arXiv subjects

Jürgen Berges

Publications and source records attributed to Jürgen Berges.

At least 19 recordsLinked to original sources

arXiv2026

Nonthermal fixed point for massless scalar field theories

We compute universal scaling exponents and scaling functions for massless scalar field theories far from equilibrium. Using a large-$N$ expansion to next-to-leading order, we investigate the nonperturbative infrared behaviour associated with the transport of a) energy or b) effective particle number towards low frequencies $ω$ and momenta $\bar p$. For massless dispersion $ω= \bar{p}$, we determine the scaling form of the distribution function whose universal power-law tail $f_S(\bar p) \sim 1/\bar{p}^κ$ is found to be a) $κ= d+1$ and b) $κ= d$ in $d=3$ spatial dimensions. Our results establish that relativistic and nonrelativistic theories do not belong to the same universality class in this case, which opens up new applications to far-from-equilibrium phenomena in high-energy and (quantum) many-body physics with linear dispersions.

hep-ph↗

arXiv2026

Renormalised thermodynamics for Bose gases from low to critical temperatures

We compute thermodynamic properties of dilute Bose gases using non-perturbative approximations of the two-particle irreducible (2PI) effective action. It is shown how to systematically renormalise the self-consistent descriptions beyond conventional Gaussian approximations such as Hartree-Fock-Bogoliubov theory. This allows us to determine the condensate depletion from low to high temperatures, including its critical behaviour at the phase transition. While the universal anomalous dimension at criticality is vanishing for Gaussian approximations, we determine its non-zero value at next-to-leading order of a self-consistent expansion in the number of field components.

cond-mat.quant-gas↗

arXiv2026

Tachyonic and parametric instabilities in an extended bosonic Josephson junction

We study the dynamics and decay of quantum phase coherence for Bose-Einstein condensates in tunnel-coupled quantum wires. The two elongated Bose-Einstein condensates exhibit a wide variety of dynamic phenomena where quantum fluctuations can lead to a rapid loss of phase coherence. We investigate the phenomenon of self-trapping in the relative population imbalance of the two condensates, particularly $π$-trapped oscillations that occur when also the relative phase is trapped. Though this state appears stable in mean-field descriptions, the $π$-trapped state becomes dynamically unstable due to quantum fluctuations. Nonequilibrium instabilities result in the generation of pairs excited from the condensate to higher momentum modes. We identify tachyonic instabilities, which are associated with imaginary parts of the dispersion relation, and parametric resonance instabilities that are triggered by oscillations of the relative phase and populations. At early times, we compute the instability chart of the characteristic modes through a linearized analysis and identify the underlying physical process. At later times, the primary instabilities trigger secondary instabilities due to the build-up of non-linearities. We perform numerical simulations in the Truncated Wigner approximation in order to observe the dynamics also in this non-linear regime. Furthermore, we discuss realistic parameters for experimental realizations of the $π$-trapped state in ultracold atom setups.

cond-mat.quant-gas↗

arXiv2025

Far from equilibrium hydrodynamics of nonthermal fixed points

Nonthermal fixed points are paradigmatic far-from-equilibrium phenomena of relevance to high-energy physics, cosmology, and cold atomic gases. We propose that, despite their intrinsically nonequilibrium nature, nonthermal fixed points give rise to hydrodynamic excitations otherwise known in the vicinity of thermal equilibrium. As a result, nonthermal fixed points can also be characterized by transport coefficients, such as a far-from-equilibrium, and therefore manifestly time-dependent, incarnation of shear viscosity. We corroborate our proposal with explicit studies using relativistic kinetic theory with binary collisions of massless particles in the 14-moment approximation and comparisons to QCD kinetic theory simulations.

