arXiv subjects

Esteban Calzetta

Publications and source records attributed to Esteban Calzetta.

At least 19 recordsLinked to original sources

arXiv2026

Scale invariant solutions in relativistic hydrodynamics

The goal of this work is to describe the scale invariant solutions of a typical relativistic hydrodynamic model. We shall take as representative model an Israel-Stewart framework, where the energy-momentum conservation laws for a conformal invariant fluid are supplemented by a Cattaneo-Maxwell equation for its viscous energy-momentum tensor. In these models the viscous energy-momentum tensor relaxes to its Landau-Lifshitz value on a finite time scale. We assume the parameters of the model depend on the speed of light $c$ in such a way that as $c\to\infty$ the fluid becomes an incompressible fluid obeying the Navier-Stokes equations. We seek the scale invariant solutions for this model and find that for finite $c$ there are two basic patterns, one which reproduces Kolmogorov turbulence when $c\to\infty$, and another whose damping rate diverges in that limit. We point out the scaling relations that allow the latter flow pattern to sustain an entropy cascade.

physics.flu-dyn↗

arXiv2026

A First-Principles Thermodynamic Uncertainty Relation for Shortcuts to Adiabaticity

We study the fundamental limitations of implementing time-dependent Hamiltonian protocols when ''time'' is provided by a quantum clock rather than an external classical parameter. For a parametric harmonic oscillator controlled through a shortcut-to-adiabaticity (STA) schedule and coupled to a minimal clock degree of freedom, tracing out the clock yields an effective reduced dynamics that is a mixture of unitary Gaussian trajectories. Within a noise-dominated regime, we compute the energetic deviation from the target STA outcome and its fluctuations, together with the fidelity to the target evolution and the purity loss of the reduced state, for vacuum and coherent initial states. Combining these observables produces a thermodynamic-uncertainty-type tradeoff that links achievable precision to an irreducible loss of purity set by the clock precision and the protocol sensitivity.

quant-ph↗

arXiv2025

Hydrodynamic models of reheating

We develop a causal hydrodynamic model that provides an effective macroscopic description of the field-theoretic dynamics during the early stages of reheating. The inflaton condensate is treated as a homogeneous background coupled to a relativistic fluid that represents its inhomogeneous fluctuations. Within the divergence-type theory framework derived from kinetic considerations, the model captures essential dissipative and non-equilibrium effects while remaining stable and causal. We find that the coupling between the oscillating condensate and the fluid induces a parametric resonance in the tensor sector, leading to the amplification of the viscous stress tensor and the generation of gravitational waves with a characteristic spectral peak. The predicted spectrum agrees with lattice simulations performed with CosmoLattice. This hydrodynamic approach offers an effective bridge between microscopic field dynamics and macroscopic cosmological observables.

hep-ph↗

arXiv2025

Statistical closures from the Martin-Siggia and Rose approach to turbulence

The goal of this paper is to study the statistical closures suggested by the Martin-Siggia and Rose approach to statistical turbulence. We find that the formalism leads to a Bethe-Salpeter equation for the three point correlation of the velocity field. In the leading order approximation this equation becomes an explicit expression. We discuss under which approximations this closure reduces to that proposed in W D McComb and S R Yoffe, A formal derivation of the local energy transfer (LET) theory of homogeneous turbulence, J. Phys. A: Math. Theor. 50, 375501 (2017). This suggests ways to improve upon this closure by dropping these restrictions, resumming the perturbative expansion and/or applying renormalization group techniques.

nlin.CD↗

arXiv2024

On the Energy Spectrum of Non-Newtonian Turbulence

The goal of this paper is to propose a theoretical framework to study homogeneous and isotropic turbulence in a viscoelastic fluid, regarded as a perturbation of a Newtonian incompressible fluid, where the fluid relaxation time, or else the Weissenberg number, plays the role of small parameter. We use a Martin-Siggia-Rose framework to obtain a formal expression for the velocity correlation function of the non-Newtonian flow, and we expand this formal expression to linear order in the relaxation time. The coefficients in this expansion are correlation functions of the base Newtonian flow. We do not derive these correlations, instead we replace them by their values according to K41 theory, which could be regarded as an extreme form of renormalization. While substantial work will be necessary to validate the model against numerical and experimental data, preliminary results are encouraging.

