Non-equilibrium Quantum Field Theory Research Articles

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.

Open quantum dynamics induced by light scalar fields

We consider the impact of a weakly coupled environment comprising a light scalar field on the open dynamics of a quantum probe field, resulting in a master equation for the probe field that features corrections to the coherent dynamics, as well as decoherence and momentum diffusion. The light scalar is assumed to couple to matter either through a nonminimal coupling to gravity or, equivalently, through a Higgs portal. Motivated by applications to experiments such as atom interferometry, we assume that the probe field can be initialized, by means of external driving, in a state that is not an eigenstate of the light scalar-field--probe system, and we derive the master equation for single-particle matrix elements of the reduced density operator of a toy model. We comment on the possibilities for experimental detection and the related challenges, and highlight possible pathways for further improvements. This derivation of the master equation requires techniques of non-equilibrium quantum field theory, including the Feynman-Vernon influence functional and thermo field dynamics, used to motivate a method of Lehmann-Symanzik-Zimmermann-like reduction. In order to obtain cutoff-independent results for the probe-field dynamics, we find that it is necessary to use a time-dependent renormalization procedure. Specifically, we show that non-Markovian effects following a quench, namely the violation of time-translational invariance due to finite-time effects, lead to a time-dependent modulation of the usual vacuum counterterms.

Dark matter Sommerfeld-enhanced annihilation and bound-state decay at finite temperature

Traditional computations of the dark matter (DM) relic abundance, for models where attractive self-interactions are mediated by light force-carriers and bound states exist, rely on the solution of a coupled system of classical on-shell Boltzmann equations. This idealized description misses important thermal effects caused by the tight coupling among force-carriers and other charged relativistic species potentially present during the chemical decoupling process. We develop for the first time a comprehensive ab initio derivation for the description of DM long-range interactions in the presence of a hot and dense plasma background directly from nonequilibrium quantum field theory. Our results clarify a few conceptional aspects of the derivation and show that under certain conditions the finite temperature effects can lead to sizable modifications of DM Sommerfeld-enhanced annihilation and bound-state decay rates. In particular, the scattering and bound states get strongly mixed in the thermal plasma environment, representing a characteristic difference from a pure vacuum theory computation. The main result of this work is a novel differential equation for the DM number density, written down in a form which is manifestly independent under the choice of what one would interpret as a bound or a scattering state at finite temperature. The collision term, unifying the description of annihilation and bound-state decay, turns out to have in general a nonquadratic dependence on the DM number density. This generalizes the form of the conventional Lee-Weinberg equation which is typically adopted to describe the freeze-out process. We prove that our number density equation is consistent with previous literature results under certain limits. In the limit of vanishing finite temperature corrections our central equation is fully compatible with the classical on-shell Boltzmann equation treatment. So far, finite temperature corrected annihilation rates for long-range force systems have been estimated from a method relying on linear response theory. We prove consistency between the latter and our method in the linear regime close to chemical equilibrium.

Nonequilibrium quantum spin dynamics from two-particle irreducible functional integral techniques in the Schwinger boson representation

We present a non-equilibrium quantum field theory approach to the initial-state dynamics of spin models based on two-particle irreducible (2PI) functional integral techniques. It employs a mapping of spins to Schwinger bosons for arbitrary spin interactions and spin lengths. At next-to-leading order (NLO) in an expansion in the number of field components, a wide range of non-perturbative dynamical phenomena are shown to be captured, including relaxation of magnetizations in a 3D long-range interacting system with quenched disorder, different relaxation behaviour on both sides of a quantum phase transition and the crossover from relaxation to arrest of dynamics in a disordered spin chain previously shown to exhibit many-body-localization. Where applicable, we employ alternative state-of-the-art techniques and find rather good agreement with our 2PI NLO results. As our method can handle large system sizes and converges relatively quickly to its thermodynamic limit, it opens the possibility to study those phenomena in higher dimensions in regimes in which no other efficient methods exist. Furthermore, the approach to classical dynamics can be investigated as the spin length is increased.

