A Bose-Einstein condensate (BEC) is a topic of significant interest within the scientific community. It is well understood that Rb-87 and Yb2Si2O7 have been utilized in experiments to explore this phenomenon. These st...A Bose-Einstein condensate (BEC) is a topic of significant interest within the scientific community. It is well understood that Rb-87 and Yb2Si2O7 have been utilized in experiments to explore this phenomenon. These studies have demonstrated that these materials can achieve the BEC phase, a state that has been experimentally validated. In this paper, we further establish, from the perspective of theoretical physics, that silicon is also capable of exhibiting BEC properties. Our approach differs from prior studies in that it uses innovatively certain boundary conditions. Specifically, we employed Yb-70 as a gamma-ray radiation source and a 1 nm linewidth (as the half-width of a 2 nm line). Additionally, we utilized the concept of half-value thickness from nuclear physics absorption models to optimize the semiconductor process. This method effectively removes ytterbium (Yb) during the process, leaving only silicon, silicon-based materials, or silicon topological superconductors on the wafer. This technical procedure results in the creation of “BEC silicon” at absolute zero temperature (0 K), introducing a novel material for BEC realization.展开更多
Time-lattice model is proposed. Using the correspondence of the model and the Ising model for simple cubic lattice system, we study the time phase transition, the electroweak phase transition, and the BEC transition f...Time-lattice model is proposed. Using the correspondence of the model and the Ising model for simple cubic lattice system, we study the time phase transition, the electroweak phase transition, and the BEC transition for time. The time field is the Higgs field. Four types of the fields are found before the electroweak phase transition, after which there is only one type of Higgs field coming from the infinite correlation of the lattice time states, going with electromagnetic field and gravitowagnetic field. The symmetry breaking and the hierarchical structures, the relation between the change in energy and the Higgs formation, the reason why there are a few antiparticles and no negative mass are explored. For the Higgs field, its energy density and time condensation are discussed. A possible mechanism of the formation of black hole is assumed.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
In this paper, we investigate the condensate fraction （CF） of fermionic pairs in the BCS-BEC crossover for three- component Fermi gas with both asymmetric interactions and unequal chemical potentials in two-dimensio...In this paper, we investigate the condensate fraction （CF） of fermionic pairs in the BCS-BEC crossover for three- component Fermi gas with both asymmetric interactions and unequal chemical potentials in two-dimensional free space. By using the functional-path-integral method, we have analytically derived the number densities and bound-state energy, from which the off-diagonal long-range order is analyzed in terms of the asymptotic behavior of the two-body density matrix. The explicit formula of CF is obtained as a function of the bound-state energy and population imbalance. It is demonstrated that the CF spectrum with respect to the bound-state energy can be used to characterize the quantum phase transition between the two kinds of Sarma phases as well as the transition from three-component to two-component superfluid. Moreover we obtain the same analytic formula of CF in the BCS superfluid phase as that of homogeneous Fermi gas with equal chemical potentials.展开更多
文摘A Bose-Einstein condensate (BEC) is a topic of significant interest within the scientific community. It is well understood that Rb-87 and Yb2Si2O7 have been utilized in experiments to explore this phenomenon. These studies have demonstrated that these materials can achieve the BEC phase, a state that has been experimentally validated. In this paper, we further establish, from the perspective of theoretical physics, that silicon is also capable of exhibiting BEC properties. Our approach differs from prior studies in that it uses innovatively certain boundary conditions. Specifically, we employed Yb-70 as a gamma-ray radiation source and a 1 nm linewidth (as the half-width of a 2 nm line). Additionally, we utilized the concept of half-value thickness from nuclear physics absorption models to optimize the semiconductor process. This method effectively removes ytterbium (Yb) during the process, leaving only silicon, silicon-based materials, or silicon topological superconductors on the wafer. This technical procedure results in the creation of “BEC silicon” at absolute zero temperature (0 K), introducing a novel material for BEC realization.
文摘Time-lattice model is proposed. Using the correspondence of the model and the Ising model for simple cubic lattice system, we study the time phase transition, the electroweak phase transition, and the BEC transition for time. The time field is the Higgs field. Four types of the fields are found before the electroweak phase transition, after which there is only one type of Higgs field coming from the infinite correlation of the lattice time states, going with electromagnetic field and gravitowagnetic field. The symmetry breaking and the hierarchical structures, the relation between the change in energy and the Higgs formation, the reason why there are a few antiparticles and no negative mass are explored. For the Higgs field, its energy density and time condensation are discussed. A possible mechanism of the formation of black hole is assumed.
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.
基金Project supported by the Graduate Outstanding Innovation Item of Shanxi Province,China (Grant No.20123005)the National Natural Science Foundation of China (Grant Nos.11075099 and 11275118)
文摘In this paper, we investigate the condensate fraction （CF） of fermionic pairs in the BCS-BEC crossover for three- component Fermi gas with both asymmetric interactions and unequal chemical potentials in two-dimensional free space. By using the functional-path-integral method, we have analytically derived the number densities and bound-state energy, from which the off-diagonal long-range order is analyzed in terms of the asymptotic behavior of the two-body density matrix. The explicit formula of CF is obtained as a function of the bound-state energy and population imbalance. It is demonstrated that the CF spectrum with respect to the bound-state energy can be used to characterize the quantum phase transition between the two kinds of Sarma phases as well as the transition from three-component to two-component superfluid. Moreover we obtain the same analytic formula of CF in the BCS superfluid phase as that of homogeneous Fermi gas with equal chemical potentials.
