264,190 research outputs found

### Finding Exponential Product Formulas of Higher Orders

In the present article, we review a continual effort on generalization of the
Trotter formula to higher-order exponential product formulas. The exponential
product formula is a good and useful approximant, particularly because it
conserves important symmetries of the system dynamics. We focuse on two
algorithms of constructing higher-order exponential product formulas. The first
is the fractal decomposition, where we construct higher-order formulas
recursively. The second is to make use of the quantum analysis, where we
compute higher-order correction terms directly. As interludes, we also have
described the decomposition of symplectic integrators, the approximation of
time-ordered exponentials, and the perturbational composition.Comment: 22 pages, 9 figures. To be published in the conference proceedings
''Quantum Annealing and Other Optimization Methods," eds. B.K.Chakrabarti and
A.Das (Springer, Heidelberg

### Optimized Negative Dimensional Integration Method (NDIM) and multiloop Feynman diagram calculation

We present an improved form of the integration technique known as NDIM
(Negative Dimensional Integration Method), which is a powerful tool in the
analytical evaluation of Feynman diagrams. Using this technique we study a $%
\phi ^{3}\oplus \phi ^{4}$ theory in $D=4-2\epsilon$ dimensions, considering
generic topologies of $L$ loops and $E$ independent external momenta, and where
the propagator powers are arbitrary. The method transforms the Schwinger
parametric integral associated to the diagram into a multiple series expansion,
whose main characteristic is that the argument contains several Kronecker
deltas which appear naturally in the application of the method, and which we
call diagram presolution. The optimization we present here consists in a
procedure that minimizes the series multiplicity, through appropriate
factorizations in the multinomials that appear in the parametric integral, and
which maximizes the number of Kronecker deltas that are generated in the
process. The solutions are presented in terms of generalized hypergeometric
functions, obtained once the Kronecker deltas have been used in the series.
Although the technique is general, we apply it to cases in which there are 2or3 different energy scales (masses or kinematic variables associated to
the external momenta), obtaining solutions in terms of a finite sum of
generalized hypergeometric series de 1 and 2 variables respectively, each of
them expressible as ratios between the different energy scales that
characterize the topology. The main result is a method capable of solving
Feynman integrals, expressing the solutions as hypergeometric series of
multiplicity $(n-1)$, where $n$ is the number of energy scales present in the
diagram.Comment: 49 pages, 14 figure

### Monopole Condensation in Lattice SU(2) QCD

This is the short review of Monte-Carlo studies of quark confinement in
lattice QCD. After abelian projections both in the maximally abelian and
Polyakov gauges, it is seen that the monopole part alone is responsible for
confinement. A block spin transformation on the dual lattice suggests that
lattice $SU(2)$ QCD is always ( for all $\beta$) in the monopole condensed
phase and so in the confinement phase in the infinite volume limit.Comment: Contribution to Confinement '95, March 1995, Osaka, Japan. Names of
figure files are corrected. 8 page uuencoded latex file and 10 ps figure

### Generalization of the Lie-Trotter Product Formula for q-Exponential Operators

The Lie-Trotter formula $e^{\hat{A}+\hat{B}} = \lim_{N\to \infty}
(e^{\hat{A}/N} e^{\hat{B}/N})^N$ is of great utility in a variety of quantum
problems ranging from the theory of path integrals and Monte Carlo methods in
theoretical chemistry, to many-body and thermostatistical calculations. We
generalize it for the q-exponential function $e_q (x) = [1+ (1-q)
x]^{(1/(1-q))}$ (with $e_1(x)=e^x$), and prove $e_q(\hat{A}+\hat{B}+(1-q)
[\hat{A}\hat{B}+\hat{B}\hat{A}] /2) = \lim_{N\to \infty}
{[e_{1-(1-q)N}(\hat{A}/N)] [e_{1-(1-q)N}(\hat{B}/N)]}^N$. This extended formula
is expected to be similarly useful in the nonextensive situationsComment: 5 pages, no figure

### Momentum distribution and correlation of two-nucleon relative motion in $^6$He and $^6$Li

The momentum distribution of relative motion between two nucleons gives
information on the correlation in nuclei. The momentum distribution is
calculated for both $^{6}$He and $^6$Li which are described in a three-body
model of $\alpha$+$N$+$N$. The ground state solution for the three-body
Hamiltonian is obtained accurately using correlated basis functions. The
momentum distribution depends on the potential model for the $N$-$N$
interaction. With use of a realistic potential, the $^6$He momentum
distribution exhibits a dip around 2 fm$^{-1}$ characteristic of $S$-wave
motion. In contrast to this, the $^6$Li momentum distribution is very similar
to that of the deuteron; no dip appears because it is filled with the $D$-wave
component arising from the tensor force.Comment: 14 pages, 9 figure

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