Hydrodynamic Description Research Articles

Relativistic Corrections in White Dwarf Asteroseismology

Abstract With the precision now afforded by modern space-based photometric observations from the retired K2 and current TESS missions, the effects of general relativity (GR) may be detectable in the light curves of pulsating white dwarfs (WDs). Almost all WD models are calculated using a Newtonian description of gravity and hydrodynamics. To determine if the inclusion of GR leads to observable effects, we used idealized models of compact stars and made side-by-side comparisons of mode periods computed using a: (i) Newtonian and (ii) GR description of the equilibrium structure and nonradial pulsations. For application to WDs, it is only necessary to include the first post-Newtonian (1pn) approximation to GR. The mathematical nature of the linear nonradial pulsation problem is then qualitatively unchanged and the GR corrections can be written as extensions of the classic Dziembowski equations. As such, GR effects might easily be included in existing asteroseismology codes. The idealized stellar models are (i) 1pn relativistic polytropes and (ii) stars with a cold degenerate electron equation of state featuring a near-surface chemical transition from μ e = 2 to μ e = 1, simulating a surface hydrogen layer. A comparison of Newtonian and 1pn normal mode periods reveals fractional differences in the order of the surface gravitational redshift z. For a typical WD, this fractional difference is ∼10−4 and is greater than the period uncertainty σ Π/Π of many WD pulsation modes observed by TESS. Consistent theoretical modeling of periods observed in these stars should, in principle, include GR effects to 1pn order.

Complex Quantum Hydrodynamics in Momentum Space with Broken Time-Reversal Symmetry

Shortly after Schrödinger’s wave mechanics in terms of complex wave functions was published, Madelung formulated this theory in terms of two real hydrodynamic-like equations. This version is also the formal basis of Bohmian mechanics, albeit with a different ontological interpretation. A point of criticism raised by Pauli against Bohmian mechanics is its missing symmetry between position and momentum that is present in classical phase space as well as in the quantum mechanical position and momentum representations. Both Madelung’s quantum hydrodynamics formulation and Bohmian mechanics are usually expressed only in position space. Recently, with the use of complex quantities, we were able to provide a hydrodynamic formulation also in momentum space. In this paper, we extend this formalism to include dissipative systems with broken time-reversal symmetry. In classical Hamiltonian mechanics and conventional quantum mechanics, closed systems with reversible time-evolution are usually considered. Extending the discussion to include open systems with dissipation, another form of symmetry is broken, that under time-reversal. There are different ways of describing such systems; for instance, Langevin and Fokker–Planck-type equations are commonly used in classical physics. We now investigate how these aspects can be incorporated into our complex hydrodynamic description and what modifications occur in the corresponding equations, not only in position, but particularly in momentum space.

Corbino magnetoresistance in neutral graphene

We explore the magnetohydrodynamics of Dirac fermions in neutral graphene in the Corbino geometry. Based on the fully consistent hydrodynamic description derived from a microscopic framework and taking into account all peculiarities of graphene-specific hydrodynamics, we report the results of a comprehensive study of the interplay of viscosity, disorder-induced scattering, recombination, energy relaxation, and interface-induced dissipation. In the clean limit, magnetoresistance of a Corbino sample is determined by viscosity. Hence the Corbino geometry could be used to measure the viscosity coefficient in neutral graphene.

Nonlinear density waves on graphene electron fluids

The hydrodynamic behavior of charged carriers leads to nonlinear phenomena such as solitary waves and shocks, among others. As an application, such waves might be exploited on plasmonic devices either for modulation or signal propagation along graphene waveguides. We study the nature of nonlinear perturbations following an approach similar to Sagdeev potential analysis and also by performing the reductive perturbation method on the hydrodynamic description of graphene electrons, taking into consideration the effect of Bohm quantum potential and odd viscosity. Thus, deriving a dissipative Kadomtsev-Petviashvili-Burgers (KPB) equation for the bidimensional flow as well as its unidimensional limit in the form of Korteweg--de Vries--Burgers (KdVB). The stability analysis of these equations unveils the existence of unstable modes that can be excited and launched through graphene plasmonic devices.

