arXiv subjects
Publications and source records attributed to S. Y. Liu.
In 2012, Andrews and Merca proved a truncated theorem on Euler's pentagonal number theorem, which opened up a new study on truncated theta series. In particular, some truncated versions of a identity of Gauss have been proved. In this article, we provide new combinatorial interpretations of the truncated versions of the identity of Gauss in terms of the minimal excludant non-overlined part of an overpartition.
We have developed a hybrid code GMEC: Gyro-kinetic Magnetohydrodynamics (MHD) Energetic-particle Code that can numerically simulate energetic particle-driven Alfvén eigenmodes and energetic particle transport in tokamak plasmas. In order to resolve the Alfvén eigenmodes with high toroidal numbers effectively, the field-aligned coordinates and meshes are adopted. The extended MHD equations are solved with five-points finite difference method and fourth order Runge-Kutta method. The gyrokinetic equations are solved by particle-in-cell (PIC) method for the perturbed energetic particle pressures that are coupled into the MHD equations. Up to now, a simplified version of the hybrid code has been completed with several successful verifications including linear simulations of toroidal Alfvén eigenmodes and reversed shear Alfvén eigenmodes.
A new magnetohydrodynamics (MHD) code based on initial value approach, GMEC_I, has been developed for simulating various MHD physics in tokamak plasmas, as the MHD foundation of the gyrokinetic-MHD energetic particle simulation code (GMEC) family. GMEC_I solves multi-level reduced-MHD models that form a hierarchy of physics complexity, which provide conveniences for the cross-code verification and the identification of key physics effect in tokamak geometry. The field-aligned coordinates are used to represent mode structure efficiently. High-order finite difference methods are used for spatial discretization. The shifted metric methods are used for numerical stability. The discrete expansion forms of physics equations in the code are generated symbolically using the compile-time symbolic solver (CSS), which is specifically developed to reduce the complexity of the high-order finite difference form of the MHD equations. Advanced computational techniques have been implemented for optimizing memory access and code parallelization that show a good efficiency using both Thread Building Block (TBB) and Message Passing Interface (MPI). Benchmarks between GMEC_I and the eigenvalue code MAS are presented for ballooning modes without and with diamagnetic drift effects, and tearing modes, which show excellent agreements.
The physical and chemical properties of cold and dense molecular clouds are key to understanding how stars form. Using the IRAM 30 m and NRO 45 m telescopes, we carried out a Multiwavelength line-Imaging survey of the 70 $μ$m dark and bright clOuds (MIAO). At a linear resolution of 0.1--0.5 pc, this work presents a detailed study of parsec-scale CO depletion and $\rm HCO^+$ deuterium (D-) fractionation toward four sources (G11.38+0.81, G15.22-0.43, G14.49-0.13, and G34.74-0.12) included in our full sample. In each source with $\rm T<20$ K and $n_{\rm H}\rm\sim10^4$--$\rm 10^5 cm^{-3}$, we compared pairs of neighboring 70 $μ$m bright and dark clumps and found that (1) the $\rm H_2$ column density and dust temperature of each source show strong spatial anticorrelation; (2) the spatial distribution of CO isotopologue lines and dense gas tracers, such as 1--0 lines of $\rm H^{13}CO^+$ and $\rm DCO^+$, are anticorrelated; (3) the abundance ratio between $\rm C^{18}O$ and $\rm DCO^+$ shows a strong correlation with the source temperature; (4) both the $\rm C^{18}O$ depletion factor and D-fraction of $\rm HCO^+$ show a robust decrease from younger clumps to more evolved clumps by a factor of more than 3; and (5) preliminary chemical modeling indicates chemical ages of our sources are ${\sim}8\times10^4$ yr, which is comparable to their free-fall timescales and smaller than their contraction timescales, indicating that our sources are likely dynamically and chemically young.
Considering the interband correlation, we present a generalized multiple-scattering approach of Green's function to investigate the effects of electron-impurity scattering on the density of states in silicene. The reduction of energy gaps in the case of relatively high chemical potential and the transformation of split-off impurity bands into band tails for low chemical potential are found. The dependency of optical conductivity on the impurity concentration is also discussed for frequency within the terahertz regime.
