arXiv subjects

Yan He

Publications and source records attributed to Yan He.

At least 73 records · Page 4Linked to original sources

arXiv2021

Multi-Matrix Verifiable Computation

The problem of securely outsourcing computation to cloud servers has attracted a large amount of attention in recent years. The verifiable computation of Gennaro, Gentry, Parno (Crypto'10) allows a client to verify the server's computation of a function with substantially less time than performing the outsourced computation from scratch. In a multi-function model (Parno, Raykova, Vaikuntanathan; TCC'12) of verifiable computation, the process of encoding function and the process of preparing input are decoupled such that any client can freely submit a computation request on its input, without having to generate an encoding of the function in advance. In this paper, we propose a multi-matrix verifiable computation scheme that allows the secure outsourcing of the matrix functions over a finite field. Our scheme is outsourceable. When it is used to outsource $m$ linear functions, the scheme is roughly $m$ times faster and has less communication cost than the previously best known scheme by Fiore and Gennaro (CCS'12), both in the client-side computation and in the server-side computation. We also show the cost saving with detailed implementations.

cs.CR↗

arXiv2021

Local Optical Conductivity of Bilayer Graphene with Kink Potential

We study the optical response of bilayer graphene with a kink potential composed of a domain wall separating two AB regions with opposite interlayer bias. The band structure and the local optical conductivity in real space are investigated in details based on a continuum model. We find that the one-dimensional chiral states localized at the domain wall contribute significantly to the local optical conductivity, which shows a clear distinction in different regions. The effects of domain wall states on optical conductivity can be detected by spatially and frequency resolved spectroscopic features. From the spectrum at various Fermi energies, important features in the band structure such as the energy separation between two chiral states can be directly measured. When the domain wall region is broad, the spatial distribution of local optical conductivity can provide important information on the bound states as well as the topological domain wall states.

cond-mat.mes-hall↗

arXiv2021

Nevanlinna Pair and Algebraic Hyperbolicity

We introduce the notion of the $\textit{Nevanlinna pair}$ for a pair $(X, D)$, where $X$ is a projective variety and $D$ is an effective Cartier divisor on $X$. This notion links and unifies the Nevanlinna theory, the complex hyperbolicity (Brody and Kobayashi hyperbolicity), the big Picard type extension theorem (more generally the Borel hyperbolicity), as well as the algebraic hyperbolicity. The key is to use the Nevanlinna theory on parabolic Riemann surfaces recently developed by Pǎun and Sibony.

math.AG↗

arXiv2021

Mobility Edges in one-dimensional Models with quasi-periodic disorder

We study the mobility edges in a variety of one-dimensional tight binding models with slowly varying quasi-periodic disorders. It is found that the quasi-periodic disordered models can be approximated by an ensemble of periodic models. The mobility edges can be determined by the overlaps of the energy bands of these periodic models. We demonstrate that this method provides an efficient way to find out the precise location of mobility edge in qusi-periodic disordered models. Based on this approximate method, we also propose an index to indicate the degree of localization of each eigenstate.

cond-mat.dis-nn↗

arXiv2021

Exact Solutions of Topological Superconductor Model with Hubbard Interactions

We study a two-dimensional model of topological superconductor with equal spin pairing and repulsive Hubbard interaction. When the pairing gap equals to the hopping constant, half of the spectrum of this model are flat bands, which makes this model exact solvable. The band structure and topological properties of the exact solutions of the interacting model are analyzed in details. It is found that the ground state corresponds to a staggered distribution of the conserved quantities.

cond-mat.supr-con↗

arXiv2021

Effects of heterostrain and lattice relaxation on optical conductivity of twisted bilayer graphene

We present a theoretical study of the effects of heterostrain and lattice relaxation on the optical conductivity of twisted bilayer graphene near the magic angle, based on the band structures obtained from a continuum model. We find that heterostrain, lattice relaxation and their combination give rise to very distinctive spectroscopic features in the optical conductivity, which can be used to probe and distinguish these effects. From the spectrum at various Fermi energies, important features in the strain- and relaxation-modified band structure such as the bandgap, bandwidth and van Hove singularities can be directly measured. The peak associated with the transition between the flat bands in the optical conductivity are highly sensitive to the direction of the strain, which can provide direct information on the strain-modified flat bands.

cond-mat.mes-hall↗

arXiv2020

Reconstruction Condition of Quantized Signals in Unlimited Sampling Framework

The latest theoretical advances in the field of unlimited sampling framework (USF) show the potential to avoid clipping problems of analog-to-digital converters (ADC). To date, most of the related works have focused on real-valued modulo samples, but little has been reported about the impact of quantization. In this paper, we study more practical USF system where modulo samples are quantized to a finite number of bits. In particular, we present a new requirement about the lower bound of sampling rate to ensure exact recovery of original signals from quantized modulo samples. The minimum sampling rate is jointly determined by signal bandwidth and quantization bits. Numerical results show that in the presence of quantization noise, signals with different waveforms and bandwidths are recovered perfectly at the new minimum sampling rate while the recovery fails at minimum sampling rate before modification, which also verifies the correctness of the theory. The trade-offs of sampling rates, quantization bits and computational complexity of recovery algorithm are also given for practitioners to weigh.