hep-th↗

arXiv2025

Extracting the symmetries of nonequilibrium quantum many-body systems

Symmetries play a pivotal role in our understanding of the properties of quantum many-body systems. While there are theorems and a well-established toolbox for systems in thermal equilibrium, much less is known about the role of symmetries and their connection to dynamics out of equilibrium. This arises due to the direct link between a system's thermal state and its Hamiltonian, which is generally not the case for nonequilibrium dynamics. Here we present a pathway to identify the effective symmetries and to extract them from data in nonequilibrium quantum many-body systems. Our approach is based on exact relations between correlation functions involving different numbers of spatial points, which can be viewed as nonequilibrium versions of (equal-time) Ward identities encoding the symmetries of the system. We derive symmetry witnesses, which are particularly suitable for the analysis of measured or simulated data at different snapshots in time. To demonstrate the potential of the approach, we apply our method to numerical and experimental data for a spinor Bose gas. We investigate the important question of a dynamical restoration of an explicitly broken symmetry of the Hamiltonian by the initial state. Remarkably, it is found that effective symmetry restoration can occur long before the system equilibrates. We also use the approach to define and identify spontaneous symmetry breaking far from equilibrium, which is of great relevance for applications to nonequilibrium phase transitions. Our work opens new avenues for the classification and analysis of quantum as well as classical many-body dynamics in a large variety of systems, ranging from ultracold quantum gases to cosmology.

cond-mat.quant-gas↗

arXiv2024

Coupling renormalization flow in the strongly interacting regime of an asymptotically free quantum field theory in four dimensions

We consider a scalar quantum field theory with global $O(N)^3$ symmetry in four Euclidean dimensions and solve it numerically in closed form in the large-N limit. For imaginary tetrahedral coupling the theory is asymptotically free, with stable and real quantum effective action. We demonstrate the dynamical build-up of a strong interaction as the correlation length increases in a regime where the coupling renormalization flow remains well defined in the infrared. This is in contrast to perturbative results of asymptotically free theories, which predict that the coupling becomes ill-defined in the infrared, like in quantum chromodynamics. These properties make the model an important laboratory for the study of strong-coupling phenomena in quantum field theory from first principles.

hep-th↗

arXiv2024

Particle production and hadronization temperature in the massive Schwinger model

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.

hep-th↗

arXiv2024

Real-time dynamics of false vacuum decay

We investigate false vacuum decay of a relativistic scalar field initialized in the metastable minimum of an asymmetric double-well potential. The transition to the true ground state is a well-defined initial-value problem in real time, which can be formulated in nonequilibrium quantum field theory on a closed time path. We employ the non-perturbative framework of the two-particle irreducible (2PI) quantum effective action at next-to-leading order in a large-N expansion. We also compare to classical-statistical field theory simulations on a lattice in the high-temperature regime. By this, we demonstrate that the real-time decay rates are comparable to those obtained from the conventional Euclidean (bounce) approach. In general, we find that the decay rates are time dependent. For a more comprehensive description of the dynamics, we extract a time-dependent effective potential, which becomes convex during the nonequilibrium transition process. By solving the quantum evolution equations for the one- and two-point correlation functions for vacuum initial conditions, we demonstrate that quantum corrections can lead to transitions that are not captured by classical-statistical approximations.

hep-th↗

arXiv2023

Probing universal dynamics with topological data analysis in a gluonic plasma

We study nonequilibrium dynamics of SU(2) lattice gauge theory in Minkowski space-time in a classical-statistical regime, where characteristic gluon occupancies are much larger than unity. In this strongly correlated system far from equilibrium, the correlations of energy and topological densities show self-similar behavior related to a turbulent cascade towards higher momentum scales. We employ persistent homology to infer topological features of the gluonic plasma via a hierarchy of simplicial and cubical complexes. All topological observables under investigation are also manifestly gauge invariant and are shown to exhibit self-similar evolution, which relate the spatial and temporal properties of the plasma in terms of universal scaling exponents and functions. The findings may help to understand the early stages of heavy-ion collisions in the limit of high energies, and our methods can also facilitate the topological analysis of other complex systems such as encountered in experiments with ultracold quantum gases.

