Condensed state physics demonstrates that the Curie temperature is the point at which spontaneous magnetization drops to zero, marking the critical transition where ferromagnetic or ferrimagnetic materials transform i...Condensed state physics demonstrates that the Curie temperature is the point at which spontaneous magnetization drops to zero, marking the critical transition where ferromagnetic or ferrimagnetic materials transform into paramagnetic substances. Below the Curie temperature, a material remains ferromagnetic;above it, the material becomes paramagnetic, with its magnetic field easily influenced by external magnetic fileds. For example, the Curie temperature of iron (Fe) is 1043 K, while that of neodymium magnets ranges from 583 to 673 K. From both physics and mathematics perspectives, examining the temperature properties of materials is essential, as it provides valuable insights into their electromagnetic and thermodynamic behaviors. This paper makes a bold assumption and, for the first time, carefully verifies the existence of a Casimir temperature at 0.00206 K under conditions of one-atomic spacing.展开更多
This paper indicates the problem of the famous Riemann hypothesis (RH), which has been well-verified by a definite answering method using a Bose-Einstein Condensate (BEC) phase. We adopt mathematical induction, mappin...This paper indicates the problem of the famous Riemann hypothesis (RH), which has been well-verified by a definite answering method using a Bose-Einstein Condensate (BEC) phase. We adopt mathematical induction, mappings, and laser photons governed by electromagnetically induced transparency (EIT) to examine the existence of the RH. In considering the well-developed as Riemann zeta function, we find that the existence of RH has a corrected and self-consistent solution. Specifically, there is the only one pole at s = 1 on the complex plane for Riemann’s functions, which generalizes to all non-trivial zeros while s > 1. The essential solution is based on the BEC phases and on the nature of the laser photon(s). This work also incorporates Heisenberg commutators [ x^,p^]=1/2in the field of quantum mechanics. We found that a satisfactory solution for the RH would be incomplete without the formalism of Heisenberg commutators, BEC phases, and EIT effects. Ultimately, we propose the application of qubits in connection with the RH.展开更多
文摘Condensed state physics demonstrates that the Curie temperature is the point at which spontaneous magnetization drops to zero, marking the critical transition where ferromagnetic or ferrimagnetic materials transform into paramagnetic substances. Below the Curie temperature, a material remains ferromagnetic;above it, the material becomes paramagnetic, with its magnetic field easily influenced by external magnetic fileds. For example, the Curie temperature of iron (Fe) is 1043 K, while that of neodymium magnets ranges from 583 to 673 K. From both physics and mathematics perspectives, examining the temperature properties of materials is essential, as it provides valuable insights into their electromagnetic and thermodynamic behaviors. This paper makes a bold assumption and, for the first time, carefully verifies the existence of a Casimir temperature at 0.00206 K under conditions of one-atomic spacing.
文摘This paper indicates the problem of the famous Riemann hypothesis (RH), which has been well-verified by a definite answering method using a Bose-Einstein Condensate (BEC) phase. We adopt mathematical induction, mappings, and laser photons governed by electromagnetically induced transparency (EIT) to examine the existence of the RH. In considering the well-developed as Riemann zeta function, we find that the existence of RH has a corrected and self-consistent solution. Specifically, there is the only one pole at s = 1 on the complex plane for Riemann’s functions, which generalizes to all non-trivial zeros while s > 1. The essential solution is based on the BEC phases and on the nature of the laser photon(s). This work also incorporates Heisenberg commutators [ x^,p^]=1/2in the field of quantum mechanics. We found that a satisfactory solution for the RH would be incomplete without the formalism of Heisenberg commutators, BEC phases, and EIT effects. Ultimately, we propose the application of qubits in connection with the RH.
