Monte Carlo Hamiltonian: the Linear Potentials

We further study the validity of the Monte Carlo Hamiltonian method. The advantage of the method, in comparison with the standard Monte Carlo Lagrangian approach, is its capability to study the excited states. We consider two quantum mechanical models: a symmetric one $V(x) = |x|/2$; and an asymmetric one $V(x)=\infty$, for $x < 0$ and $V(x)=x$, for $x \ge 0$. The results for the spectrum, wave functions and thermodynamical observables are in agreement with the analytical or Runge-Kutta calculations.Comment: Latex file, 8 figure

Predicted ΛΛˉ\Lambda\bar{\Lambda} and Ξ−Ξˉ+\Xi^-\bar{\Xi}^+ decay modes of the charmoniumlike Y(4230)Y(4230)

In this work, we predict the light hadronic decay channels $Y(4230)\to\Lambda\bar{\Lambda}$ and $\Xi^-\bar{\Xi}^+$ when treating the $Y(4230)$ as a vector charmonium state. By the hadronic loop mechanism, the branching ratios of the $Y(4230)\to\Lambda\bar{\Lambda}$ and $\Xi^-\bar{\Xi}^+$ processes are calculated. In addition, we discuss the possibility of carrying out the search for the signal of the $Y(4230)$ through $\Lambda\bar{\Lambda}$ and $\Xi^-\bar{\Xi}^+$ channels from the $e^+e^-$ annihilation. Assuming $Y(4230)$ exist in $\Lambda\bar{\Lambda}$ and $\Xi^-\bar{\Xi}^+$ channel, we also present the time-like electromagnetic form factors (EMFFs) at $\sqrt{s}=m_{Y(4230)}$.Comment: 8 pages, 9 figures and 2 table

Novel π\pi-type vortex in a nanoscale extreme type-II superconductor: Induced by quantum-size effect

By numerically solving the Bogoliubov-de Gennes equations, we report a novel $\pi$-type vortex state whose order parameter near the core undergoes an extraordinary $\pi$-phase change for a quantum-confined extreme type-II $s$-wave superconductor. Its supercurrent behaves as the cube of the radial coordinate near the core, and its local density of states spectrum exhibits a significant negative-shifted zero-bias peak. Such $\pi$-type vortex state is induced by quantum-size effect, and can survive thermal smearing at temperatures up to a critical value $T_\tau$. The Anderson's approximation indicates that the $\pi$-type vortex may remain stable under sufficiently week magnetic field in the case less deep in the type-II limit. Moreover, we find that its appearance is governed by the sample size and $k_F\xi_0$ with $k_F$ the Fermi wave number and $\xi_0$ the zero-temperature coherence length. Similar effects may be expected in quantum-confined ultracold superfluid Fermi gasses, or even high-$T_c$ superconductors with proper $k_F\xi_0$ value.Comment: 6 figure

Implications for the non-Gaussianity of curvature perturbation from pulsar timing arrays

The recently released data by pulsar timing array (PTA) collaborations present strong evidence for a stochastic signal consistent with a gravitational-wave background. Assuming this signal originates from scalar-induced gravitational waves, we jointly use the PTA data from the NANOGrav 15-yr data set, PPTA DR3, and EPTA DR2 to probe the small-scale non-Gaussianity. We put the first-ever constraint on the non-Gaussianity parameter, finding $|F_\mathrm{NL}|\lesssim 13.9$ for a lognormal power spectrum of the curvature perturbations. Furthermore, we obtain $-13.9 \lesssim F_\mathrm{NL}\lesssim -0.1$ to prevent excessive production of primordial black holes. Moreover, the multi-band observations with the space-borne gravitational-wave detectors, such as LISA/Taiji/TianQin, will provide a complementary investigation of primordial non-Gaussianity. Our findings pave the way to constrain inflation models with PTA data.Comment: 8 pages, 2 figures, 1 table; Refs added; Supplementary Material added; Accepted by PRD as a Lette