eess.SP↗

arXiv2020

Optical Conductivity of Twisted Bilayer Graphene Near the Magic Angle

We theoretically study the band structure and optical conductivity of twisted bilayer graphene (TBG) near the magic angle considering the effects of lattice relaxation. We show that the optical conductivity spectrum is characterized by a series of peaks associated with the van Hove singularities in the band structure, and the peak energies evolve systematically with the twist angle. Lattice relaxation effects in TBG modify its band structure, especially the flat bands, which lead to significant shifts of the peaks in optical conductivity. These results demonstrate that spectroscopic features in the optical conductivity can serve as fingerprints for exploring the band structure, band gap and lattice relaxation in magic angle TBG as well as identifying its rotation angle.

cond-mat.mes-hall↗

arXiv2020

Towards Class-incremental Object Detection with Nearest Mean of Exemplars

Incremental learning is a form of online learning. Incremental learning can modify the parameters and structure of the deep learning model so that the model does not forget the old knowledge while learning new knowledge. Preventing catastrophic forgetting is the most important task of incremental learning. However, the current incremental learning is often only for one type of input. For example, if the input images are of the same type, the current incremental model can learn new knowledge while not forgetting old knowledge. However, if several categories are added to the input graphics, the current model will not be able to deal with it correctly, and the accuracy will drop significantly. Therefore, this paper proposes a kind of incremental method, which adjusts the parameters of the model by identifying the prototype vector and increasing the distance of the vector, so that the model can learn new knowledge without catastrophic forgetting. Experiments show the effectiveness of our proposed method.

cs.CV↗

arXiv2020

Ring-Frustrated Non-Hermitian $XY$ Model

We study a non-Hermitian version of XY closed chain with odd number of lattice sites. We consider both anti-ferromagnetic coupling and also a symmetric non-collinear spin coupling. It is found that the energy spectrum is real in certain region of the parameter space. In contrast to previous non-Hermitian models, the ground state is a state with one mode occupied inside this real energy spectrum region, instead of the artificially identified vacuum state. At the same time, there appears a gapless excitation, which is made by kink like spin configurations. It is also found that this kink phase has non-trivial topological invariant.

quant-ph↗

arXiv2020

Exact Solution to Sodium-Iridate-BCS-Hubbard Model along the Symmetric Line: Non-trivial topology in the ferromagnetic order

We study the sodium-iridates model on the honeycomb lattice with both BCS pairing potential and Hubbard interaction term. It is shown that this model can be exactly solved with appropriate choices of amplitude of pairing gaps, where the interacting terms are transformed to external field terms. The band structures of these exact solutions on both torus and cylinder geometry are discussed in great details. It is found that the ground state assumes an anti-ferromagnetic configuration, which breaks the time reversal symmetry spontaneously and renders the superconductor topologically trivial. On the other hand, the nontrivial topology is preserved with ferromagnetic configuration and can be characterized by the isospin Chern number.

cond-mat.str-el↗

arXiv2020

Ubiquity of zeros of Loschmidt amplitude for mixed states in different physical processes and their implications

The Loschmidt amplitude of the purified states of mixed-state density matrices is shown to have zeros when the system undergoes a quasistatic, quench, or Uhlmann process. While the Loschmidt-amplitude zero of a quench process corresponds to a dynamical quantum phase transition (DQPT) accompanied by the diverging dynamical free energy, the Loschmidt-amplitude zero of the Uhlmann process corresponds to a topological phase transition (TQPT) accompanied by a jump of the Uhlmann phase. Although the density matrix remains intact in a quasistatic process, the Loschmidt amplitude can have zeros not associated with a phase transition. We present examples of two-level and three-level systems exhibiting finite- or infinite- temperature DQPTs and finite-temperature TQPTs associated with the Loschmidt-amplitude zeros. Moreover, the dynamical phase or geometrical phase of mixed states can be extracted from the Loschmidt amplitude. Those phases may become quantized or exhibit discontinuity at the Loschmidt-amplitude zeros. A spinor representation of the purified states of a general two-level system is presented to offer more insights into the change of purification in different processes. The quasistatic process, for example, is shown to cause a rotation of the spinor.

