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The fluid-dynamical modeling of a nuclear collision at high energy usually starts shortly after the collision. A major source of uncertainty comes from the detailed modeling of the initial state. While the collision itself likely involves far-from-equilibrium dynamics, it is not excluded that a fluid theory of second order can reasonably well describe its soft features. Here we explore this possibility and discuss how the state before the collision can be described in that setup, what are the requirements from relativistic causality to the form of the equations of motion, how much entropy production can result from shear and bulk viscous dissipation during the initial longitudinal dynamics, and how one can thus obtain sensible initial conditions for the subsequent transverse expansion. While we do here only first steps, we outline a larger program. If the latter could be successfully completed it could lead to a dynamical description of heavy-ion collisions where the only uncertainty lies in the thermodynamic and transport properties of quantum chromodynamics., Comment: 19 pages, 13 figures

To capture the dynamics of macroscopic non-relativistic fluids consisting of very many atoms, it is typically sufficient to truncate the gradient expansion at order zero, leading to ideal fluid dynamics, or at order one, leading to the Navier-Stokes theory. For mesoscopic fluids consisting of a small number of atoms, second-order corrections can become significant. We investigate here specifically superfluids at vanishing temperature, and identify relevant second-order terms of quantum origin that contribute already in a static situation. The general form of these terms arises from an extension of the Gross-Pitaevskii theory. In the context of density functional theory, they are named after C. von Weizs\"acker. We assess the influence of these terms on numerical solutions of second-order fluid dynamic equations for the expansion of a mesoscopic ultra-cold Fermi gas released from an anisotropic harmonic trap in two spatial dimensions.

The production of quantum field excitations or particles in cosmological spacetimes is a hallmark prediction of curved quantum field theory. The generation of cosmological perturbations from quantum fluctuations in the early universe constitutes an important application. The problem can be quantum-simulated in terms of structure formation in an interacting Bose-Einstein condensate (BEC) with time-dependent s-wave scattering length. Here, we explore a mapping between cosmological particle production in general (D+1)-dimensional spacetimes and scattering problems described by the non-relativistic stationary Schr\"odinger equation in one dimension. Through this mapping, intuitive explanations for emergent spatial structures in both the BEC and the cosmological system can be obtained for a large class of analogue cosmological scenarios, ranging from power-law expansions to periodic modulations. The investigated cosmologies and their scattering analogues are tuned to be implemented in a (2+1)-dimensional quantum field simulator., Comment: References and new section added. (22 + 14) pages, (13 + 7) figures, (1+1) tables

We study the time evolution of a state of a relativistic quantum field theory restricted to a spatial subregion $\Omega$. More precisely, we use the Feynman-Vernon influence functional formalism to describe the dynamics of the field theory in the interior of $\Omega$ arising after integrating out the degrees of freedom in the exterior. We show how the influence of the environment gets encoded in a boundary term. Furthermore, we derive a stochastic equation of motion for the field expectation value in the interior. We find that the boundary conditions obtained in this way are energy non-conserving and non-local in space and time. Our results find applications in understanding the emergence of local thermalization in relativistic quantum field theories and the relationship between quantum field theory and relativistic fluid dynamics., Comment: 17 pages, 4 figures

We study the pair production, string breaking, and hadronization of a receding electron-positron pair using the bosonized version of the massive Schwinger model in quantum electrodynamics in 1+1 space-time dimensions. Specifically, we study the dynamics of the electric field in Bjorken coordinates by splitting it into a coherent field and its Gaussian fluctuations. We find that the electric field shows damped oscillations, reflecting pair production. Interestingly, the computation of the asymptotic total particle density per rapidity interval for large masses can be fitted using a Boltzmann factor, where the temperature can be related to the hadronization temperature in QCD. Lastly, we discuss the possibility of an analog quantum simulation of the massive Schwinger model using ultracold atoms, explicitly matching the potential of the Schwinger model to the effective potential for the relative phase of two linearly coupled Bose-Einstein condensates., Comment: 15 pages, 8 figures. v2: 2 references added includes minor clarifications, matches published version

