arXiv subjects

Juhao Wu

Publications and source records attributed to Juhao Wu.

At least 19 recordsLinked to original sources

arXiv2026

Scalar Casimir Effect on a Two-Dimensional Sphere with a Wu--Yang Magnetic Monopole

We investigate the Casimir effect of a complex scalar field on a two-dimensional sphere threaded by a fixed Wu--Yang magnetic monopole at the center. In this background the charged scalar field is a section of a nontrivial complex line bundle over $S^2$, reflecting the monopole's nontrivial topology. We solve the Klein--Gordon equation analytically and compute the Casimir energy using a generalized Abel--Plana formula for multivalued functions. We find that the monopole can reverse the sign of the Casimir pressure, turning an attractive force into a repulsive one when the monopole strength is sufficiently large. This behavior persists across a broad range of curvature couplings and suggests that Wu--Yang monopoles may provide a source of repulsive vacuum stress, with possible implications for gravitational and cosmological settings.

hep-th↗

arXiv2025

Non-degenerate Ground State of the Spin-Boson Model under Abelian Diagonalization

By utilizing a unitary transformation, we derive the necessary and sufficient conditions for the degeneracy between the even- and odd-parity energy states of the spin-boson model (SBM). Employing the Rayleigh quotient of matrix algebra, we rigorously prove that the ground state energy of the SBM is lower than the systems lowest possible degenerate energy and possesses a definite parity. Based on the necessary and sufficient conditions for parity breaking, we provide an analytical expression for the parity-breaking critical value, which is closely related to the expansion order and computational accuracy. This expression reproduces the SBM phase diagram obtained by quantum Monte Carlo (QMC) and logarithmic discretization numerical renormalization group (NRG) methods. However, this phase diagram does not characterize the ground state of the system.

cond-mat.str-el↗

arXiv2025

Davenport-Heilbronn Function Ratio Properties and Non-Trivial Zeros Study

This paper systematically investigates the analytic properties of the ratio $f(s)/f(1-s) = X(s)$ based on the Davenport-Heilbronn functional equation $f(s) = X(s)f(1-s)$. We propose a novel method to analyze the distribution of non-trivial zeros through the monotonicity of the ratio $|f(s)/f(1-s)|$. Rigorously proving that non-trivial zeros can only lie on the critical line $\sigma=1/2$, we highlight two groundbreaking findings: 1. Contradiction of Off-Critical Zeros: Numerical "exceptional zeros" (e.g., Spira, 1994) violate the theoretical threshold $\kappa=1.21164$ and conflict with the monotonicity constraint of $|X(s)|=1$. 2. Essential Difference Between Approximate and Strict Zeros: Points satisfying $f(s) \to 0$ do not constitute strict zeros unless verified by analyticity. This work provides a new perspective for studying zero distributions of $L$-functions related to the Riemann Hypothesis.

math.GM↗

arXiv2024

MegActor-$\Sigma$: Unlocking Flexible Mixed-Modal Control in Portrait Animation with Diffusion Transformer

Diffusion models have demonstrated superior performance in the field of portrait animation. However, current approaches relied on either visual or audio modality to control character movements, failing to exploit the potential of mixed-modal control. This challenge arises from the difficulty in balancing the weak control strength of audio modality and the strong control strength of visual modality. To address this issue, we introduce MegActor-$\Sigma$: a mixed-modal conditional diffusion transformer (DiT), which can flexibly inject audio and visual modality control signals into portrait animation. Specifically, we make substantial advancements over its predecessor, MegActor, by leveraging the promising model structure of DiT and integrating audio and visual conditions through advanced modules within the DiT framework. To further achieve flexible combinations of mixed-modal control signals, we propose a ``Modality Decoupling Control" training strategy to balance the control strength between visual and audio modalities, along with the ``Amplitude Adjustment" inference strategy to freely regulate the motion amplitude of each modality. Finally, to facilitate extensive studies in this field, we design several dataset evaluation metrics to filter out public datasets and solely use this filtered dataset to train MegActor-$\Sigma$. Extensive experiments demonstrate the superiority of our approach in generating vivid portrait animations, outperforming previous methods trained on private dataset.