quant-ph↗

arXiv2020

Non-Hermitian generalizations of extended Su-Schrieffer-Heeger models

Non-Hermitian generalizations of the Su-Schrieffer-Heeger (SSH) models with higher periods of the hopping coefficients, called the SSH3 and SSH4 models, are analyzed. The conventional construction of the winding number fails for the Hermitian SSH3 model, but the non-Hermitian generalization leads to a topological system due to a point gap on the complex plane. The non-Hermitian SSH3 model thus has a winding number and exhibits the non-Hermitian skin effect. Moreover, the SSH3 model has two types of localized states and a zero-energy state associated with special symmetries. The total Zak phase of the SSH3 model exhibits quantization, and its finite value indicates coexistence of the two types of localized states. Meanwhile, the SSH4 model resembles the SSH model, and its non-Hermitian generalization also exhibits the non-Hermitian skin effect. A careful analysis of the non-Hermitian SSH4 model with different boundary conditions shows the bulk-boundary correspondence is restored with the help of the generalized Brillouin zone or the real-space winding number. The physics of the non-Hermitian SSH3 and SSH4 models may be tested in cold-atom or other simulators.

cond-mat.quant-gas↗

arXiv2020

Complete Strain Mapping of Nanosheets of Tantalum Disulfide

Quasi-two-dimensional (quasi-2D) materials hold promise for future electronics because of their unique band structures that result in electronic and mechanical properties sensitive to crystal strains in all three dimensions. Quantifying crystal strain is a prerequisite to correlating it with the performance of the device, and calls for high resolution but spatially resolved rapid characterization methods. Here we show that using fly-scan nano X-ray diffraction we can accomplish a tensile strain sensitivity below 0.001% with a spatial resolution of better than 80 nm over a spatial extent of 100 $μ$m on quasi 2D flakes of 1T-TaS2. Coherent diffraction patterns were collected from a $\sim$ 100 nm thick sheet of 1T-TaS2 by scanning 12keV focused X-ray beam across and rotating the sample. We demonstrate that the strain distribution around micron and sub-micron sized 'bubbles' that are present in the sample may be reconstructed from these images. The experiments use state of the art synchrotron instrumentation, and will allow rapid and non-intrusive strain mapping of thin film samples and electronic devices based on quasi 2D materials.

cond-mat.mtrl-sci↗

arXiv2020

Non-Hermitian three-dimensional two-band Hopf insulator

The Hopf insulator is a three-dimensional topological insulator outside the standard classification of topological insulators. Here we consider two types of non-Hermitian Hopf insulators, one without and one with the non-Hermitian skin effect. The isolated gapless points of the Hermitian model are broadened into finite regimes in the non-Hermitian models. However, the modulus of the Hopf index remains quantized in the gapped regions. The model without the non-Hermitian skin effect allows an accurate evaluation of its generalized Hopf index and energy spectrum, showing an agreement between the gapless-regime estimations from the systems with periodic- and open- boundary conditions. Near the zero-energy plane, Fermi rings can be observed whenever the Hopf index is quantized at nonzero values, and there is a bulk-boundary correspondence between the modulus of the Hopf index and the number of Fermi rings. The other model manifests the non-Hermitian skin effect in the generalized Brillouin zone and shows the skewed profiles of the bulk states. The Hopf index and energy spectrum are shown to be sensitive to the boundary condition in the presence of the non-Hermitian skin effect.

cond-mat.mes-hall↗

arXiv2020

Fully nonlinear equations of Krylov type on Riemannian manifolds with negative curvature

In this paper, we consider fully nonlinear equations of Krylov type on Riemannian manifolds with negative curvature which naturally arise in conformal geometry. Moreover, we prove the a priori estimates for solutions to these equations and establish the existence results. Our results can be viewed as an extension of previous results given by Gursky-Viaclovsky and Li-Sheng.

math.AP↗

arXiv2020

Dynamic process and Uhlmann process: Incompatibility and dynamic phase of mixed quantum states

While a pure quantum state may accumulate both the Berry phase and dynamic phase as it undergoes a cyclic path in the parameter space, the situation is more complicated when mixed quantum states are considered. From the Ulhmann bundle, a mixed quantum state can accumulate the Ulhmann phase if the parallel-transport condition is satisfied. However, we show that the Ulhmann process is in general not compatible with the evolution equation of the density matrix governed by the Hamiltonian. Thus, a mixed quantum state usually accumulates a dynamic phase during its time evolution. We present the expression of the dynamic phase for mixed quantum states. In examples of quasi-static one-dimensional two-band models and simple harmonic oscillator, the dynamic phase can take multiple discrete values at infinitely high temperature due to the resonant points. However, the behavior differs if the energy spectrum is continuous without a band gap. Moreover, there is no natural analog of the dynamic phase in classical systems.

quant-ph↗

arXiv2019

Variable-coefficient symbolic computation approach for finding multiple rogue wave solutions of nonlinear system with variable coefficients

In this paper, a variable-coefficient symbolic computation approach is proposed to solve the multiple rogue wave solutions of nonlinear equation with variable coefficients. As an application, a (2+1)-dimensional variable-coefficient Kadomtsev-Petviashvili equation is investigated. The multiple rogue wave solutions are obtained and their dynamics features are shown in some 3D and contour plots.

nlin.PS↗