456 research outputs found
Nonperturbative Effects on T_c of Interacting Bose Gases in Power-Law Traps
The critical temperature T_c of an interacting Bose gas trapped in a general
power-law potential V(x)=\sum_i U_i|x_i|^{p_i} is calculated with the help of
variational perturbation theory. It is shown that the interaction-induced shift
in T_c fulfills the relation (T_c-T_c^0)/T_c^0= D_1(eta)a + D'(eta)a^{2 eta}+
O(a^2) with T_c^0 the critical temperature of the trapped ideal gas, a the
s-wave scattering length divided by the thermal wavelength at T_c, and
eta=1/2+\sum_i 1/p_i the potential-shape parameter. The terms D_1(eta)a and
D'(eta) a^{2 eta} describe the leading-order perturbative and nonperturbative
contributions to the critical temperature, respectively. This result
quantitatively shows how an increasingly inhomogeneous potential suppresses the
influence of critical fluctuations. The appearance of the a^{2 eta}
contribution is qualitatively explained in terms of the Ginzburg criterion.Comment: Author Information under
http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of
paper (including all PS fonts) at
http://www.physik.fu-berlin.de/~kleinert/35
Stability of 3D Cubic Fixed Point in Two-Coupling-Constant \phi^4-Theory
For an anisotropic euclidean -theory with two interactions [u
(\sum_{i=1^M {\phi}_i^2)^2+v \sum_{i=1}^M \phi_i^4] the -functions are
calculated from five-loop perturbation expansions in
dimensions, using the knowledge of the large-order behavior and Borel
transformations. For , an infrared stable cubic fixed point for
is found, implying that the critical exponents in the magnetic phase
transition of real crystals are of the cubic universality class. There were
previous indications of the stability based either on lower-loop expansions or
on less reliable Pad\'{e approximations, but only the evidence presented in
this work seems to be sufficently convincing to draw this conclusion.Comment: Author Information under
http://www.physik.fu-berlin.de/~kleinert/institution.html . Paper also at
http://www.physik.fu-berlin.de/~kleinert/kleiner_re250/preprint.htm
Perturbation Theory for Path Integrals of Stiff Polymers
The wormlike chain model of stiff polymers is a nonlinear -model in
one spacetime dimension in which the ends are fluctuating freely. This causes
important differences with respect to the presently available theory which
exists only for periodic and Dirichlet boundary conditions. We modify this
theory appropriately and show how to perform a systematic large-stiffness
expansions for all physically interesting quantities in powers of ,
where is the length and the persistence length of the polymer. This
requires special procedures for regularizing highly divergent Feynman integrals
which we have developed in previous work. We show that by adding to the
unperturbed action a correction term , we can calculate
all Feynman diagrams with Green functions satisfying Neumann boundary
conditions. Our expansions yield, order by order, properly normalized
end-to-end distribution function in arbitrary dimensions , its even and odd
moments, and the two-point correlation function
Non-abelian descendant of abelian duality in a two-dimensional frustrated quantum magnet
Several recent works on quantum criticality beyond the Landau-Ginzburg-Wilson
paradigm have led to a number of field theories, potentially important for
certain two-dimensional magnetic insulating systems, where criticality is not
very well understood. This situation highlights the need for non-perturbative
information about criticality in two spatial dimensions (three space-time
dimensions), which is a longstanding challenge. As a step toward addressing
these issues, we present evidence that the O(4) vector model is dual to a
theory of Dirac fermions coupled to both SU(2) and U(1) gauge fields. Both
field theories arise as low-energy, long-wavelength descriptions of a
frustrated XY model on the triangular lattice. Abelian boson-vortex duality of
the lattice model, together with the emergence of larger non-abelian symmetry
at low energies, leads to this rare example of duality in two spatial
dimensions involving non-abelian global symmetry and fermions, but without
supersymmetry. The duality can also be viewed as a bosonization of the Dirac
fermion gauge theory.Comment: 12 pages + 3 appendices. 3 figures. Minor change, typos correcte
Screened Perturbation Theory to Three Loops
The thermal physics of a massless scalar field with a phi^4 interaction is
studied within screened perturbation theory (SPT). In this method the
perturbative expansion is reorganized by adding and subtracting a mass term in
the lagrangian. We consider several different mass prescriptions that
generalize the one-loop gap equation to two-loop order. We calculate the
pressure and entropy to three-loop order and the screening mass to two-loop
order. In contrast to the weak-coupling expansion, the SPT-improved
approximations appear to converge even for rather large values of the coupling
constant.Comment: 30 pages, 10 figure