cs.CV↗

arXiv2024

MegActor: Harness the Power of Raw Video for Vivid Portrait Animation

Despite raw driving videos contain richer information on facial expressions than intermediate representations such as landmarks in the field of portrait animation, they are seldom the subject of research. This is due to two challenges inherent in portrait animation driven with raw videos: 1) significant identity leakage; 2) Irrelevant background and facial details such as wrinkles degrade performance. To harnesses the power of the raw videos for vivid portrait animation, we proposed a pioneering conditional diffusion model named as MegActor. First, we introduced a synthetic data generation framework for creating videos with consistent motion and expressions but inconsistent IDs to mitigate the issue of ID leakage. Second, we segmented the foreground and background of the reference image and employed CLIP to encode the background details. This encoded information is then integrated into the network via a text embedding module, thereby ensuring the stability of the background. Finally, we further style transfer the appearance of the reference image to the driving video to eliminate the influence of facial details in the driving videos. Our final model was trained solely on public datasets, achieving results comparable to commercial models. We hope this will help the open-source community.The code is available at https://github.com/megvii-research/MegFaceAnimate.

cs.CV↗

arXiv2020

On the gauge transformation for the rotation of the singular string in the Dirac monopole theory

In the Dirac theory of the quantum-mechanical interaction of a magnetic monopole and an electric charge, the vector potential is singular from the origin to infinity along certain direction - the so called Dirac string. Imposing the famous quantization condition, the singular string attached to the monopole can be rotated arbitrarily by a gauge transformation, and hence is not physically observable. By deriving its analytical expression and analyzing its properties, we show that the gauge function $χ({\bf r})$ which rotates the string to another one has quite complicated behaviors depending on which side from which the position variable ${\bf r}$ gets across the plane expanded by the two strings. Consequently, some misunderstandings in the literature are clarified.

physics.gen-ph↗

arXiv2020

A few properties of the ratio of Davenport-Heilbronn Functions

Starting from the Davenport-Heilbronn function equation: $f(s) = X(s) f(1-s)$, we discover the four properties of the meromorphic function $X(s)$ defined as the ratio of the Davenport-Heilbronn functions: $\frac{f(s)}{f(1-s)} = X(s)$, and three corresponding lemmas. For the first time, we propose to study the distribution of the non-trivial zeros of the Davenport-Heilbronn function by exploring the monotonicity of the similarity ratio $\left| \frac{f(s)}{f(1-s)} \right|$. We point out that for the $f(s)$ which satisfies the Davenport-Heilbronn function equation, the existence of non-trivial zeros outside of the critical line $\{ s_n | σ\neq 1/2 \}$ presents two puzzles: 1) $f(s_n) \neq f(1 - s_n)$; 2) the existence of non-trivial zeros $\{ s_n | σ\neq 1/2 \}$ is in contradiction of the monotonicity of the similar ratio $\left| \frac{f(s)}{f(1-s)}\right|$.

math.NT↗

arXiv2020

A Proof of Riemann Hypothesis

The meromorphic function $W(s)$ introduced in the Riemann-Zeta function $ζ(s) = W(s) ζ(1-s)$ maps the line of $s = 1/2 + it$ onto the unit circle in $W$-space. $|W(s)| = 0$ gives the trivial zeroes of the Riemann-Zeta function $ζ(s)$. In the range: $0 < |W(s)| \neq 1$, $ζ(s)$ does not have nontrivial zeroes. $|W(s)|=1$ is the necessary condition for the nontrivial zeros of the Riemann-Zeta function. Writing $s = σ+ it$, in the range: $0 \leq σ\leq 1$, but $σ\neq 1/2$, even if $|W(s)|=1$, the Riemann-Zeta function $ζ(s)$ is non-zero. Based on these arguments, the nontrivial zeros of the Riemann-Zeta function $ζ(s)$ can only be on the $s = 1/2 + it$ critical line. Therefore a proof of the Riemann Hypothesis is presented.