Creation and Evolution of Particle Number Asymmetry in an Expanding Universe

We introduce a model which may generate particle number asymmetry in an expanding Universe. The model includes CP violating and particle number violating interactions. The model consists of a real scalar field and a complex scalar field. Starting with an initial condition specified by a density matrix, we show how the asymmetry is created through the interaction and how it evolves at later time. We compute the asymmetry using non-equilibrium quantum field theory and as a first test of the model, we study how the asymmetry evolves in the flat limit.

Leptogenesis from oscillations of heavy neutrinos with large mixing angles

The extension of the Standard Model by heavy right-handed neutrinos can simultaneously explain the observed neutrino masses via the seesaw mechanism and the baryon asymmetry of the Universe via leptogenesis. If the mass of the heavy neutrinos is below the electroweak scale, they may be found at the LHC, BELLE II, NA62, the proposed SHiP experiment or a future high-energy collider. In this mass range, the baryon asymmetry is generated via CP-violating oscillations of the heavy neutrinos during their production. We study the generation of the baryon asymmetry of the Universe in this scenario from first principles of non-equilibrium quantum field theory,including spectator processes and feedback effects. We eliminate several uncertainties from previous calculations and find that the baryon asymmetry of the Universe can be explained with larger heavy neutrino mixing angles, increasing the chance for an experimental discovery. For the limiting cases of fast and strongly overdamped oscillations of right-handed neutrinos, the generation of the baryon asymmetry can be calculated analytically up to corrections of order one.

Renormalization out of equilibrium in a superrenormalizable theory

We discuss the renormalization of the initial value problem in Nonequilibrium Quantum Field Theory within a simple, yet instructive, example and show how to obtain a renormalized time evolution for the two-point functions of a scalar field and its conjugate momentum at all times. The scheme we propose is applicable to systems that are initially far from equilibrium and compatible with non-secular approximation schemes which capture thermalization. It is based on Kadanoff-Baym equations for non-Gaussian initial states, complemented by usual vacuum counterterms. We explicitly demonstrate how various cutoff-dependent effects peculiar to nonequilibrium systems, including time-dependent divergences or initial-time singularities, are avoided by taking an initial non-Gaussian three-point vacuum correlation into account.

Equilibration of a quantum field in de Sitter space-time

We address the following question: To what extent can a quantum field tell if it has been placed in de Sitter space? Our approach is to use the techniques of non-equilibrium quantum field theory to compute the time evolution of a state which starts off in flat space for (conformal) times $\eta<\eta_0$, and then evolves in a de Sitter background turned on instantaneously at $\eta=\eta_0$. We find that the answer depends on what quantities one examines. We study a range of them, all based on two-point correlation functions, and analyze which ones approach the standard Bunch-Davies values over time. The outcome of this analysis suggests that the nature of the equilibration process in this system is similar to that in more familiar systems.

Relic density computations at NLO: infrared finiteness and thermal correction

Abstract There is an increasing interest in accurate dark matter relic density predictions, which requires next-to-leading order (NLO) calculations. The method applied up to now uses zero-temperature NLO calculations of annihilation cross sections in the standard Boltzmann equation for freeze-out, and is conceptually problematic, since it ignores the finite-temperature infrared (IR) divergences from soft and collinear radiation and virtual effects. We address this problem systematically by starting from non-equilibrium quantum field theory, and demonstrate on a realistic model that soft and collinear temperature-dependent divergences cancel in the collision term. Our analysis provides justification for the use of the freeze-out equation in its conventional form and determines the leading finite-temperature correction to the annihilation cross section. This turns out to have a remarkably simple structure.

