Microscopic theory of particle-vibration coupling

Eugene R. Marshalek

Nandita Rudra, P. Rudra

M. Baldo, P. F. Bortignon

。 Cao, Ligang

A. Kuriyama, M. Yamamura

A microscopic theory is proposed to describe not only the pairing rotation, the pairing vibrations and the independent-particle motions, but also their mutual couplings in a consistent manner. With the aid of a BCS-type wave packet and a quasi-particle coherent state, the quantal system is translated into a corresponding classical one. First, we develop a canonical form in a classical image. This classical system obeys certain constraints, by which the double counting in the degrees of freedom is avoided. Then, the quantization is performed with the use of the Dirac theory of a canonical system with constraints. The original fermion operators themselves are expressed in terms of three types of degrees of freedom, which correspond to the pairing rotation, the pairing vibrations and the independent-quasi-particle motions, respectively.

Jiaqing Yan

Current classical wave theory and quantum physics systems usually simplify the wave behavior of microscopic particles such as photons, electrons, and protons into reciprocating vibrations in a two-dimensional plane, and define the standard wavelength and wave period by the extreme distance between wave crests and troughs along the propagation direction (X-direction). This study proposes that microscopic particles are not limited to vibration in a single plane, but continuously exhibit the characteristics of 360° spatial three-dimensional omnidirectional micro-vibration during propagation. Each vibration of a particle in an inclined direction has its corresponding wave crest and trough, but the projection of such extreme values in the propagation X-direction is too small to be recognized as an effective measurement extreme. A particle needs to undergo tens of thousands of alternating vibrations in three-dimensional directions before a vibration direction exactly perpendicular to the X-propagation direction appears, forming a recognizable real wave crest and trough in the X-direction. The traditional wave model only selects the extreme values in the X-direction to determine the wavelength, ignoring the vibration patterns in other directions, which is a macroscopic equivalent approximation and cannot fully reflect the real state of microscopic particle motion. This study further discusses the ability of this model to explain typical microscopic phenomena such as electron diffraction and particle scattering, providing a new theoretical perspective for in-depth understanding of the wave mechanism of microscopic particles.