Heavy quarks (i.e. charm and beauty) in heavy-ion collisions are initially produced out of kinetic equilibrium via hard partonic scattering processes. However, recent measurements of anisotropic flow of charmed hadrons pose the question regarding the thermalization of heavy quarks in the quark-gluon plasma (QGP). Exploiting a mapping between transport theory and fluid dynamics, we develop a fluid-dynamic description for charm quarks and show results for charm-hadron momentum distributions. Inspired by recent Lattice-QCD (LQCD) calculations, we show that a late hydrodynamization within the lifetime of the QGP is possible also for beauty quarks., Comment: 4 pages, 2 figures, Contribution to Quark Matter 2023. arXiv admin note: substantial text overlap with arXiv:2307.15580

A method to calculate hadron momentum spectra after feed down from resonance decays in the context of ultra-relativistic heavy ion collisions described by relativistic fluid dynamics is presented. The conceptual setup uses the Cooper-Frye freeze-out integration together with an integral operator describing resonance decays. We provide explicit expressions for the integration over the freeze-out surface for a smooth and symmetric background solution, as well as for linearized perturbations around it. A major advantage of our method is that many integrals can be precomputed independently of a concrete hydrodynamic simulation. Additionally, we examine the influence of adding heavier resonances to the decay chain on the spectrum of pions and show how to include a phase with partial chemical equilibrium in order to separate the chemical from the kinetic freeze-out., Comment: 37 pages, 4 figures

Hydrodynamics provides a successful framework to effectively describe the dynamics of complex many-body systems ranging from subnuclear to cosmological scales by introducing macroscopic quantities such as particle densities and fluid velocities. According to textbook knowledge, it requires coarse graining over microscopic constituents to define a macroscopic fluid cell, which is large compared to the interparticle spacing and the mean free path. In addition, the entire system must consist of many such fluid cells. The latter requirement on the system size has been challenged by experiments on high-energy heavy-ion collisions, where collective particle emission, typically associated with the formation of a hydrodynamic medium, has been observed with few tens of final-state particles. Here, we demonstrate emergence of hydrodynamics in a system with significantly less constituents. Our observation challenges the requirements for a hydrodynamic description, as in our system all relevant length scales, i.e. the system size, the inter-particle spacing, and the mean free path are comparable. The single particle resolution, deterministic control over particle number and interaction strength in our experiment allow us to explore the boundaries between a microscopic description and a hydrodynamic framework in unprecedented detail., Comment: 11 pages, 6 figures

Exploiting a mapping between transport theory and fluid dynamics, we show how a fluid-dynamic description of the diffusion of charm quarks in the QCD plasma is feasible. We show results for spectra of charmed hadrons obtained with a fluid-dynamic description of the quark-gluon plasma (QGP) coupled with the conservation of a heavy-quark - antiquark current. We compare our calculations with the most recent experimental data in order to provide further constraints on the transport coefficients of the QGP., Comment: Hard Probes 2023

Relative entropy is a powerful measure of the dissimilarity between two statistical field theories in the continuum. In this work, we study the relative entropy between Gaussian scalar field theories in a finite volume with different masses and boundary conditions. We show that the relative entropy depends crucially on $d$, the dimension of Euclidean space. Furthermore, we demonstrate that the mutual information between two disjoint regions in $\mathbb{R}^d$ is finite if the two regions are separated by a finite distance and satisfies an area law. We then construct an example of "touching" regions between which the mutual information is infinite. We argue that the properties of mutual information in scalar field theories can be explained by the Markov property of these theories., Comment: 89 pages, 9 figures

A fluid-dynamic approach to charm-quark diffusion in the quark-gluon plasma (QGP) is developed for the first time. Results for integrated yields and momentum distributions of charmed hadrons obtained with a fluid-dynamic description for the dynamics of the QGP coupled to an additional heavy-quark-antiquark current are shown. In addition to the thermodynamic Equation of State (EoS), this description uses a heavy-quark diffusion constant which we take from Lattice QCD calculations. The results describe quantitatively experimental data measured at the LHC at the center-of-mass energy of $\sqrt{s_{\rm NN}}$ = 5.02 TeV up to $p_{\rm T}\sim$ 4-5 GeV/$c$, showing that charm quarks undergo a very fast hydrodynamization in the medium created by ultrarelativistic heavy-ion collisions., Comment: 11 pages, 6 figures

