Optical Reciprocity Induced Symmetry of the Scattering Eigenstates in Non-PT\cal PT-Symmetric Heterostructures

The scattering matrix $S$ obeys the unitary relation $S^\dagger S=1$ in a Hermitian system and the symmetry property ${\cal PT}S{\cal PT}=S^{-1}$ in a Parity-Time (${\cal PT}$) symmetric system. Here we report a different symmetry relation of the $S$ matrix in a one-dimensional heterostructure, which is given by the amplitude ratio of the incident waves in the scattering eigenstates. It originates from the optical reciprocity and holds independent of the Hermiticity or $\cal PT$ symmetry of the system. Using this symmetry relation, we probe a quasi-transition that is reminiscent of the spontaneous symmetry breaking of a $\cal PT$-symmetric $S$ matrix, now with unbalanced gain and loss and even in the absence of gain. We show that the additional symmetry relation provides a clear evidence of an exceptional point, even when all other signatures of the $\cal PT$ symmetry breaking are completely erased. We also discuss the existence of a final exceptional point in this correspondence, which is attributed to asymmetric reflections from the two sides of the heterostructure.Comment: 5 pages, 4 figure

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

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

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