159 research outputs found
Convergence of the Linear Delta Expansion in the Critical O(N) Field Theory
The linear delta expansion is applied to the 3-dimensional O(N) scalar field
theory at its critical point in a way that is compatible with the large-N
limit. For a range of the arbitrary mass parameter, the linear delta expansion
for converges, with errors decreasing like a power of the order n in
delta. If the principal of minimal sensitivity is used to optimize the
convergence rate, the errors seem to decrease exponentially with n.Comment: 26 pages, latex, 8 figure
The Density Matrix Renormalization Group applied to single-particle Quantum Mechanics
A simplified version of White's Density Matrix Renormalization Group (DMRG)
algorithm has been used to find the ground state of the free particle on a
tight-binding lattice. We generalize this algorithm to treat the tight-binding
particle in an arbitrary potential and to find excited states. We thereby solve
a discretized version of the single-particle Schr\"odinger equation, which we
can then take to the continuum limit. This allows us to obtain very accurate
results for the lowest energy levels of the quantum harmonic oscillator,
anharmonic oscillator and double-well potential. We compare the DMRG results
thus obtained with those achieved by other methods.Comment: REVTEX file, 21 pages, 3 Tables, 4 eps Figure
Precise variational tunneling rates for anharmonic oscillator with g<0
We systematically improve the recent variational calculation of the imaginary
part of the ground state energy of the quartic anharmonic oscillator.
The results are extremely accurate as demonstrated by deriving, from the
calculated imaginary part, all perturbation coefficients via a dispersion
relation and reproducing the exact values with a relative error of less than
. A comparison is also made with results of a Schr\"{o}dinger
calculation based on the complex rotation method.Comment: PostScrip
Improved Conformal Mapping of the Borel Plane
The conformal mapping of the Borel plane can be utilized for the analytic
continuation of the Borel transform to the entire positive real semi-axis and
is thus helpful in the resummation of divergent perturbation series in quantum
field theory. We observe that the rate of convergence can be improved by the
application of Pad\'{e} approximants to the Borel transform expressed as a
function of the conformal variable, i.e. by a combination of the analytic
continuation via conformal mapping and a subsequent numerical approximation by
rational approximants. The method is primarily useful in those cases where the
leading (but not sub-leading) large-order asymptotics of the perturbative
coefficients are known.Comment: 6 pages, LaTeX, 2 tables; certain numerical examples adde
Critical thermodynamics of three-dimensional MN-component field model with cubic anisotropy from higher-loop \epsilon expansion
The critical thermodynamics of an -component field model with cubic
anisotropy relevant to the phase transitions in certain crystals with
complicated ordering is studied within the four-loop \ve expansion using the
minimal subtraction scheme. Investigation of the global structure of RG flows
for the physically significant cases M=2, N=2 and M=2, N=3 shows that the model
has an anisotropic stable fixed point with new critical exponents. The critical
dimensionality of the order parameter is proved to be equal to
, that is exactly half its counterpart in the real hypercubic
model.Comment: 9 pages, LaTeX, no figures. Published versio
Improved perturbation theory in the vortex liquids state of type II superconductors
We develop an optimized perturbation theory for the Ginzburg - Landau
description of thermal fluctuations effects in the vortex liquids. Unlike the
high temperature expansion which is asymptotic, the optimized expansion is
convergent. Radius of convergence on the lowest Landau level is in
2D and in 3D. It allows a systematic calculation of magnetization
and specific heat contributions due to thermal fluctuations of vortices in
strongly type II superconductors to a very high precision. The results are in
good agreement with existing Monte Carlo simulations and experiments.
Limitations of various nonperturbative and phenomenological approaches are
noted. In particular we show that there is no exact intersection point of the
magnetization curves both in 2D and 3D.Comment: 24 pages, 9 figure
On the Divergence of Perturbation Theory. Steps Towards a Convergent Series
The mechanism underlying the divergence of perturbation theory is exposed.
This is done through a detailed study of the violation of the hypothesis of the
Dominated Convergence Theorem of Lebesgue using familiar techniques of Quantum
Field Theory. That theorem governs the validity (or lack of it) of the formal
manipulations done to generate the perturbative series in the functional
integral formalism. The aspects of the perturbative series that need to be
modified to obtain a convergent series are presented. Useful tools for a
practical implementation of these modifications are developed. Some resummation
methods are analyzed in the light of the above mentioned mechanism.Comment: 42 pages, Latex, 4 figure
Separase: a universal trigger for sister chromatid disjunction but not chromosome cycle progression
Separase is a protease whose liberation from its inhibitory chaperone Securin triggers sister chromatid disjunction at anaphase onset in yeast by cleaving cohesin's kleisin subunit. We have created conditional knockout alleles of the mouse Separase and Securin genes. Deletion of both copies of Separase but not Securin causes embryonic lethality. Loss of Securin reduces Separase activity because deletion of just one copy of the Separase gene is lethal to embryos lacking Securin. In embryonic fibroblasts, Separase depletion blocks sister chromatid separation but does not prevent other aspects of mitosis, cytokinesis, or chromosome replication. Thus, fibroblasts lacking Separase become highly polyploid. Hepatocytes stimulated to proliferate in vivo by hepatectomy also become unusually large and polyploid in the absence of Separase but are able to regenerate functional livers. Separase depletion in bone marrow causes aplasia and the presumed death of hematopoietic cells other than erythrocytes. Destruction of sister chromatid cohesion by Separase may be a universal feature of mitosis in eukaryotic cells
Solvable simulation of a double-well problem in PT symmetric quantum mechanics
Within quantum mechanics which works with parity-pseudo-Hermitian
Hamiltonians we study the tunneling in a symmetric double well formed by two
delta functions with complex conjugate strengths. The model is exactly solvable
and exhibits several interesting features. Besides an amazingly robust absence
of any PT symmetry breaking, we observe a quasi-degeneracy of the levels which
occurs all over the energy range including the high-energy domain. This pattern
is interpreted as a manifestation of certain "quantum beats".Comment: 12 pages incl. 7 figure
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