The solution of Kardar-Parisi-Zhang equation (KPZ equation) is solved formally via Cole-Hopf transformation $h=log u$, where $u$ is the solution of multiplicative stochastic heat equation(SHE). In earlier works by Chatterjee and Dunlap, Caravenna, Su
n, and Zygouras, and Gu, they consider the solution of two dimensional KPZ equation via the solution $u_varepsilon$ of SHE with flat initial condition and with noise which is mollified in space on scale in $varepsilon$ and its strength is weakened as $beta_varepsilon=hat{beta} sqrt{frac{2pi varepsilon}{-log varepsilon}}$, and they prove that when $hat{beta}in (0,1)$, $frac{1}{beta_varepsilon}(log u_varepsilon-mathbb{E}[log u_varepsilon])$ converges in distribution to a solution of Edward-Wilkinson model as a random field. In this paper, we consider a stochastic heat equation $u_varepsilon$ with general initial condition $u_0$ and its transformation $F(u_varepsilon)$ for $F$ in a class of functions $mathfrak{F}$, which contains $F(x)=x^p$ ($0<pleq 1$) and $F(x)=log x$. Then, we prove that $frac{1}{beta_varepsilon}(F(u_varepsilon(t,x))-mathbb{E}[F(u_varepsilon(t,x))])$ converges in distribution to Gaussian random variables jointly in finitely many $Fin mathfrak{F}$, $t$, and $u_0$. In particular, we obtain the fluctuations of solutions of stochastic heat equations and KPZ equations jointly converge to solutions of SPDEs which depends on $u_0$. Our main tools are It^os formula, the martingale central limit theorem, and the homogenization argument as in the works by Cosco and the authors. To this end, we also prove the local limit theorem for the partition function of intermediate $2d$-directed polymers
We propose a mechanism of the spin Seebeck effect attributed to excitonic condensation in a nonmagnetic insulator. We analyze a half-filled two-orbital Hubbard model with a crystalline field splitting in the strong coupling limit. In this model, the
competition between the crystalline field and electron correlations brings about an excitonic insulating state, where the two orbitals are spontaneously hybridized. Using the generalized spin-wave theory and Boltzmann transport equation, we find that a spin current generated by a thermal gradient is observed in the excitonic insulating state without magnetic fields. The spin Seebeck effect originates from spin-split collective excitation modes although the ground state does not exhibit any magnetic orderings. This peculiar phenomenon is inherent in the excitonic insulating state, whose order parameter is time-reversal odd and yields a spin splitting for the collective excitation modes. We also find that the spin current is strongly enhanced and its direction is inverted in the vicinity of the phase transition to another magnetically ordered phase. We suggest that the present phenomenon is possibly observed in perovskite cobaltites with the GdFeO$_3$-type lattice distortion.
There have been recently several works studying the regularized stochastic heat equation (SHE) and Kardar-Parisi-Zhang (KPZ) equation in dimension $dgeq 3$ as the smoothing parameter is switched off, but most of the results did not hold in the full t
emperature regions where they should. Inspired by martingale techniques coming from the directed polymers literature, we first extend the law of large numbers for SHE obtained in [MSZ16] to the full weak disorder region of the associated polymer model and to more general initial conditions. We further extend the Edwards-Wilkinson regime of the SHE and KPZ equation studied in [GRZ18,MU17,DGRZ20] to the full $L^2$-region, along with multidimensional convergence and general initial conditions for the KPZ equation (and SHE), which were not proven before. To do so, we rely on a martingale CLT combined with a refinement of the local limit theorem for polymers.
Effects of the spin-orbit coupling (SOC) and magnetic field on excitonic insulating (EI) states are investigated. We introduce the two-orbital Hubbard model with the crystalline field splitting, which is a minimal model for discussing the exciton con
densation in strongly correlated electron systems, and analyze its effective Hamiltonian in the strong correlation limit by using the mean-field theory. In the absence of the SOC and magnetic field, the ground state changes from the nonmagnetic band-insulating state to the EI state by increasing the Hund coupling. In an applied magnetic field, the magnetic moment appears in the EI state, which is continuously connected to the forced ferromagnetic state. On the other hand, in the presence of the SOC, they are separated by a phase boundary. We find that the magnetic susceptibility is strongly enhanced in the EI phase near the boundary with a small SOC. This peculiar behavior is attributed to the low-energy fluctuation of the spin nematicity inherent in the high-spin local state stabilized by the Hund coupling. The present study not only reveals the impact of the SOC for the EI state but also sheds light on the role of quantum fluctuations of the spin nematicity for the EI state.
