arXiv subjects

Kejiang Zhou

Publications and source records attributed to Kejiang Zhou.

5 recordsLinked to original sources

arXiv2026

Mathematical Basis for Analyzing Superconducting Phase Transitions Using Catastrophe Theory

We establish a rigorous mathematical bridge from quantum many-body path integrals to the cusp catastrophe model by Lyapunov-Schmidt reduction, which provides a theoretical foundation for analyzing superconducting phase transition using the catastrophe theory. First, it is proved that, near the critical point the infinite-dimensional effective action is diffeomorphic to a finite-dimensional catastrophe. Secondly, starting from Ginzburg-Landau free energy functional, the Euler-Lagrange partial differential equation can be reduced to the cusp catastrophe model. Thirdly, the fermionic imaginary-time path integral to the cusp catastrophe is derived through the Hubbard-Stratonovich transformation, Matsubara frequency expansion, and Grassmann algebra. Furthermore, we connect this framework with the adsorption potential theory we proposed, elucidating the catastrophic topological nature of the electron pairing mechanism in high-temperature superconductivity. The precise microscopic derivation of the adsorption potential from first-principles electronic structure calculations would strengthen the predictive power of the theory.

cond-mat.supr-con↗

arXiv2026

Interfacial charge-induced adsorption mode for electron pairing in high-temperature superconductors

The electron pairing mechanism by the interfacial charge-induced adsorption mode of high-temperature superconductors is revealed. For the YBCO superconductors, the coupling of electrons and valence-flexible state of oxygen ions forms a charge-regulated interfacial layer induced by the adsorption potential, and electrons are paired by sharing the optimized interfacial structure and exchanging the adsorption mode, generating strong attraction to form Cooper pairs. Then the effective interaction potential between electrons is exactly derived in details, as well as the electron-adsorption-mode coupling strength, in which the adsorption coupling constant is up to 43.4. Furthermore, we verify that d-wave come from the anisotropy of interfacial adsorption forces, and explain the pseudo-energy gap behavior. By using the one-dimensional Ginzburg-Landau equation in the absence of a magnetic field, we obtain the coherence length expression, and the coherence length calculated is very close to the literature results. By establishing the energy gap equation, we obtain the superconducting gap , which is very close to the measured result of 17meV by Scanning Tunneling Microscopy/Spectroscopy. These quantitative predictions close to the known results could verify our theoretical framework.

cond-mat.supr-con↗

arXiv2026

Bilattice-Catastrophe Isomorphism for Four-Valued Logic in Digital Systems

Belnap's four-valued logic, distinguished by its inherent bilattice structure, provides a natural algebraic bridge between discrete Four-valued logic (4VL) in circuit and continuous catastrophe theory (CT). Building on the rigorous verification of the bilattice-catastrophe isomorphism theorem, we establish a categorical correspondence spanning the catastrophe category, interlaced bilattice category, and 4VL category, with the cusp catastrophe emerging as the canonical CT counterpart to 4VL.This unification provides a foundational framework for explaining 4VL's robustness. Crucially, we demonstrate that the four-valued algebra FOUR is the minimal complete algebraic structure capable of describing continuous-discrete interfaces with involution symmetry. Unlike the empirical adoption of X and Z in engineering practice, our work reveals their mathematical necessity: X and Z are topological invariants of discretized continuous dynamical systems, encoding fundamental properties of catastrophe-induced discontinuities. The work enables cross-disciplinary extensions to uncertainty propagation, complex system modeling, and fault-tolerant design.

cond-mat.dis-nn↗

arXiv2025

Thermodynamic adsorption potential of superconductors

Based on the general thermodynamic analysis of Polanyi adsorption potential, the adsorption potential condition for superconductors is obtained exactly by using the quantum state equation we presented. Because this adsorption potential results in changes of electron concentration, temperature and pressure in a certain volume (adsorption space) adjacent to the surface of the lattice, the composition and structure of superconductors are of course decisive for the adsorption potential. Then we calculate the molar adsorption potentials for those typical superconductors, and find that it is positively correlated to the superconductivity temperature , which reveals that those high-superconductors are mainly determined by the higher molar adsorption potentials. In addition, the adsorption potential at still works despite the disappearance of the energy gap of the BCS theory. This shows that beyond the electron-phonon interaction mechanism, the Cooper-paired electrons are mainly formed by this physical adsorption potential for high-superconductors. This adsorption potential theory could explain almost all common facts about high-temperature superconductors, including many anomalies of the normal and superconducting states.

cond-mat.supr-con↗

arXiv2022

Revisiting quantum relativistic effects from phase transition by catastrophe theory

In this paper we start from the Schrödinger equation to revisit some classical quantum mechanics from the perspective of phase transition process. Here the relativistic effect of particles moving at high speed can be regarded as the phase transition process when the velocity variable increases. Considering that the catastrophe models could describe qualitatively any phase transition process, we adopt the simplest folding catastrophe type as the potential function in the Schrödinger equation to obtain a revised Schrödinger relativistic equation through the dimensionless analysis first, and then further to derive out the steady-state Klein-Gordon equation and Dirac relativistic equation gradually. These results reveal that the quantum relativistic effect could be considered as the phase transition process, which could be described by adopting the catastrophe models as the potential function in the classical Schrödinger equation.

quant-ph↗