Study on space-time structure of Higgs boson decay using HBT correlation Method in e+^+e−^- collision at s\sqrt{s}=250 GeV

The space-time structure of the Higgs boson decay are carefully studied with the HBT correlation method using e$^+$e$^-$ collision events produced through Monte Carlo generator PYTHIA 8.2 at $\sqrt{s}$=250GeV. The Higgs boson jets (Higgs-jets) are identified by H-tag tracing. The measurement of the Higgs boson radius and decay lifetime are derived from HBT correlation of its decay final state pions inside Higgs-jets in the e$^+$e$^-$ collisions events with an upper bound of $R_H \le 1.03\pm 0.05$ fm and $\tau_H \le (1.29\pm0.15)\times 10^{-7}$ fs. This result is consistent with CMS data.Comment: 7 pages,3 figure

Quantum Tunneling of Spin Particles in Periodic Potentials with Asymmetric Twin Barriers

The tunneling effect of a periodic potential with an asymmetric twin barrier per period is calculated using the instanton method. The model is derived from the Hamiltonian of a small ferromagnetic particle in an external magnetic field using the spin-coherent-state path integral. The instantons in two neighbouring barriers differ and lead to different level shifts $\triangle\epsilon_1, \triangle\epsilon_2$. We derive with Bloch theory the energy spectrum which has formally the structure of an energy band. The spectrum depends on both level shifts. The removal of Kramer's degeneracy by an external magnetic field is discussed. In addition we find a new kind of quenching of macroscopic quantum coherence which is irrelevant to Kramer's degeneracy.Comment: 18 pages, LaTex, one figur

Scattering in PT\cal PT and RT\cal RT Symmetric Multimode Waveguides: Generalized Conservation Laws and Spontaneous Symmetry Breaking beyond One Dimension

We extend the generalize conservation law of light propagating in a one-dimensional $\cal PT$-symmetric system, i.e., $|T-1|=\sqrt{R_LR_R}$ for the transmittance $T$ and the reflectance $R_{L,R}$ from the left and right, to a multimode waveguide with either $\cal PT$ or $\cal RT$ symmetry, in which higher dimensional investigations are necessary. These conservation laws exist not only in a matrix form for the transmission and reflection matrices; they also exist in a scalar form for real-valued quantities by defining generalized transmittance and reflectance. We then discuss, for the first time, how a multimode $\cal PT$-symmetric waveguide can be used to observe spontaneous symmetry breaking of the scattering matrix, which typically requires tuning the non-hermiticity of the system (i.e. the strength of gain and loss). Here the advantage of using a multimode waveguide is the elimination of tuning any system parameters: the transverse mode order $m$ plays the role of the symmetry breaking parameter, and one observes the symmetry breaking by simply performing scattering experiment in each waveguide channel at a single frequency and fixed strength of gain and loss.Comment: 8 pages, 6 figure

Generalization and Equilibrium in Generative Adversarial Nets (GANs)

We show that training of generative adversarial network (GAN) may not have good generalization properties; e.g., training may appear successful but the trained distribution may be far from target distribution in standard metrics. However, generalization does occur for a weaker metric called neural net distance. It is also shown that an approximate pure equilibrium exists in the discriminator/generator game for a special class of generators with natural training objectives when generator capacity and training set sizes are moderate. This existence of equilibrium inspires MIX+GAN protocol, which can be combined with any existing GAN training, and empirically shown to improve some of them.Comment: This is an updated version of an ICML'17 paper with the same title. The main difference is that in the ICML'17 version the pure equilibrium result was only proved for Wasserstein GAN. In the current version the result applies to most reasonable training objectives. In particular, Theorem 4.3 now applies to both original GAN and Wasserstein GA

Application of Instantons: Quenching of Macroscopic Quantum Coherence and Macroscopic Fermi-Particle Configurations

Starting from the coherent state representation of the evolution operator with the help of the path-integral, we derive a formula for the low-lying levels $E = \epsilon_0 - 2\triangle\epsilon cos (s+\xi)\pi$ of a quantum spin system. The quenching of macroscopic quantum coherence is understood as the vanishing of $cos (s+\xi)\pi$ in disagreement with the suppression of tunneling (i.e. $\triangle\epsilon = 0$) as claimed in the literature. A new configuration called the macroscopic Fermi-particle is suggested by the character of its wave function. The tunneling rate ($(2\triangle\epsilon)/(\pi)$) does not vanish, not for integer spin s nor for a half-integer value of s, and is calculated explicitly (for the position dependent mass) up to the one-loop approximation.Comment: 13 pages, LaTex, no figure