47 research outputs found
Renormalization-group investigation of a superconducting -phase transition using five loops calculations
We have studied a Fermi system with attractive -symmetric interaction
at the finite temperatures by the quantum field renormalization group (RG)
method. The RG functions have been calculated in the framework of dimensional
regularization and minimal subtraction scheme up to five loops. It has been
found that for the RG flux leaves the system's stability region --
the system undergoes a first order phase transition. To estimate the
temperature of the transition to superconducting or superfluid phase the RG
analysis for composite operators has been performed using three-loops
approximation. As the result this analysis shows that for systems
estimated phase transition temperature is higher then well known theoretical
estimations based on continuous phase transition formalism
Kraichnan model of passive scalar advection
A simple model of a passive scalar quantity advected by a Gaussian
non-solenoidal ("compressible") velocity field is considered. Large order
asymptotes of quantum-field expansions are investigated by instanton approach.
The existence of finite convergence radius of the series is proved, a position
and a type of the corresponding singularity of the series in the regularization
parameter are determined. Anomalous exponents of the main contributions to the
structural functions are resummed using new information about the series
convergence and two known orders of the expansion.Comment: 21 page
Renormalization Group in Non-Relativistic Quantum Statistics
Dynamic behaviour of a boson gas near the condensation transition in the
symmetric phase is analyzed with the use of an effective large-scale model derived from
time-dependent Green functions at finite temperature. A renormalization-group analysis
shows that the scaling exponents of critical dynamics of the effective multi-charge model
coincide with those of the standard model A. The departure of this result from the descrip tion of the superfluid transition by either model E or F of the standard phenomenological
stochastic models is corroborated by the analysis of a generalization of model F, which
takes into account the effect of compressible fluid velocity. It is also shown that, con trary to the single-charge model A, there are several correction exponents in the effective
model, which are calculated at the leading order of the = 4 − d expansion
Effective large-scale model of boson gas from microscopic theory
An effective large-scale model of interacting boson gas at low temperatures is constructed from first principles. The starting point is the generating function of time-dependent Green functions at finite temperature. The perturbation expansion is worked out for the generic case of finite time interval and grand-canonical density operator with the use of the S-matrix functional for the generating function. Apparent infrared divergences of the perturbation expansion are pointed out. Regularization via attenuation of propagators is proposed and the relation to physical dissipation is studied. Problems of functional-integral representation of Green functions are analyzed. The proposed large-scale model is explicitly renormalized at the leading order
Renormalization Group in Non-Relativistic Quantum Statistics
Dynamic behaviour of a boson gas near the condensation transition in the
symmetric phase is analyzed with the use of an effective large-scale model derived from time-dependent Green functions at finite temperature. A renormalization-group analysis shows that the scaling exponents of critical dynamics of the effective multi-charge model coincide with those of the standard model A. The departure of this result from the description of the superfluid transition by either model E or F of the standard phenomenological stochastic models is corroborated by the analysis of a generalization of model F, which takes into account the effect of compressible fluid velocity. It is also shown that, contrary to the single-charge model A, there are several correction exponents in the effective model, which are calculated at the leading order of the ɛ= 4 − d expansion