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Heng Guo

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Published work

40 published item(s)

preprint2026arXiv

PolarVLM: Bridging the Semantic-Physical Gap in Vision-Language Models

Mainstream vision-language models (VLMs) fundamentally struggle with severe optical ambiguities, such as reflections and transparent objects, due to the inherent limitations of standard RGB inputs. While polarization imaging captures polarimetric physical parameters that resolve these ambiguities, existing methods are constrained by fixed-format outputs and remain isolated from open-ended reasoning. To bridge this semantic-physical gap, we introduce PolarVLM, the first multimodal framework integrating polarimetric physical parameters into VLMs. By employing a dual-stream architecture and a progressive two-stage training strategy, PolarVLM effectively prevents physical misinterpretations while preserving general visual abilities. Complementing our architecture, we construct PolarVQA, the first benchmark for polarization-aware VQA, featuring 75K physics-grounded instruction-tuning pairs targeting reflective and transparent scenes. Experiments show that PolarVLM surpasses the RGB baseline by 25.4% overall across five evaluation tasks, with remarkable gains of 26.6% in reflection recognition and 34.0% in glass counting, successfully unlocking physics-aware semantic understanding.

preprint2023arXiv

ECSAS: Exploring Critical Scenarios from Action Sequence in Autonomous Driving

Critical scenario generation requires the ability of sampling critical combinations from the infinite parameter space in the logic scenario. Existing solutions aim to explore the correlation of action parameters in the initial scenario rather than action sequences. How to model action sequences so that one can further consider the effects of different action parameters in the scenario is the bottleneck of the problem. In this paper, we attack the problem by proposing the ECSAS framework. Specifically, we first propose a description language, BTScenario, allowing us to model action sequences of the scenarios. We then use reinforcement learning to search for combinations of critical action parameters. To increase efficiency, we further propose several optimizations, including action masking and replay buffer. We have implemented ECSAS, and experimental results show that it is more efficient than native approaches such as random and combination testing in various nontrivial scenarios.

preprint2022arXiv

A New Probabilistic V-Net Model with Hierarchical Spatial Feature Transform for Efficient Abdominal Multi-Organ Segmentation

Accurate and robust abdominal multi-organ segmentation from CT imaging of different modalities is a challenging task due to complex inter- and intra-organ shape and appearance variations among abdominal organs. In this paper, we propose a probabilistic multi-organ segmentation network with hierarchical spatial-wise feature modulation to capture flexible organ semantic variants and inject the learnt variants into different scales of feature maps for guiding segmentation. More specifically, we design an input decomposition module via a conditional variational auto-encoder to learn organ-specific distributions on the low dimensional latent space and model richer organ semantic variations that is conditioned on input images.Then by integrating these learned variations into the V-Net decoder hierarchically via spatial feature transformation, which has the ability to convert the variations into conditional Affine transformation parameters for spatial-wise feature maps modulating and guiding the fine-scale segmentation. The proposed method is trained on the publicly available AbdomenCT-1K dataset and evaluated on two other open datasets, i.e., 100 challenging/pathological testing patient cases from AbdomenCT-1K fully-supervised abdominal organ segmentation benchmark and 90 cases from TCIA+&BTCV dataset. Highly competitive or superior quantitative segmentation results have been achieved using these datasets for four abdominal organs of liver, kidney, spleen and pancreas with reported Dice scores improved by 7.3% for kidneys and 9.7% for pancreas, while being ~7 times faster than two strong baseline segmentation methods(nnUNet and CoTr).

preprint2022arXiv

Edge-preserving Near-light Photometric Stereo with Neural Surfaces

This paper presents a near-light photometric stereo method that faithfully preserves sharp depth edges in the 3D reconstruction. Unlike previous methods that rely on finite differentiation for approximating depth partial derivatives and surface normals, we introduce an analytically differentiable neural surface in near-light photometric stereo for avoiding differentiation errors at sharp depth edges, where the depth is represented as a neural function of the image coordinates. By further formulating the Lambertian albedo as a dependent variable resulting from the surface normal and depth, our method is insusceptible to inaccurate depth initialization. Experiments on both synthetic and real-world scenes demonstrate the effectiveness of our method for detailed shape recovery with edge preservation.