physics.flu-dyn↗

arXiv2024

Propagation speeds of relativistic conformal fluids from a generalized relaxation time approximation

We compute the propagation speeds for a conformal real relativistic fluid. We begin from a kinetic equation in the relaxation time approximation, where the relaxation time is an arbitrary function of the particle energy in the Landau frame. We propose a parameterization of the one particle distribution function designed to contain a second order Chapman-Enskog solution as a particular case. We derive the hydrodynamic equations applying the moments method to this parameterized one particle distribution function, and solve for the propagation speeds of linearized scalar, vector and tensor perturbations. For relaxation times of the form $\tau=\tau_0(-\beta_{\mu}p^{\mu})^{-a}$, with $-\infty< a<2$, where $\beta_{\mu}=u_{\mu}/T$ is the temperature vector in the Landau frame, we show that the Anderson-Witting prescription $a=1$ yields the fastest speeds.

hep-th↗

arXiv2023

Limits on quantum measurement engines

A quantum measurement involves energy exchanges between the system to be measured and the measuring apparatus. Some of them involve energy losses, for example because energy is dissipated into the environment or is spent in recording the measurement outcome. Moreover, these processes take time. For this reason, these exchanges must be taken into account in the analysis of a quantum measurement engine, and set limits to its efficiency and power. We propose a quantum engine based on a spin 1/2 particle in a magnetic field and study its fundamental limitations due to the quantum nature of the evolution. The coupling with the electromagnetic vacuum is taken into account and plays the role of a measurement apparatus. We fully study its dynamics, work, power and efficiency.

quant-ph↗

arXiv2023

A coherent full microwave scattering formulation for random layered media

We present a fully coherent, analytic model of the backscattering intensity in all HH, HV, VH and VV channels, for the volume scattering of radiation from a layer of finite thickness, such as a vegetation layer over bare soil. We aim for a simple, not numerically intensive model which could be used either as forward model in a Bayesian estimation scheme, or else as a preliminary means to identify key features of a concrete problem, for its further analysis by more sophisticated theoretical and numerical approaches.

physics.optics↗

arXiv2022

Field Theory Approaches to Relativistic Hydrodynamics

Just as non relativistic fluids, oftentimes we find relativistic fluids in situations where random fluctuations cannot be ignored, thermal and turbulent fluctuations being the most relevant examples. Because of the theory's inherent nonlinearity, fluctuations induce deep and complex changes in the dynamics of the system. The Martin-Siggia-Rose technique is a powerful tool that allows us to translate the original hydrodynamic problem into a quantum field theory one, thus taking advantage of the progress in the treatment of quantum fields out of equilibrium. To demonstrate this technique, we shall consider the thermal fluctuations of the spin two modes of a relativistic fluid, in a theory where hydrodynamics is derived by taking moments of the Boltzmann equation under the relaxation time approximation.

hep-ph↗

arXiv2021

Steady asymptotic equilibria in conformal relativistic fluids

When one considers a shock wave in the frame where the shock is at rest, on either side one has a steady flow which converges to equilibrium away from the shock. However, hydrodynamics is unable to describe this flow if the asymptotic velocity is higher than the characteristic speed of the theory. We obtain an exact solution for the decay rate to equilibrium for a conformal fluid in kinetic theory under the relaxation time approximation, and compare it to two hydrodynamic schemes, one accounting for the second moments of the distribution function and thus equivalent, in the small deviations from equilibrium limit, to an Israel-Stewart framework, and another accounting for both second and third moments. While still having a finite characteristic speed, the second model is a significant improvement on the first.