Hydrodynamic gauge fixing and higher order hydrodynamic expansion

Hydrodynamics is a powerful emergent theory for the large-scale behaviours in many-body systems, quantum or classical. It is a gradient series expansion, where different orders of spatial derivatives provide an effective description on different length scales. We report the first fully general derivation of third-order, or ‘dispersive’, terms in the hydrodynamic expansion. Our derivation is based on general principles of statistical mechanics, along with the assumption that the complete set of local and quasi-local conserved densities constitutes a good set of emergent degrees of freedom. We obtain fully general Kubo-like expressions for the associated hydrodynamic coefficients (also known as Burnett coefficients), and we determine their exact form in quantum integrable models, introducing in this way purely quantum higher-order terms into generalised hydrodynamics. We emphasise the importance of hydrodynamic gauge fixing at diffusive order, where we claim that it is parity-time-reversal, and not time-reversal, invariance that is at the source of Einstein’s relation, Onsager’s reciprocal relations, the Kubo formula and entropy production. At higher hydrodynamic orders we introduce a more general, nth order ‘symmetric’ gauge, which we show implies the validity of the higher-order hydrodynamic description.

Intrinsic Interface Adsorption Drives Selectivity in Atomically Smooth Nanofluidic Channels.

Specific molecular interactions underlie unexpected and useful phenomena in nanofluidic systems, but these require descriptions that go beyond traditional macroscopic hydrodynamics. In this letter, we demonstrate how equilibrium molecular dynamics simulations and linear response theory can be synthesized with hydrodynamics to provide a comprehensive characterization of nanofluidic transport. Specifically, we study the pressure driven flows of ionic solutions in nanochannels comprised of two-dimensional crystalline substrates made from graphite and hexagonal boron nitride. While simple hydrodynamic descriptions do not predict a streaming electrical current or salt selectivity in such simple systems, we observe that both arise due to the intrinsic molecular interactions that act to selectively adsorb ions to the interface in the absence of a net surface charge. Notably, this emergent selectivity indicates that these nanochannels can serve as desalination membranes.

Charge transport, information scrambling and quantum operator-coherence in a many-body system with U(1) symmetry

In this work, we derive an exact hydrodynamical description for the coupled, charge and operator dynamics, in a quantum many-body system with U(1) symmetry. Using an emergent symmetry in the complex Brownian SYK model with charge conservation, we map the operator dynamics in the model to the imaginary-time dynamics of an SU(4) spin-chain. We utilize the emergent SU(4) description to demonstrate that the U(1) symmetry causes quantum-coherence to persist even after disorder-averaging, in sharp contrast to models without symmetries. In line with this property, we write down a ‘restricted’ Fokker-Planck equation for the out-of-time ordered correlator (OTOC) in the large-N limit, which permits a classical probability description strictly in the incoherent sector of the global operator-space. We then exploit this feature to describe the OTOC in terms of a Fisher-Kolmogorov-Petrovsky-Piskun (FKPP)-equation which couples the operator with the charge and is valid at all time-scales and for arbitrary charge-density profiles. The coupled equations obtained belong to a class of models also used to describe the population dynamics of bacteria embedded in a diffusive media. We simulate them to explore operator-dynamics in a background of non-uniform charge configuration, which reveals that the charge transport can strongly affect dynamics of operators, including those that have no overlap with the charge.

Assessing the ultracentral flow puzzle in hydrodynamic modeling of heavy-ion collisions

An outstanding problem in heavy-ion collisions is the inability for models to accurately describe ultra-central experimental flow data, despite that being precisely the regime where a hydrodynamic description should be most applicable. We reassess the status of this puzzle by computing the flow in ultra-central collisions obtained from multiple recent Bayesian models that were tuned to various observables in different collision systems at typical centralities. While central data can now be described with better accuracy than in previous calculations, tension with experimental observation remains and worsens as one goes to ultra-central collisions. Tuning the model parameters cannot remove this tension without destroying the fit at other centralities. As such, new elements are likely needed in the standard modeling of heavy-ion collisions.

Quantum kinetics of quenched two-dimensional Bose superfluids

We study theoretically the nonequilibrium dynamics of a two-dimensional (2D) uniform Bose superfluid following a quantum quench, from its short-time (prethermal) coherent dynamics to its long-time thermalization. Using a quantum hydrodynamic description combined with a Keldysh field formalism, we derive quantum kinetic equations for the low-energy phononic excitations of the system and characterize both their normal and anomalous momentum distributions. We apply this formalism to the interaction quench of a 2D Bose gas and study the ensuing dynamics of its quantum structure factor and coherence function, both recently measured experimentally. Our results indicate that, in two dimensions, a description in terms of independent quasiparticles becomes quickly inaccurate and should be systematically questioned when dealing with nonequilibrium scenarios.

