Critical behavior of weakly interacting bosons: A functional renormalization group approach

We present a detailed investigation of the momentum-dependent self-energy Sigma(k) at zero frequency of weakly interacting bosons at the critical temperature T_c of Bose-Einstein condensation in dimensions 3<=D<4. Applying the functional renormalization group, we calculate the universal scaling function for the self-energy at zero frequency but at all wave vectors within an approximation which truncates the flow equations of the irreducible vertices at the four-point level. The self-energy interpolates between the critical regime k > k_c, where k_c is the crossover scale. In the critical regime, the self-energy correctly approaches the asymptotic behavior Sigma(k) \propto k^{2 - eta}, and in the short-wavelength regime the behavior is Sigma(k) \propto k^{2(D-3)} in D>3. In D=3, we recover the logarithmic divergence Sigma(k) \propto ln(k/k_c) encountered in perturbation theory. Our approach yields the crossover scale k_c as well as a reasonable estimate for the critical exponent eta in D=3. From our scaling function we find for the interaction-induced shift in T_c in three dimensions, Delta T_c / T_c = 1.23 a n^{1/3}, where a is the s-wave scattering length and n is the density, in excellent agreement with other approaches. We also discuss the flow of marginal parameters in D=3 and extend our truncation scheme of the renormalization group equations by including the six- and eight-point vertex, which yields an improved estimate for the anomalous dimension eta \approx 0.0513. We further calculate the constant lim_{k->0} Sigma(k)/k^{2-eta} and find good agreement with recent Monte-Carlo data.Comment: 23 pages, 7 figure

Self-energy and critical temperature of weakly interacting bosons

Using the exact renormalization group we calculate the momentum-dependent self-energy Sigma (k) at zero frequency of weakly interacting bosons at the critical temperature T_c of Bose-Einstein condensation in dimensions 3 <= D < 4. We obtain the complete crossover function interpolating between the critical regime k << k_c, where Sigma (k) propto k^{2 - eta}, and the short-wavelength regime k >> k_c, where Sigma (k) propto k^{2 (D-3)} in D> 3 and Sigma (k) \propto ln (k/k_c) in D=3. Our approach yields the crossover scale k_c on the same footing with a reasonable estimate for the critical exponent eta in D=3. From our Sigma (k) we find for the interaction-induced shift of T_c in three dimensions Delta T_c / T_c approx 1.23 a n^{1/3}, where a is the s-wave scattering length and n is the density.Comment: 4 pages,1 figur

Deformation of anisotropic Fermi surfaces due to electron-electron interactions

We analyze the deformations of the Fermi surface induced by electron-electron interactions in anisotropic two dimensional systems. We use perturbation theory to treat, on the same footing, the regular and singular regions of the Fermi surface. It is shown that, even for weak local coupling, the self-energy presents a nontrivial behavior showing momentum dependence and interplay with the Fermi surface shape. Our scheme gives simple analytical expressions based on local features of the Fermi surface.Comment: 7 pages, 3 figure

Exact integral equation for the renormalized Fermi surface

The true Fermi surface of a fermionic many-body system can be viewed as a fixed point manifold of the renormalization group (RG). Within the framework of the exact functional RG we show that the fixed point condition implies an exact integral equation for the counterterm which is needed for a self-consistent calculation of the Fermi surface. In the simplest approximation, our integral equation reduces to the self-consistent Hartree-Fock equation for the counterterm.Comment: 5 pages, 1 figur

Conserving Gapless Mean-Field Theory for Weakly Interacting Bose Gases

This paper presents a conserving gapless mean-field theory for weakly interacting Bose gases. We first construct a mean-field Luttinger-Ward thermodynamic functional in terms of the condensate wave function $\Psi$ and the Nambu Green's function $\hat{G}$ for the quasiparticle field. Imposing its stationarity respect to $\Psi$ and $\hat{G}$ yields a set of equations to determine the equilibrium for general non-uniform systems. They have a plausible property of satisfying the Hugenholtz-Pines theorem to provide a gapless excitation spectrum. Also, the corresponding dynamical equations of motion obey various conservation laws. Thus, the present mean-field theory shares two important properties with the exact theory: ``conserving'' and ``gapless.'' The theory is then applied to a homogeneous weakly interacting Bose gas with s-wave scattering length $a$ and particle mass $m$ to clarify its basic thermodynamic properties under two complementary conditions of constant density $n$ and constant pressure $p$. The superfluid transition is predicted to be first-order because of the non-analytic nature of the order-parameter expansion near $T_{c}$ inherent in Bose systems, i.e., the Landau-Ginzburg expansion is not possible here. The transition temperature $T_{c}$ shows quite a different interaction dependence between the $n$-fixed and $p$-fixed cases. In the former case $T_{c}$ increases from the ideal gas value $T_{0}$ as $T_{c}/T_{0}= 1+ 2.33 an^{1/3}$, whereas it decreases in the latter as $T_{c}/T_{0}= 1- 3.84a(mp/2\pi\hbar^{2})^{1/5}$. Temperature dependences of basic thermodynamic quantities are clarified explicitly.Comment: 19 pages, 8 figure

Mapping the contribution of β3-containing GABA(A )receptors to volatile and intravenous general anesthetic actions