nucl-th↗

arXiv2021

Linearized dispersion relations in viscous relativistic hydrodynamics

We compute the dispersion relations for scalar, vector and tensor modes of a viscous relativistic fluid, linearized around an equilibrium solution, for a divergence type theory (which, in the linearized theory, includes Israel-Stewart and anisotropic hydrodynamics as particular cases) and contrast them to the corresponding results derived from kinetic theory under the relaxation time approximation, and from causal first order theories. We conclude that all approaches give similar dynamics for the scalar and vector modes, while the particular divergence type theory presented here also contains propagating damped tensor waves, in agreement with kinetic theory. Non hydrodynamic tensor modes are also a feature of holographic fluids. These results support the application of hydrodynamics in problems involving the interaction between fluids and gravitational waves.

hep-ph↗

arXiv2021

Primordial Weibel instability

We study the onset of vector instabilities in the post-inflationary epoch of the Universe as a mechanism for primordial magnetic fields amplification. We assume the presence of a charged spectator scalar field arbitrarily coupled to gravity during Inflation in its vacuum de Sitter state. Gravitational particle creation takes place at the transition from Inflation to the subsequent Reheating stage and thus the vacuum field state becomes an excited many particles one. Consequently this state can be described as a real fluid, and we build out the hydrodynamic framework using second order theories for relativistic fluids with a relaxation time prescription for the collision integral. Given the high-temperature regime and the vanishing scalar curvature of the Universe during Reheating (radiation-dominated-type era), the fluid can be regarded as a conformal one. The large quantum fluctuations induced by the rapid transition from inflationary to effectively radiation dominated expansion become statistical fluctuations whereby both a charge excess and anisotropic pressures are produced in any finite domain. The precise magnitude of the effect for each scale is determined by the size of the averaging domain and the coupling to curvature. We look at domains which are larger than the horizon at the beginning of Reheating, but much smaller than our own horizon, and show that in a finite fraction of them the anisotropy and charge excess provide suitable conditions for a Weibel instability. If moreover the duration of reheating is shorter than the relaxation time of the fluid, then this instability can compensate or even overcome the conformal dilution of a primordial magnetic field. We show that the non-trivial topology of the magnetic field encoded in its magnetic helicity is also amplified if present.

astro-ph.HE↗

arXiv2020

Fully developed relativistic turbulence

We use a simple model consisting of energy-momentum tensor conservation and a Maxwell-Cattaneo equation for its viscous part to study nonlinear phenomena in a real relativistic fluid. We focus on new types of behavior without nonrelativistic equivalents, such as an entropy cascade driven by fluctuations in the tensor degrees of freedom of the theory. We write down the von K\'arm\'an-Howarth equations for this kind of turbulence, and consider the correlations corresponding to fully developed turbulence.

gr-qc↗

arXiv2020

Nonlinear Fluctuations in Relativistic Causal Fluids

In the Second Order Theories (SOT) of real relativistic fluids, the non-ideal properties of the flows are described by a new set of dynamical tensor variables. In this work we explore the non-linear dynamics of those variables in a conformal fluid. Among all possible SOTs, we choose to work with the Divergence Type Theories (DTT) formalism, which ensures that the second law of thermodynamics is fulfilled non-perturbatively. The tensor modes include two divergence-free modes which have no analog in theories based on covariant generalizations of the Navier-Stokes equation, and that are particularly relevant because they couple linearly to a gravitational field. To study the dynamics of this irreducible tensor sector, we observe that in causal theories such as DTTs, thermal fluctuations induce a stochastic stirring force, which excites the tensor modes while preserving energy momentum conservation. From fluctuation-dissipation considerations it follows that the random force is Gaussian with a white spectrum. The irreducible tensor modes in turn excite vector modes, which back-react on the tensor sector, thus producing a consistent non-linear, second order description of the divergence-free tensor dynamics. Using the Martin-Siggia-Rose (MSR) formalism plus the Two-Particle Irreducible Effective Action (2PIEA) formalism, we obtain the one-loop corrected equations for the relevant two-point correlation functions of the model: the retarded propagator and the Hadamard function. The overall result of the self-consistent dynamics of the irreducible tensor modes at this order is a depletion of the spectrum in the UV sector, which suggests that tensor modes could sustain an inverse entropy cascade.