Two-dimensional van der Waals materials have recently been established experimentally as a highly-tunable condensed matter platform, facilitating the controlled manipulation of band structures and interactions. In several of these materials, Dirac cones are present in the low-energy regime near the Fermi level. Thus, fermionic excitations emerging in these materials close to the Dirac cones have a linear dispersion relation near the Fermi surface as massless relativistic Dirac fermions. Here, we study low-energy fermionic excitations of such Dirac materials in the presence of a mass gap that may be generated by symmetry breaking. Introducing a dynamical Fermi velocity and/or time-dependent mass gap for the Dirac quasiparticles, we exhibit the emergence of an analog of cosmological fermion pair production in terms of observables such as the expected occupation number or two-point correlation functions. We find that it is necessary and sufficient for quasiparticle production that only the ratio between the mass gap and the Fermi velocity is time-dependent. In this way, we establish that highly-tunable Dirac materials can serve as analog models for cosmological spacetime geometries, in particular, for Friedmann-Lema\^itre-Robertson-Walker expanding cosmologies. We briefly discuss possibilities for experimental realization, Comment: 15 pages, 4 figures

Large-scale structure formation is studied in a kinetic theory approach, extending the standard perfect pressureless fluid description for dark matter by including the velocity dispersion tensor as a dynamical degree of freedom. The evolution of power spectra for density, velocity and velocity dispersion degrees of freedom is investigated in a non-perturbative approximation scheme based on the Dyson$\unicode{x2013}$Schwinger equation. In particular, the generation of vorticity and velocity dispersion is studied and predictions for the corresponding power spectra are made, which qualitatively agree well with results obtained from $N$-body simulations. It is found that velocity dispersion grows strongly due to non-linear effects and at late times its mean value seems to be largely independent of the initial conditions. By taking this into account, a rather realistic picture of non-linear large-scale structure formation can be obtained, albeit the numerical treatment remains challenging, especially for very cold dark matter models., Comment: 43 pages, 15 figures

Information geometry provides differential geometric concepts like a Riemannian metric, connections and covariant derivatives on spaces of probability distributions. We discuss here how these concepts apply to quantum field theories in the Euclidean domain which can also be seen as statistical field theories. The geometry has a dual affine structure corresponding to sources and field expectation values seen as coordinates. A key concept is a new generating functional, which is a functional generalization of the Kullback-Leibler divergence. From its functional derivatives one can obtain connected as well as one-particle irreducible correlation functions. It also encodes directly the geometric structure, i. e. the Fisher information metric and the two dual connections, and it determines asymptotic probabilities for field configurations through Sanov's theorem., Comment: references added

An exact functional renormalization group flow equation is derived for the divergence functional which is a generalization of the Kullback-Leibler divergence to quantum field theories in the Euclidean domain. It compares distributions with different sources and field expectation values. The renormalization group flow for a regularized version of this functional connects two limits: one where the functional is known in terms of the microscopic action or probability distribution, and the other where all fluctuations are taken into account. In the latter limit one can obtain full correlation functions from functional derivatives of the divergence functional. The flow equation provides a possiblity to determine this functional non-perturbatively., Comment: references added

Particle momentum distributions originating from a quark-gluon plasma as produced in high-energy nuclear collisions can be influenced by thermal fluctuations in fluid dynamic fields. We study this effect by generalizing the commonly used kinetic freeze-out prescription by allowing for small fluctuations around an average in fluid velocity, chemical potentials and temperature. This leads to the appearance of specific two-body momentum correlations. Combining a blast-wave parametrization of the kinetic freeze-out surface with the thermal correlation functions of an ideal resonance gas, we perform an exploratory study of angular net-charge correlations induced by thermal fluctuations around vanishing chemical potential. We note a diffusion of the near-side peak around $\Delta y=\Delta\phi=0$ induced by variances of different chemical potentials, which could be investigated experimentally., Comment: 15 pages; 2 figures

Phonons have the characteristic linear dispersion relation of massless relativistic particles. They arise as low energy excitations of Bose-Einstein condensates and, in nonhomogeneous situations, are governed by a space- and time-dependent acoustic metric. We discuss how this metric can be experimentally designed to realize curved spacetime geometries, in particular, expanding Friedmann-Lema\^itre-Robertson-Walker cosmologies, with negative, vanishing, or positive spatial curvature. A nonvanishing Hubble rate can be obtained through a time-dependent scattering length of the background condensate. For relativistic quantum fields this leads to the phenomenon of particle production, which we describe in detail. We explain how particle production and other interesting features of quantum field theory in curved spacetime can be tested in terms of experimentally accessible correlation functions., Comment: 19 pages, 11 figures

