45,020 research outputs found
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 and with the inner derivation .
Physically the present noncommutative derivatives express quantum fluctuations
and responses.Comment: Latex file, 29 pages, no figur
BPS Analysis of the Charged Soliton Solutions of D-brane Worldvolume Theory from the Viewpoint of Target-space Supersymmetry
We investigate BPS properties of the charged soliton solutions of D-brane
worldvolume theory, which is described by the supersymmetric Dirac-Born-Infeld
action, by means of the N=2 target-space supersymmetry algebra. Our results
agree with those obtained previously. We also extend our BPS analysis to the
case where axion background exists.Comment: 11 pages, LaTeX, 3 eps figures, v2: references corrected, a note
added, minor changes, v3: references corrected, notes added, equations added,
discussions adde
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
by a magnetic field ) of the =1/2 ferromagnetic Heisenberg chain and the
classical Heisenberg chain are calculated at low temperatures In both
chains the nonlinear susceptibilities diverge as and a linear
susceptibilities diverge as The arbitrary spin Heisenberg
ferromagnet has a scaling relation between and
The scaling function
=(2/3)-(44/135) + O() is common to all values of spin
Comment: 16 pages (revtex 2.0) + 6 PS figures upon reques
Dynamics of the superfluid to Mott insulator transition in one dimension
We numerically study the superfluid to Mott insulator transition for bosonic
atoms in a one dimensional lattice by exploiting a recently developed
simulation method for strongly correlated systems. We demonstrate this methods
accuracy and applicability to Bose-Hubbard model calculations by comparison
with exact results for small systems. By utilizing the efficient scaling of
this algorithm we then concentrate on systems of comparable size to those
studied in experiments and in the presence of a magnetic trap. We investigate
spatial correlations and fluctuations of the ground state as well as the nature
and speed at which the superfluid component is built up when dynamically
melting a Mott insulating state by ramping down the lattice potential. This is
performed for slow ramping, where we find that the superfluid builds up on a
time scale consistent with single-atom hopping and for rapid ramping where the
buildup is much faster than can be explained by this simple mechanism. Our
calculations are in remarkable agreement with the experimental results obtained
by Greiner et al. [Nature (London) 415, 39 (2002)].Comment: 14 pages, 11 figures, RevTex 4. Replaced with published versio
Role of quark-quark correlation in baryon structure and non-leptonic weak transitions of hyperons
We study the role of quark-quark correlation in the baryon structure and, in
particular, the hyperon non-leptonic weak decay, which is sensitive to the
correlation between quarks in the spin-0 channel. We rigorously solve
non-relativistic three-body problem for SU(3) ground state baryons to take into
account the quark-pair correlation explicitly. With the suitable attraction in
the spin-0 channel, resulting static baryon properties as well as the parity
conserving weak decay amplitudes agree with the experimental values. Special
emphasis is placed also on the effect of the SU(6) spin-flavor symmetry
breaking on the baryon structure. Although the SU(6) breaking effects on the
local behavior of the quark wave functions are considerable due to the spin-0
attraction, the calculated magnetic moments are almost the same as the naive
SU(6) expectations
Inelastic final-state interaction
The final-state interaction in multichannel decay processes is sytematically
studied with application to B decay in mind. Since the final-state inteaction
is intrinsically interwoven with the decay interaction in this case, no simple
phase theorem like "Watson's theorem" holds for experimentally observed final
states. We first examine in detail the two-channel problem as a toy-model to
clarify the issues and to remedy common mistakes made in earlier literature.
Realistic multichannel problems are too challenging for quantitative analysis.
To cope with mathematical complexity, we introduce a method of approximation
that is applicable to the case where one prominant inelastic channel dominates
over all others. We illustrate this approximation method in the amplitude of
the decay B to pi K fed by the intermediate states of a charmed meson pair.
Even with our approximation we need more accurate information of strong
interactions than we have now. Nonethless we are able to obtain some insight in
the issue and draw useful conclusions on general fearyres on the strong phases.Comment: The published version. One figure correcte
Density of Yang-Lee zeros for the Ising ferromagnet
The densities of Yang-Lee zeros for the Ising ferromagnet on the
square lattice are evaluated from the exact grand partition functions
(). The properties of the density of Yang-Lee zeros are discussed as
a function of temperature and system size . The three different classes
of phase transitions for the Ising ferromagnet, first-order phase transition,
second-order phase transition, and Yang-Lee edge singularity, are clearly
distinguished by estimating the magnetic scaling exponent from the
densities of zeros for finite-size systems. The divergence of the density of
zeros at Yang-Lee edge in high temperatures (Yang-Lee edge singularity), which
has been detected only by the series expansion until now for the square-lattice
Ising ferromagnet, is obtained from the finite-size data. The identification of
the orders of phase transitions in small systems is also discussed using the
density of Yang-Lee zeros.Comment: to appear in Physical Review
Massless and massive one-loop three-point functions in negative dimensional approach
In this article we present the complete massless and massive one-loop
triangle diagram results using the negative dimensional integration method
(NDIM). We consider the following cases: massless internal fields; one massive,
two massive with the same mass m and three equal masses for the virtual
particles. Our results are given in terms of hypergeometric and
hypergeometric-type functions of external momenta (and masses for the massive
cases) where the propagators in the Feynman integrals are raised to arbitrary
exponents and the dimension of the space-time D. Our approach reproduces the
known results as well as other solutions as yet unknown in the literature.
These new solutions occur naturally in the context of NDIM revealing a
promising technique to solve Feynman integrals in quantum field theories
Commuting quantum transfer matrix approach to intrinsic Fermion system: Correlation length of a spinless Fermion model
The quantum transfer matrix (QTM) approach to integrable lattice Fermion
systems is presented. As a simple case we treat the spinless Fermion model with
repulsive interaction in critical regime. We derive a set of non-linear
integral equations which characterize the free energy and the correlation
length of for arbitrary particle density at any finite
temperatures. The correlation length is determined by solving the integral
equations numerically. Especially in low temperature limit this result agrees
with the prediction from conformal field theory (CFT) with high accuracy.Comment: 17 page
- …