math.GM↗

arXiv2015

High Efficiency, Multi-Terawatt X-ray free electron lasers

We study high efficiency, multi-terawatt peak power, few angstrom wavelength, X-ray Free Electron Lasers (X-ray FELs). To obtain these characteristics we consider an optimized undulator design: superconducting, helical, with short period and built-in strong focusing. This design reduces the length of the breaks between modules, decreasing diffraction effects, and allows using a stronger transverse electron focusing. Both effects reduce the gain length and the overall undulator length. The peak power and efficiency depend on the transverse electron beam distribution and on time dependent effects, like synchrotron sideband growth. The last effect is identified as the main cause for reduction of electron beam microbunching and FEL peak power. We show that the optimal functional form for the undulator magnetic field tapering profile, yielding the maximum output power, depends significantly on these effects. The output power achieved when neglecting time dependent effects for an LCLS-like X-ray FEL with a 100 m long tapered undulator is 7.3 TW, a 14 $\%$ electron beam energy extraction efficiency. When these effects are included the highest peak power is achieved reducing the tapering rate, thus minimizing the reduction in electron micro-bunching due to synchrotron sideband growth. The maximum efficiency obtained for this case is 9 $\%$, corresponding to 4.7 TW peak radiation power. Possible methods to suppress the synchrotron sidebands, and further enhance the FEL peak power, up to about 6 TW by increasing the seed power, are discussed.

physics.acc-ph↗

arXiv2015

Tapering studies for Terawatt level X-ray FELs with a superconducting undulator

We study the tapering optimization scheme for a short period, less than two cm, superconducting undulator, and show that it can generate 4 keV X-ray pulses with peak power in excess of 1 terawatt, using LCLS electron beam parameters. We study the effect of undulator module length relative to the FEL gain length for continous and step-wise taper profiles. For the optimal section length of 1.5m we study the evolution of the FEL process for two different superconducting technologies NbTi and Nb3Sn. We discuss the major factors limiting the maximum output power, particle detrapping around the saturation location and time dependent detrapping due to generation and amplification of sideband modes.

physics.acc-ph↗

arXiv2014

Transverse pulse shaping and optimization of a tapered hard X-ray free electron laser

Multidimensional optimization schemes for TW hard X-Ray free electron lasers are applied to the cases of transversely uniform and parabolic electron beam distributions and compared to examples of transversely Gaussian beams. The optimizations are performed for a $200$m undulator and a resonant wavelength of $λ_r=1.5Å$ using the fully 3-dimensional FEL particle code GENESIS. Time dependent simulations showed that the maximum radiation power is larger for flatter transverse distributions due to enhanced optical guiding in the tapered section of the undulator. For a transversely Gaussian beam the maximum output power was found to be $\text{P}_{max}$=$1.56$ TW compared to $2.26$ TW for the parabolic case and $2.63$ TW for the uniform case. Spectral data also showed a 30-70$\%$ reduction in energy deposited in the sidebands for the uniform and parabolic beams compared with a Gaussian. An analysis of the maximum power as a function of detuning from resonance shows that redshifting the central wavelength by $Δλ/ λ<ρ$ increases the power for all three transverse electron distributions.

physics.acc-ph↗

arXiv2011

Generation of Coherent X-Ray Radiation Through Modulation Compression

In this paper, we propose a scheme to generate tunable coherent X-ray radiation for future light source applications. This scheme uses an energy chirped electron beam, a laser modulator, a laser chirper and two bunch compressors to generate a prebunched kilo-Ampere current electron beam from a few tens Ampere electron beam out of a linac. The initial modulation energy wavelength can be compressed by a factor of $1+h_b R_{56}^a$ in phase space, where $h_b$ is the energy bunch length chirp introduced by the laser chirper, $R_{56}^a$ is the momentum compaction factor of the first bunch compressor. As an illustration, we present an example to generate more than 400 MW, 170 attoseconds pulse, 1 nm coherent X-ray radiation using a 60 Ampere electron beam out of the linac and 200 nm laser seed. Both the final wavelength and the radiation pulse length in the proposed scheme are tunable by adjusting the compression factor and the laser parameters.

