Effective non-Hermitian Hamiltonian and continuum shell model

Abstract

The intrinsic dynamics of a system with open decay channels is described by an effective non-Hermitian Hamiltonian which at the same time allows one to find the external dynamics, - reaction cross sections. We discuss ways of incorporating this approach into the shell model context. Several examples of increasing complexity, from schematic models to realistic nuclear calculations (chain of oxygen isotopes), are presented. The approach is capable of describing a multitude of phenomena in a unified way combining physics of structure and reactions. Self-consistency of calculations and threshold energy dependence of the coupling to the continuum are crucial for the description of loosely bound states.

16 pages, 12 figures

References in corpus (13)

• Gamow Shell Model Description of Neutron-Rich Nuclei
• Two-Particle Resonant States in a Many-Body Mean Field
• Exact solution of the nuclear pairing problem
• Study of the ${}^{7}Be(p,\gamma {)}^{8}B$ and ${}^{7}Li(n,\gamma {)}^{8}Li$ capture reactions using the shell model embedded in the continuum
• Dynamics of quantum systems
• Analysis of the 16O(p,gamma)17F capture reaction using the shell model embedded in the continuum
• Effective Coupling for Open Billiards
• A Simple Mode on a Highly Excited Background: Collective Strength and Damping in the Continuum
• Conductance of Open Quantum Billiards and Classical Trajectories
• Whispering gallery modes in open quantum billiards
• Interfering Doorway States and Giant Resonances. I: Resonance Spectrum and Multipole Strengths
• Interfering Doorway States and Giant Resonances. II: Transition Strengths
• Statistical aspects of nuclear coupling to continuum

Cited by in corpus (54)

• Correspondence between winding numbers and skin modes in non-hermitian systems
• Effective operator formalism for open quantum systems
• Interference traps waves in open system: Bound states in the continuum
• Bloch bound states in the radiation continuum in a periodic array of dielectric rods
• Discrete and continuum spectra in the unified shell model approach
• Continuum Shell Model
• Two-proton radioactivity
• Bound states in the continuum in photonic structures
• Super-Radiant Dynamics, Doorways, and Resonances in Nuclei and Other Open Mesoscopic Systems
• Superradiance Transition in Transport Through Nanosystems
• Complex coupled-cluster approach to an ab-initio description of open quantum systems
• Gamow shell model and realistic nucleon-nucleon interactions
• Superradiance Transition in Photosynthetic Light-Harvesting Complexes
• Avoided crossings and bound states in the continuum in low-contrast dielectric gratings
• Non-exponential and oscillatory decays in quantum mechanics
• Robust bound states in the continuum in Kerr microcavity embedded in photonic crystal waveguide
• $\alpha$-cluster structure of ${}^{18}$O
• Resonances of 7He in the complex scaling method
• Nuclear pairing: new perspectives
• Transport Through Nanostructures with Asymmetric Coupling to the Leads
• Polarization-based branch selection of bound states in the continuum in dielectric waveguide modes anti-crossed by a metal grating
• An above-barrier narrow resonance in ${}^{15}$F
• Effective Interaction Techniques for the Gamow Shell Model
• Topological superconductivity and Majorana states in low-dimensional systems
• Subradiant hybrid states in the open 3D Anderson-Dicke model
• Probing the Non-exponential Decay Regime in Open Quantum Systems
• Effects of anisotropy and Coulomb interactions on quantum transport in a quadruple quantum-dot structure
• The Landau--Zener Problem with Decay and with Dephasing
• Bound states in the continuum and exceptional points in dielectric waveguide equipped with a metal grating
• Doorway states in nuclear reactions as a manifestation of the "super-radiant" mechanism
• Porter-Thomas distribution in unstable many-body systems
• Description of the 17F(p,gamma)18Ne radiative capture reaction in the continuum shell model
• "Super-radiance" and the width of exotic baryons
• Fano effect in Aharonov-Bohm ring with topologically superconducting bridge
• Degenerate bound states in the continuum in square and triangular open acoustic resonators
• A maximum likelihood method to correct for missed levels based on the ${\Delta }_3(L)$ statistic
• Exploring quantum dynamics in an open many-body system: Transition to superradiance
• Superradiance Transition and Nonphotochemical Quenching in Photosynthetic Complexes
• Collapse of the Fano Resonance Caused by the Nonlocality of the Majorana State
• The influence of Coulomb correlations on nonequilibrium quantum transport in quadruple quantum-dot structure
• Two-electron bound states in continuum in quantum dots
• The nuclear pairing problem: new perspectives
• Bound States in the Continuum and Fano Resonances in the Dirac Cone Spectrum
• Probing eigenfunction nonorthogonality by parametric shifts of resonance widths
• Resonance scattering and singularities of the scattering function
• Spectral Singularities and Zero Energy Bound States
• Beam energy dependence of Coulomb-nuclear interference in the breakup of 11Be
• Effects due to Resonant and Continuum States on the Neutrino-Nucleus Cross Section
• A comparative study on different non-Hermitian approaches for modeling open quantum systems
• Influence of Impurity on the Rate of Single Photon Superradiance in Disordered N Qubit Chain
• Superradiance Transition in Graphene
• Concurrent Skin-scale-free Localization and Criticality under Möbius Boundary Conditions in a Non-Hermitian Ladder
• Unified Multipole Bott Indices for Non-Hermitian Skin Effect in Different Orders
• Complex Band Structure and Bound States in the Continuum: A Unified Theoretical Framework