1,452 research outputs found
Strong-coupling expansion for the momentum distribution of the Bose Hubbard model with benchmarking against exact numerical results
A strong-coupling expansion for the Green's functions, self-energies and
correlation functions of the Bose Hubbard model is developed. We illustrate the
general formalism, which includes all possible inhomogeneous effects in the
formalism, such as disorder, or a trap potential, as well as effects of thermal
excitations. The expansion is then employed to calculate the momentum
distribution of the bosons in the Mott phase for an infinite homogeneous
periodic system at zero temperature through third-order in the hopping. By
using scaling theory for the critical behavior at zero momentum and at the
critical value of the hopping for the Mott insulator to superfluid transition
along with a generalization of the RPA-like form for the momentum distribution,
we are able to extrapolate the series to infinite order and produce very
accurate quantitative results for the momentum distribution in a simple
functional form for one, two, and three dimensions; the accuracy is better in
higher dimensions and is on the order of a few percent relative error
everywhere except close to the critical value of the hopping divided by the
on-site repulsion. In addition, we find simple phenomenological expressions for
the Mott phase lobes in two and three dimensions which are much more accurate
than the truncated strong-coupling expansions and any other analytic
approximation we are aware of. The strong-coupling expansions and scaling
theory results are benchmarked against numerically exact QMC simulations in two
and three dimensions and against DMRG calculations in one dimension. These
analytic expressions will be useful for quick comparison of experimental
results to theory and in many cases can bypass the need for expensive numerical
simulations.Comment: 48 pages 14 figures RevTe
Geometrical Aspects on Parameter estimation of stochastic gravitational wave background: beyond the Fisher analysis
The maximum likelihood method is often used for parameter estimation in
gravitational wave astronomy. Recently, an interesting approach was proposed by
Vallisneri to evaluate the distributions of parameter estimation errors
expected for the method. This approach is to statistically analyze the local
peaks of the likelihood surface, and works efficiently even for signals with
low signal-to-noise ratios. Focusing special attention to geometric structure
of the likelihood surface, we follow the proposed approach and derive formulae
for a simplified model of data analysis where the target signal has only one
intrinsic parameter, along with its overall amplitude. Then we apply our
formulae to correlation analysis of stochastic gravitational wave background
with a power-law spectrum. We report qualitative trends of the formulae using
numerical results specifically obtained for correlation analysis with two
Advanced-LIGO detectors.Comment: 23 pages, to be published in PR
Axiomatic Bargaining Theory on Opportunity Assignments
This paper discusses issues of axiomatic bargaining problems over opportunity assignments. The fair arbitrator uses the principle of "equal opportunity" for all players to make the recommendation on re- source allocations. A framework in such a context is developed and several classical solutions to standard bargaining problems are reformulated and axiomatically characterized. Working Paper 06-4
Coarse-grained loop algorithms for Monte Carlo simulation of quantum spin systems
Recently, Syljuasen and Sandvik proposed a new framework for constructing
algorithms of quantum Monte Carlo simulation. While it includes new classes of
powerful algorithms, it is not straightforward to find an efficient algorithm
for a given model. Based on their framework, we propose an algorithm that is a
natural extension of the conventional loop algorithm with the split-spin
representation. A complete table of the vertex density and the worm-scattering
probability is presented for the general XXZ model of an arbitrary S with a
uniform magnetic field.Comment: 12 pages, 7 figures, insert a word "squared" in the first line of the
caption of Fig.7 and correct the label of vertical axis of Fig.
Moduli Space Dimensions of Multi-Pronged Strings
The numbers of bosonic and fermionic zero modes of multi-pronged strings are
counted in super-Yang-Mills theory and compared with those of the
IIB string theory. We obtain a nice agreement for the fermionic zero modes,
while our result for the bosonic zero modes differs from that obtained in the
IIB string theory. The possible origin of the discrepancy is discussedComment: 15 pages, 2 figure
Quadrupolar Order in Isotropic Heisenberg Models with Biquadratic Interaction
Through Quantum Monte Carlo simulation, we study the biquadratic-interaction
model with the SU(2) symmetry in two and three dimensions. The zero-temperature
phase diagrams for the two cases are identical and exhibit an intermediate
phase characterized by finite quadrupole moment, in agreement with mean-field
type arguments and the semi-classical theory. In three dimensions, we
demonstrate that the model in the quadrupolar regime has a phase transition at
a finite temperature. In contrast to predictions by mean-field theories, the
phase transition to the quadrupolar phase turns out to be of the second order.
We also examine the critical behavior in the two marginal cases with the SU(3)
symmetry.Comment: 4 pages 5 figure
The axial anomaly and the phases of dense QCD
The QCD axial anomaly, by coupling the chiral condensate and BCS pairing
fields of quarks in dense matter, leads to a new critical point in the QCD
phase diagram \cite{HTYB,chiral2}, which at sufficiently low temperature should
terminate the line of phase transitions between chirally broken hadronic matter
and color superconducting quark matter. The critical point indicates that
matter at low temperature should cross over smoothly from the hadronic to the
quark phase, as suggested earlier on the basis of symmetry. We review here the
arguments, based on a general Ginzburg-Landau effective Lagrangian, for the
existence of the new critical point, as well as discuss possible connections
between the QCD phase structure and the BEC-BCS crossover in ultracold trapped
atomic fermion systems at unitarity. and implications for the presence of quark
matter in neutron stars.Comment: 8 pages, Proceedings of Quark Matter 2008, Jaipu
Securing Basic Well-being for All
The purpose of this paper is to examine the possibility of a social choice rule to implement a social policy for securing basic well-being for all. The paper introduces a new scheme of social choice, called a social relation function (SRF), which associates a reflexive and transitive binary relation over a set of social policies to each profile of individual well-being appraisals and each profile of group evaluations. As part of the domains of SRFs, the available class of group evaluations is constrained by three conditions. Furthermore, the non-negative response (NR) and the weak Pareto condition (WP) are introduced. NR demands giving priority to group evaluation, while treating the groups as formally equal relative to each other. WP requires treating impartially the well-being appraisals of all individuals. In conclusion, this paper shows that under some reasonable assumptions, there exists an SRF that satisfies NR and WP
Spin fluctuations in CuGeO probed by light scattering
We have measured temperature dependence of low-frequency Raman spectra in
CuGeO, and have observed the quasi-elastic scattering in the
polarization above the spin-Peierls transition temperature. We attribute it to
the fluctuations of energy density in the spin system. The magnetic specific
heat and an inverse of the magnetic correlation length can be derived from the
quasi-elastic scattering. The inverse of the magnetic correlation length is
proportional to at high temperatures. We compare the
specific heat with a competing- model. This model cannot explain
quantitatively both the specific heat and the magnetic susceptibility with the
same parameters. The origin of this discrepancy is discussed.Comment: 17 pages, REVTeX, 5 Postscript figures; in press in PR
Universal relations in the finite-size correction terms of two-dimensional Ising models
Quite recently, Izmailian and Hu [Phys. Rev. Lett. 86, 5160 (2001)] studied
the finite-size correction terms for the free energy per spin and the inverse
correlation length of the critical two-dimensional Ising model. They obtained
the universal amplitude ratio for the coefficients of two series. In this study
we give a simple derivation of this universal relation; we do not use an
explicit form of series expansion. Moreover, we show that the Izmailian and
Hu's relation is reduced to a simple and exact relation between the free energy
and the correlation length. This equation holds at any temperature and has the
same form as the finite-size scaling.Comment: 4 pages, RevTeX, to appear in Phys. Rev. E, Rapid Communication
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