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J. Berges

Publications and source records attributed to J. Berges.

At least 73 records · Page 4Linked to original sources
arXiv2004

Introduction to Nonequilibrium Quantum Field Theory

There has been substantial progress in recent years in the quantitative understanding of the nonequilibrium time evolution of quantum fields. Important topical applications, in particular in high energy particle physics and cosmology, involve dynamics of quantum fields far away from the ground state or thermal equilibrium. In these cases, standard approaches based on small deviations from equilibrium, or on a sufficient homogeneity in time underlying kinetic descriptions, are not applicable. A particular challenge is to connect the far-from-equilibrium dynamics at early times with the approach to thermal equilibrium at late times. Understanding the ``link'' between the early- and the late-time behavior of quantum fields is crucial for a wide range of phenomena. For the first time questions such as the explosive particle production at the end of the inflationary universe, including the subsequent process of thermalization, can be addressed in quantum field theory from first principles. The progress in this field is based on efficient functional integral techniques, so-called n-particle irreducible effective actions, for which powerful nonperturbative approximation schemes are available. Here we give an introduction to these techniques and show how they can be applied in practice. Though we focus on particle physics and cosmology applications, we emphasize that these techniques can be equally applied to other nonequilibrium phenomena in complex many body systems.

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arXiv2004

n-Particle irreducible effective action techniques for gauge theories

A loop or coupling expansion of a so-called n-particle irreducible (nPI) generating functional provides a well-defined approximation scheme in terms of self-consistently dressed propagators and n-point vertices. A self-consistently complete description determines the functional for arbitrarily high n to a given order in the expansion. We point out an equivalence hierarchy for nPI effective actions, which allows one to obtain a self-consistently complete result in practice. The method is applied to a SU(N) gauge theory with fermions up to four-loop or O(g^6) corrections. For non-equilibrium we discuss the connection to kinetic theory. The leading-order on-shell results in g can be obtained from the three-loop effective action approximation, which already includes in particular all diagrams enhanced by the Landau Pomeranchuk Migdal effect. Furthermore, we compare the effective action approach with Schwinger-Dyson (SD) equations. By construction, SD equations are expressed in terms of loop diagrams including both classical and dressed vertices, which leads to ambiguities of whether classical or dressed ones should be employed at a given truncation order. We point out that these problems are absent using effective action techniques. We show that a wide class of truncations of SD equations cannot be obtained from the nPI effective action. In turn, our results can be used to resolve SD ambiguities of whether classical or dressed vertices should be employed at a given truncation order.

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arXiv2004

Critical phenomena from the two-particle irreducible 1/N expansion

The 1/N expansion of the two-particle irreducible (2PI) effective action is employed to compute universal properties at the second-order phase transition of an O(N)-symmetric N-vector model directly in three dimensions. At next-to-leading order the approach cures the spurious small-N divergence of the standard (1PI) 1/N expansion for a computation of the critical anomalous dimension eta(N), and leads to improved estimates already for moderate values of N.

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arXiv2004

Critical Phenomena in Continuous Dimension

We present a calculation of critical phenomena directly in continuous dimension d employing an exact renormalization group equation for the effective average action. For an Ising-type scalar field theory we calculate the critical exponents nu(d) and eta(d) both from a lowest--order and a complete first--order derivative expansion of the effective average action. In particular, this can be used to study critical behavior as a function of dimensionality at fixed temperature.

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arXiv2003

Parametric resonance in quantum field theory

We present the first study of parametric resonance in quantum field theory from a complete next-to-leading order calculation in a 1/N-expansion of the 2PI effective action, which includes scattering and memory effects. We present a complete numerical solution for an O(N)-symmetric scalar theory and provide an approximate analytic description of the nonlinear dynamics in the entire amplification range. We find that the classical resonant amplification at early times is followed by a collective amplification regime with explosive particle production in a broad momentum range, which is not accessible in a leading-order calculation.

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arXiv2003

Thermalization of fermionic quantum fields

We solve the nonequilibrium dynamics of a 3+1 dimensional theory with Dirac fermions coupled to scalars via a chirally invariant Yukawa interaction. The results are obtained from a systematic coupling expansion of the 2PI effective action to lowest non-trivial order, which includes scattering as well as memory and off-shell effects. The dynamics is solved numerically without further approximation, for different far-from-equilibrium initial conditions. The late-time behavior is demonstrated to be insensitive to the details of the initial conditions and to be uniquely determined by the initial energy density. Moreover, we show that at late time the system is very well characterized by a thermal ensemble. In particular, we are able to observe the emergence of Fermi--Dirac and Bose--Einstein distributions from the nonequilibrium dynamics.

