arXiv subjects

Nicki Mullins

Publications and source records attributed to Nicki Mullins.

14 recordsLinked to original sources

arXiv2026

Fluctuation--response relations from an emergent $\mathbb{Z}_2$ symmetry in the rotating stochastic Landau model

In this work, we investigate the extent to which fluctuation--response relations emerge from coarse-grained stochastic dynamics alone, and which aspects instead depend on additional information about the system. To address this question, we study the rotating stochastic Landau model, an exactly solvable system describing an overdamped charged Brownian particle in a constant magnetic field, coupled dissipatively to a rotating environment, whose steady state supports circulating probability currents. Using the Martin--Siggia--Rose path integral, we show that there is an emergent $\mathbb{Z}_2$ symmetry transformation that implements the time-reversed dynamics and changes the action by a boundary term. Comparison with the Crooks fluctuation theorem identifies this term with the entropy associated with transitions between steady-state configurations. After coupling the theory to external sources, the same symmetry yields Ward identities relating fluctuations and response. These identities follow entirely from the coarse-grained stochastic theory and do not fix the noise strength. Finally, upon imposing the Einstein relation, we show that they coincide with the high-temperature fluctuation--dissipation relations implied by the rotating Kubo--Martin--Schwinger condition for a microscopic Gibbs ensemble.

cond-mat.stat-mech↗

arXiv2026

Jet Momentum Broadening in Viscous QCD Matter: A Moment Expansion Approach

We formulate out-of-equilibrium jet momentum broadening in QCD effective kinetic theory through a moment expansion of the medium distribution function, a method traditionally used to derive relativistic viscous hydrodynamics from kinetic theory. We explicitly compute the leading near-equilibrium contribution to the spatial jet broadening tensor $\hat q^{ij}$ within the 14-moment approximation, and show that it is controlled by the medium shear-stress tensor. This provides a direct map from QCD effective kinetic theory to event-by-event viscous hydrodynamic simulations, converting local shear-stress fields into anisotropic corrections to jet broadening in heavy-ion collisions.

hep-ph↗

arXiv2026

Covariant diffusion tensor for jet momentum broadening out of equilibrium

Jets are produced in the earliest stages of heavy-ion collisions, where they can interact with a medium that is not yet close to local equilibrium. Motivated by this, we generalize the usual jet transport coefficient $\hat q$ to a Lorentz-covariant diffusion tensor $\hat q^{\mu\nu}$ within a leading-order elastic (Boltzmann/Fokker--Planck) description of jet--medium interactions. The tensor formulation organizes medium effects in a frame-covariant way and reveals additional information beyond the standard scalar definition, including energy diffusion and off-diagonal components that encode correlations between energy and momentum exchange which are absent (or redundant) in equilibrium. We illustrate the formalism in (tree-level) massless $\lambda\varphi^4$ theory for isotropic but out-of-equilibrium states. For sufficiently large jet momentum, quantum statistical effects become subleading, so that the non-equilibrium evolution can be studied reliably in the classical (Boltzmann) limit. This allows us to solve the corresponding Boltzmann equation for the medium and determine the time dependence of $\hat q^{\mu\nu}$ as the system approaches equilibrium. We find that out-of-equilibrium corrections can either enhance or reduce jet momentum broadening, depending on the initial distribution function.

hep-ph↗

arXiv2026

Solving BDNK diffusion using physics-informed neural networks

In this work, we reformulate the relativistic BDNK (Bemfica-Disconzi-Noronha-Kovtun) diffusion equation in flux-conservative form, and solve the resulting equations in $(1+1)$D using both a second-order Kurganov-Tadmor finite volume scheme and physics-informed neural networks (PINNs). In particular, we introduce the SA-PINN-ACTO framework, which combines the self-adaptive PINN technique with an exact enforcement of initial and periodic boundary conditions through an algebraic transform of the network's raw output, allowing the network to focus solely on minimizing the PDE residual. We test both approaches on smooth and discontinuous initial data, for both trivial and dynamically evolving velocity and temperature BDNK backgrounds, and for two characteristic speeds. The SA-PINN-ACTO method matches the converged Kurganov-Tadmor solutions for smooth profiles, while for discontinuous profiles the errors increase, reflecting an expected limitation of PINNs near sharp gradients.

