2,029 research outputs found
Optimized perturbation method for the propagation in the anharmonic oscillator potential
The application of the optimized expansion for the quantum-mechanical
propagation in the anharmonic potential is discussed for real and
imaginary time. The first order results in the imaginary time formalism provide
approximations to the free energy and particle density which agree well with
the exact results in the whole range of temperatures.Comment: 13 pages, plain LATEX, 3 compressed and uuencoded Postscript figures,
submitted to Phys.Lett.
Addendum to paper: Strong-Coupling Behavior of -Theories and Critical Exponents [Phys. Rev. D 57, 2264 (1998)]
The graphical extrapolation procedure to infinite order of variational
perturbation theory in a recent calculation of critical exponents of
three-dimensional -theories at infinite couplings is improved by
another way of plotting the results.Comment: Author Information under
http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of
paper also at
http://www.physik.fu-berlin.de/~kleinert/kleiner_re257a/preprint.htm
PT-symmetric operators and metastable states of the 1D relativistic oscillators
We consider the one-dimensional Dirac equation for the harmonic oscillator
and the associated second order separated operators giving the resonances of
the problem by complex dilation. The same operators have unique extensions as
closed PT-symmetric operators defining infinite positive energy levels
converging to the Schroedinger ones as c tends to infinity. Such energy levels
and their eigenfunctions give directly a definite choice of metastable states
of the problem. Precise numerical computations shows that these levels coincide
with the positions of the resonances up to the order of the width. Similar
results are found for the Klein-Gordon oscillators, and in this case there is
an infinite number of dynamics and the eigenvalues and eigenvectors of the
PT-symmetric operators give metastable states for each dynamics.Comment: 13 pages, 2 figure
Optimized Perturbation Methods for the Free Energy of the Anharmonic Oscillator
Two possibile applications of the optimized expansion for the free energy of
the quantum-mechanical anharmonic oscillator are discussed. The first method is
for the finite temperature effective potential; the second one, for the
classical effective potential. The results of both methods show a quick
convergence and agree well with the exact free energy in the whole range of
temperatures. Postscript figures are available under request to AO email
[email protected]: 8 pages, preprin
Effective Hamiltonian with holomorphic variables
The pure-quantum self-consistent harmonic approximation (PQSCHA) permits to
study a quantum system by means of an effective classical Hamiltonian. In this
work the PQSCHA is reformulated in terms of the holomorphic variables connected
to a set of bosonic operators. The holomorphic formulation, based on the
olomorphic path integral for the Weyl symbol of the density matrix, makes it
possible to directly approach general Hamiltonians given in terms of bosonic
creation and annihilation operators.Comment: Proceedings of the Conference "Path Integrals from peV to TeV - 50
Years from Feynman's paper" (Florence, August 1998) -- 2 pages, ReVTe
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