Direct images of bundles under Frobenius morphisms

Let $X$ be a smooth projective variety of dimension $n$ over an algebraically closed field $k$ with ${\rm char}(k)=p>0$ and $F:X\to X_1$ be the relative Frobenius morphism. For any vector bundle $W$ on $X$, we prove that instability of $F_*W$ is bounded by instability of $W\otimes{\rm T}^{\ell}(\Omega^1_X)$ ($0\le \ell\le n(p-1)$)(Corollary \ref{cor3.8}). When $X$ is a smooth projective curve of genus $g\ge 2$, it implies $F_*W$ being stable whenever $W$ is stable.Comment: the final version to appear in Invent. math. (2008

Fourier transform and rigidity of certain distributions

Let $E$ be a finite dimensional vector space over a local field, and $F$ be its dual. For a closed subset $X$ of $E$, and $Y$ of $F$, consider the space $D^{-\xi}(E;X,Y)$ of tempered distributions on $E$ whose support are contained in $X$ and support of whose Fourier transform are contained in $Y$. We show that $D^{-\xi}(E;X,Y)$ possesses a certain rigidity property, for $X$, $Y$ which are some finite unions of affine subspaces.Comment: 10 page

Objective and efficient terahertz signal denoising by transfer function reconstruction

As an essential processing step in many disciplines, signal denoising efficiently improves data quality without extra cost. However, it is relatively under-utilized for terahertz spectroscopy. The major technique reported uses wavelet denoising in the time-domain, which has a fuzzy physical meaning and limited performance in low-frequency and water-vapor regions. Here, we work from a new perspective by reconstructing the transfer function to remove noise-induced oscillations. The method is fully objective without a need for defining a threshold. Both reflection imaging and transmission imaging were conducted. The experimental results show that both low- and high-frequency noise and the water-vapor influence were efficiently removed. The spectrum accuracy was also improved, and the image contrast was significantly enhanced. The signal-to-noise ratio of the leaf image was increased up to 10 dB, with the 6 dB bandwidth being extended by over 0.5 THz

Creation of collective many-body states and single photons from two-dimensional Rydberg lattice gases

The creation of collective many-body quantum states from a two-dimensional lattice gas of atoms is studied. Our approach relies on the van-der-Waals interaction that is present between alkali metal atoms when laser excited to high-lying Rydberg s-states. We focus on a regime in which the laser driving is strong compared to the interaction between Rydberg atoms. Here energetically low-lying many-particle states can be calculated approximately from a quadratic Hamiltonian. The potential usefulness of these states as a resource for the creation of deterministic single-photon sources is illustrated. The properties of these photon states are determined from the interplay between the particular geometry of the lattice and the interatomic spacing.Comment: 12 pages, 8 figure

Toward precision mass measurements of neutron-rich nuclei relevant to rr-process nucleosynthesis

The open question of where, when, and how the heavy elements beyond iron enrich our Universe has triggered a new era in nuclear physics studies.\ Of all the relevant nuclear physics inputs, the mass of very neutron-rich nuclides is a key quantity for revealing the origin of heavy elements beyond iron.\ Although the precise determination of this property is a great challenge, enormous progress has been made in recent decades, and it has contributed significantly to both nuclear structure and astrophysical nucleosynthesis studies.\ In this review, we first survey our present knowledge of the nuclear mass surface, emphasizing the importance of nuclear mass precision in $r$-process calculations.\ We then discuss recent progress in various methods of nuclear mass measurement with a few selected examples.\ For each method, we focus on recent breakthroughs and discuss possible ways of improving the weighing of $r$-process nuclides.Comment: 10 figures, review articles in Frontiers of Physic

Multivalley engineering in semiconductor microcavities

We consider exciton-photon coupling in semiconductor microcavities in which separate periodic potentials have been embedded for excitons and photons. We show theoretically that this system supports degenerate ground-states appearing at non-zero in-plane momenta, corresponding to multiple valleys in reciprocal space, which are further separated in polarization corresponding to a polarization-valley coupling in the system. Aside forming a basis for valleytronics, the multivalley dispersion is predicted to allow for spontaneous momentum symmetry breaking and two-mode squeezing under non-resonant and resonant excitation, respectively.Comment: Manuscript: 7 pages, 7 figures, published in Scientific Reports 7, 45243 (2017

Time-Reversal Symmetry Breaking and Spontaneous Anomalous Hall Effect in Fermi Fluids

We study the spontaneous non-magnetic time-reversal symmetry breaking in a two-dimensional Fermi liquid without breaking either the translation symmetry or the U(1) charge symmetry. Assuming that the low-energy physics is described by fermionic quasiparticle excitations, we identified an "emergent" local $U(1)^N$ symmetry in momentum space for an $N$-band model. For a large class of models, including all one-band and two-band models, we found that the time-reversal and chiral symmetry breaking can be described by the $U(1)^N$ gauge theory associated with this emergent local $U(1)^N$ symmetry. This conclusion enables the classification of the time-reversal symmetry-breaking states as types I and II, depending on the type of accompanying spatial symmetry breaking. The properties of each class are studied. In particular, we show that the states breaking both time-reversal and chiral symmetries are described by spontaneously generated Berry phases. We also show examples of the time-reversal symmetry-breaking phases in several different microscopically motivated models and calculate their associated Hall conductance within a mean-field approximation. The fermionic nematic phase with time-reversal symmetry breaking is also presented and the possible realizations in strongly correlated models such as the Emery model are discussed.Comment: 18 pages, 8 figure

Spontaneous spin-polarized current in a nonuniform Rashba interaction system

We investigate the electron transport through a two-dimensional semiconductor with a nonuniform Rashba spin-orbit interaction. Due to the combination of the coherence effect and the Rashba interaction, a spontaneous spin-polarized current emerges in the absence of any magnetic material and magnetic field. For a two-terminal device, only the local current contains polarization; however, with a four-terminal setup, a polarized total current is produced. This phenomenon may offer a novel way for generating a spin-polarized current, replacing the traditional spin-injection method.Comment: 4 pages, 4 figure

Opposite spin accumulations on the transverse edges by the confining potential

We show that the spin-orbit interaction induced by the boundary confining potential causes opposite spin accumulations on the transverse edges in a zonal two-dimensional electron gas in the presence of external longitudinal electric field. While the bias is reversed, the spin polarized direction is also reversed. The intensity of the spin accumulation is proportional to the bias voltage. In contrast to the bulk extrinsic and intrinsic spin Hall effects, the spin accumulation by the confining potential is almost unaffected by impurity and survives even in strong disorder. The result provides a new mechanism to explain the recent experimental data.Comment: 5 pages, 6 figure