nucl-th↗

arXiv2025

A new effective theory for stochastic relativistic hydrodynamics

Thermal fluctuations are a fundamental feature of dissipative systems that are essential for understanding physics near the expected critical point of QCD and in small systems. When such fluctuations are modeled naively in relativistic systems, strange features can appear such as negative self-correlation functions. We construct an effective theory for nonlinear stochastic relativistic hydrodynamics that ensure a well-posed mathematical formulation. Using Crooks fluctuation theorem, we derive a symmetry of the effective action that incorporates fluctuations through a suitable free energy functional. For divergence type theories, the action can then be fully specified using a single vector generating current. The equations of motion obtained using this procedure are guaranteed to be flux conservative and symmetric hyperbolic when the dynamics is causal. This ensures that these equations are well-posed (for suitable initial data) and are in a form that can easily be simulated, including with Metropolis techniques.

nucl-th↗

arXiv2025

Emergent Viscous Hydrodynamics From a Single Quantum Particle

We investigate an explicit example of how spatial decoherence can lead to hydrodynamic behavior in the late-time, long-wavelength regime of open quantum systems. We focus on the case of a single non-relativistic quantum particle linearly coupled to a thermal bath of noninteracting harmonic oscillators at temperature $T$, a la Caldeira and Leggett. Taking advantage of decoherence in the position representation, we expand the reduced density matrix in powers of the off-diagonal spatial components, so that high-order terms are suppressed at late times. Truncating the resulting power series at second order leads to a set of dissipative transient hydrodynamic equations similar to the non-relativistic limit of equations widely used in simulations of the quark-gluon plasma formed in ultrarelativistic heavy-ion collisions. Transport coefficients are directly determined by the damping constant $\gamma$, which quantifies the influence of the environment. The asymptotic limit of our hydrodynamic equations reduces to the celebrated Navier-Stokes equations for a compressible fluid in the presence of a drag force. Our results shed new light on the onset of hydrodynamic behavior in open quantum systems where a system with few degrees of freedom is coupled to a large thermal environment.

cond-mat.stat-mech↗

arXiv2025

Effective action for relativistic hydrodynamics from Crooks fluctuation theorem

A new effective theory framework for fluctuating hydrodynamics in the relativistic regime is derived using standard thermodynamical principles and general properties of non-equilibrium stochastic dynamics. For the first time, we establish clear and concise conditions for ensuring that the resulting effective theories are causal, stable, and well-posed within general relativity. These properties are independent of spacetime foliation and are valid in the full nonlinear regime. Out-of-equilibrium fluctuations are constrained by a relativistically covariant version of Crooks fluctuation theorem, which determines how the entropy production is distributed even when the system is driven by an external force. This leads to an emerging $\mathbb{Z}_2$ symmetry responsible for imposing fluctuation-dissipation relations for n-point correlation functions, which matches the standard constraints for the Schwinger-Keldysh effective action.

nucl-th↗

arXiv2024

Consistent inclusion of fluctuations in first-order causal and stable relativistic hydrodynamics

We construct, for the first time, a Bemfica-Disconzi-Noronha-Kovtun (BDNK) theory for linear stochastic fluctuations, which is proved to be mathematically consistent, causal, and covariantly stable. The Martin-Siggia-Rose action is shown to be bilocal in most cases, and the noise is not white. The presence of nonhydrodynamic modes induces long-range correlations in the primary fluid variables (temperature, chemical potential, and flow velocity). However, correlators of conserved densities remain localized in space, and coincide with those calculated within fluctuating Isreal-Stewart theory. We show that, in some cases, there is a nonlocal change of variables that maps the Israel-Stewart action into the BDNK action.

nucl-th↗

arXiv2024

Modelling stochastic fluctuations in relativistic kinetic theory

Using the information current, we develop a Lorentz-covariant framework for modeling equilibrium fluctuations in relativistic kinetic theory in the grand-canonical ensemble. The resulting stochastic theory is proven to be causal and covariantly stable, and its predictions do not depend on the choice of spacetime foliation used to define the grand-canonical probabilities. As expected, in a box containing $N{>}5$ particles, Boltzmann's molecular chaos postulate is broken with (almost exact) probability $N^{-1/2}$, leading to a breakdown of the Boltzmann equation in small systems. We also verify that, in ultrarelativistic gases, transient hydrodynamics already accounts for at least 80% of the equilibrium fluctuations of the stress-energy tensor at a given time. Finally, we compute the correlators at non-equal times for two selected collision kernels: That of a chemically active diluted solution, and that of ultrarelativistic scalar particles self-interacting via a quartic potential. For the former, we compute the density-density correlators analytically in real space, and dehydrodynamization of the stochastic theory is proven to occur whenever the mean free path diverges at high energy.