Aims. We study a sample of eight B[e] stars with uncertain evolutionary status to shed light on the origin of their circumstellar dust. Methods. We performed a diagnostic analysis on the spectral energy distribution beyond infrared wavelengths, and conducted a census of neighboring region of each target to ascertain its evolutionary status. Results. In comparison to pre-main sequence Herbig stars, these B[e] stars show equally substantial excess emission in the near-infrared, indicative of existence of warm dust, but much reduced excess at longer wavelengths, so the dusty envelopes should be compact in size. Isolation from star-forming regions excludes the possibility of their pre-main sequence status. Six of our targets, including HD 50138, HD 45677, CD-245721, CD-49 3441, MWC 623, and HD 85567, have been previously considered as FS CMa stars, whereas HD 181615/6 and HD 98922 are added to the sample by this work. We argue that the circumstellar grains of these isolated B[e] stars, already evolved beyond the pre-main sequence phase, should be formed in situ. This is in contrast to Herbig stars, which inherit large grains from parental molecular clouds. It has been thought that HD 98922, in particular, is a Herbig star because of its large infrared excess, but we propose it being in a more evolved stage. Because dust condenses out of stellar mass loss in an inside-out manner, the dusty envelope is spatially confined, and anisotropic mass flows, or anomalous optical properties of tiny grains, lead to the generally low line-of-sight extinction toward these stars.
Considering finite-temperature screened electron-impurity scattering, we present a kinetic equation approach to investigate transport properties of two-dimensional massive fermions in silicene. We find that the longitudinal conductivity is always nonvanishing when chemical potential lies within the energy gap. This residual conductivity arises from interband correlation and strongly depends on strength of electron-impurity scattering. We also clarify that the electron-impurity interaction makes substantial contributions to the spin- and valley-Hall conductivities, which, however, are almost independent of impurity density. The dependencies of longitudinal conductivity as well as of spin- and valley-Hall conductivities on chemical potential, on temperature, and on gap energy are analyzed.
We examine the effect of changing the linear polarization angle $θ$ of incident microwaves with respect to the dc current on radiation-induced magnetoresistance oscillations in a two-dimensional (2D) system within the balance-equation formulation of the photon-assisted magnetotransport model, considering the radiative decay as the sole damping mechanism. At an extremum the amplitude of oscillatory magnetoresistance $R_{xx}$ exhibits a sinusoidal, up to a factor of 5, magnitude variation with rotating the polarization angle $θ$. The maximal amplitude shows up generally at a nonzero $θ$, which is dependent upon the extremum in question, the 2D electron setup, the radiation frequency and the magnetic field orientation. These results provide a natural explanation for the experimental observations by Mani {\it et al.} [Phys. Rev. B {\bf 84}, 085308 (2011)], and Ramanayaka {\it et al.} [Phys. Rev. B {\bf 85}, 205315 (2012)].
Considering screeening of electron scattering interactions in terms of the finite-temperature STLS theory and solving the linearized Boltzmann equation (with no appeal to a relaxation time approximation), we present a theoretical analysis of the low-temperature Seebeck effect in two-dimensional semiconductors with dilute electron densities. We find that the temperature ($T$) dependencies of the diffusion and phonon-drag thermoelectric powers ($S_d$ and $S_g$) can no longer be described by the conventional simple power-laws. As temperature increases, $|S_d|/T$ decreases when $T\gtrsim 0.1 ε_F$ ($ε_F$ is the Fermi energy), while $|S_g|$ first increases and then falls, resulting a peak located at a temperature between Bloch-Grüneisen temperature and $ε_F$.
Nonlinear magnetotransport of a microwave-irradiated high mobility two-dimensional electron system under a finite direct current excitation is analyzed using a dc-controlled scheme with photon-assisted transition mechanism. The predicted amplitudes, extrema and nodes of the oscillatory differential resistance versus the magnetic field and the current density, are in excellent agreement with the recent experimental observation [Hatke et al. Phys. Rev. B 77, 201304(R) (2008)].
We present a kinetic equation approach to investigate dc transport properties of graphene in the diffusive regime considering long-range electron-impurity scattering. In our study, the effects of interband correlation (or polarization) on conductivity are taken into account. We find that the conductivity contains not only the usual term inversely proportional to impurity density $N_i$, but also an anomalous term that is linear in $N_i$. This leads to a minimum in the density dependence of conductivity when the electron density $N_{\rm e}$ is equal to a critical value, $N_c$. For $N_{\rm e}>N_c$ the conductivity varies almost linearly with the electron density, while it is approximately inversely proportional to $N_{\rm e}$ when $N_{\rm e}<N_c$ in the diffusive regime. The effects of various scattering potentials on the conductivity minimum are also analyzed. Using typical experimental parameters, we find that for RPA screened electron-impurity scattering the minimum conductivity is about $5.1 e^2/h$ when $N_{\rm e}\approx 0.32N_i$.
Motivated by a recent experiment[Nature {\bf 442}, 176 (2006)], we present a quantitative microscopic theory to investigate the inverse spin-Hall effect with spin injection into aluminum considering both intrinsic and extrinsic spin-orbit couplings using the orthogonalized-plane-wave method. Our theoretical results are in good agreement with the experimental data. It is also clear that the magnitude of the anomalous Hall resistivity is mainly due to contributions from extrinsic skew scattering, while its spatial variation is determined by the intrinsic spin-orbit coupling.