Motivated by the possibility to use Bose-Einstein condensates as quantum simulators for spacetime curvature, we study a massless relativistic scalar quantum field in spatially curved Friedmann-Lema\^itre-Robertson-Walker universes with $d=2+1$ spacetime dimensions. In particular, we investigate particle production caused by a time-dependent background geometry, by means of the spectrum of fluctuations and several two-point field correlation functions. We derive new analytical results for several expansion scenarios., Comment: 17 pages, 6 figures

The observed large-scale structure in our Universe is seen as a result of quantum fluctuations amplified by spacetime evolution. This, and related problems in cosmology, asks for an understanding of the quantum fields of the standard model and dark matter in curved spacetime. Even the reduced problem of a scalar quantum field in an explicitly time-dependent spacetime metric is a theoretical challenge and thus a quantum field simulator can lead to new insights. Here, we demonstrate such a quantum field simulator in a two-dimensional Bose-Einstein condensate with a configurable trap and adjustable interaction strength to implement this model system. We explicitly show the realisation of spacetimes with positive and negative spatial curvature by wave packet propagation and confirm particle pair production in controlled power-law expansion of space. We find quantitative agreement with new analytical predictions for different curvatures in time and space. This benchmarks and thereby establishes a quantum field simulator of a new class. In the future, straightforward upgrades offer the possibility to enter new, so far unexplored, regimes that give further insight into relativistic quantum field dynamics., Comment: 9 pages, 6 figures

Fluid dynamic considerations are used to determine the electric current spectral density in the regime of small energies and momenta. The spectral density in this regime is parameterized by the electric conductivity, the charge susceptibility, and the relaxation time for the electric current, which is needed for relativistic causality. Experimentally, the spectral function can be accessed through the production rates of photons and dileptons in the expanding quark-gluon plasma. We use fluid dynamic simulations of high energy nuclear collisions, together with the transport limit of the spectral density, to obtain photon and dielectron spectra for different values of the conductivity and relaxation times. The yields of photon and dileptons produced in the plasma are compared to the background from decays of short-lived hadrons. We discuss how experiments can constrain the electrical conductivity and associated relaxation time of the quark-gluon plasma., Comment: 5 pages, 4 figures

Collective phenomena in quantum many-body systems are often described in terms of hydrodynamics, an appropriate framework when the involved particle numbers are effectively macroscopic. We propose to use experiments on expanding clouds of few and many interacting cold atoms to investigate the emergence of hydrodynamics as a function of particle number. We consider gases confined in two-dimensional elliptically-deformed traps, and we employ the manifestation of elliptic flow as an indicator of collective behavior. We quantify the response of the gas to the deformation of the trapping potential, and show how such information can be used to establish how many atoms are needed for the system to develop a degree of collectivity comparable to that expected in the hydrodynamic limit. This method permits one, in particular, to exploit observations made in expanding atomic gases to shed light on the apparent hydrodynamic behaviour of mesoscopic systems of quarks and gluons formed in the scattering of light ions in high-energy collider experiments., Comment: 28 pages, 8 figures

The functional renormalisation group is employed to study the non-linear regime of late-time cosmic structure formation. This framework naturally allows for non-perturbative approximation schemes, usually guided by underlying symmetries or a truncation of the theory space. An extended symmetry that is related to Galilean invariance is studied and corresponding Ward identities are derived. These are used to obtain (formally) closed renormalisation group flow equations for two-point correlation functions in the limit of large wave numbers (small scales). The flow equations are analytically solved in an approximation that is connected to the 'sweeping effect' previously described in the context of fluid turbulence., Comment: 16 pages, corrected typos

Entropic uncertainty is a well-known concept to formulate uncertainty relations for continuous variable quantum systems with finitely many degrees of freedom. Typically, the bounds of such relations scale with the number of oscillator modes, preventing a straight-forward generalization to quantum field theories. In this work, we overcome this difficulty by introducing the notion of a functional relative entropy and show that it has a meaningful field theory limit. We present the first entropic uncertainty relation for a scalar quantum field theory and exemplify its behavior by considering few particle excitations and the thermal state. Also, we show that the relation implies the multidimensional Heisenberg uncertainty relation., Comment: 11 pages, 1 figure, published version

