Related papers: Derivative expansion in the HAL QCD method for a s…
We discuss differential-- versus integral--equation based methods describing out--of thermal equilibrium systems and emphasize the importance of a well defined reduction to statistical observables. Applying the projection operator approach,…
We make a detailed comparison between the direct method and the HAL QCD potential method for the baryon-baryon interactions, taking the $\Xi\Xi$ system at $m_\pi= 0.51$ GeV in 2+1 flavor QCD and using both smeared and wall quark sources.…
A recently formulated version of the eigenchannel method [R. Szmytkowski, Ann. Phys. (N.Y.) {\bf 311}, 503 (2004)] is applied to quantum scattering of Schr\"odinger particles from non-local separable potentials. Eigenchannel vectors and…
We investigate the $I=1$ $\pi \pi$ interaction using the HAL QCD method in lattice QCD. We employ the (2+1)-flavor gauge configurations on $32^3 \times 64$ lattice at the lattice spacing $a \approx 0.0907$ fm and $m_{\pi} \approx 411$ MeV,…
In this article, we report the $\rho$ resonance study using the HAL QCD method. We calculate the $I=1$ $\pi \pi$ potential at $m_{\pi} \approx 0.41$ GeV by a combination of the one-end trick, sequential propagator and covariant…
It has been recognized recently that fractional calculus is useful for handling scaling structures and processes. We begin this survey by pointing out the relevance of the subject to physical situations. Then the essential definitions and…
We present a new numerical method for accurate computations of solutions to (linear) one dimensional Schr\"odinger equations with periodic potentials. This is a prominent model in solid state physics where we also allow for perturbations by…
We derive a general formalism that relates the spectrum of two-particle systems in a finite volume to physical scattering amplitudes, taking into account the presence of any left-hand branch cuts due to single-particle exchanges. The method…
This article analysis differential equations which represents damped and fractional oscillators. First, it is shown that prior to using physical quantities in fractional calculus, it is imperative that they are turned dimensionless.…
We carry out a detailed analysis of a time dispersive dissipative (TDD) string, using our recently developed conservative and Hamiltonian extensions of TDD systems. This analysis of the TDD string includes, in particular: (i) an explicit…
Perturbation expansions appear to be divergent series in many physically interesting situations, including in quantum field theories like quantum electrodynamics (QED) and quantum chromodynamics (QCD), where the perturbative coefficients…
We derive parametric travelling-wave solutions of non-linear QCD equations. They describe the evolution towards saturation in the geometric scaling region. The method, based on an expansion in the inverse of the wave velocity, leads to a…
We present a lattice QCD study of the phase shift of $I{=}2$ $\pi\pi$ scattering on the basis of two different approaches: the standard finite volume approach by Luscher and the recently introduced HAL QCD potential method. Quenched QCD…
The time-dependent fields obtained by solving partial differential equations in two and more dimensions quickly overwhelm the analytical capabilities of the human brain. A meaningful insight into the temporal behaviour can be obtained by…
A new exponentially fitted version of the Discrete Variational Derivative method for the efficient solution of oscillatory complex Hamiltonian Partial Differential Equations is proposed. When applied to the nonlinear Schroedinger equation,…
An approach based on splitting the reaction potential into a finite range part and a long range tail part to describe few-body scattering in the case of a Coulombic interaction is proposed. The solution to the Schr\"odinger equation for the…
We develop a functional derivative approach to calculate the chemical potentials of the second-order perturbation theory (MP2). In the functional derivative approach, the correlation part of the MP2 chemical potential, which is the…
We review recent progress of the HAL QCD method which was recently proposed to investigate hadron interactions in lattice QCD. The strategy to extract the energy-independent non-local potential in lattice QCD is explained in detail. The…
Time-dependent quantum mechanics provides an intuitive picture of particle propagation in external fields. Semiclassical methods link the classical trajectories of particles with their quantum mechanical propagation. Many analytical results…
Shape derivative is an important analytical tool for studying scattering problems involving perturbations in scatterers. Many applications, including inverse scattering, optimal design, and uncertainty quantification, are based on shape…