Non-equilibrium Quantum Field Theory Research Articles

From QFT to Boltzmann: freeze-in in the presence of oscillating condensates

Scalar dark matter (DM), and axions in particular, have an irreducible abundance of particles produced by freeze-in due to portal interactions with the Standard Model plasma in the early Universe. In addition, vacuum misalignment and other mechanisms can lead to the presence of a cold, oscillating condensate. Therefore, generically, the evolution of the DM in both forms, condensate and particles, needs to be studied simultaneously. In non-equilibrium quantum field theory, the condensate and particles are described by one- and two-point functions, respectively. The fundamental coupled equations of motion (EoMs) of these objects are non-local. To simplify the EoMs and bring them into a familiar form for relic abundance calculations, we perform a Markovianization process for a quasi-harmonically oscillating homogeneous condensate, leading to local EoMs for the particle distribution function and the envelope function of condensate oscillation. This reduces the dynamics to a pair of coupled Boltzmann equations, and we derive explicitly the form of the collision operators for all particle and condensate interactions.

Towards a Field-Theory based Relativistic Quantum Information

We present our program for the development of quantum informational concepts in relativistic systems in terms of the unequal-time correlation functions of quantum fields. We employ two formalisms that provide the basis for further developments. (i) The Quantum Temporal Probabilities (QTP) Method for quantum field measurements and (ii) the Closed-Time-Path (CTP) formalism for causal time evolutions. We present the main ideas of QTP and we show how it relates to the CTP formalism, allowing us to express concepts of measurement theory in terms of path-integrals. We also present many links of our program to non-equilibrium quantum field theories. Details can be found in a recent paper by the authors [1].

Quantum field theory based quantum information: Measurements and correlations

This is the first in a series of papers aiming to develop a relativistic quantum information theory in terms of unequal-time correlation functions in quantum field theory. In this work, we highlight two formalisms which together can provide a useful theoretical platform suitable for further developments: (1) Quantum field measurements using the Quantum Temporal Probabilities (QTP) method; (2) Closed-Time-Path (CTP) formalism for causal time evolutions. QTP incorporates the detector into the quantum description, while emphasizing that the records of measurement are macroscopic and can be expressed in terms of classical spacetime coordinates. We first present a new, elementary derivation of the QTP formulas for the probabilities of n measurement events. We then demonstrate the relation of QTP with the Closed-Time-Path formalism, by writing an explicit formula that relates the associated generating functionals. We exploit the path integral representation of the CTP formalism, in order to express the measured probabilities in terms of path integrals. After this, we provide some simple applications of the QTP formalism. In particular, we show how Unruh–DeWitt detector models and Glauber’s photodetection theory appear as limiting cases. Finally, with quantum correlation being the pivotal notion in relativistic quantum information and measurements, we highlight the role played by the CTP two-particle irreducible effective action which enables one to tap into the resources of non-equilibrium quantum field theory for our stated purpose.

New method for directly computing reduced density matrices

We demonstrate the power of a first principle-based and practicable method that allows for the perturbative computation of reduced density matrix elements of an open quantum system without making use of any master equations. The approach is based on techniques from non-equilibrium quantum field theory like thermo field dynamics, the Schwinger-Keldsyh formalism, and the Feynman-Vernon influence functional. It does not require the Markov approximation and is essentially a Lehmann-Szymanzik-Zimmermann-like reduction. In order to illustrate this method, we consider a real scalar field as an open quantum system interacting with an environment comprising another real scalar field. We give a general formula that allows for the perturbative computation of density matrix elements for any number of particles in a momentum basis. Finally, we consider a simple toy model and use this formula to obtain expressions for some of the system's reduced density matrix elements.

Density Matrix Formalism for Interacting Quantum Fields

We provide a description of interacting quantum fields in terms of density matrices for any occupation numbers in Fock space in a momentum basis. As a simple example, we focus on a real scalar field interacting with another real scalar field, and present a practicable formalism for directly computing the density matrix elements of the combined scalar–scalar system. For deriving the main formula, we use techniques from non-equilibrium quantum field theory like thermo-field dynamics and the Schwinger–Keldysh formalism. Our results allow for studies of particle creation/annihilation processes at finite times and other non-equilibrium processes, including those found in the theory of open quantum systems.

Dissipation of oscillating scalar backgrounds in an FLRW universe

We study the dissipation of oscillating scalar backgrounds in a spatially flat Friedmann-Lemaître-Robertson-Walker universe using non-equilibrium quantum field theory. To be concrete, a Z2-symmetric two-scalar model with quartic interactions is used. For quasi-harmonic oscillations, we adopt the multi-scale analysis to obtain analytical approximate expressions for the evolution of the scalar background in terms of the retarded self-energy and retarded proper four-vertex function. Different from the case in flat spacetime, we find that in an expanding universe the condensate decay in this model can be complete only if the imaginary part of the retarded self-energy is not negligibly small. The microphysical interpretation of the imaginary parts of the retarded self-energy and retarded proper four-vertex function in terms of particle production is also discussed.

