The traditional theory of wave-particle duality holds that microscopic particles are both particles and waves. This view arises from the limitations of early experimental techniques, which equate the statistical wave behavior of a large number of particles directly with the essential properties of a single particle, leading to problems such as logical inconsistency and vague physical picture. Based on modern single-particle emission experiments and basic physical logic, this paper proposes a new explanation: the essential nature of microscopic particles is always particle, not wave; the observed wave property originates from the inherent, continuous, and omnidirectional tiny vibration of particles themselves, which is an external manifestation of particle motion rather than an intrinsic attribute. The strength of a particle’s wave property is closely related to its mass: the smaller the mass, the more significant the vibration and the stronger the wave property; the larger the mass, the weaker the vibration and the less obvious the wave property. Wave-like phenomena such as double-slit interference are the statistical distribution results of landing positions caused by the inherent vibration of numerous particles. This paper reconstructs the physical essence of wave-particle phenomena with concise and self-consistent logic, providing a more intuitive and unified new idea for understanding the microscopic world.
GW calculations with a fully self-consistent Green's function
G and screened interaction
W---based on the iterative solution of the Dyson equation---provide a consistent framework for the description of ground- and excited-state properties of interacting many-body systems. We show that for closed-shell systems self-consistent
GW reaches the same final Green's function regardless of the initial reference state. Self-consistency systematically improves ionization energies and total energies of closed-shell systems compared to
G0W0 based on Hartree-Fock and (semi)local density-functional theory. These improvements also translate to the electron density, as exemplified by an improved description of dipole moments, and permit us to assess the quality of ground-state properties such as bond lengths and vibrational frequencies.
We study ground-state properties of a two-site, two-electron Holstein model describing two molecules coupled indirectly via electron-phonon interaction by using both exact diagonalization and self-consistent diagrammatic many-body perturbation theory. The Hartree and self-consistent Born approximations used in the present work are studied at different levels of self-consistency. The governing equations are shown to exhibit multiple solutions when the electron-phonon interaction is sufficiently strong, whereas at smaller interactions, only a single solution is found. The additional solutions at larger electron-phonon couplings correspond to symmetry-broken states with inhomogeneous electron densities. A comparison to exact results indicates that this symmetry breaking is strongly correlated with the formation of a bipolaron state in which the two electrons prefer to reside on the same molecule. The results further show that the Hartree and partially self-consistent Born solutions obtained by enforcing symmetry do not compare well with exact energetics, while the fully self-consistent Born approximation improves the qualitative and quantitative agreement with exact results in the same symmetric case. This together with a presented natural occupation number analysis supports the conclusion that the fully self-consistent approximation describes partially the bipolaron crossover. These results contribute to better understanding how these approximations cope with the strong localizing effect of the electron-phonon interaction.