Quantum effect in the diffusion along a potential barrier: Comments on the synthesis of superheavy elements

We discuss a quantum effect in the diffusion process by developing a theory, which takes the finite curvature of the potential field into account. The transport coefficients of our theory satisfy the well-known fluctuation-dissipation theorem in the limit of Markovian approximation in the cases of diffusion in a flat potential and in a potential well. For the diffusion along a potential barrier, the diffusion coefficient can be related to the friction coefficient by an analytic continuation of the fluctuation-dissipation theorem for the case of diffusion along a potential well in the asymptotic time, but contains strong non-Markovian effects at short times. By applying our theory to the case of realistic values of the temperature, the barrier curvature, and the friction coefficient, we show that the quantum effects will play significant roles in describing the synthesis of superheavy elements, i.e., the evolution from the fusion barrier to the conditional saddle, in terms of a diffusion process. We especially point out the importance of the memory effect, which increases at lower temperatures. It makes the net quantum effects enhance the probability of crossing the conditional saddle.Comment: 12 pages, 3 figures, accepted for publication in Phys. Rev.

The dual nature of 5f electrons and origin of heavy fermions in U compounds

We develop a theory for the electronic excitations in UPt$_3$ which is based on the localization of two of the $5f$ electrons. The remaining $f$ electron is delocalized and acquires a large effective mass by inducing intra-atomic excitations of the localized ones. The measured deHaas-vanAlphen frequencies of the heavy quasiparticles are explained as well as their anisotropic heavy mass. A model calculation for a small cluster reveals why only the largest of the different $5f$ hopping matrix elements is operative causing the electrons in other orbitals to localize.Comment: 6 pages, 3 figure

Electromagnon dispersion probed by inelastic X-ray scattering in LiCrO2

Inelastic X-ray scattering with meV energy resolution (IXS) is an ideal tool to measure collective excitations in solids and liquids. In non-resonant scattering condition, the cross-section is strongly dominated by lattice vibrations (phonons). However, it is possible to probe additional degrees of freedom such as magnetic fluctuations that are strongly coupled to the phonons. The IXS spectrum of the coupled system contains not only the phonon dispersion but also the so far undetected magnetic correlation function. Here we report the observation of strong magnon-phonon coupling in LiCrO2 that enables the measurement of magnetic correlations throughout the Brillouin zone via IXS. We find electromagnon excitations and electric dipole active two-magnon excitations in the magnetically ordered phase and heavily damped electromagnons in the paramagnetic phase of LiCrO2. We predict that several (frustrated) magnets with dominant direct exchange and non-collinear magnetism show surprisingly large IXS cross-section for magnons and multi-magnon processes

Remarks on hard Lefschetz conjectures on Chow groups

We propose two conjectures of Hard Lefschetz type on Chow groups and prove them for some special cases. For abelian varieties, we shall show they are equivalent to well-known conjectures of Beauville and Murre.Comment: to appear in Sciences in China, Ser. A Mathematic

Influence of tunneling on electron screening in low energy nuclear reactions in laboratories

Using a semiclassical mean field theory, we show that the screening potential exhibits a characteristic radial variation in the tunneling region in sharp contrast to the assumption of the constant shift in all previous works. Also, we show that the explicit treatment of the tunneling region gives a larger screening energy than that in the conventional approach, which studies the time evolution only in the classical region and estimates the screening energy from the screening potential at the external classical turning point. This modification becomes important if the electronic state is not a single adiabatic state at the external turning point either by pre-tunneling transitions of the electronic state or by the symmetry of the system even if there is no essential change with the electronic state in the tunneling region.Comment: 3 figure

Temperature Dependence of Zero-Bias Resistances of a Single Resistance-Shunted Josephson Junction

Zero-bias resistances of a single resistance-shunted Josephson junction are calculated as a function of the temperature by means of the path-integral Monte Carlo method in case a charging energy $E_{\rm C}$ is comparable with a Josephson energy $E_{\rm J}$. The low-temperature behavior of the zero-bias resistance changes around $\alpha=R_{\rm Q}/R_{\rm S}=1$, where $R_{\rm S}$ is a shunt resistance and $R_{\rm Q}=h/(2e)^2$. The temperature dependence of the zero-bias resistance shows a power-law-like behavior whose exponent depends on $E_{\rm J}/E_{\rm C}$. These results are compared with the experiments on resistance-shunted Josephson junctions

Absence of a fuzzy S4S^4 phase in the dimensionally reduced 5d Yang-Mills-Chern-Simons model

We perform nonperturbative studies of the dimensionally reduced 5d Yang-Mills-Chern-Simons model, in which a four-dimensional fuzzy manifold, ``fuzzy S$^{4}$'', is known to exist as a classical solution. Although the action is unbounded from below, Monte Carlo simulations provide an evidence for a well-defined vacuum, which stabilizes at large $N$, when the coefficient of the Chern-Simons term is sufficiently small. The fuzzy S$^{4}$ prepared as an initial configuration decays rapidly into this vacuum in the process of thermalization. Thus we find that the model does not possess a ``fuzzy S$^{4}$ phase'' in contrast to our previous results on the fuzzy S$^{2}$.Comment: 11 pages, 2 figures, (v2) typos correcte