arXiv subjects
Publications and source records attributed to Yu Shi.
Study on pre- and postselected quantum system indicates that ``product rule'' and ``sum rule'' for elements of reality should be abandoned. We show that this so-called non-partial realism can refute arguments against hidden variables in a unified way, and might save local realism.
For spontaneous breaking of global or gauge symmetry, it is superfluous to assume that the vacuum expectation value of the scalar field manifesting the symmetry is nonvanishing. The vacuum with spontaneous symmetry breaking simply corresponds to nonzero number of particles of one or more components of the real scalar field.
Spontaneous symmetry breaking originats in quantum mechanical measurement of the relevant observable defining the physical situation, order parameter is the average of this observable. A modification is made on the random-phase postulate validating the ensemble description. Off-diagonal long-range order, macroscopic wavefunction and interference effects in many-particle systems present when there is a so-called nucleation of quantum state, which is proposed to be the origin of spontaneous gauge symmetry breaking, for which nonconservation of particle number N is not essential. The approach based on nonvanishing expectation of the field operator, $<\hatψ(\vec{r})>$, is only a coherent-state approximation in thermodynamic limit. When $N \to \infty$, this approach is equivalent, but $<\hatψ(\vec{r})>$ is not the macroscopic wavefunction.
Yang's $η$ pairing operator is generalized to explore off-diagonal long-range order in the Hubbard bilayer with an arbitrary chemical potential. With this operator and a constraint condition on annihilation and creation operators, we construct explicitly eigenstates which possess simultaneously three kinds of off-diagonal long-range order, i.e., the intralayer one and the interlayer one for on-site pairing, and that for interlayer nearest-neighbor pairing. As in the simple Hubbard model there is also an SO(4) symmetry, with the the generators properly defined. A sufficient condition leads to at least one of the above three kinds of off-diagonal long-range order. A constraint relation among different kinds of off-diagonal long-range order is also given. There exists a triplet of collective modes if the U(1) symmetry of a subgroup is spontaneously broken.
The power-law dependence of the angle in the angular projection of galaxy distribution is explained by assuming that in the spherical shells within a small angle the distributions are also fractal. If this local angular fractal is possessed, a fractal structure is angularly-isotropic at each occupied point though inhomogeneous, and is compatible with the present evidence claimed to be of homogeneity for galaxy distribution. Further, it is most likely to be isotropic rather than only angularly-isotropic. Several related issues are discussed.
It is shown that calculus can apply on a fractal structure with the condition that the infinitesimal limit of change of the variable is larger than the lower cut-off of the fractal structure, and an assumption called local decomposability. As an application, it is shown that the angular projection of a fractal distribution in 3-dimensional space is not homogeneous at sufficiently large angles. Therefore the angular projection of galaxy distribution for sufficiently large angles can discriminate the fractal and the homogeneity pictures.
Analytical investigation is made on the two-dimensional traffic-flow model with alternative movement and exclude-volume effect between right and up arrows [Phys. Rev. {\bf A} 46 R6124 (1992)]. Several exact results are obtained, including the upper critical density above which there are only jamming configurations, and the lower critical density below which there are only moving configurations. The observed jamming transition takes place at another critical density $p_{c}(N)$, which is in the intermidiate region between the lower and upper critical densities. It is derived that $p_{c}(N)\,=\,CN^α$, where $C$ and $α$ are determined to be respectively $0.76$ and $-0.14$ from previous numerical simulation. This transition is suggested to be a second-order phase transition, the order parameter is found. The nature of self-organization, ergodicity breaking and synchronization are discussed, Comparison with the sandpile model is made.
Some conceptual issues in the semi-classical approaches to giant magnetoresistance in magnetic multilayers are discussed.
We investigate correlations among pitches in several songs and pieces of piano music by mapping them to one-dimensional walks. Two kinds of correlations are studied, one is related to the real values of frequencies while they are treated only as different symbols for another. Long-range power law behavior is found in both kinds. The first is more meaningful. The structure of music, such as beat, measure and stanza, are reflected in the change of scaling exponents. Some interesting features are observed. Our results demonstrate the viewpoint that the fundamental principle of music is the balance between repetition and contrast.