable, semilocally critical CDW states to the strange metallic region.
    
    Phys. Rev. Lett. 120, 171603 (April 2018).
    
    

19. Chasing the cuprates with dilatonic dyons
    Amoretti, Andrea; Baggioli, Matteo; Magnoli, Nicodemo; Musso, Daniele
    
    Magnetic field and momentum dissipation are key ingredients in describing condensed matter systems. We include them in gauge/gravity and systematically explore the bottom-up panorama of holographic IR effective field theories based on bulk Einstein-Maxwell Lagrangians plus scalars. The class of solutions here examined appears insufficient to capture the phenomenology of charge transport in the cuprates. We analyze in particular the temperature scaling of the resistivity and of the Hall angle. Keeping an open attitude, we illustrate weak and strong points of the approach.
    
    JHEP 06 113 (June 2016).
    
    

20. Bounds on charge and heat diffusivities in momentum dissipating holography
    Amoretti, Andrea; Braggio, Alessandro; Magnoli, Nicodemo; Musso, Daniele
    
    Inspired by a recently conjectured universal bound for thermo-electric diffusion constants in quantum critical, strongly coupled systems and relying on holographic analytical computations, we investigate the possibility of formulating Planckian bounds in different holographic models featuring momentum dissipation. For a certain family of solutions to a simple massive gravity dilaton model at zero charge density we find linear in temperature resistivity and entropy density alongside a constant electric susceptibility. In addition we explicitly find that the sum of the thermo-electric diffusion constants is bounded.
    
    JHEP 07 102 (July 2015).
    
    

21. Analytic dc thermoelectric conductivities in holography with massive gravitons
    Amoretti, Andrea; Braggio, Alessandro; Maggiore, Nicola; Magnoli, Nicodemo; Musso, Daniele
    
    We provide an analytical derivation of the thermoelectric transport coefficients of the simplest momentum-dissipating model in gauge/gravity where the lack of momentum conservation is realized by means of explicit graviton mass in the bulk. We rely on the procedure recently described by Donos and Gauntlett for holographic models where momentum dissipation is realized through nontrivial scalars. The analytical approach confirms and supports the results found previously by means of numerical computations and the associated holographic renormalization procedure. Importantly, it also provides a precise identification of the range of validity of the hydrodynamic approximation.
    
    Phys.Rev.D 91 2, 025002 (January 2015).
    
    

22. Thermo-electric transport in gauge/gravity models with momentum dissipation
    Amoretti, Andrea; Braggio, Alessandro; Maggiore, Nicola; Magnoli, Nicodemo; Musso, Daniele
    
    We present a systematic definition and analysis of the thermo-electric linear response in gauge/gravity systems focusing especially on models with massive gravity in the bulk and therefore momentum dissipation in the dual field theory. A precise treatment of finite counter-terms proves to be essential to yield a consistent physical picture whose hydrodynamic and beyond-hydrodynamics behaviors noticeably match with field theoretical expectations. The model furnishes a possible gauge/gravity description of the crossover from the quantum-critical to the disorder-dominated Fermi-liquid behaviors, as expected in graphene.
    
    JHEP 09 160 (September 2014).