33 research outputs found
Applying generalized Pad\'e approximants in analytic QCD models
A method of resummation of truncated perturbation series, related to diagonal
Pad\'e approximants but giving results independent of the renormalization
scale, was developed more than ten years ago by us with a view of applying it
in perturbative QCD. We now apply this method in analytic QCD models, i.e.,
models where the running coupling has no unphysical singularities, and we show
that the method has attractive features such as a rapid convergence. The method
can be regarded as a generalization of the scale-setting methods of Stevenson,
Grunberg, and Brodsky-Lepage-Mackenzie. The method involves the fixing of
various scales and weight coefficients via an auxiliary construction of
diagonal Pad\'e approximant. In low-energy QCD observables, some of these
scales become sometimes low at high order, which prevents the method from being
effective in perturbative QCD where the coupling has unphysical singularities
at low spacelike momenta. There are no such problems in analytic QCD.Comment: 14 pages; extended presentation of the analytic QCD models in Sec.IV;
two references added ([37,38]); version to appear in Phys.Rev.
On kinetic Boltzmann equations and related hydrodynamic flows with dry viscosity
A two-component particle model of Boltzmann-Vlasov type kinetic equations in the form of special nonlinear integro-differential hydrodynamic systems on an infinite-dimensional functional manifold is discussed. We show that such systems are naturally connected with the nonlinear kinetic Boltzmann-Vlasov equations for some one-dimensional particle flows with pointwise interaction potential between particles. A new type of hydrodynamic two-component Benney equations is constructed and their Hamiltonian structure is analyzed
Nonmonotonic Decay of Nonequilibrium Polariton Condensate in Direct-Gap Semiconductors
Time evolution of a nonequilibrium polariton condensate has been studied in
the framework of a microscopic approach. It has been shown that due to
polariton-polariton scattering a significant condensate depletion takes place
in a comparatively short time interval. The condensate decay occurs in the form
of multiple echo signals. Distribution-function dynamics of noncondensate
polaritons have been investigated. It has been shown that at the initial stage
of evolution the distribution function has the form of a bell. Then
oscillations arise in the contour of the distribution function, which further
transform into small chaotic ripples. The appearance of a short-wavelength wing
of the distribution function has been demonstrated. We have pointed out the
enhancement and then partial extinction of the sharp extra peak arising within
the time interval characterized by small values of polariton condensate density
and its relatively slow changes.Comment: 20 pages, LaTeX 2.09; in press in PR
Summing Divergent Perturbative Series in a Strong Coupling Limit. The Gell-Mann - Low Function of the \phi^4 Theory
An algorithm is proposed for determining asymptotics of the sum of a
perturbative series in the strong coupling limit using given values of the
expansion coefficients. Operation of the algorithm is illustrated by test
examples, method for estimating errors is developed, and an optimization
procedure is described. Application of the algorithm to the theory
gives a behavior at large for its Gell-Mann
-- Low function. The fact that the exponent is close to unity can be
interpreted as a manifestation of the logarithmic branching of the type
(with ), which is
confirmed by independent evidence. In any case, the theory is
internally consistent. The procedure of summing perturbartive series with
arbitrary values of expansion parameter is discussed.Comment: 23 pages, PD
What are the experimentally observable effects of vertex corrections in superconductors?