BACKGROUND: Agents belonging to diverse chemical classes are used clinically as general anesthetics. The molecular targets mediating their actions are however still only poorly defined. Both chemical diversity and substantial differences in the clinical actions of general anesthetics suggest that general anesthetic agents may have distinct pharmacological targets. It was demonstrated previously that the immobilizing action of etomidate and propofol is completely, and the immobilizing action of isoflurane partly mediated, by β3-containing GABA(A )receptors. This was determined by using the β3(N265M) mice, which carry a point mutation known to decrease the actions of general anesthetics at recombinant GABA(A )receptors. In this communication, we analyzed the contribution of β3-containing GABA(A )receptors to the pharmacological actions of isoflurane, etomidate and propofol by means of β3(N265M) mice. RESULTS: Isoflurane decreased core body temperature and heart rate to a smaller degree in β3(N265M) mice than in wild type mice, indicating a minor but significant role of β3-containing GABA(A )receptors in these actions. Prolonged time intervals in the ECG and increased heart rate variability were indistinguishable between genotypes, suggesting no involvement of β3-containing GABA(A )receptors. The anterograde amnesic action of propofol was indistinguishable in β3(N265M) and wild type mice, suggesting that it is independent of β3-containing GABA(A )receptors. The increase of heart rate variability and prolongation of ECG intervals by etomidate and propofol were also less pronounced in β3(N265M) mice than in wild type mice, pointing to a limited involvement of β3-containing GABA(A )receptors in these actions. The lack of etomidate- and propofol-induced immobilization in β3(N265M) mice was also observed in congenic 129X1/SvJ and C57BL/6J backgrounds, indicating that this phenotype is stable across different backgrounds. CONCLUSION: Our results provide evidence for a defined role of β3-containing GABA(A )receptors in mediating some, but not all, of the actions of general anesthetics, and confirm the multisite model of general anesthetic action. This pharmacological separation of anesthetic endpoints also suggests that subtype-selective substances with an improved side-effect profile may be developed

Anaesthesiological strategies in elective craniotomy: randomized, equivalence, open trial – The NeuroMorfeo trial

<p>Abstract</p> <p>Background</p> <p>Many studies have attempted to determine the <it>"best" </it>anaesthetic technique for neurosurgical procedures in patients without intracranial hypertension. So far, no study comparing intravenous (IA) with volatile-based neuroanaesthesia (VA) has been able to demonstrate major outcome differences nor a superiority of one of the two strategies in patients undergoing elective supratentorial neurosurgery. Therefore, current practice varies and includes the use of either volatile or intravenous anaesthetics in addition to narcotics. Actually the choice of the anaestesiological strategy depends only on the anaesthetists' preferences or institutional policies.</p> <p>This trial, named NeuroMorfeo, aims to assess the equivalence between volatile and intravenous anaesthetics for neurosurgical procedures.</p> <p>Methods/Design</p> <p>NeuroMorfeo is a multicenter, randomized, open label, controlled trial, based on an equivalence design. Patients aged between 18 and 75 years, scheduled for elective craniotomy for supratentorial lesion without signs of intracranial hypertension, in good physical state (ASA I-III) and Glasgow Coma Scale (GCS) equal to 15, are randomly assigned to one of three anaesthesiological strategies (two VA arms, sevoflurane + fentanyl or sevoflurane + remifentanil, and one IA, propofol + remifentanil). The equivalence between intravenous and volatile-based neuroanaesthesia will be evaluated by comparing the intervals required to reach, after anaesthesia discontinuation, a modified Aldrete score ≥ 9 (primary end-point). Two statistical comparisons have been planned:</p> <p>1) sevoflurane + fentanyl vs. propofol + remifentanil;</p> <p>2) sevoflurane + remifentanil vs. propofol + remifentanil.</p> <p>Secondary end-points include: an assessment of neurovegetative stress based on (a) measurement of urinary catecholamines and plasma and urinary cortisol and (b) estimate of sympathetic/parasympathetic balance by power spectrum analyses of electrocardiographic tracings recorded during anaesthesia; intraoperative adverse events; evaluation of surgical field; postoperative adverse events; patient's satisfaction and analysis of costs.</p> <p>411 patients will be recruited in 14 Italian centers during an 18-month period.</p> <p>Discussion</p> <p>We presented the development phase of this anaesthesiological on-going trial. The recruitment started December 4^th, 2007 and up to 4^th, December 2008, 314 patients have been enrolled.</p

The nonperturbative functional renormalization group and its applications

The renormalization group plays an essential role in many areas of physics, both conceptually and as a practical tool to determine the long-distance low-energy properties of many systems on the one hand and on the other hand search for viable ultraviolet completions in fundamental physics. It provides us with a natural framework to study theoretical models where degrees of freedom are correlated over long distances and that may exhibit very distinct behavior on different energy scales. The nonperturbative functional renormalization-group (FRG) approach is a modern implementation of Wilson's RG, which allows one to set up nonperturbative approximation schemes that go beyond the standard perturbative RG approaches. The FRG is based on an exact functional flow equation of a coarse-grained effective action (or Gibbs free energy in the language of statistical mechanics). We review the main approximation schemes that are commonly used to solve this flow equation and discuss applications in equilibrium and out-of-equilibrium statistical physics, quantum many-particle systems, high-energy physics and quantum gravity.Comment: v2) Review article, 93 pages + bibliography, 35 figure