hep-ph↗

arXiv2023

Asymptotic freedom in a strongly interacting scalar quantum field theory in four Euclidean dimensions

We show that scalar quantum field theory in four Euclidean dimensions with global $O(N)^3$ symmetry and imaginary tetrahedral coupling is asymptotically free and bounded from below in the large-N limit. While the Hamiltonian is non-Hermitian, the full quantum effective action for the large-N theory only depends on the square of that coupling which is real. A perturbative analysis uncovers that the renormalization group flow of the quartic couplings connects a Gaussian ultraviolet fixed point to a strongly interacting theory in the infrared. This realizes a renormalizable field theory which exhibits non-trivial dynamics, such as direct scattering, while still being analytically tractable also non-perturbatively. Our findings open up a way to address outstanding problems in strongly coupled theories from first principles.

hep-th↗

arXiv2023

Order parameters for gauge invariant condensation far from equilibrium

Nuclear collisions at sufficiently high energies are expected to produce far-from-equilibrium matter with a high density of gluons at early times. We show gauge condensation, which occurs as a consequence of the large density of gluons. To identify this condensation phenomenon, we construct two local gauge-invariant observables that carry the macroscopic zero mode of the gauge condensate. The first order parameter for gauge condensation investigated here is the correlator of the spatial Polyakov loop. We also consider, for the first time, the correlator of the gauge invariant scalar field, associated to the exponent of the Polyakov loop. Using real-time lattice simulations of classical-statistical $SU(2)$ gauge theory, we find gauge condensation on a system-size dependent time scale $t_{\text{cond}} \sim L^{1/ζ}$ with a universal scaling exponent $ζ$. Furthermore, we suggest an effective theory formulation describing the dynamics using one of the order parameters identified. The formation of a condensate at early times may have intriguing implications for the early stages in heavy ion collisions.

hep-ph↗

arXiv2022

Stable and unstable perturbations in universal scaling phenomena far from equilibrium

We study the dynamics of perturbations around nonthermal fixed points associated to universal scaling phenomena in quantum many-body systems far from equilibrium. For an N-component scalar quantum field theory in 3+1 space-time dimensions, we determine the stability scaling exponents using a self-consistent large-N expansion to next-to-leading order. Our analysis reveals the presence of both stable and unstable perturbations, the latter leading to quasi-exponential deviations from the fixed point in the infrared. We identify a tower of far-from-equilibrium quasi-particle states and their dispersion relations by computing the spectral function. With the help of linear response theory, we demonstrate that unstable dynamics arises from a competition between elastic scattering processes among the quasi-particle states. What ultimately renders the fixed point dynamically attractive is the phenomenon of a scaling instability, which is the universal scaling of the unstable regime towards the infrared due to a self-similar quasi-particle cascade. Our results provide ab initio understanding of emergent stability properties in self-organized scaling phenomena.

hep-ph↗

arXiv2022

Thermalization dynamics of a gauge theory on a quantum simulator

Gauge theories form the foundation of modern physics, with applications ranging from elementary particle physics and early-universe cosmology to condensed matter systems. We perform quantum simulations of the unitary dynamics of a U(1) symmetric gauge field theory and demonstrate emergent irreversible behavior. The highly constrained gauge theory dynamics is encoded in a one-dimensional Bose--Hubbard simulator, which couples fermionic matter fields through dynamical gauge fields. We investigate global quantum quenches and the equilibration to a steady state well approximated by a thermal ensemble. Our work may enable the investigation of elusive phenomena, such as Schwinger pair production and string-breaking, and paves the way for simulating more complex higher-dimensional gauge theories on quantum synthetic matter devices.

cond-mat.quant-gas↗

arXiv2022

Stability analysis of non-thermal fixed points in longitudinally expanding kinetic theory