We study how inhomogeneities of the cosmological fluid fields backreact on the homogeneous part of energy density and how they modify the Friedmann equations. In general, backreaction requires to go beyond the pressureless ideal fluid approximation, and this can lead to a reduced growth of cosmological large scale structure. Since observational evidence favours evolution close to the standard growing mode in the linear regime, we focus on two-component fluids in which the non-ideal fluid is gravitationally coupled to cold dark matter and in which a standard growing mode persists. This is realized, e.g. for a baryonic fluid coupled to cold dark matter. We calculate the backreaction for this case and for a wide range of other two-fluid models. Here the effect is either suppressed because the non-ideal matter properties are numerically too small, or because they lead to a too stringent UV cut-off of the integral over the power spectrum that determines backreaction. We discuss then matter field backreaction from a broader perspective and generalize the formalism such that also far-from-equilibrium scenarios relevant to late cosmological times and non-linear scales can be addressed in the future., Comment: 11 pages, 3 figures

We derive entropic inseparability criteria for the phase space representation of quantum states. In contrast to criteria involving differential entropies of marginal phase space distributions, our criteria are based on a joint distribution known as the Husimi Q-distribution. This distribution is experimentally accessible in cold atoms, circuit QED architectures and photonic systems and bears practical advantages compared to the detection of marginals. We exemplify the strengths of our entropic approach by considering several classes of non-Gaussian states where second-order criteria fail. We show that our criteria certify entanglement in previously undetectable regions highlighting the strength of using the Husimi Q-distribution for entanglement detection., Comment: 7 pages, 2 figures

We investigate the massive Schwinger model in $d=1+1$ dimensions using bosonization and the nonperturbative functional renormalization group. In agreement with previous studies we find that the phase transition, driven by a change of the ratio $m/e$ between the mass and the charge of the fermions, belongs to the two-dimensional Ising universality class. The temperature and vacuum angle dependence of various physical quantities (chiral density, electric field, entropy density) are also determined and agree with results obtained from density matrix renormalization group studies. Screening of fractional charges and deconfinement occur only at infinite temperature. Our results exemplify the possibility to obtain virtually all physical properties of an interacting system from the functional renormalization group., Comment: 14 pages, 9 figures

The Wehrl entropy is an entropy associated to the Husimi quasi-probability distribution. We discuss how it can be used to formulate entropic uncertainty relations and for a quantification of entanglement in continuous variables. We show that the Wehrl-Lieb inequality is closer to equality than the usual Bia{\l}ynicki-Birula and Mycielski entropic uncertainty relation almost everywhere. Furthermore, we show how a Wehrl mutual information can be used to obtain a measurable perfect witness for pure state bipartite entanglement, which additionally provides a lower bound on the entanglement entropy., Comment: 15 pages, 3 figures

The quantum effective action yields equations of motion and correlation functions including all quantum corrections. We discuss here how it encodes also Noether currents at the full quantum level. Interestingly, the construction can be generalized beyond the standard symmetry transformations that leave the action invariant. We also discuss an extended set of transformations, which change the action by a term that is locally known on the level of the quantum effective action. Associated to such extended gauge transformations are currents for which we obtain a divergence-type equation of motion, but they are not conserved. We call them non-conserved Noether currents. We discuss in particular symmetries and extended transformations associated to space-time geometry for relativistic quantum field theories. These encompass local dilatations or Weyl gauge transformation, local Lorentz transformations and local shear transformations. Together they constitute the symmetry group of the frame bundle GL$(d)$. The corresponding non-conserved Noether currents are the dilatation or Weyl current, the spin current and the shear current. In particular for the latter we obtain a new divergence-type equations of motion., Comment: 25 pages

Quantum uncertainty relations are formulated in terms of relative entropy between distributions of measurement outcomes and suitable reference distributions with maximum entropy. This type of entropic uncertainty relation can be applied directly to observables with either discrete or continuous spectra. We find that a sum of relative entropies is bounded from above in a nontrivial way, which we illustrate with some examples., Comment: 10 pages, no figures