The two-particle irreducible effective action for classical stochastic processes

By combining the two-particle-irreducible (2PI) effective action common in non-equilibrium quantum field theory with the classical Martin–Siggia–Rose formalism, self-consistent equations of motion for the first and second cumulants of non-linear classical stochastic processes are constructed. Such dynamical equations for correlation and response functions are important in describing non-equilibrium systems, where equilibrium fluctuation–dissipation relations are unavailable. The method allows to evolve stochastic systems from arbitrary Gaussian initial conditions. In the non-linear case, it is found that the resulting integro-differential equations can be solved with considerably reduced computational effort compared to state-of-the-art stochastic Runge–Kutta methods. The details of the method are illustrated by several physical examples.

Coupled hydrodynamics in dipole-conserving quantum systems

We investigate the coupled dynamics of charge and energy in interacting lattice models with dipole conservation. We formulate a generic hydrodynamic theory for this combination of fractonic constraints and numerically verify its applicability to the late-time dynamics of a specific bosonic quantum system by developing a microscopic non-equilibrium quantum field theory. Employing a self-consistent $1/N$ approximation in the number of field components, we extract all entries of a generalized diffusion matrix and determine their dependence on microscopic model parameters. We discuss the relation of our results to experiments in ultracold atom quantum simulators.

General Markovian equation for scalar fields in a slowly evolving background

We present a general and model-independent method to obtain an effective Markovian quantum kinetic equation for the expectation value of a slowly evolving scalar field in an adiabatically evolving background from first principles of nonequilibrium quantum field theory. The method requires almost no assumptions about the field's interactions and the composition of the background, except that 1) the coupling constants shall be small enough for perturbation theory to be applicable, 2) there is a clear separation between microphysical time scales and the rate at which bulk properties change, and 3) higher time derivatives of the field remain small. The resulting Markovian equation of motion is expressed in terms of an effective potential and friction coefficients. Motivated by cosmological applications we focus on spatially homogeneous and isotropic systems, but the approach could also be applied to spatial gradients.

Quantum noise of gravitons and stochastic force on geodesic separation

In this work we consider the effects of gravitons and their fluctuations on the dynamics of two masses using the Feynman-Vernon influence functional formalism, applied earlier to nonequilibrium quantum field theory [Calzetta and Hu, Nonequilibrium Quantum Field Theory (Cambridge University Press, Cambridge, England, 2008)] and semiclassical stochastic gravity [Hu and Verdaguer, Semiclassical and Stochastic Gravity: Quantum Field Effects on Curved Spacetime (Cambridge University Press, Cambridge, England, 2020)], and most recently, to this problem by Parikh et al., [Phys. Rev. Lett. 127, 081602 (2021); Phys. Rev. D 104, 046021 (2021)]. The Hadamard function of the gravitons yields the noise kernel acting as a stochastic tensorial force in a Langevin equation governing the motion of the separation of the two masses. The fluctuations of the separation due to the graviton noise are then solved for various quantum states including the Minkowski vacuum, thermal, coherent and squeezed states. The previous considerations of Parikh et al. are only for some selected modes of the graviton, while in this work we have included all graviton modes and polarizations. We comment on the possibility of detecting these fluctuations in primordial gravitons using interferometors with long baselines in deep space experiments.

Cutting rules on a cylinder: a simplified diagrammatic approach to quantum kinetic theory

Nonequilibrium quantum field theory is often used to derive an approximation for the evolution of number densities and asymmetries in astroparticle models when a more precise treatment of quantum thermal effects is required. This work presents an alternative framework using the zero-temperature quantum field theory, S-matrix unitarity, and classical Boltzmann equation as starting points leading to a set of rules for calculations of thermal corrections to reaction rates. Statistical factors due to on-shell intermediate states are obtained from the cuts of forward diagrams with multiple spectator lines. It turns out that it is equivalent to cutting closed diagrams on a cylindrical surface.

Intrinsic Entropy of Squeezed Quantum Fields and Nonequilibrium Quantum Dynamics of Cosmological Perturbations.