Time variation of particle and antiparticle asymmetry in an expanding universe

Particle number violating interactions wash out the primordial asymmetry of particle number density generated by some interaction satisfying Sakharov conditions for baryogenesis. In this paper, we study how the primordial asymmetry evolves in time under the presence of particle number violating interactions and in the environment of expanding universe. We introduce a complex scalar model with particle number violating mass terms and calculate the time evolution of the particle number density with non-equilibrium quantum field theory. We show how the time evolution of the number density depends on parameters, including the chemical potential related with the particle number, temperature, size of the particle number violating mass terms, and the expansion rate of the universe. Depending upon whether the chemical potential is larger or smaller than the rest mass of the scalar particle, behaviors of the number density are very different to each other. When the chemical potential is smaller than the mass, the interference among the contribution of oscillators with various momenta reduces the number density in addition to the dilution due to the expansion of universe. In opposite case, the oscillation of the particle number density lasts for a long time and the cancellation due to the interference does not occur.

Leptogenesis in crossing and runaway regimes

We study the impact of effective thermal masses and widths on resonant leptogenesis. We identify two distinct possibilities which we refer to as crossing and runaway regimes. In the runaway regime the mass difference grows monotonously with temperature, whereas it initially decreases in the crossing regime, such that the effective masses become equal at some temperature. Following the conventional logic the source of the asymmetry would vanish in the latter case. Using non-equilibrium quantum field theory, we analytically demonstrate that the vanishing of the difference of the effective masses does however neither imply a suppression nor a strong enhancement of the source for the lepton asymmetry. In the vicinity of the crossing point the asymmetry calculated in an (improved) Boltzmann limit develops a spurious peak, which signals the breakdown of the quasiparticle approximation. In the exact result this spurious enhancement is compensated by coherent transitions between the two mass shells. Despite the breakdown of the quasiparticle approximation off-shell contributions remain negligibly small even at the crossing point.

Quantum and medium effects in (resonant) leptogenesis

Leptogenesis offers a very attractive explanation for the origin of the baryon asymmetry of the universe. Such scenarios based on leptonic CP–violation can be realized already within minimalistic seesaw extensions of the standard model. Apart from model building issues the answer to the question of whether a given particle theory can explain the observed baryon number density depends also on the detailed statistical evolution of the asymmetry. The CP–violation within a given model leads to an asymmetry only if it is accompanied by an out–of–equilibrium evolution in the early universe. Most existing analyses employ Boltzmann–like equations (BEs) to describe it. In this context fundamental issues arise which can be addressed in the framework of non–equilibrium quantum field theory (NEQFT). Here, the relevance of quantum and medium effects for thermal leptogenesis is investigated. Within the 2PI–formalism of NEQFT, questions such as that for the justification of the particle picture arise naturally in subsequent approximations when BEs are to be derived. This specific problem is particularly important in the case of resonant leptogenesis where the relevant particle states are almost degenerate in mass. It is found that Boltzmann like equations can (only) be obtained in certain cases. But it is then possible to account for corrections due to quantum and medium effects.

Unruh effect under non-equilibrium conditions: oscillatory motion of an Unruh-DeWitt detector

The Unruh effect refers to the thermal fluctuations a detector experiences while undergoing linear motion with uniform acceleration in a Minkowski vacuum. This thermality can be demonstrated by tracing the vacuum state of the field over the modes beyond the accelerated detector's event horizon. However, the event horizon is well-defined only if the detector moves with eternal uniform linear acceleration. This idealized condition cannot be fulfilled in realistic situations when the motion unavoidably involves periods of non-uniform acceleration. Many experimental proposals to test the Unruh effect are of this nature. Often circular or oscillatory motion, which lacks an obvious geometric description, is considered in such proposals. The proper perspective for theoretically going beyond, or experimentally testing, the Unruh-Hawking effect in these more general conditions has to be offered by concepts and techniques in non-equilibrium quantum field theory. In this paper we provide a detailed analysis of how an Unruh-DeWitt detector undergoing oscillatory motion responds to the fluctuations of a quantum field. Numerical results for the late-time temperatures of the oscillating detector are presented. We comment on the digressions of these results from what one would obtain from a naive application of Unruh's result.