The computational analysis of the Cauchy problem for semi-linear Klein-Gordon equations in the de Sitter spacetime is considered. Several simulations are performed to show the time-global behaviors of the solutions of the equations in the spacetime b
ased on the structure-preserving scheme. It is remarked that the sufficiently large Hubble constant yields the strong diffusion-effect which gives the long and stable simulations for the defocusing semi-linear terms. The reliability of the simulations is confirmed by the preservation of the numerically modified Hamiltonian of the equations.
We theoretically study finite temperature properties of interacting fermion systems under geometrical frustration in the charge degree of freedom. Physical quantities such as charge structure factors, the specific heat, and the entropy, of the two-di
mensional model of interacting spinless fermions on an anisotropic triangular lattice are numerically calculated using the thermal pure quantum state. By considering the Coulomb interactions up to the next-nearest-neighbor bonds, we elucidate that in the highly frustrated region where a long-period stripe-type charge order (CO) is the ground state, fluctuations of different stripe-type CO patterns become large at finite temperatures. When we further introduce $1/r$-type long-range Coulomb interactions, the ground state unexpectedly recovers the non-stripe-type 3-fold CO pattern characteristic of triangular lattice models with short-range interactions. Our results imply that the BEDT-TTF-based organic conductors exhibiting glass-like behavior locates in the region of the intermediate strength of long-range interactions, where both the stripe- and non-stripe-type CO fluctuations are prominent.
We investigated the star formation activities in the AFGL333 region, which is in the vicinity of the W4 expanding bubble, by conducting NH3 (1,1), (2,2), and (3,3) mapping observations with the 45 m Nobeyama Radio Telescope at an angular resolution o
f 75. The morphology of the NH3 (1,1) map shows a bow-shape structure with the size of 2.0 x 0.6 pc as seen in the dust continuum. At the interface between the W4 bubble and the dense NH3 cloud, the compact HII region G134.2+0.8, associated with IRAS02245+6115, is located. Interestingly, just north and south of G134.2+0.8 we found NH3 emission exhibiting large velocity widths of ~ 2.8 km/s, compared to 1.8 km/s at the other positions. As the possibility of mechanical energy injection through the activity of YSO(s) is low, we considered the origin of the large turbulent gas motion as indication of interaction between the compact HII region and the periphery of the dense molecular cloud. We also found expanding motion of the CO emission associated with G134.2+0.8. The overall structure of the AFGL333-Ridge might have been formed by the expanding bubble of W4. However, the small velocity widths observed west of IRAS02245+6115, around the center of the dense molecular cloud, suggest that interaction with the compact HII region is limited. Therefore the YSOs (dominantly Class 0/I) in the core of the AFGL333-Ridge dense molecular cloud most likely formed in quiescent mode. As has been previously suggested for the large scale star formation in the W3 giant molecular cloud, our results show an apparent coexistence of induced and quiescent star formation in this region. It appears that star formation in the AFGL333 region has proceeded without significant external triggers, but accompanying stellar feedback environment.
We have derived and implemented a stress tensor formulation for the van derWaals density functional (vdW-DF) with spin-polarization-dependent gradient correction (GC) recently proposed by the authors [J. Phys. Soc. Jpn. 82, 093701 (2013)] and applied
it to nonmagnetic and magnetic molecular crystals under ambient condition. We found that the cell parameters of the molecular crystals obtained with vdW-DF show an overall improvement compared with those obtained using local density and generalized gradient approximations. In particular, the original vdW-DF with GC gives the equilibrium structural parameters of solid oxygen in the {alpha}-phase, which are in good agreement with the experiment.
We present an ab initio approach for evaluating a free energy profile along a reaction coordinate by combining logarithmic mean force dynamics (LogMFD) and first-principles molecular dynamics. The mean force, which is the derivative of the free energ
y with respect to the reaction coordinate, is estimated using density functional theory (DFT) in the present approach, which is expected to provide an accurate free energy profile along the reaction coordinate. We apply this new method, first-principles LogMFD (FP-LogMFD), to a glycine dipeptide molecule and reconstruct one- and two-dimensional free energy profiles in the framework of DFT. The resultant free energy profile is compared with that obtained by the thermodynamic integration method and by the previous LogMFD calculation using an empirical force-field, showing that FP-LogMFD is a promising method to calculate free energy without empirical force-fields.
We propose a practical approach to spin-polarized systems within the van der Waals density functional (vdW-DF). The method was applied to a gas phase oxygen molecule and a parallel (H-type) pair of oxygen molecules. It was found that vdW-DF improves
the equilibrium distance and binding energy. In particular, one type of vdW-DF can describe such systems reasonably well. The van der Waals interaction has been confirmed to have an energy comparable to the magnetic one, while emerging at a distance rather longer than the latter.