Density contrasts in the universe are governed by scalar cosmological perturbations which, when expressed in terms of gauge-invariant variables, contain a classical component from scalar metric perturbations and a quantum component from inflaton field fluctuations. It has long been known that the effect of cosmological expansion on a quantum field amounts to squeezing. Thus, the entropy of cosmological perturbations can be studied by treating them in the framework of squeezed quantum systems. Entropy of a free quantum field is a seemingly simple yet subtle issue. In this paper, different from previous treatments, we tackle this issue with a fully developed nonequilibrium quantum field theory formalism for such systems. We compute the covariance matrix elements of the parametric quantum field and solve for the evolution of the density matrix elements and the Wigner functions, and, from them, derive the von Neumann entropy. We then show explicitly why the entropy for the squeezed yet closed system is zero, but is proportional to the particle number produced upon coarse-graining out the correlation between the particle pairs. We also construct the bridge between our quantum field-theoretic results and those using the probability distribution of classical stochastic fields by earlier authors, preserving some important quantum properties, such as entanglement and coherence, of the quantum field.

Oscillating scalar dissipating in a medium

We study how oscillations of a scalar field condensate are damped due to dissipative effects in a thermal medium. Our starting point is a non-linear and non-local condensate equation of motion descending from a 2PI-resummed effective action derived in the Schwinger-Keldysh formalism appropriate for non-equilibrium quantum field theory. We solve this non-local equation by means of multiple-scale perturbation theory appropriate for time-dependent systems, obtaining approximate analytic solutions valid for very long times. The non-linear effects lead to power-law damping of oscillations, that at late times transition to exponentially damped ones characteristic for linear systems. These solutions describe the evolution very well, as we demonstrate numerically in a number of examples. We then approximate the non-local equation of motion by a Markovianised one, resolving the ambiguities appearing in the process, and solve it utilizing the same methods to find the very same leading approximate solution. This comparison justifies the use of Markovian equations at leading order. The standard time-dependent perturbation theory in comparison is not capable of describing the non-linear condensate evolution beyond the early time regime of negligible damping. The macroscopic evolution of the condensate is interpreted in terms of microphysical particle processes. Our results have implications for the quantitative description of the decay of cosmological scalar fields in the early Universe, and may also be applied to other physical systems.

Collisional strong-field QED kinetic equations from first principles

Starting from nonequilibrium quantum field theory on a closed time path, we derive kinetic equations for the strong-field regime of quantum electrodynamics (QED) using a systematic expansion in the gauge coupling $e$. The strong field regime is characterized by a large photon field of order $\mathcal{O}(1/e)$, which is relevant for the description of, e.g., intense laser fields, the initial stages of off-central heavy ion collisions, and condensed matter systems with net fermion number. The strong field enters the dynamical equations via both quantum Vlasov and collision terms, which we derive to order $\mathcal{O}(e^2)$. The kinetic equations feature generalized scattering amplitudes that have their own equation of motion in terms of the fermion spectral function. The description includes single photon emission, electron-positron pair photoproduction, vacuum (Schwinger) pair production, their inverse processes, medium effects and contributions from the field, which are not restricted to the so-called locally-constant crossed field approximation. This extends known kinetic equations commonly used in strong-field QED of intense laser fields. In particular, we derive an expression for the asymptotic fermion pair number that includes leading-order collisions and remains valid for strongly inhomogeneous fields. For the purpose of analytically highlighting limiting cases, we also consider plane-wave fields for which it is shown how to recover Furry-picture scattering amplitudes by further assuming negligible occupations. Known on-shell descriptions are recovered in the case of simply peaked ultrarelativistic fermion occupations. Collisional strong-field equations are necessary to describe the dynamics to thermal equilibrium starting from strong-field initial conditions.

Nonequilibrium Dynamics of the Chiral Quark Condensate under a Strong Magnetic Field

Strong magnetic fields impact quantum-chromodynamics (QCD) properties in several situations; examples include the early universe, magnetars, and heavy-ion collisions. These examples share a common trait—time evolution. A prominent QCD property impacted by a strong magnetic field is the quark condensate, an approximate order parameter of the QCD transition between a high-temperature quark-gluon phase and a low-temperature hadronic phase. We use the linear sigma model with quarks to address the quark condensate time evolution under a strong magnetic field. We use the closed time path formalism of nonequilibrium quantum field theory to integrate out the quarks and obtain a mean-field Langevin equation for the condensate. The Langevin equation features dissipation and noise kernels controlled by a damping coefficient. We compute the damping coefficient for magnetic field and temperature values achieved in peripheral relativistic heavy-ion collisions and solve the Langevin equation for a temperature quench scenario. The magnetic field changes the dissipation and noise pattern by increasing the damping coefficient compared to the zero-field case. An increased damping coefficient increases fluctuations and time scales controlling condensate’s short-time evolution, a feature that can impact hadron formation at the QCD transition. The formalism developed here can be extended to include other order parameters, hydrodynamic modes, and system’s expansion to address magnetic field effects in complex settings as heavy-ion collisions, the early universe, and magnetars.