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arXiv2003

Quark and Nuclear Matter in the Linear Chiral Meson Model

We present an analytical description of the phase transitions from a nucleon gas to nuclear matter and from nuclear matter to quark matter within the same model. The equation of state for quark and nuclear matter is encoded in the effective potential of a linear sigma model. We exploit an exact differential equation for its dependence upon the chemical potential $μ$ associated to conserved baryon number. An approximate solution for vanishing temperature is used to discuss possible phase transitions as the baryon density increases. For a nucleon gas and nuclear matter we find a substantial density enhancement as compared to quark models which neglect the confinement to baryons. The results point out that the latter models are not suitable to discuss the phase diagram at low temperature.

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arXiv2002

Nonequilibrium quantum fields with large fluctuations

We consider the nonequilibrium evolution of an O(N)-symmetric scalar quantum field theory using a systematic two-particle irreducible 1/N-expansion to next-to-leading order, which includes scattering and memory effects. The corresponding ``full Kadanoff-Baym equations'' are solved numerically without further approximations. This allows one to obtain a controlled nonperturbative description of far-from-equilibrium dynamics and the late-time approach to quantum thermal equilibrium. Employing in addition a first-order gradient expansion for the Wigner transformed correlators we derive kinetic equations. In contrast to standard descriptions based on loop expansions, our equations remain valid for nonperturbatively large fluctuations. As an application, we discuss the fluctuation dominated regime following parametric resonance in quantum field theory.

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arXiv2002

Far-from-equilibrium dynamics with broken symmetries from the 2PI-1/N expansion

We derive the nonequilibrium real-time evolution of an O(N) - invariant scalar quantum field theory in the presence of a nonvanishing expectation value of the quantum field. Using a systematic 1/N expansion of the 2PI effective action to next-to-leading order, we obtain nonperturbative evolution equations which include scattering and memory effects. The equivalence of the direct method, which requires the resummation of an infinite number of skeleton diagrams, with the auxiliary-field formalism, which involves only one diagram at next-to-leading order, is shown.

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arXiv2002

Nonequilibrium Quantum Fields and the Classical Field Theory Limit

We calculate the far-from-equilibrium dynamics and thermalization both for the quantum and the classical O(N)--model. The early and late-time behavior can be described from the 2PI--loop expansion for weak couplings or the nonperturbative 2PI--1/N expansion of the effective action beyond leading order. A comparison with exact simulations in 1+1 dimensions in the classical limit shows that the 2PI--1/N expansion at next-to-leading order gives quantitatively precise results already for moderate values of N. We derive a criterion for the validity of the classical approximation and verify it by comparing far-from-equilibrium quantum and classical dynamics. At late times one observes the expected deviations due to the difference between classical and quantum thermal equilibrium.

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arXiv2001

Quantum Fields far from Equilibrium and Thermalization

I review the use of the 2PI effective action in nonequilibrium quantum field theory. The approach enables one to find approximation schemes which circumvent long-standing problems of non-thermal or secular (unbounded) late-time evolutions encountered in standard loop or 1/N expansions of the 1PI effective action. It is shown that late-time thermalization can be described from a numerical solution of the three-loop 2PI effective action for a scalar $ϕ^4$--theory in 1+1 dimensions (with Jurgen Cox, hep-ph/0006160). Quantitative results far from equilibrium beyond the weak coupling expansion can be obtained from the 1/N expansion of the 2PI effective action at next-to-leading order (NLO), calculated for a scalar O(N) symmetric quantum field theory (hep-ph/0105311). Extending recent calculations in classical field theory by Aarts et al. (hep-ph/0007357) and by Blagoev et al. (hep-ph/0106195) to $N>1$ we show that the NLO approximation converges to exact (MC) results already for moderate values of $N$ (with Gert Aarts, hep-ph/0107129). I comment on characteristic time scales in scalar quantum field theory and the applicability of classical field theory for sufficiently high initial occupation numbers.