Applicability of the Linear delta Expansion for the lambda phi^4 Field Theory at Finite Temperature in the Symmetric and Broken Phases
The thermodynamics of a scalar field with a quartic interaction is studied
within the linear delta expansion (LDE) method. Using the imaginary-time
formalism the free energy is evaluated up to second order in the LDE. The
method generates nonperturbative results that are then used to obtain
thermodynamic quantities like the pressure. The phase transition pattern of the
model is fully studied, from the broken to the symmetry restored phase. The
results are compared with those obtained with other nonperturbative methods and
also with ordinary perturbation theory. The results coming from the two main
optimization procedures used in conjunction with the LDE method, the Principle
of Minimal Sensitivity (PMS) and the Fastest Apparent Convergence (FAC) are
also compared with each other and studied in which cases they are applicable or
not. The optimization procedures are applied directly to the free energy.Comment: 13 pages, 10 eps figures, revtex, replaced with published versio
Non-adiabatic Josephson Dynamics in Junctions with in-Gap Quasiparticles
Conventional models of Josephson junction dynamics rely on the absence of low
energy quasiparticle states due to a large superconducting gap. With this
assumption the quasiparticle degrees of freedom become "frozen out" and the
phase difference becomes the only free variable, acting as a fictitious
particle in a local in time Josephson potential related to the adiabatic and
non-dissipative supercurrent across the junction. In this article we develop a
general framework to incorporate the effects of low energy quasiparticles
interacting non-adiabatically with the phase degree of freedom. Such
quasiparticle states exist generically in constriction type junctions with high
transparency channels or resonant states, as well as in junctions of
unconventional superconductors. Furthermore, recent experiments have revealed
the existence of spurious low energy in-gap states in tunnel junctions of
conventional superconductors - a system for which the adiabatic assumption
typically is assumed to hold. We show that the resonant interaction with such
low energy states rather than the Josephson potential defines nonlinear
Josephson dynamics at small amplitudes.Comment: 9 pages, 1 figur
Solution to the 3-Loop -Derivable Approximation for Massless Scalar Thermodynamics
We develop a systematic method for solving the 3-loop -derivable
approximation to the thermodynamics of the massless field theory. The
method involves expanding sum-integrals in powers of and m/T, where g is
the coupling constant, m is a variational mass parameter, and T is the
temperature. The problem is reduced to one with the single variational
parameter m by solving the variational equations order-by-order in and
m/T. At the variational point, there are ultraviolet divergences of order
that cannot be removed by any renormalization of the coupling constant. We
define a finite thermodynamic potential by truncating at order in g
and m/T. The associated thermodynamic functions seem to be perturbatively
stable and insensitive to variations in the renormalization scale.Comment: 57 pages, 10 figure
Thermodynamics and Phase Structure of the Two-Flavor Nambu--Jona-Lasinio Model Beyond Large-N_c
The optimized perturbation theory (OPT) method is applied to the
version of the Nambu--Jona-Lasinio (NJL) model both at zero and at finite
temperature and/or density. At the first nontrivial order the OPT exhibits a
class of 1/N_c corrections which produce nonperturbative results that go beyond
the standard large-N_c, or mean-field approximation. The consistency of the OPT
method with the Goldstone theorem at this order is established, and appropriate
OPT values of the basic NJL (vacuum) parameters are obtained by matching the
pion mass and decay constant consistently. Deviations from standard large-N_c
relations induced by OPT at this order are derived, for example, for the
Gell--Mann-Oakes-Renner relation. Next, the results for the critical quantities
and the phase diagram of the model, as well as a number of other
thermodynamical quantities of interest, are obtained with OPT and then
contrasted with the corresponding results at large N_c.Comment: 29 pages, 20 figures, revtex. Minor corrections. In press Phys. Rev.
Operator Transformations Between Exactly Solvable Potentials and Their Lie Group Generators
One may obtain, using operator transformations, algebraic relations between
the Fourier transforms of the causal propagators of different exactly solvable
potentials. These relations are derived for the shape invariant potentials.
Also, potentials related by real transformation functions are shown to have the
same spectrum generating algebra with Hermitian generators related by this
operator transformation.Comment: 13 pages with one Postscript figure, uses LaTeX2e with revte
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