Hydrodynamics of dipole-conserving fluids.

Dipole-conserving fluids serve as examples of kinematically constrained systems that can be understood on the basis of symmetry. They are known to display various exotic features including glassylike dynamics, subdiffusive transport, and immobile excitations' dubbed fractons. Unfortunately, such systems have so far escaped a complete macroscopic formulation as viscous fluids. In this work, we construct a consistent hydrodynamic description for fluids invariant under translation, rotation, and dipole shift symmetry. We use symmetry principles to formulate a thermodynamic theory for dipole-conserving systems at equilibrium and apply irreversible thermodynamics in order to elucidate dissipative effects. Remarkably, we find that the inclusion of the energy conservation not only renders the longitudinal modes diffusive rather than subdiffusive but also diffusion is present even at the lowest order in the derivative expansion. This work paves the way towards an effective description of many-body systems with constrained dynamics such as ensembles of topological defects, fracton phases of matter, and certain models of glasses.

Quantum transitions from superfluid to insulating phases in disordered Bose systems

By the example of Heisenberg d-dimensional disordered non-frustrated antiferromagnets, we discuss quantum transitions at d≥2 from magnetically ordered (superfluid) to various disorder-induced insulating phases (Bose-glass, Mott-glass, etc.) in Bose systems with quenched disorder. We perform a scaling consideration as well as a discussion based on the hydrodynamic description of long-wavelength excitations and on the assumption that the ordered part of the system shows fractal properties near the transition point. We propose that the scaling ansatz for the singular part of the free energy suggested before for the transition to the Bose-glass phase is applicable also for other transitions if the quenched disorder does not produce a local imbalance in sublattices magnetizations. We show using the scaling consideration that η=2−z and β=νd/2, where η, β, and ν, are critical exponents of the correlation function, the order parameter, and the correlation length, respectively, and z is the dynamical critical index. These relations were missed in previous analytical discussions of Bose-glass and Mott-glass phases. They signify, in particular, that z=d/2 for the transition to the Mott-glass phase and that the density of states of localized excitations shows a superuniversal (i.e., independent of d) behavior near the transitions. Being derived solely from the scaling analysis, the above relations for η and β are valid also for the transition to the random-singlet phase.

Cosmic-ray-driven galactic winds: transport modes of cosmic rays and Alfvén-wave dark regions

ABSTRACTFeedback mediated by cosmic rays (CRs) is an important process in galaxy formation. Because CRs are long-lived and because they are transported along the magnetic field lines independently of any gas flow, they can efficiently distribute their feedback energy within the galaxy. We present an in-depth investigation of (i) how CRs launch galactic winds from a disc that is forming in a $10^{11} \, \rm {M}_\odot$ halo and (ii) the state of CR transport inside the galactic wind. To this end, we use the arepo moving-mesh code and model CR transport with the two-moment description of CR hydrodynamics. This model includes the CR interaction with the gyroresonant Alfvén waves that enable us to self-consistently calculate the CR diffusion coefficient and CR transport speeds based on coarse-grained models for plasma physical effects. This delivers insight into key questions such as whether the effective CR transport is streaming-like or diffusive-like, how the CR diffusion coefficient and transport speed change inside the circumgalactic medium, and to what degree the two-moment approximation is needed to faithfully capture these effects. We find that the CR-diffusion coefficient reaches a steady state in most environments with the notable exception of our newly discovered Alfvén-wave dark regions where the toroidal wind magnetic field is nearly perpendicular to the CR pressure gradient so that CRs are unable to excite the gyroresonant Alfvén waves. However, CR transport itself cannot reach a steady state and is not well described by either the CR streaming paradigm, the CR diffusion paradigm, or a combination of both.

Nonlocal Fourier modal method for analyzing nonlocal plasmonic periodic nanostructures

In accordance with growing scientific interests in nanoplasmonic structures, along with the increasing ability to fabricate them using proper nanotechnologies, we have developed a methodology to incorporate nonlocal optical responses, described with a simple hydrodynamic model, into the numerical Fourier modal method (FMM) technique to enable broadening of the simulation portfolio of such physical phenomena in plasmonic nanostructures. Here, we have newly incorporated the nonlocal response approximation (NRA) into the periodic FMM technique (called NonLocFMM) described with a proper hydrodynamic model, and we show in several examples that this implementation is capable of numerically analyzing periodic plasmonic systems, such as nonlocal periodic multilayers and resonant gratings. The implementation was performed in such a way that a future possible generalization of the hydrodynamic nonlocal description will be feasible, as well as the aperiodization of the technique. Such an extension is, indeed, viable and will be the subject of a subsequent paper.

