Juergen Berges

Color superconductivity and chiral symmetry restoration at non-zero baryon density and temperature ☆

We explore the phase diagram of strongly interacting matter as a function of temperature and baryon number density, using a class of models for two-flavor QCD in which the interaction between quarks is modelled by that induced by instantons. Our treatment allows us to investigate the possible simultaneous formation of condensates in the conventional quark-anti-quark channel (breaking chiral symmetry) and in a quark-quark channel leading to color superconductivity: the spontaneous breaking of color symmetry via the formation of quark Cooper pairs. At low temperatures, chiral symmetry restoration occurs via a first-order transition between a phase with low (or zero) baryon density and a high density color superconducting phase. We find color superconductivity in the high density phase for temperatures less than of order tens to 100 MeV, and find coexisting 〈qq〉 and 〈qq〉 condensates in this phase in the presence of a current quark mass. At high temperatures, the chiral phase transition is second order in the chiral limit and is a smooth crossover for non-zero current quark mass. A tricritical point separates the first-order transition at high densities from the second-order transition at high temperatures. In the presence of a current quark mass this tricritical point becomes a second-order phase transition with Ising model exponents, suggesting that a long correlation length may develop in heavy ion collisions in which the phase transition is traversed at the appropriate density.

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 f...

Controlled nonperturbative dynamics of quantum fields out-of-equilibrium

Abstract 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.

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 two-particle irreducible 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.

Thermalization of fermionic quantum fields

Abstract 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 nontrivial 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.

UNLOCKING COLOR AND FLAVOR IN SUPERCONDUCTING STRANGE QUARK MATTER

Abstract We explore the phase diagram of strongly interacting matter with massless u and d quarks as a function of the strange quark mass m s and the chemical potential μ for baryon number. Neglecting electromagnetism, we describe the different baryonic and quark matter phases at zero temperature. For quark matter, we support our model-independent arguments with a quantitative analysis of a model which uses a four-fermion interaction abstracted from single-gluon exchange. For any finite m s , at sufficiently large μ we find quark matter in a color-flavor-locked state which leaves a global vector-like SU (2) color+ L + R symmetry unbroken. As a consequence, chiral symmetry is always broken in sufficiently dense quark matter. As the density is reduced, for sufficiently large m s we observe a first-order transition from the color-flavor-locked phase to color superconducting phase analogous to that in two-flavor QCD. At this unlocking transition chiral symmetry is restored. For realistic values of m s our analysis indicates that chiral symmetry breaking may be present for all densities down to those characteristic of baryonic matter. This supports the idea that quark matter and baryonic matter may be continuously connected in nature. We map the gaps at the quark Fermi surfaces in the high density color-flavor-locked phase onto gaps at the baryon Fermi surfaces at low densities.

Magnetic fields within color superconducting neutron star cores

Abstract We discuss the Meissner effect for a color superconductor formed by cold dense quark matter. Though color and ordinary electromagnetism are broken in a color superconductor, there is a linear combination of the photon and a gluon that remains massless. Consequently, a color superconducting region may be penetrated by an external magnetic field. We show that at most a small fraction of the magnetic field is expelled, and if the screening distance is the smallest length scale in the problem there is no expulsion at all. We calculate the behavior of the magnetic field for a spherical geometry relevant for compact stars. If a neutron star contains a quark matter core, this core is a color superconductor. Our results demonstrate that such cores admit magnetic fields without restricting them to quantized flux tubes. Such magnetic fields within color superconducting neutron star cores are stable on time scales longer than the age of the universe, even if the spin period of the neutron star is changing.

Classical Aspects of Quantum Fields Far from Equilibrium

We consider the time evolution of nonequilibrium quantum scalar fields in the O(N) model, using the next-to-leading order 1/N expansion of the two-particle irreducible effective action. A comparison with exact numerical simulations in 1+1 dimensions in the classical limit shows that the 1/N expansion gives quantitatively precise results already for moderate values of N. For sufficiently high initial occupation numbers the time evolution of quantum fields is shown to be accurately described by classical physics. Eventually the correspondence breaks down due to the difference between classical and quantum thermal equilibrium.

Nonequilibrium time evolution of the spectral function in quantum field theory

Transport or kinetic equations are often derived assuming a quasiparticle ~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 111 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 the presence of strong qualitative changes in the effective particle distribution. These results may be used to make further analytical progress toward a quantum Boltzmann equation including off-shell effects and a nonzero width.

n-particle irreducible effective action techniques for gauge theories

A loop or coupling expansion of a so-called