We use the Hamiltonian formulation of kinetic theory to perform a stability analysis of non-thermal fixed points in a non-Abelian plasma. We construct a perturbative expansion of the Fokker-Planck collision kernel in an adiabatic approximation and show that the (next-to-)leading order solutions reproduce the known non-thermal fixed point scaling exponents. Working at next-to-leading order, we derive the stability equations for scaling exponents and find the relaxation rate to the non-thermal fixed point. This approach provides the basis for an understanding of the prescaling phenomena observed in QCD kinetic theory and non-relativistic Bose gas systems.

hep-ph↗

arXiv2022

Condensation and thermalization of an easy-plane ferromagnet in a spinor Bose gas

The extensive control of spin makes spintronics a promising candidate for future scalable quantum devices. For the generation of spin-superfluid systems, a detailed understanding of the build-up of coherence and relaxation is necessary. However, to determine the relevant parameters for robust coherence properties and faithfully witnessing thermalization, the direct access to space- and time-resolved spin observables is needed. Here, we study the thermalization of an easy-plane ferromagnet employing a homogeneous one-dimensional spinor Bose gas. Building on the pristine control of preparation and readout we demonstrate the dynamic emergence of long-range coherence for the spin field and verify spin-superfluidity by experimentally testing Landau's criterion. We reveal the structure of the emergent quasi-particles: one 'massive'(Higgs) mode, and two 'massless' (Goldstone) modes - a consequence of explicit and spontaneous symmetry breaking, respectively. Our experiments allow for the first time to observe the thermalization of an easy-plane ferromagnetic Bose gas; we find agreement for the relevant momentum-resolved observables with a thermal prediction obtained from an underlying microscopic model within the Bogoliubov approximation. Our methods and results pave the way towards a quantitative understanding of condensation dynamics in large magnetic spin systems and the study of the role of entanglement and topological excitations for its thermalization.

cond-mat.quant-gas↗

arXiv2022

Equal-time approach to real-time dynamics of quantum fields

We employ the equal-time formulation of quantum field theory to derive effective kinetic theories, first for a weakly coupled non-relativistic Bose gas, and then for a strongly correlated system of self-interacting N-component fields. Our results provide the link between state-of-the-art measurements of equal-time effective actions using quantum simulator platforms, as employed in Refs. [1, 2], and observables underlying effective kinetic or hydrodynamic descriptions. New non-perturbative approximation schemes can be developed and certified this way, where the a priori time-local formulation of the equal-time effective action has crucial advantages over the conventional closed-time-path approach which is non-local in time.

cond-mat.quant-gas↗

arXiv2022

Non-equilibrium dynamics of fluctuations in an ultra-cold atomic mixture

We investigate an ultra-cold mixture of Bose gases interacting via spin-changing collisions by studying the dynamics of spin fluctuations. The experimental implementation employs $^{23}$Na and $^{7}$Li atoms, which are prepared out of equilibrium across a wide range of initial conditions. We identify three regimes in the dynamics of the system for different initial states: a long-lived metastable regime, an instability range with strong growth of fluctuations, and a fast relaxing regime approaching thermal equilibrium. Theoretical modelling of the data allows us to reconstruct effective potentials which characterize the different dynamical regimes of the system.

cond-mat.quant-gas↗

arXiv2021

Finding self-similar behavior in quantum many-body dynamics via persistent homology

Inspired by topological data analysis techniques, we introduce persistent homology observables and apply them in a geometric analysis of the dynamics of quantum field theories. As a prototype application, we consider data from a classical-statistical simulation of a two-dimensional Bose gas far from equilibrium. We discover a continuous spectrum of dynamical scaling exponents, which provides a refined classification of nonequilibrium self-similar phenomena. A possible explanation of the underlying processes is provided in terms of mixing strong wave turbulence and anomalous vortex kinetics components in point clouds. We find that the persistent homology scaling exponents are inherently linked to the geometry of the system, as the derivation of a packing relation reveals. The approach opens new ways of analyzing quantum many-body dynamics in terms of robust topological structures beyond standard field theoretic techniques.

cond-mat.quant-gas↗