Long time dynamics of a single-particle extended quantum walk on a one-dimensional lattice with complex hoppings: a generalized hydrodynamic description

We study a single-particle continuous-time quantum walk on a one-dimensional spatial lattice with complex nearest neighbour (NN) and next-nearest neighbour (NNN) hopping amplitudes. We show that the model allows for controlled information transfer and directional biasing without a biased initial state. Specifically, we show that for an unbiased initial state, complex couplings lead to chiral propagation and a causal cone structure asymmetric about the origin. We provide a hydrodynamic description for the dynamics in the large space–time limit. We obtain a global ‘quasi-stationary state’ which can be described in terms of the local quasi-particle densities satisfying Euler type of hydrodynamic equations and characterized by an infinite set of conservation laws. Further, we show that higher-order hydrodynamic equations can be used to describe the anomalous sub-diffusive scaling near the extremal fronts. The long-time behaviour for any complex NNN hopping with a nonzero real component is similar to that of purely real hopping; at a critical coupling strength, there is a Lifshitz transition where the topology of the causal structure changes from a regime with one causal cone to a regime with two nested (asymmetric) causal cones. For purely imaginary NNN hopping, there is a transition from one causal cone to a regime with two partially overlapping cones which can be attributed to the existence of degenerate maximal fronts. Both the nature of the Lifshitz transition and the scaling behaviour at the critical coupling are different in the two cases. We also discuss possible experimental realizations of such a model.

A hydrodynamical description of gravitational waves

It is easy to reason that gravity might be the effect of a fluid in disguise, as it will naturally arise in emergent gravity models where gravity is due to the effect of some fundamental particles, with the latter expected to behave collectively like a fluid at the macroscopic scale. We call this the fluid/gravity equivalence. The key difficulty with the fluid/gravity equivalence is to find the correct metric–fluid relation (the relation between the emergent metric and the fluid properties) so that the fluid not only has physically acceptable properties but also obeys the usual hydrodynamic equations, while at the same time the emergent metric also obeys the Einstein equations. Faced with the problem, we have previously made a tentative proposal of the metric–fluid relation, focusing only on obtaining physically acceptable predictions on the fluid properties. In this paper, however, we find that for the general gravitational wave spacetime near the null infinity, the underlying fluid not only has physically acceptable properties, but also satisfies the expected relativistic hydrodynamic equations in the Minkowski background, thus providing a concrete example satisfying both of the major requirements expected for the fluid/gravity equivalence.

Hydrodynamic lubrication in colloidal gels.

Colloidal gels are elasto-plastic materials composed of an out-of-equilibrium, self-assembled network of micron-sized (solid) particles suspended in a fluid. Recent work has shown that far-field hydrodynamic interactions do not change gel structure, only the rate at which the network forms and ages. However, during gel formation, the interplay between short-ranged attractions leading to gelation and equally short-ranged hydrodynamic lubrication interactions remains poorly understood. Here, we therefore study gelation using a range of hydrodynamic descriptions: from single-body (Brownian Dynamics), to pairwise (Rotne-Prager-Yamakawa), to (non-)lubrication-corrected many-body (Stokesian Dynamics). We confirm the current understanding informed by simulations accurate in the far-field. Yet, we find that accounting for lubrication can strongly impact structure at low colloid volume fraction. Counterintuitively, strongly dissipative lubrication interactions also accelerate the aging of a gel, irrespective of colloid volume fraction. Both elements can be explained by lubrication forces facilitating collective dynamics and therefore phase-separation. Our findings indicate that despite the computational cost, lubricated hydrodynamic modeling with many-body far-field interactions is needed to accurately capture the evolution of the gel structure.

Using baryonic charge balance functions to resolve questions about the baryo-chemistry of the quark gluon plasma

Baryon annihilations during the hadronic stage of heavy-ion collisions affects final-state baryon and antibaryon yields and final-state correlations of baryons and antibaryons. Understanding annihilation is important for addressing questions about the chemistry at the beginning of the hadronic stage and for interpreting charge-balance correlations involving baryons. Here, charge balance functions, using protons and antiprotons binned by relative momentum, rapidity, and azimuthal angle are shown to clarify the amount of annihilation in the hadronic stage. This enables a more accurate extraction of the baryo-chemistry at the beginning of the hadronic stage. Understanding annihilation is also crucial if charge balance correlations are to be used to infer the chemistry of the earliest stages of a heavy-ion collision. Calculations are presented based on microscopic simulations of the hadronic stage coupled to a hydrodynamic description of the earlier stage, along with a detailed modeling of correlations of protons and antiprotons, known as charge-balance functions.