nucl-th↗

arXiv2024

Causal and Stable Relativistic Hydrodynamic Fluctuations

When two nuclei collide close to the speed of light, a fluid state known as the quark-gluon plasma is formed. Attempts to understand the dynamics of this fluid have generated significant research into dissipative relativistic fluid dynamics. The fluctuation-dissipation theorem implies that any dissipative dynamical system will also experience thermal fluctuations; however, such fluctuations are not typically included in the modeling of the quark-gluon plasma. This work discusses a new method of determining whether a hydrodynamic framework is consistent with thermal fluctuations. We develop a new method for calculating the noise correlator of relativistic hydrodynamic systems and apply it to Israel-Stewart theory in a general hydrodynamic frame.

nucl-th↗

arXiv2023

A new approach to stochastic relativistic fluid dynamics from information flow

We present a new general formalism for introducing thermal fluctuations in relativistic hydrodynamics, which incorporates recent developments on the causality and stability of relativistic hydrodynamic theories. Our approach is based on the information current, which measures the net amount of information carried by perturbations around equilibrium in a relativistic many-body system. The resulting noise correlators are guaranteed to be observer-independent for thermodynamically stable models. We obtain an effective action within our formalism and discuss its properties.

nucl-th↗

arXiv2023

Relativistic hydrodynamic fluctuations from an effective action: causality, stability, and the information current

Causality is necessary for retarded Green's functions to remain retarded in all inertial frames in relativity, which ensures that dissipation of fluctuations is a Lorentz invariant concept. For first-order BDNK theories with stochastic fluctuations, introduced via the Schwinger-Keldysh formalism, we show that imposing causality and stability leads to correlation functions of hydrodynamic fluctuations that only display the expected physical properties at small frequencies and wavenumber, i.e., within the expected regime of validity of the first-order approach. For second-order theories of Israel and Stewart type, constructed using the information current such that entropy production is always non-negative, a stochastic formulation is presented using the Martin-Siggia-Rose approach where imposing causality and stability leads to correlators with the desired properties. We also show how Green's functions can be determined from such an action. We identify a $\mathbb{Z}_2$ symmetry, analogous to the Kubo-Martin-Schwinger symmetry, under which this Martin-Siggia-Rose action is invariant. This modified Kubo-Martin-Schwinger symmetry provides a new guide for the effective action formulation of hydrodynamic systems with dynamics not solely governed by conservation laws. Furthermore, this symmetry ensures that the principle of detailed balance is valid in a covariant manner. We employ the new symmetry to further clarify the connection between the Schwinger-Keldysh and Martin-Siggia-Rose approaches, establishing a precise link between these descriptions in second-order theories of relativistic hydrodynamics. Finally, the modified Kubo-Martin-Schwinger symmetry is used to determine the corresponding action describing diffusion in Israel-Stewart theories in a general hydrodynamic frame.

hep-th↗

arXiv2023

Stochastic fluctuations in relativistic fluids: causality, stability, and the information current

We develop a general formalism for introducing stochastic fluctuations around thermodynamic equilibrium which takes into account, for the first time, recent developments on the causality and stability properties of relativistic hydrodynamic theories. The method is valid for any covariantly stable theory of relativistic viscous fluid dynamics derived from a covariant maximum entropy principle. We illustrate the formalism with some applications, showing how it could be used to consistently introduce fluctuations in a model of relativistic heat diffusion, and in conformally invariant Israel-Stewart theory in a general hydrodynamic frame. The latter example is used to study the hydrodynamic frame dependence of the symmetric two-point function of fluctuations of the energy-momentum tensor.

nucl-th↗

arXiv2022

Far-from-equilibrium kinetic dynamics of $λϕ^4$ theory in an expanding universe

We investigate the far-from-equilibrium behavior of the Boltzmann equation for a gas of massless scalar field particles with quartic (tree level) self-interactions ($λϕ^4$) in Friedmann-Lemaitre-Robertson-Walker spacetime. Using a new covariant generating function for the moments of the Boltzmann distribution function, we analytically determine a subset of the spectrum and the corresponding eigenfunctions of the linearized Boltzmann collision operator. We show how the covariant generating function can be also used to find the exact equations for the moments in the full nonlinear regime. Different than the case of a ultrarelativistic gas of hard spheres (where the total cross section is constant), for $λϕ^4$ the fact that the cross section decreases with energy implies that moments of arbitrarily high order directly couple to low order moments. Numerical solutions for the scalar field case are presented and compared to those found for a gas of hard spheres.

hep-ph↗