The second law of thermodynamics is discussed and reformulated from a quantum information theoretic perspective for open quantum systems using relative entropy. Specifically, the relative entropy of a quantum state with respect to equilibrium states is considered and its monotonicity property with respect to an open quantum system evolution is used to obtain second law-like inequalities. We discuss this first for generic quantum systems in contact with a thermal bath and subsequently turn to a formulation suitable for the description of local dynamics in a relativistic quantum field theory. A local version of the second law similar to the one used in relativistic fluid dynamics can be formulated with relative entropy or even relative entanglement entropy in a space-time region bounded by two light cones. We also give an outlook towards isolated quantum field theories and discuss the role of entanglement for relativistic fluid dynamics., Comment: 15 pages, 3 figures

A new truncation scheme based on the cumulant expansion of the one-particle phase-space distribution function for dark matter particles is developed. Extending the method of moments in relativistic kinetic theory, we derive evolution equations which supplement the covariant conservation of the energy-momentum tensor and particle number current. Truncating the cumulant expansion we obtain a closed, covariant and hyperbolic system of equations which can be used to model the evolution of a general relativistic non-ideal fluid. As a working example we consider a Friedmann-Lema\^itre-Robertson-Walker cosmology with dynamic pressure and solve for the time evolution of the effective equation of state parameter., Comment: 10 pages, 1 figure

Four models for the initial conditions of a fluid dynamic description of high energy heavy ion collisions are analysed and compared. We study expectation values and event-by-event fluctuations in the initial transverse energy density profiles from Pb-Pb collisions. Specifically, introducing a Fourier-Bessel mode expansion for fluctuations, we determine expectation values and two-mode correlation functions of the expansion coefficients. The analytically solveable independent point-sources model is compared to an initial state model based on Glauber theory and two models based on the Color Glass Condensate framework. We find that the large wavelength modes of all investigated models show universal properties for central collisions and also discuss to which extent general properties of initial conditions can be understood analytically., Comment: 18 pages, 8 figures, results are attached as ancillary files; presentation in section IV rephrased for clarification, typos corrected, references added

The existing transformation from a relativistic real scalar field to a complex non-relativistic scalar field by Namjoo, Guth, and Kaiser is generalized from Minkowski space to a more general background metric. In that case the transformation is not purely algebraic any more but determined by a differential equation. We apply the generalized transformation to a real scalar with $\phi^4$ interaction on an Friedmann-Lema\^itre-Robertson-Walker cosmologically expanding background and calculate the resulting non-relativistic action up to second order in small parameters. We also show that the transformation can be interpreted as a Bogoliubov transformation between relativistic and non-relativistic creation and annihilation operators and comment on emerging symmetries in the non-relativistic theory.

Thermodynamics is usually developed starting from entropy and the maximum entropy principle. We investigate here to what extent one can replace entropy with relative entropy which has several advantages, for example in the context of local quantum field theory. We find that the principle of maximum entropy can be replaced by a principle of minimum expected relative entropy. Various ensembles and their thermodynamic potentials can be defined through relative entropy. We also show that thermal fluctuations are in fact governed by a relative entropy. Furthermore we reformulate the third law of thermodynamics using relative entropy only., Comment: 14 pages, 1 figure

Real Clifford algebras for arbitrary number of space and time dimensions as well as their representations in terms of spinors are reviewed and discussed. The Clifford algebras are classified in terms of isomorphic matrix algebras of real, complex or quaternionic type. Spinors are defined as elements of minimal or quasi-minimal left ideals within the Clifford algebra and as representations of the pin and spin groups. Two types of Dirac adjoint spinors are introduced carefully. The relation between mathematical structures and applications to describe relativistic fermions is emphasized throughout., Comment: 42 pages

Dark matter evolution during the process of cosmological structure formation can be described in terms of a one-particle irreducible effective action at a characteristic scale $k_m$ and a loop expansion below this scale, based on the effective propagators and vertices. We calculate the form of the effective vertices and compute the bispectrum of density perturbations within a one-loop approximation. We find that the effective vertices play a subdominant role as compared to the effective viscosity and sound velocity that modify the (inverse) propagators. For the bispectrum we reproduce the results of standard perturbation theory in the range where it is applicable, and find a slightly improved agreement with N-body simulations at larger wavenumbers., Comment: 24 pages, 9 figures