hep-th↗

arXiv2020

Dissipative type theories for Bjorken and Gubser flows

We use the dissipative type theory (DTT) framework to solve for the evolution of conformal fluids in Bjorken and Gubser flows from isotropic initial conditions. The results compare well with both exact and other hydrodynamic solutions in the literature. At the same time, DTTs enforce the Second Law of thermodynamics as an exact property of the formalism, at any order in deviations from equilibrium, and are easily generalizable to more complex situations.

nucl-th↗

arXiv2020

Nonlinear Dynamics of Tensor Modes in Conformal Real Relativistic Fluids

In the Second Order Theories (SOT) of real relativistic fluids, the non-ideal properties are described by a new set of dynamical tensor variables. In this work we explore the non-linear dynamics of those modes in a conformal fluid. Among all possible SOTs, we choose to work with the Divergence Type Theories (DTT) formalism, which ensures that the second law of thermodynamics is satisfied non-perturbatively. In considering a perturbative scheme within this formalism, at next to leading order a set of Maxwell-Cattaneo equations is obtained, as in e.g. Israel-Stewart theories. The tensor modes include two divergence-free modes which have no analog in theories based on covariant Navier-Stokes equations, and that are particularly relevant because they may couple linearly to a gravitational field. To study the dynamics of this irreducible tensor sector, we observe that in causal theories such as DTTs, thermal fluctuations induce a stochastic stirring force in the equations of motion, which excites the tensor modes while preserving energy momentum conservation. From fluctuation-dissipation considerations, it follows that the random force is Gaussian with a white spectrum. The irreducible tensor modes in turn excite vector modes, which back-react on the tensor sector, thus producing a consistent non-linear, second order description of the divergence-free tensor dynamics. Using the Martin-Siggia-Rose (MSR) formalism we obtain the two-point correlation function for these tensor modes at next to leading order, and the induced stochastic component of the energy-momentum tensor. We find that the thermal fluctuations induce a scale invariant spectrum at short scales, while preserving a white spectrum at large scales. This result suggests that tensor modes could sustain an entropy cascade.

hep-th↗

arXiv2019

The importance of being measurement

Energy exchanges under form of heat is neither the most natural or efficient way to operate an engine in the quantum realm. Recently there have been in the literature several proposals for "quantum measurement engines" where energy is fed into the machine by operations which otherwise would be conducive to quantum measurements on the working substance (henceforth "the system"). In the analysis of the working of these devices, oftentimes it is assumed that the only effect of measurement is to turn the state of the system from whatever prior state to an eigenstate of the measured property, and energy exchanges are determined therefrom. This ignores the intricacies of the quantum measurement process. We propose a simple model of a quantum measurement engine where the measurement process may be analyzed in detail, and therefore energy exchanges, and limitations on their duration, may be traced more fully.

quant-ph↗

arXiv2018

Not quite free shortcuts to adiabaticity

Given the increasing use of shotcuts to adiabaticity (STA) to optimize power and efficiency of quantum heat engines, it becomes a relevant question if there are any theoretical limits to their application. We argue that quantum fluctuations in the control device which implements the shortcut deflect the system from the adiabatic path. This not only induces transitions to unwanted final states but also changes the system energy, so that using the STA has a definite cost in terms of conventional work definitions. This may be the ultimate cost of an adiabatic shortcut, in the sense that it is present even for a frictionless, zero temperature driving. We estimate the effect, to lowest nontrivial order in the derivatives of the time-dependent frequency, on a parametric harmonic oscillator, thus providing a consistency condition for the validity of the classical approximation.

quant-ph↗