297 research outputs found
Very-high-precision solutions of a class of Schr{\"o}dinger equations
We investigate a method to solve a class of Schr{\"o}dinger equation
eigenvalue problems numerically to very high precision (from thousands to a
million of decimals). The memory requirement, and the number of high precision
algebraic operations, of the method scale essentially linearly with when
only eigenvalues are computed. However, since the algorithms for multiplying
high precision numbers scale at a rate between and , the time requirement of our method increases somewhat faster
than .Comment: 4 page contribution to proceedings of the Conference on Computational
Physics, June 23rd-26th 2010 in Trondheim (submitted to Computer Physics
Communications
The hunting motif in the literature of the United States:1782-1992.
The thesis analyses a representative but by no means complete selection of American hunting texts from 1782 to 1992. The first chapter gives an overview of the history of hunting and important contemporary and related literature. It looks at characters such as Daniel Boone and David Crockett, assesses the changes hunting underwent and mentions the recent developments, such as the rise of the horror thriller. The following twelve chapters analyse novels and short stories by twelve different authors. The main research results are: 1) The establishment of a tripartite structure. Hunting texts can be divided into political, pro-hunting and anti-hunting texts. Pro-hunting text tend to have a self-confident firstperson narrator. Anti-hunting texts tend to have a less confident third-person narrator. 2) The use of either an anthropocentric or a biocentric perspective. 3) The animal described in hunting stories is of exceptional size, danger, or beauty. One effect of this is an increased polarisation between hunter and hunted. 4) Several writers employ binary oppositions as a stylistic device, such as life versus death, bravery versus fear, or man versus animal. 5) The hunter is usually described as a lonely, ‘wifeless’ man, either without any relationship at all, or incapable of entering into a relationship. He has also an unusually high potential of aggression, an urge to kill. The diversity and versatility of the hunting motif as well as the large group of texts discovered, and listed in an appendix, demonstrates that hunting stories are an important part of American literature and culture
Observing Quantum Tunneling in Perturbation Series
We apply Borel resummation method to the conventional perturbation series of
ground state energy in a metastable potential, . We observe
numerically that the discontinuity of Borel transform reproduces the imaginary
part of energy eigenvalue, i.e., total decay width due to the quantum
tunneling. The agreement with the exact numerical value is remarkable in the
whole tunneling regime 0.Comment: 12 pages, 2 figures. Phyzzx, Tables.tex, The final version to appear
in Phys. Lett.
Multi-Instantons and Exact Results III: Unified Description of the Resonances of Even and Odd Anharmonic Oscillators
This is the third article in a series of three papers on the resonance energy
levels of anharmonic oscillators. Whereas the first two papers mainly dealt
with double-well potentials and modifications thereof [see J. Zinn-Justin and
U. D. Jentschura, Ann. Phys. (N.Y.) 313 (2004), pp. 197 and 269], we here focus
on simple even and odd anharmonic oscillators for arbitrary magnitude and
complex phase of the coupling parameter. A unification is achieved by the use
of PT-symmetry inspired dispersion relations and generalized quantization
conditions that include instanton configurations. Higher-order formulas are
provided for the oscillators of degrees 3 to 8, which lead to subleading
corrections to the leading factorial growth of the perturbative coefficients
describing the resonance energies. Numerical results are provided, and
higher-order terms are found to be numerically significant. The resonances are
described by generalized expansions involving intertwined non-analytic
exponentials, logarithmic terms and power series. Finally, we summarize
spectral properties and dispersion relations of anharmonic oscillators, and
their interconnections. The purpose is to look at one of the classic problems
of quantum theory from a new perspective, through which we gain systematic
access to the phenomenologically significant higher-order terms.Comment: 51 pages, LaTeX, Latin2 font
Calculation of the Characteristic Functions of Anharmonic Oscillators
The energy levels of quantum systems are determined by quantization
conditions. For one-dimensional anharmonic oscillators, one can transform the
Schrodinger equation into a Riccati form, i.e., in terms of the logarithmic
derivative of the wave function. A perturbative expansion of the logarithmic
derivative of the wave function can easily be obtained. The Bohr-Sommerfeld
quantization condition can be expressed in terms of a contour integral around
the poles of the logarithmic derivative. Its functional form is B_m(E,g) = n +
1/2, where B is a characteristic function of the anharmonic oscillator of
degree m, E is the resonance energy, and g is the coupling constant. A
recursive scheme can be devised which facilitates the evaluation of
higher-order Wentzel-Kramers-Brioullin (WKB) approximants. The WKB expansion of
the logarithmic derivative of the wave function has a cut in the tunneling
region. The contour integral about the tunneling region yields the instanton
action plus corrections, summarized in a second characteristic function
A_m(E,g). The evaluation of A_m(E,g) by the method of asymptotic matching is
discussed for the case of the cubic oscillator of degree m=3.Comment: 11 pages, LaTeX; three further typographical errors correcte
Effective Potential for Complex Langevin Equations
We construct an effective potential for the complex Langevin equation on a
lattice. We show that the minimum of this effective potential gives the
space-time and Langevin time average of the complex Langevin field. The loop
expansion of the effective potential is matched with the derivative expansion
of the associated Schwinger-Dyson equation to predict the stationary
distribution to which the complex Langevin equation converges.Comment: 23 pages, 2 figure
Evaluation of overlaps between arbitrary Fermionic quasiparticle vacua
We derive an expression that allows for the unambiguous evaluation of the
overlap between two arbitrary quasiparticle vacua, including its sign. Our
expression is based on the Pfaffian of a skew-symmetric matrix, extending the
formula recently proposed by [L. M. Robledo, Phys. Rev. C 79, 021302(R) (2009)]
to the most general case, including the one of the overlap between two
different blocked n-quasiparticle states for either even or odd systems. The
powerfulness of the method is illustrated for a few typical matrix elements
that appear in realistic angular-momentum-restored Generator-Coordinate Method
calculations when breaking time-reversal invariance and using the full model
space of occupied single-particle states.Comment: 10 pages, 3 figure
Semi-Lorentz invariance, unitarity, and critical exponents of symplectic fermion models
We study a model of N-component complex fermions with a kinetic term that is
second order in derivatives. This symplectic fermion model has an Sp(2N)
symmetry, which for any N contains an SO(3) subgroup that can be identified
with rotational spin of spin-1/2 particles. Since the spin-1/2 representation
is not promoted to a representation of the Lorentz group, the model is not
fully Lorentz invariant, although it has a relativistic dispersion relation.
The hamiltonian is pseudo-hermitian, H^\dagger = C H C, which implies it has a
unitary time evolution. Renormalization-group analysis shows the model has a
low-energy fixed point that is a fermionic version of the Wilson-Fisher fixed
points. The critical exponents are computed to two-loop order. Possible
applications to condensed matter physics in 3 space-time dimensions are
discussed.Comment: v2: Published version, minor typose correcte
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
Asymptotics of Expansion of the Evolution Operator Kernel in Powers of Time Interval
The upper bound for asymptotic behavior of the coefficients of expansion of
the evolution operator kernel in powers of the time interval \Dt was
obtained. It is found that for the nonpolynomial potentials the coefficients
may increase as . But increasing may be more slow if the contributions with
opposite signs cancel each other. Particularly, it is not excluded that for
number of the potentials the expansion is convergent. For the polynomial
potentials \Dt-expansion is certainly asymptotic one. The coefficients
increase in this case as , where is the order of
the polynom. It means that the point \Dt=0 is singular point of the kernel.Comment: 12 pp., LaTe
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