In a quantum field theory, apparent thermalization can be a consequence of entanglement as opposed to scatterings. We discuss here how this can help to explain open puzzles such as the success of thermal models in electron-positron collisions. It turns out that an expanding relativistic string described by the Schwinger model (which also underlies the Lund model) has at early times an entanglement entropy that is extensive in rapidity. At these early times, the reduced density operator is of thermal form, with an entanglement temperature $T_\tau=\hbar/(2\pi k_B\tau)$, even in the absence of any scatterings., Comment: Contribution to the proceedings of Quark Matter 2018, to appear in Nuclear Physics A

The current state of research on high-energy heavy ion physics, including its motivations and purpose is reviewed from a theorist's perspective. Possible future directions are discussed, in particular the possibility of investigating the regime of small transverse momenta in more detail and an improved interplay between experiments and dedicated theory development., Comment: Contribution to the proceedings of the Sixth Annual Conference on Large Hadron Collider Physics (LHCP2018)

Cosmological perturbation theory for the late Universe dominated by dark matter is extended beyond the perfect fluid approximation by taking the dark matter velocity dispersion tensor as an additional field into account. A proper tensor decomposition of the latter leads to two additional scalar fields, as well as a vector and a tensor field. Most importantly, the trace of the velocity dispersion tensor can have a spatially homogeneous and isotropic expectation value. While it decays at early times, we show that a back-reaction effect quadratic in perturbations makes it grow strongly at late times. We compare sterile neutrinos as a candidate for comparatively warm dark matter to weakly interacting massive particles as a rather cold dark matter candidate and show that the late time growth of velocity dispersion is stronger for the latter. Another feature of a non-vanishing velocity dispersion expectation value is that it destroys the apparent self-consistency of the single-stream approximation and allows thereby to treat times and scales beyond shell-crossing., Comment: 37 pages, 11 figures

As a result of a non-trivial mixing matrix, neutrinos cannot be simultaneously in a flavor and mass eigenstate. We formulate and discuss information entropic relations that quantify the associated quantum uncertainty. We also formulate a protocol to determine the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix from quantum manipulations and measurements on an entangled lepton-neutrino pair. The entangled state features neutrino oscillations in a conditional probability involving measurements on the lepton and the neutrino. They can be switched off by choosing a specific observable on the lepton side which is determined by the PMNS matrix. The parameters of the latter, including the CP-violating phase $\delta$, can be obtained by guessing them and improving the guess by minimizing the remaining oscillations., Comment: 16 pages, 2 figures

The fluid dynamics of a relativistic fireball with longitudinal and transverse expansion is described using a background-fluctuation splitting. Symmetry representations of azimuthal rotations and longitudinal boosts are used for a classification of initial state configurations and their fluid dynamic propagation in terms of a mode expansion. We develop an accurate and efficient numerical scheme based on the pseudo-spectral method to solve the resulting hyperbolic partial differential equations. Comparison to the analytically known Gubser solution underlines the high accuracy of this technique. We also present first applications of FluiduM to central heavy ion collisions at the LHC energies featuring a realistic thermodynamic equations of state as well as shear and bulk viscous dissipation., Comment: 36 pages, 12 figures

In the context of ultra-relativistic nuclear collisions, we present a fast method for calculating the final particle spectra after the direct decay of resonances from a Cooper-Frye integral over the freeze-out surface. The method is based on identifying components of the final particle spectrum that transform in an irreducible way under rotations in the fluid-restframe. Corresponding distribution functions can be pre-computed including all resonance decays. Just a few of easily tabulated scalar functions then determine the Lorentz invariant decay spectrum from each space-time point, and simple integrals of these scalar functions over the freeze-out surface determine the final decay products. This by-passes numerically costly event-by-event calculations of the intermediate resonances. The method is of considerable practical use for making realistic data to model comparisons of the identified particle yields and flow harmonics, and for studying the viscous corrections to the freeze-out distribution function., Comment: 14 pages, 5 figures, for the code to compute irreducible components of the decay distribution see https://github.com/amazeliauskas/FastReso ; v2 small clarifications, added a figure, updated references, published version