We calculate the effects of vertex corrections, of non-constant density of
states and of a (self-consistently determined) phonon self-energy for the
Holstein model on a 3D cubic lattice. We replace vertex corrections with a
Coulomb pseudopotential, mu*, adjusted to give the same Tc, and repeat the
calculations, to see which effects are a distinct feature of vertex
corrections. This allows us to determine directly observable effects ofvertex
corrections on a variety of thermodynamic properties of superconductors. To
this end, we employ conserving approximations (in the local approximation) to
calculate the superconducting critical temperatures, isotope coefficients,
superconducting gaps, free-energy differences and thermodynamic critical fields
for a range of parameters. We find that the dressed value of lambda is
significantly larger than the bare value. While vertex corrections can cause
significant changes in all the above quantities (even whenthe bare
electron-phonon coupling is small), the changes can usually be well-modeled by
an appropriate Coulomb pseudopotential. The isotope coefficient proves to be
the quantity that most clearly shows effects of vertex corrections that can not
be mimicked by a mu*.Comment: 28 pages, 12 figure
Polaron Variational Methods In The Particle Representation Of Field Theory : I. General Formalism
We apply nonperturbative variational techniques to a relativistic scalar
field theory in which heavy bosons (``nucleons'') interact with light scalar
mesons via a Yukawa coupling. Integrating out the meson field and neglecting
the nucleon vacuum polarization one obtains an effective action in terms of the
heavy particle coordinates which is nonlocal in the proper time. As in
Feynman's polaron approach we approximate this action by a retarded quadratic
action whose parameters are to be determined variationally on the pole of the
two-point function. Several ans\"atze for the retardation function are studied
and for the most general case we derive a system of coupled variational
equations. An approximate analytic solution displays the instability of the
system for coupling constants beyond a critical value.Comment: 33 pages standard LaTeX, 3 uuencoded gzipped postscript figures
embedded with psfig.st
Statistical Mechanics and the Physics of the Many-Particle Model Systems
The development of methods of quantum statistical mechanics is considered in
light of their applications to quantum solid-state theory. We discuss
fundamental problems of the physics of magnetic materials and the methods of
the quantum theory of magnetism, including the method of two-time temperature
Green's functions, which is widely used in various physical problems of
many-particle systems with interaction. Quantum cooperative effects and
quasiparticle dynamics in the basic microscopic models of quantum theory of
magnetism: the Heisenberg model, the Hubbard model, the Anderson Model, and the
spin-fermion model are considered in the framework of novel
self-consistent-field approximation. We present a comparative analysis of these
models; in particular, we compare their applicability for description of
complex magnetic materials. The concepts of broken symmetry, quantum
protectorate, and quasiaverages are analyzed in the context of quantum theory
of magnetism and theory of superconductivity. The notion of broken symmetry is
presented within the nonequilibrium statistical operator approach developed by
D.N. Zubarev. In the framework of the latter approach we discuss the derivation
of kinetic equations for a system in a thermal bath. Finally, the results of
investigation of the dynamic behavior of a particle in an environment, taking
into account dissipative effects, are presented.Comment: 77 pages, 1 figure, Refs.37
Nonequilibrium Quantum Dynamics of Second Order Phase Transitions
We use the so-called Liouville-von Neumann (LvN) approach to study the
nonequilibrium quantum dynamics of time-dependent second order phase
transitions. The LvN approach is a canonical method that unifies the functional
Schr\"{o}dinger equation for the quantum evolution of pure states and the LvN
equation for the quantum description of mixed states of either equilibrium or
nonequilibrium. As nonequilibrium quantum mechanical systems we study a
time-dependent harmonic and an anharmonic oscillator and find the exact Fock
space and density operator for the harmonic oscillator and the nonperturbative
Gaussian Fock space and density operator for the anharmonic oscillator. The
density matrix and the coherent, thermal and coherent-thermal states are found
in terms of their classical solutions, for which the effective Hamiltonians and
equations of motion are derived. The LvN approach is further extended to
quantum fields undergoing time-dependent second order phase transitions. We
study an exactly solvable model with a finite smooth quench and find the
two-point correlation functions. Due to the spinodal instability of long
wavelength modes the two-point correlation functions lead to the
-scaling relation during the quench and the Cahn-Allen scaling
relation after the completion of quench. Further, after the finite
quench the domain formation shows a time-lag behavior at the cubic power of
quench period. Finally we study the time-dependent phase transition of a
self-interacting scalar field.Comment: discussion on back-reaction added, typos corrected, references added,
final version for PR
Convergence and Gauge Dependence Properties of the Resummed One-loop Quark-Quark Scattering Amplitude in Perturbative QCD
The one-loop QCD effective charge for quark-quark scattering
is derived by diagrammatic resummation of the one-loop amplitude using an
arbitary covariant gauge. Except for the particular choice of gauge parameter
, is found to {\it increase} with increasing
physical scale, , as or . For ,
decreases with increasing and satisfies a renormalisation group equation.
Also, except for the case , convergence radii of geometric series
are found to impose upper limits on .Comment: 28 pages, 5 tables, 5 figures. v3 The one-loop amplitudes in Section
2 are recalculated using dimensional regularisation, and several errors in
the on-shell calculation of Reference[1] are pointed out. v4 one figure
removed one added. Three tables and new text in Section 5 added. Published
versio