preprint2022arXiv

Improved bounds for randomly colouring simple hypergraphs

We study the problem of sampling almost uniform proper $q$-colourings in $k$-uniform simple hypergraphs with maximum degree $Δ$. For any $δ> 0$, if $k \geq\frac{20(1+δ)}δ$ and $q \geq 100Δ^{\frac{2+δ}{k-4/δ-4}}$, the running time of our algorithm is $\tilde{O}(\mathrm{poly}(Δk)\cdot n^{1.01})$, where $n$ is the number of vertices. Our result requires fewer colours than previous results for general hypergraphs (Jain, Pham, and Voung, 2021; He, Sun, and Wu, 2021), and does not require $Ω(\log n)$ colours unlike the work of Frieze and Anastos (2017).

preprint2022arXiv

Inapproximability of counting hypergraph colourings

Recent developments in approximate counting have made startling progress in developing fast algorithmic methods for approximating the number of solutions to constraint satisfaction problems (CSPs) with large arities, using connections to the Lovasz Local Lemma. Nevertheless, the boundaries of these methods for CSPs with non-Boolean domain are not well-understood. Our goal in this paper is to fill in this gap and obtain strong inapproximability results by studying the prototypical problem in this class of CSPs, hypergraph colourings. More precisely, we focus on the problem of approximately counting $q$-colourings on $K$-uniform hypergraphs with bounded degree $Δ$. An efficient algorithm exists if $Δ\lesssim \frac{q^{K/3-1}}{4^KK^2}$ (Jain, Pham, and Vuong, 2021; He, Sun, and Wu, 2021). Somewhat surprisingly however, a hardness bound is not known even for the easier problem of finding colourings. For the counting problem, the situation is even less clear and there is no evidence of the right constant controlling the growth of the exponent in terms of $K$. To this end, we first establish that for general $q$ computational hardness for finding a colouring on simple/linear hypergraphs occurs at $Δ\gtrsim Kq^K$, almost matching the algorithm from the Lovasz Local Lemma. Our second and main contribution is to obtain a far more refined bound for the counting problem that goes well beyond the hardness of finding a colouring and which we conjecture that is asymptotically tight (up to constant factors). We show in particular that for all even $q\geq 4$ it is NP-hard to approximate the number of colourings when $Δ\gtrsim q^{K/2}$.

preprint2022arXiv

Swendsen-Wang dynamics for the ferromagnetic Ising model with external fields

We study the sampling problem for the ferromagnetic Ising model with consistent external fields, and in particular, Swendsen-Wang dynamics on this model. We introduce a new grand model unifying two closely related models: the subgraph world and the random cluster model. Through this new viewpoint, we show: (1) polynomial mixing time bounds for Swendsen-Wang dynamics and (edge-flipping) Glauber dynamics of the random cluster model, generalising the bounds and simplifying the proofs for the no-field case by Guo and Jerrum (2018); (2) near linear mixing time for the two dynamics above if the maximum degree is bounded and all fields are (consistent and) bounded away from $1$.

preprint2020arXiv

Kaluza-Klein modes of $U(1)$ gauge vector field on brane with codimension-$d$

From the paper [JHEP 01 (2019) 021], it is known that the effective action of a massless $U(1)$ gauge vector field on a codimension-2 brane is gauge invariant due to the coupling between the vector Kaluza-Klein (KK) modes with two types of scalar KK modes. It is interesting to generalize this result to a brane world model with an arbitrary number of extra dimensions. In this work, we first investigate the case with three extra dimensions. After KK decomposition, there are three types of scalar KK modes. In addition to the mutual coupling between these scalar modes, there are also coupling between the scalar and the vector KK modes. The coupling constants are not all independent. The relationships between the coupling constants enable us to obtain a gauge invariant effective action, from which we can see that the masses of the vector KK modes depend on all the three extra dimensions. The masses of the scalar modes, however, depend only on two of the three extra dimensions. Then we generalize the results into branes with codimension $d$ ($d=1, 2...$), and find that $d$ will directly affect the masses of the KK modes. But there is always a gauge invariant effective action for the massive vector KK modes.