We develop a novel real-time approach to computing the entanglement between spatial regions for Gaussian states in quantum field theory. The entanglement entropy is characterized in terms of local correlation functions on space-like Cauchy hypersurfaces. The framework is applied to explore an expanding light cone geometry in the particular case of the Schwinger model for quantum electrodynamics in 1+1 space-time dimensions. We observe that the entanglement entropy becomes extensive in rapidity at early times and that the corresponding local reduced density matrix is a thermal density matrix for excitations around a coherent field with a time dependent temperature. Since the Schwinger model successfully describes many features of multiparticle production in $e^+ e^-$ collisions, our results provide an attractive explanation in this framework for the apparent thermal nature of multiparticle production even in the absence of significant final state scattering., Comment: 39 pages, 4 figures

Dissipative relativistic fluid dynamics is not always causal and can favor superluminal signal propagation under certain circumstances. On the other hand, high-energy nuclear collisions have a microscopic description in terms of QCD and are expected to follow the causality principle of special relativity. We discuss under which conditions the fluid evolutions for a radial expansion are hyperbolic and how the properties of the solutions are encoded in the associated characteristic curves. The expansion dynamics is causal in relativistic sense if the characteristic velocities are smaller than the speed of light. We obtain a concrete inequality from this constraint and discuss how it can be violated for certain initial conditions. We argue that causality poses a bound to the applicability of relativistic fluid dynamics. }, Comment: 23 pages, 13 figures; Added references, corrected typos, added discussion as section 2, results unchanged

A surprising result in $e^+ e^-$ collisions is that the particle spectra from the string formed between the expanding quark-antiquark pair have thermal properties even though scatterings appear not to be frequent enough to explain this. We address this problem by considering the finite observable interval of a relativistic quantum string in terms of its reduced density operator by tracing over the complement region. We show how quantum entanglement in the presence of a horizon in spacetime for the causal transfer of information leads locally to a reduced mixed-state density operator. For very early proper time $\tau$, we show that the entanglement entropy becomes extensive and scales with the rapidity. At these early times, the reduced density operator is of thermal form, with an entanglement temperature $T_\tau=\hbar/(2\pi k_B \tau)$, even in the absence of any scatterings., Comment: 5 pages, 3 figures, published version

Following an approach of Matarrese and Pietroni, we derive the functional renormalization group (RG) flow of the effective action of cosmological large-scale structures. Perturbative solutions of this RG flow equation are shown to be consistent with standard cosmological perturbation theory. Non-perturbative approximate solutions can be obtained by truncating the a priori infinite set of possible effective actions to a finite subspace. Using for the truncated effective action a form dictated by dissipative fluid dynamics, we derive RG flow equations for the scale dependence of the effective viscosity and sound velocity of non-interacting dark matter, and we solve them numerically. Physically, the effective viscosity and sound velocity account for the interactions of long-wavelength fluctuations with the spectrum of smaller-scale perturbations. We find that the RG flow exhibits an attractor behaviour in the IR that significantly reduces the dependence of the effective viscosity and sound velocity on the input values at the UV scale. This allows for a self-contained computation of matter and velocity power spectra for which the sensitivity to UV modes is under control., Comment: In revised version, affiliations corrected

The analytic continuation from the Euclidean domain to real space of the one-particle irreducible quantum effective action is discussed in the context of generalized local equilibrium states. Discontinuous terms associated with dissipative behavior are parametrized in terms of a conveniently defined sign operator. A generalized variational principle is then formulated, which allows to obtain causal and real dissipative equations of motion from the analytically continued quantum effective action. Differential equations derived from the implications of general covariance determine the space-time evolution of the temperature and fluid velocity fields and allow for a discussion of entropy production including a local form of the second law of thermodynamics., Comment: 34 pages, improved discussion of dissipative terms in energy momentum tensor, references added

There are interesting parallels between the physics of heavy ion collisions and cosmology. Both systems are out-of-equilibrium and relativistic fluid dynamics plays an important role for their theoretical description. From a comparison one can draw interesting conclusions for both sides. For heavy ion physics it could be rewarding to attempt a theoretical description of fluid perturbations similar to cosmological perturbation theory. In the context of late time cosmology, it could be interesting to study dissipative properties such as shear and bulk viscosity and corresponding relaxation times in more detail. Knowledge and experience from heavy ion physics could help to constrain the microscopic properties of dark matter from observational knowledge of the cosmological fluid properties., Comment: 8 pages, Plenary contribution to the proceedings of Quark Matter 2015, Kobe, Japan