Systematic approach toΔL=1processes in thermal leptogenesis

In this work we study the contribution to leptogenesis from Delta L=1 decay and scattering processes mediated by the Higgs with quarks in the initial and final states using the formalism of non-equilibrium quantum field theory. Starting from fundamental equations for correlators of the quantum fields we derive quantum-corrected Boltzmann and rate equations for the total lepton asymmetry improved in that they include quantum-statistical effects and medium corrections to the quasiparticle properties. To compute the collision term we take into account one- and two-loop contributions to the lepton self-energy and use the extended quasiparticle approximation for the Higgs two-point function. The resulting CP-violating and washout reaction densities are numerically compared to the conventional ones.

Systematic approach to thermal leptogenesis

In this work we study thermal leptogenesis using non-equilibrium quantum field theory. Starting from fundamental equations for correlators of the quantum fields we describe the steps necessary to obtain quantum kinetic equations for quasiparticles. These can easily be compared to conventional results and overcome conceptional problems inherent in the canonical approach. Beyond CP-violating decays we include also those scattering processes which are tightly related to the decays in a consistent approximation of fourth order in the Yukawa couplings. It is demonstrated explicitly how the S-matrix elements for the scattering processes in the conventional approach are related to two- and three-loop contributions to the effective action. We derive effective decay and scattering amplitudes taking medium corrections and thermal masses into account. In this context we also investigate CP-violating Higgs decay within the same formalism. From the kinetic equations we derive rate equations for the lepton asymmetry improved in that they include quantum-statistical effects and medium corrections to the quasiparticle properties.

Leptogenesis from a GeV seesaw without mass degeneracy

For Leptogenesis based on the type-I seesaw mechanism, we present a systematic calculation of lepton-number violating and purely flavoured asymmetries within nonequilibrium Quantum Field Theory. We show that sterile neutrinos with non-degenerate masses in the GeV range can explain the baryon asymmetry of the Universe via flavoured Leptogenesis. This is possible due to the interplay of thermal and flavour effects. Our approach clarifies the relation between Leptogenesis from the oscillations of sterile neutrinos and the more commonly studied scenarios from decays and inverse decays. We explain why lower mass bounds for non-degenerate sterile neutrinos derived for Leptogenesis from out-of-equilibrium decays do not apply to flavoured Leptogenesis with GeV-scale neutrinos.

Real-time quantum dynamics of heavy-quark systems at high temperature

On the basis of the closed-time-path formalism of nonequilibrium quantum field theory, we derive the real-time quantum dynamics of heavy-quark systems. Even though our primary goal is the description of heavy quarkonia, our method allows a unified description of the propagation of single heavy quarks as well as their bound states. To make calculations tractable, we deploy leading-order perturbation theory and consider the nonrelativistic limit. Various dynamical equations, such as the master equation for quantum Brownian motion and the time-evolution equation for heavy-quark and quarkonium forward correlators, are obtained from a single operator: the renormalized effective Hamiltonian. We are thus able to reproduce previous results of perturbative calculations of the drag force and the complex potential simultaneously. In addition, we present stochastic time-evolution equations for the heavy-quark and quarkonium wave function, which are equivalent to the dynamical equations.

The Boltzmann equation from quantum field theory

We show from first principles the emergence of classical Boltzmann equations from relativistic nonequilibrium quantum field theory as described by the Kadanoff–Baym equations. Our method applies to a generic quantum field, coupled to a collection of background fields and sources, in a homogeneous and isotropic spacetime. The analysis is based on analytical solutions to the full Kadanoff–Baym equations, using the WKB approximation. This is in contrast to previous derivations of kinetic equations that rely on similar physical assumptions, but obtain approximate equations of motion from a gradient expansion in momentum space. We show that the system follows a generalized Boltzmann equation whenever the WKB approximation holds. The generalized Boltzmann equation, which includes off-shell transport, is valid far from equilibrium and in a time dependent background, such as the expanding universe.