The magnetoresistance oscillations in high-mobility two-dimensional electron systems induced by two radiation fields of frequencies 31 GHz and 47 GHz, are analyzed in a wide magnetic-field range down to 100 G, using the balance-equation approach to magnetotransport for high-carrier-density systems. The frequency mixing processes are shown to be important. The predicted peak positions, relative heights, radiation-intensity dependence and their relation with monochromatic resistivities are in good agreement with recent experimental finding [M. A. Zudov {\it et al.} Phys. Rev. Lett. 96, 236804 (2006)].
We employ a helicity-basis kinetic equation approach to investigate the anomalous Hall effect in two-dimensional narrow-band semiconductors considering both Rashba and extrinsic spin-orbit (SO) couplings, as well as a SO coupling directly induced by an external driving electric field. Taking account of long-range electron-impurity scattering up to the second Born approximation, we find that the various components of the anomalous Hall current fit into two classes: (a) side-jump and (b) skew scattering anomalous Hall currents. The side-jump anomalous Hall current involves contributions not only from the extrinsic SO coupling but also from the SO coupling due to the driving electric field. It also contains a component which arises from the Rashba SO coupling and relates to the off-diagonal elements of the helicity-basis distribution function. The skew scattering anomalous Hall effect arises from the anisotropy of the diagonal elements of the distribution function and it is a result of both the Rashba and extrinsic SO interactions. Further, we perform a numerical calculation to study the anomalous Hall effect in a typical InSb/AlInSb quantum well. The dependencies of the side-jump and skew scattering anomalous Hall conductivities on magnetization and on the Rashba SO coupling constant are examined.
The frequency dependence of the peak-valley pairs occurring in the magnetoresistivity of a two-dimensional electron system under enhanced microwave irradiation, which are considered to associate with multiphoton processes, is examined in the sub-cyclotron-frequency range, based on a theoretical treatment with photon-assisted electron transitions due to impurity scattering. It is shown that with equivalent radiation power (producing the same height of the main oscillation peak), much more and stronger multi-photon structures show up at lower frequency, and when frequency increases all these structures rapidly weaken, diminish and finally disappear completely. These are in agreement with the recent experimental observation [cond-mat/0608633].
Employing a nonequilibrium Green's function approach, we examine the effects of long-range hole-impurity scattering on spin-Hall current in $p$-type bulk semiconductors within the framework of the self-consistent Born approximation. We find that, contrary to the null effect of short-range scattering on spin-Hall current, long-range collisions do produce a nonvanishing contribution to the spin-Hall current, which is independent of impurity density in the diffusive regime and relates only to hole states near the Fermi surface. The sign of this contribution is opposite to that of the previously predicted disorder-independent spin-Hall current, leading to a sign change of the total spin-Hall current as hole density varies. Furthermore, we also make clear that the disorder-independent spin-Hall effect is a result of an interband polarization directly induced by the dc electric field with contributions from all hole states in the Fermi sea.
A nonequilibrium Green's function approach is employed to investigate the spin-Hall effect in diffusive two-dimensional electron systems with Rashba spin-orbit interaction. Considering a long-range electron-impurity scattering potential in the self-consistent Born approximation, we find that the spin-Hall effect arises from two distinct interband polarizations in helicity basis: a disorder-unrelated polarization directly induced by the electric field and a polarization mediated by electron-impurity scattering. The disorder-unrelated polarization is associated with all electron states below the Fermi surface and produces the original intrinsic spin-Hall current, while the disorder-mediated polarization emerges with contribution from the electron states near the Fermi surface and gives rise to an additional contribution to the spin-Hall current. Within the diffusive regime, the total spin-Hall conductivity vanishes in {\it infinitely large} samples, independently of temperature, of the spin-orbit coupling constant, of the impurity density, and of the specific form of the electron-impurity scattering potential. However, in a {\it finite-size} Rashba two-dimensional semiconductor, the spin-Hall conductivity no longer always vanishes. Depending on the sample size in the micrometer range, it can be positive, zero or negative with a maximum absolute value reaching as large as $e/8π$ order of magnitude at low temperatures. As the sample size increases, the total spin-Hall conductivity oscillates with a decreasing amplitude. We also discuss the temperature dependence of the spin-Hall conductivity for different sample sizes.
Recently discovered new structures and zero-resistance states outside the well-known oscillations are demonstrated to arise from multiphoton assisted processes, by a detailed analysis of microwave photoresistance in two-dimensional electron systems under enhanced radiation. The concomitant resistance dropping and peak narrowing observed in the experiments are also reproduced. We show that the radiation-induced suppression of average resistance comes from virtual photon effect and exists throughout the whole magnetic field range.