physics.acc-ph↗

arXiv2011

Generation of Multi-Color Attosecond X-Ray Radiation Through Modulation Compression

In this paper, we propose a scheme to generate tunable multi-color attosecond coherent X-ray radiation for future light source applications. This scheme uses an energy chirped electron beam, a laser modulators, a laser chirper and two bunch compressors to generate a multi-spike prebunched kilo-Ampere current electron beam from a few tens Ampere electron beam out of a linac. Such an electron beam transports through a series of undulator radiators and bunch compressors to generate multi-color coherent X-ray radiation. As an illustration, we present an example to generate two attosecond pulses with $2.2$ nm and $3$ nm coherent X-ray radiation wavelength and more than $200$ MW peak power using a $30$ Ampere $200$ nm laser seeded electron beam.

physics.acc-ph↗

arXiv2003

Coupled-Bunch Beam Breakup due to Resistive-Wall Wake

The coupled-bunch beam breakup problem excited by the resistive wall wake is formulated. An approximate analytic method of finding the asymptotic behavior of the transverse bunch displacement is developed and solved.

physics.acc-ph↗

arXiv2003

Impact of the Wiggler Coherent Synchrotron Radiation Impedance on the Beam Instability

Coherent Synchrotron Radiation (CSR) can play an important role by not only increasing the energy spread and emittance of a beam, but also leading to a potential instability. Previous studies of the CSR induced longitudinal instability were carried out for the CSR impedance due to dipole magnets. However, many storage rings include long wigglers where a large fraction of the synchrotron radiation is emitted. This includes high-luminosity factories such as DAPHNE, PEP-II, KEK-B, and CESR-C as well as the damping rings of future linear colliders. In this paper, the instability due to the CSR impedance from a wiggler is studied assuming a large wiggler parameter $K$. The primary consideration is a low frequency microwave-like instability, which arises near the pipe cut-off frequency. Detailed results are presented on the growth rate and threshold for the damping rings of several linear collider designs. Finally, the optimization of the relative fraction of damping due to the wiggler systems is discussed for the damping rings.

physics.acc-ph↗

arXiv2003

Calculation of the Coherent Synchrotron Radiation Impedance from a Wiggler

Most studies of Coherent Synchrotron Radiation (CSR) have only considered the radiation from independent dipole magnets. However, in the damping rings of future linear colliders, a large fraction of the radiation power will be emitted in damping wigglers. In this paper, the longitudinal wakefield and impedance due to CSR in a wiggler are derived in the limit of a large wiggler parameter $K$. After an appropriate scaling, the results can be expressed in terms of universal functions, which are independent of $K$. Analytical asymptotic results are obtained for the wakefield in the limit of large and small distances, and for the impedance in the limit of small and high frequencies.

physics.acc-ph↗

arXiv1998

Bose Condensation and Superfluidity in Finite Rotating Bose Systems

There is a long standing problem about how close a connection exists between superfluidity and Bose condensation. Employing recent technology, for the case of confined finite Bose condensed systems in TOP traps, these questions concerning superfluidity and Bose condensation can be partially resolved if the velocity profile of the trapped atoms can be directly measured.

cond-mat.stat-mech↗

arXiv1998

Bose Condensates in TOP Traps Exhibit Circulating Superfluid Flows

For spin one atoms localized in a quadrapole magnetic field gradient, the atoms may be impeded from spin flipping their way out from the center of the trap by the application of a rotating uniform magnetic field. From a quantum mechanical viewpoint, such a trap for a Bose condensate is equivalent to having a superfluid in a rotating bucket. Vorticity is then expected to be induced in the condensate fluid flow without the application of any further external perturbations.

cond-mat.stat-mech↗