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arXiv2001

Controlled nonperturbative dynamics of quantum fields out of equilibrium

We compute the nonequilibrium real-time evolution of an O(N)-symmetric scalar quantum field theory from a systematic 1/N expansion of the 2PI effective action to next-to-leading order, which includes scattering and memory effects. In contrast to the standard 1/N expansion of the 1PI effective action, the next-to-leading order expansion in presence of a possible expectation value for the composite operator leads to a bounded time evolution where the truncation error may be controlled by higher powers in 1/N. We present a detailed comparison with the leading-order results and determine the range of validity of standard mean field type approximations. We investigate ``quench'' and ``tsunami'' initial conditions frequently used to mimic idealized far-from-equilibrium pion dynamics in the context of heavy-ion collisions. For spatially homogeneous initial conditions we find three generic regimes, characterized by an early-time exponential damping, a parametrically slow (power-law) behavior at intermediate times, and a late-time exponential approach to thermal equilibrium. The different time scales are obtained from a numerical solution of the time-reversal invariant equations in 1+1 dimensions without further approximations. We discuss in detail the out-of-equilibrium behavior of the nontrivial n-point correlation functions as well as the evolution of a particle number distribution and inverse slope parameter.

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arXiv2001

Nonequilibrium time evolution of the spectral function in quantum field theory

Transport or kinetic equations are often derived assuming a quasi-particle (on-shell) representation of the spectral function. We investigate this assumption using a three-loop approximation of the 2PI effective action in real time, without a gradient expansion or on-shell approximation. For a scalar field in 1+1 dimensions the nonlinear evolution, including the integration over memory kernels, can be solved numerically. We find that a spectral function approximately described by a nonzero width emerges dynamically. During the nonequilibrium time evolution the Wigner transformed spectral function is slowly varying, even in presence of strong qualitative changes in the effective particle distribution. These results may be used to make further analytical progress towards a quantum Boltzmann equation including off-shell effects and a nonzero width.

hep-ph↗
arXiv2000

Higgs description of two-flavor QCD vacuum

A Higgs description for the QCD vacuum in the limit of two quark flavors is proposed. Complete ``spontaneous breaking'' of color symmetry is realized by condensation of an adjoint quark-antiquark and a quark-quark pair. The vacuum is invariant under isospin symmetry applying color and flavor transformations simultaneously. All elementary excitations acquire integral charges. The dressed microscopic quark and gluon degrees of freedom can be identified with the macroscopic baryon and vector meson degrees of freedom. In addition to the nucleons we find soliton--type fermions with integer isospin. Their presence provides an important test accessible to lattice QCD simulations.

hep-ph↗
arXiv2000

Quark description of nuclear matter

We discuss the role of an adjoint chiral condensate for color superconducting quark matter. Its presence leads to color-flavor locking in two-flavor quark matter. Color is broken completely as well as chiral symmetry in the two-flavor theory with coexisting adjoint quark-antiquark and antitriplet quark-quark condensates. The qualitative properties of this phase match the properties of ordinary nuclear matter without strange baryons. This complements earlier proposals by Schafer and Wilczek for a quark description of hadronic phases. We show for a class of models with effective four-fermion interactions that adjoint chiral and diquark condensates do not compete, in the sense that simultaneous condensation occurs for sufficiently strong interactions in the adjoint chiral channel.

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arXiv2000

Thermalization of Quantum Fields from Time-Reversal Invariant Evolution Equations

We study the time evolution of correlation functions in closed quantum systems for nonequilibrium ensembles of initial conditions. For a scalar quantum field theory we show that generic time-reversal invariant evolutions approach equilibrium at large times. The calculation provides a first principles justification of Boltzmann's conjecture that the large-time behavior of isolated macroscopic systems can be described by thermal ensemble averages.

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arXiv2000

Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics

We review the use of an exact renormalization group equation in quantum field theory and statistical physics. It describes the dependence of the free energy on an infrared cutoff for the quantum or thermal fluctuations. Non-perturbative solutions follow from approximations to the general form of the coarse-grained free energy or effective average action. They interpolate between the microphysical laws and the complex macroscopic phenomena. Our approach yields a simple unified description for O(N)-symmetric scalar models in two, three or four dimensions, covering in particular the critical phenomena for the second-order phase transitions, including the Kosterlitz-Thouless transition and the critical behavior of polymer chains. We compute the aspects of the critical equation of state which are universal for a large variety of physical systems and establish a direct connection between microphysical and critical quantities for a liquid-gas transition. Universal features of first-order phase transitions are studied in the context of scalar matrix models. We show that the quantitative treatment of coarse graining is essential for a detailed estimate of the nucleation rate. We discuss quantum statistics in thermal equilibrium or thermal quantum field theory with fermions and bosons and we describe the high temperature symmetry restoration in quantum field theories with spontaneous symmetry breaking. In particular, we explore chiral symmetry breaking and the high temperature or high density chiral phase transition in quantum chromodynamics using models with effective four-fermion interactions.

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