Coarse graining and first order phase transitions

We discuss the dependence of the coarse grained free energy and the classical interface tension on the coarse graining scale $k$. A stable range appears only if the renormalized dimensionless couplings at the critical temperature are small. This gives a quantitative criterion for the validity of computations within Langer's theory of spontaneous bubble nucleation.Comment: 14 pages, 5 figure

Renormalized thermodynamics from the 2PI effective action

High-temperature resummed perturbation theory is plagued by poor convergence properties. The problem appears for theories with bosonic field content such as QCD, QED or scalar theories. We calculate the pressure as well as other thermodynamic quantities at high temperature for a scalar one-component field theory, solving a three-loop 2PI effective action numerically without further approximations. We present a detailed comparison with the two-loop approximation. One observes a strongly improved convergence behavior as compared to perturbative approaches. The renormalization employed in this work extends previous prescriptions, and is sufficient to determine all counterterms required for the theory in the symmetric as well as the spontaneously broken phase.Comment: 20 pages, 7 figures; PRD version, references added, very minor change

Solving non-perturbative flow equations

Non-perturbative exact flow equations describe the scale dependence of the effective average action. We present a numerical solution for an approximate form of the flow equation for the potential in a three-dimensional N-component scalar field theory. The critical behaviour, with associated critical exponents, can be inferred with good accuracy.Comment: Latex, 14 pages, 2 uuencoded figure

Turning a First Order Quantum Phase Transition Continuous by Fluctuations: General Flow Equations and Application to d-Wave Pomeranchuk Instability

We derive renormalization group equations which allow us to treat order parameter fluctuations near quantum phase transitions in cases where an expansion in powers of the order parameter is not possible. As a prototypical application, we analyze the nematic transition driven by a d-wave Pomeranchuk instability in a two-dimensional electron system. We find that order parameter fluctuations suppress the first order character of the nematic transition obtained at low temperatures in mean-field theory, so that a continuous transition leading to quantum criticality can emerge

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 $\mu$ 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.Comment: 27 pages, Int.J.Mod.Phys.A versio

Quantum-mechanical tunnelling and the renormalization group

We explore the applicability of the exact renormalization group to the study of tunnelling phenomena. We investigate quantum-mechanical systems whose energy eigenstates are affected significantly by tunnelling through a barrier in the potential. Within the approximation of the derivative expansion, we find that the exact renormalization group predicts the correct qualitative behaviour for the lowest energy eigenvalues. However, quantitative accuracy is achieved only for potentials with small barriers. For large barriers, the use of alternative methods, such as saddle-point expansions, can provide quantitative accuracy.Comment: 9 pages, 5 figures, to appear in Phys. Lett.

Renormalization-group study of weakly first-order phase transitions

We study the universal critical behaviour near weakly first-order phase transitions for a three-dimensional model of two coupled scalar fields -- the cubic anisotropy model. Renormalization-group techniques are employed within the formalism of the effective average action. We calculate the universal form of the coarse-grained free energy and deduce the ratio of susceptibilities on either side of the phase transition. We compare our results with those obtained through Monte Carlo simulations and the epsilon-expansion.Comment: 8 pages, 4 figures in eps forma

Non-equilibrium dynamics of a Bose-Einstein condensate in an optical lattice

The dynamical evolution of a Bose-Einstein condensate trapped in a one-dimensional lattice potential is investigated theoretically in the framework of the Bose-Hubbard model. The emphasis is set on the far-from-equilibrium evolution in a case where the gas is strongly interacting. This is realized by an appropriate choice of the parameters in the Hamiltonian, and by starting with an initial state, where one lattice well contains a Bose-Einstein condensate while all other wells are empty. Oscillations of the condensate as well as non-condensate fractions of the gas between the different sites of the lattice are found to be damped as a consequence of the collisional interactions between the atoms. Functional integral techniques involving self-consistently determined mean fields as well as two-point correlation functions are used to derive the two-particle-irreducible (2PI) effective action. The action is expanded in inverse powers of the number of field components N, and the dynamic equations are derived from it to next-to-leading order in this expansion. This approach reaches considerably beyond the Hartree-Fock-Bogoliubov mean-field theory, and its results are compared to the exact quantum dynamics obtained by A.M. Rey et al., Phys. Rev. A 69, 033610 (2004) for small atom numbers.Comment: 9 pages RevTeX, 3 figure

The Universal Equation of State near the Critical Point of QCD

We study the universal properties of the phase diagram of QCD near the critical point using the exact renormalization group. For two-flavour QCD and zero quark masses we derive the universal equation of state in the vicinity of the tricritical point. For non-zero quark masses we explain how the universal equation of state of the Ising universality class can be used in order to describe the physical behaviour near the line of critical points. The effective exponents that parametrize the growth of physical quantities, such as the correlation length, are given by combinations of the critical exponents of the Ising class that depend on the path along which the critical point is approached. In general the critical region, in which such quantities become large, is smaller than naively expected.Comment: 22 pages, 4 figures, new analytical calculations in sections 4 and 6, references added, version to appear in Nucl. Phys.