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Nuclear Theory·nucl-th

Monday·October 2, 2017

7 papers—3 primary·4 cross-listed

All7Primary3Cross-lists4
  1. 04

    Relation between scattering amplitude and Bethe-Salpeter wave function in quantum field theory

    Takeshi Yamazaki🇯🇵 · Yoshinobu Kuramashi🇯🇵

    We reexamine the relations between the Bethe-Salpeter (BS) wave function of two particles, the on-shell scattering amplitude, and the effective potential in quantum filed theory. It is emphasized that there is an exact relation between the BS wave function inside the interaction range and the scattering amplitude, and the reduced BS wave function, which is defined in this article, plays an essential role in this relation. Based on the exact relation, we show that the solution of Schrödinger equation with the effective potential gives us a correct on-shell scattering amplitude only at the momentum where the effective potential is calculated, while wrong results are obtained from the Schrödinger equation at general momenta. We also discuss about a momentum expansion of the reduced BS wave function and an uncertainty of the scattering amplitude stemming from the choice of the interpolating operator in the BS wave function. The theoretical conclusion obtained in this article could give hints to understand the inconsistency observed in lattice QCD calculation of the two-nucleon channels with different approaches.

    ↳ hep-latnucl-thPRD(2017)·27 citations
  2. 05

    Semiclassical catastrophe theory of simple bifurcations

    A.G. Magner · K. Arita

    The Fedoriuk-Maslov catastrophe theory of caustics and turning points is extended to solve the bifurcation problems by the improved stationary phase method (ISPM). The trace formulas for the radial power-law (RPL) potentials are presented by the ISPM based on the second- and third-order expansion of the classical action near the stationary point. A considerable enhancement of contributions of the two orbits (pair of consisting of the parent and newborn orbits) at their bifurcation is shown. The ISPM trace formula is proposed for a simple bifurcation scenario of Hamiltonian systems with continuous symmetries, where the contributions of the bifurcating parent orbits vanish upon approaching the bifurcation point due to the reduction of the end-point manifold. This occurs since the contribution of the parent orbits is included in the term corresponding to the family of the newborn daughter orbits. Taking this feature into account, the ISPM level densities calculated for the RPL potential model are shown to be in good agreement with the quantum results at the bifurcations and asymptotically far from the bifurcation points.

    ↳ math.DSnlin.CDnucl-thPRE(2017)·6 citations
  3. 06

    Statistics of a simple transmission mode on a lossy chaotic background

    Dmitry V. Savin

    Scattering on a resonance state coupled to a complicated background is a typical problem for mesoscopic quantum many-body systems as well as for wave propagation in the presence of a complex environment. On average, such a simple mode acquires an effective damping, the so-called "spreading" width, due to mixing with the background states. Modeling the latter by random matrix theory and employing the strength function formalism, we derive the joint distribution of the reflection and total transmission at arbitrary absorption in the background. The distribution is found to possess a remarkable symmetry between its reflection and transmission sectors, which is controlled by the ratio of the spreading to escape width. This in turn results in a symmetry relation between the marginal densities, despite the absence of the flux conservation at finite absorption. As an application, we study the statistics of total losses in the system at arbitrary coupling to the background.

    ↳ cond-mat.mes-hallmath-phmath.MPnucl-th+1PRResearch(2020)·4 citations
  4. 07

    QCD at finite isospin chemical potential

    Bastian B. Brandt🇩🇪 · Gergely Endrodi🇩🇪 · Sebastian Schmalzbauer🇩🇪

    We investigate the properties of QCD at finite isospin chemical potential at zero and non-zero temperatures. This theory is not affected by the sign problem and can be simulated using Monte-Carlo techniques. With increasing isospin chemical potential and temperatures below the deconfinement transition the system changes into a phase where charged pions condense, accompanied by an accumulation of low modes of the Dirac operator. The simulations are enabled by the introduction of a pionic source into the action, acting as an infrared regulator for the theory, and physical results are obtained by removing the regulator via an extrapolation. We present an update of our study concerning the associated phase diagram using 2+1 flavours of staggered fermions with physical quark masses and the comparison to Taylor expansion. We also present first results for our determination of the equation of state at finite isospin chemical potential and give an example for a cosmological application. The results can also be used to gain information about QCD at small baryon chemical potentials using reweighting with respect to the pionic source parameter and the chemical potential and we present first steps in this direction.

    ↳ hep-lathep-phnucl-thEPJ Web Conf.(2018)·67 citations

Affiliations

first authorsco-authorsvia INSPIRE