Doping dependence of the upper critical field in La_{2-x}Sr_xCuO_4 from specific heat

The low-temperature specific heat of La_{2-x}Sr_xCuO_4 (LSCO) single crystals in magnetic field H up to 12 T has been examined over a wide range of doping (0.063=< p =<0.238). From this we have mapped the upper critical field H_{c2} of LSCO across the entire superconducting diagram. It is found that the H_{c2} shows a doping dependence similar to that of the critical temperature T_c. We have discussed the implications of the result and proposed that there may be an effective superconducting energy scale responsible for the H_{c2} behavior in the underdoped region.Comment: 6 pages,3 figures,1 tabl

Smooth densities of the laws of perturbed diffusion processes

Under some regularity conditions on $b$, $\sigma$ and $\alpha$, we prove that the following perturbed stochastic differential equation \begin{equation} X_t=x+\int_0^t b(X_s)ds+\int_0^t \sigma(X_s) dB_s+\alpha \sup_{0 \le s \le t} X_s, \ \ \ \alpha<1 \end{equation} admits smooth densities for all $0 \le t \le t_0$, where $t_0>0$ is some finite number

Gravitational waves with dark matter minispikes: the combined effect

It was shown that the dark matter(DM) minihalo around an intermediate mass black hole(IMBH) can be redistributed into a cusp, called the DM minispike. We consider an intermediate-mass-ratio inspiral consisting of an IMBH harbored in a DM minispike with nonannihilating DM particles and a small black hole(BH) orbiting around it. We investigate gravitational waves(GWs) produced by this system and analyze the waveforms with the comprehensive consideration of gravitational pull, dynamical friction and accretion of the minispike and calculate the time difference and phase difference caused by it. We find that for a certain range of frequency, the inspiralling time of the system is dramatically reduced for smaller central IMBH and large density of DM. For the central IMBH with $10^5M_\odot$, the time of merger is ahead, which can be distinguished by LISA, Taiji and Tianqin. We focus on the effect of accretion and compare it with that of gravitational pull and friction. We find that the accretion mass is a small quantity compared to the initial mass of the small BH and the accretion effect is inconspicuous compared with friction. However, the accumulated phase shift caused by accretion is large enough to be detected by LISA, Taiji and Tianqin, which indicate that the accretion effect can not be ignored in the detection of GWs.Comment: 10 pages, 14 figure