81,328 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

### Long-distance final-state interactions and J/psi decay

To understand the short-distance vs long-distance final-state interactions,
we have performed a detailed amplitude analysis for the two-body decay, J/psi
into vector and pseudoscalar mesons. The current data favor a large relative
phase nearly 90 degrees between the three-gluon and one-photon decay
amplitudes. The source of this phase is apparently in the long-distance
final-state interaction. Nothing anomalous is found in the magnitudes of the
three-gluon and one-photon amplitudes. We discuss implications of this large
relative phase in the weak decay of heavy particles.Comment: 11 pages, RevTe

### General Formulation of Quantum Analysis

A general formulation of noncommutative or quantum derivatives for operators
in a Banach space is given on the basis of the Leibniz rule, irrespective of
their explicit representations such as the G\^ateaux derivative or commutators.
This yields a unified formulation of quantum analysis, namely the invariance of
quantum derivatives, which are expressed by multiple integrals of ordinary
higher derivatives with hyperoperator variables. Multivariate quantum analysis
is also formulated in the present unified scheme by introducing a partial inner
derivation and a rearrangement formula. Operator Taylor expansion formulas are
also given by introducing the two hyperoperators $\delta_{A \to B} \equiv
-\delta_A^{-1} \delta_B$ and $d_{A \to B} \equiv \delta_{(-\delta_A^{-1}B) ;
A}$ with the inner derivation $\delta_A : Q \mapsto [A,Q] \equiv AQ-QA$.
Physically the present noncommutative derivatives express quantum fluctuations
and responses.Comment: Latex file, 29 pages, no figur

### Analytic study of disoriented chiral condensate

Evolution of disoriented chiral condenstates is studied with the classical
sigma model in 3+1 dimensions. By smoothly connecting a chiral symmetric
solution of the formation period to a solution of the decay period, we obtain a
complete spacetime evolution of the pion field for a simple and physically
interesting source. The formation process is discussed quantitatively from the
viewpoint of the axial-vector isospin conservation.Comment: Latex with no figure, 18 pages. Full postscript available from
http://theor1.lbl.gov/www/theorygroup/papers/38931.p

### Final state interaction in heavy hadron decay

I present a critical account of the final-state interaction (FSI) in two-body
B decays from viewpoint of the hadron picture. I emphasize that the phase and
the magnitude of decay amplitude are related to each other by a dispersion
relation. In a model phase of FSI motivated by experiment, I illustrate how
much the magnitude of amplitude can deviate from its factorization value by the
FSI.Comment: 8 pages in sprocl.tex with 4 eps figures. A talk presented at the
Third International Conference on B Physics and CP Violation, (Taipei,
December 1999

### Aging dynamics of ferromagnetic and reentrant spin glass phases in stage-2 Cu$_{0.80}$C$_{0.20}$Cl$_{2}$ graphite intercalation compound

Aging dynamics of a reentrant ferromagnet stage-2
Cu$_{0.8}$Co$_{0.2}$Cl$_{2}$ graphite intercalation compound has been studied
using DC magnetic susceptibility. This compound undergoes successive
transitions at the transition temperatures $T_{c}$ ($\approx 8.7$ K) and
$T_{RSG}$ ($\approx 3.3$ K). The relaxation rate $S_{ZFC}(t)$ exhibits a
characteristic peak at $t_{cr}$ below $T_{c}$. The peak time $t_{cr}$ as a
function of temperature $T$ shows a local maximum around 5.5 K, reflecting a
frustrated nature of the ferromagnetic phase. It drastically increases with
decreasing temperature below $T_{RSG}$. The spin configuration imprinted at the
stop and wait process at a stop temperature $T_{s}$ ($<T_{c}$) during the
field-cooled aging protocol, becomes frozen on further cooling. On reheating,
the memory of the aging at $T_{s}$ is retrieved as an anomaly of the
thermoremnant magnetization at $T_{s}$. These results indicate the occurrence
of the aging phenomena in the ferromagnetic phase ($T_{RSG}<T<T_{c}$) as well
as in the reentrant spin glass phase ($T<T_{RSG}$).Comment: 9 pages, 9 figures; submitted to Physical Review

### Quantum phase transitions in the sub-ohmic spin-boson model: Failure of the quantum-classical mapping

The effective theories for many quantum phase transitions can be mapped onto
those of classical transitions. Here we show that such a mapping fails for the
sub-ohmic spin-boson model which describes a two-level system coupled to a
bosonic bath with power-law spectral density, J(omega) ~ omega^s. Using an
epsilon expansion we prove that this model has a quantum transition controlled
by an interacting fixed point at small s, and support this by numerical
calculations. In contrast, the corresponding classical long-range Ising model
is known to have an upper-critical dimension at s = 1/2, with mean-field
transition behavior controlled by a non-interacting fixed point for 0 < s <
1/2. The failure of the quantum-classical mapping is argued to arise from the
long-ranged interaction in imaginary time in the quantum model.Comment: 4 pages, 3 figs; (v2) discussion extended; (v3) marginal changes,
final version as published; (v4) added erratum pointing out that main
conclusions were incorrect due to subtle failures of the NR

### The Free Energy and the Scaling Function of the Ferromagnetic Heisenberg Chain in a Magnetic Field

A nonlinear susceptibilities (the third derivative of a magnetization $m_S$
by a magnetic field $h$ ) of the $S$=1/2 ferromagnetic Heisenberg chain and the
classical Heisenberg chain are calculated at low temperatures $T.$ In both
chains the nonlinear susceptibilities diverge as $T^{-6}$ and a linear
susceptibilities diverge as $T^{-2}.$ The arbitrary spin $S$ Heisenberg
ferromagnet $[$ ${\cal H} = \sum_{i=1}^{N} \{ - J{\bf S}_{i} {\bf S}_{i+1} -
(h/S) S_{i}^{z} \}$ $(J>0),$ $]$ has a scaling relation between $m_S,$ $h$ and
$T:$ $m_S(T,h) = F( S^2 Jh/T^2).$ The scaling function
$F(x)$=(2$x$/3)-(44$x^{3}$/135) + O($x^{5}$) is common to all values of spin
$S.$Comment: 16 pages (revtex 2.0) + 6 PS figures upon reques

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