Action complexity of charged black holes with higher derivative interactions

Quantum complexity of CFT states can be computed holographically from the dual gravitational solutions. In this paper, we have studied the late time growth of holographic complexity of a charged black hole in five-dimensional, Anti-de Sitter spacetime in the presence of quartic derivative interaction terms using the Complexity = Action conjecture. These interaction terms in the gravitational action can lead to the violation of Llyod's bound. The dual CFT is known to admit a hydrodynamic description where the KSS bound is also violated due to the presence of higher derivative terms in the bulk action. The origin of terms which violate both the bounds are the same for the gravitational action of consideration. We have also discussed the late time complexity growth rate of the Jackiw-Teitelboim (JT) model with higher derivative corrections.

The invariant ion-acoustic waves in the plasma

The space plasmas have been found empirically to be separated into those residing far from the classical thermal equilibrium and those residing near equilibrium. The modern formalism of the kappa distributions explains this distinction under the value of the kappa index, the intensive parameter that characterizes thermodynamics together with temperature. Recent studies have suggested that by defining an invariant kappa index as the zero dimensionality spectral index, kappa _{0}, which is independent of the dimensionality, the degrees of freedom, or the numbers of particles, one may separately consider the physical and thermodynamic feature of the kappa index in space plasmas by utilizing kappa _{0}. This study extends the mentioned idea to the ion-acoustic waves (IAWs) in the astrophysical plasmas in order to deriving an invariant formalism for the IAWs including the pure thermodynamic features of the background particles. This paper is based on the kinetic theory formalism and the hydrodynamic fluid description for extracting the characteristics of the invariant IAWs. Relying on the Vlasov–Poisson equations, considering a low-frequency band for the weakly damped ion oscillations, we have derived the most generalized formalism of the ion-sound speed in space plasmas in terms of the extended polytropic indices of the plasma species, gamma _{j}, and also the generalized formalism of Landau damping for the invariant IAWs in terms of kappa _{0}, wavelength, and temperatures of the plasma species. In the hydrodynamic description, we have normalized the fluid parameters in terms of the generalized quantities, including the extended formulations of the ion-sound speed and Debye length. Then, by using the perturbation expansion in linear and nonlinear regimes, we may find some other issues in the formalism of the invariant IAWs, such as the effect of the perturbed potential degrees of freedom, d_{Phi }, the isothermal/extended phase speed of the IAWs, and the combined effects of the wave steepening and dispersion of ion waves. We have also derived a generalized KdV equation and its solitary wave solutions in an invariant formalism. Based on the empirical evidences in space plasmas, the far-equilibrium plasmas are characterized by 0<kappa _{0}<1 (0<gamma _{j}<0.5), while the near-equilibrium plasmas are labeled with kappa _{0}>1 (0.5<gamma _{j}<1). We have numerically analyzed our solutions from the anti-equilibrium states at kappa _{0}rightarrow 0 (gamma _{j}rightarrow 0) towards the equilibrium states at kappa _{0}gg 1 (gamma _{j}rightarrow 1). Our theoretical study provides strong evidence, for the first time, about the distinction of plasmas under the value of the kappa index. Our analysis confirms the distinction of the involved IAWs diagrams in the two mentioned regions, where the transition from far-equilibrium states to the near-equilibrium states may occur in the vicinity kappa _{0}sim 1 (gamma _{j}sim 0.5), denoting the escape state of the evolution.

Thermoviscous hydrodynamics in nondegenerate dipolar Bose gases

We present a hydrodynamic model of ultracold, but not yet quantum condensed, dipolar Bosonic gases. Such systems present both $s$-wave and dipolar scattering, the latter of which results in anisotropic transport tensors of thermal conductivity and viscosity. This work presents an analytic derivation of the viscosity tensor coefficients, utilizing the methods established in [Wang et al., arXiv:2205.10465], where the thermal conductivities were derived. Taken together, these transport tensors then permit a comprehensive description of hydrodynamics that is now embellished with dipolar anisotropy. An analysis of attenuation in linear waves illustrates the effect of this anisotropy in dipolar fluids, where we find a clear dependence on the dipole orientation relative to the direction of wave propagation.