Dark matter bound-state formation at higher order: a non-equilibrium quantum field theory approach

The formation of meta-stable dark matter bound states in coannihilating scenarios could efficiently occur through the scattering with a variety of Standard Model bath particles, where light bosons during the electroweak cross over or even massless photons and gluons are exchanged in the t-channel. The amplitudes for those higher-order processes, however, are divergent in the collinear direction of the in- and out-going bath particles if the mediator is massless. To address the issue of collinear divergences, we derive the bound-state formation collision term in the framework of non-equilibrium quantum field theory. The main result is an expression for a more general cross section, which allows to compute higher-order bound-state formation processes inside the primordial plasma background in a comprehensive manner. Based on this result, we show that next-to-leading order contributions, including the bath-particle scattering, are i) collinear finite and ii) generically dominate over the on-shell emission for temperatures larger than the absolute value of the binding energy. Based on a simplified model, we demonstrate that the impact of these new effects on the thermal relic abundance is significant enough to make it worthwhile to study more realistic coannihilation scenarios.

An Analytical Multiple-Temperature Model for Flash Laser Irradiation on Single-Layer Graphene.

A Multiple-Temperature Model is proposed to describe the flash laser irradiation of a single layer of graphene. Zhukovsky’s mathematical approach is applied to solve the Fourier heat equations based upon quantum concepts, including heat operators. Easy solutions were inferred with respect to classical mathematics. Thus, simple equations were set for the electrons and phonon temperatures in the case of flash laser treatment of a single layer of graphene. Our method avoids the difficulties and extensive time-consuming nonequilibrium green function method or quantum field theories when applied in a condensed matter. Simple expressions were deduced that could prove useful for researchers.

Out-of-horizon correlations following a quench in a relativistic quantum field theory

One of the manifestations of relativistic invariance in non-equilibrium quantum field theory is the “horizon effect” a.k.a. light-cone spreading of correlations: starting from an initially short-range correlated state, measurements of two observers at distant space-time points are expected to remain independent until their past light-cones overlap. Surprisingly, we find that in the presence of topological excitations correlations can develop outside of horizon and indeed even between infinitely distant points. We demonstrate this effect for a wide class of global quantum quenches to the sine-Gordon model. We point out that besides the maximum velocity bound implied by relativistic invariance, clustering of initial correlations is required to establish the “horizon effect”. We show that quenches in the sine-Gordon model have an interesting property: despite the fact that the initial states have exponentially decaying correlations and cluster in terms of the bosonic fields, they violate the clustering condition for the soliton fields, which is argued to be related to the non-trivial field topology. The nonlinear dynamics governed by the solitons makes the clustering violation manifest also in correlations of the local bosonic fields after the quench.

Nonlocal emergent hydrodynamics in a long-range quantum spin system

Generic short-range interacting quantum systems with a conserved quantity exhibit universal diffusive transport at late times. We employ non-equilibrium quantum field theory and semi-classical phase-space simulations to show how this universality is replaced by a more general transport process in a long-range XY spin chain at infinite temperature with couplings decaying algebraically with distance as $r^{-\alpha}$. While diffusion is recovered for $\alpha>1.5$, longer-ranged couplings with $0.5<\alpha\leq 1.5 $ give rise to effective classical L\'evy flights; a random walk with step sizes drawn from a distribution with algebraic tails. We find that the space-time dependent spin density profiles are self-similar, with scaling functions given by the stable symmetric distributions. As a consequence, for $0.5<\alpha\leq1.5$ autocorrelations show hydrodynamic tails decaying in time as $t^{-1/(2\alpha-1)}$ and linear-response theory breaks down. Our findings can be readily verified with current trapped ion experiments.

Leptogenesis via varying Weinberg operator: the Closed-Time-Path approach

In this work we provide a detailed study of the CP violating phase transition (CPPT) which is a new mechanism proposed to produce a baryon asymmetry. This mechanism exploits the Weinberg operator whose coefficient is dynamically realised from the vacuum expectation values (VEVs) of new scalars. In the specific case of the first order phase transition, the scalar VEVs vary in the bubble wall which separates the two phases. This results in a spacetime varying coefficient for the Weinberg operator. The interference of two Weinberg operators at different spacetime points generates a CP asymmetry between lepton and anti-lepton production/annihilation processes, which eventually results in an asymmetry between baryon and anti-baryon number densities in the early Universe. We present the calculation of the lepton asymmetry, based on non-equilibrium quantum field theory methods, in full. We consider the influence of the bubble wall characteristics and the impact of thermal effects on the lepton asymmetry and draw a comparison between the CPPT mechanism and electroweak baryogenesis.