preprint2020arXiv

Perfect sampling from spatial mixing

We introduce a new perfect sampling technique that can be applied to general Gibbs distributions and runs in linear time if the correlation decays faster than the neighborhood growth. In particular, in graphs with sub-exponential neighborhood growth like $\mathbb{Z}^d$, our algorithm achieves linear running time as long as Gibbs sampling is rapidly mixing. As concrete applications, we obtain the currently best perfect samplers for colorings and for monomer-dimer models in such graphs.

preprint2020arXiv

Rapid mixing from spectral independence beyond the Boolean domain

We extend the notion of spectral independence (introduced by Anari, Liu, and Oveis Gharan [ALO20]) from the Boolean domain to general discrete domains. This property characterises distributions with limited correlations, and implies that the corresponding Glauber dynamics is rapidly mixing. As a concrete application, we show that Glauber dynamics for sampling proper $q$-colourings mixes in polynomial-time for the family of triangle-free graphs with maximum degree $Δ$ provided $q\ge (α^*+δ)Δ$ where $α^*\approx 1.763$ is the unique solution to $α^*=\exp(1/α^*)$ and $δ>0$ is any constant. This is the first efficient algorithm for sampling proper $q$-colourings in this regime with possibly unbounded $Δ$. Our main tool of establishing spectral independence is the recursive coupling by Goldberg, Martin, and Paterson [GMP05].

preprint2020arXiv

Towards a Fast Steady-State Visual Evoked Potentials (SSVEP) Brain-Computer Interface (BCI)

Steady-state visual evoked potentials (SSVEP) brain-computer interface (BCI) provides reliable responses leading to high accuracy and information throughput. But achieving high accuracy typically requires a relatively long time window of one second or more. Various methods were proposed to improve sub-second response accuracy through subject-specific training and calibration. Substantial performance improvements were achieved with tedious calibration and subject-specific training; resulting in the user's discomfort. So, we propose a training-free method by combining spatial-filtering and temporal alignment (CSTA) to recognize SSVEP responses in sub-second response time. CSTA exploits linear correlation and non-linear similarity between steady-state responses and stimulus templates with complementary fusion to achieve desirable performance improvements. We evaluated the performance of CSTA in terms of accuracy and Information Transfer Rate (ITR) in comparison with both training-based and training-free methods using two SSVEP data-sets. We observed that CSTA achieves the maximum mean accuracy of 97.43$\pm$2.26 % and 85.71$\pm$13.41 % with four-class and forty-class SSVEP data-sets respectively in sub-second response time in offline analysis. CSTA yields significantly higher mean performance (p<0.001) than the training-free method on both data-sets. Compared with training-based methods, CSTA shows 29.33$\pm$19.65 % higher mean accuracy with statistically significant differences in time window less than 0.5 s. In longer time windows, CSTA exhibits either better or comparable performance though not statistically significantly better than training-based methods. We show that the proposed method brings advantages of subject-independent SSVEP classification without requiring training while enabling high target recognition performance in sub-second response time.

preprint2016arXiv

New localization mechanism and Hodge duality for $q-$form field

In this paper, we investigate the problem of localization and the Hodge duality for a $q-$form field on a $p-$brane with codimension one. By a general Kaluza-Klein (KK) decomposition without gauge fixing, we obtain two Schrödinger-like equations for two types of KK modes of the bulk $q-$form field, which determine the localization and mass spectra of these KK modes. It is found that there are two types of zero modes (the $0-$level modes): a $q-$form zero mode and a $(q-1)-$form one, which cannot be localized on the brane at the same time. For the $n-$level KK modes, there are two interacting KK modes, a massive $q-$form KK mode and a massless $(q-1)-$form one. By analyzing gauge invariance of the effective action and choosing a gauge condition, the $n-$level massive $q-$form KK mode decouples from the $n-$level massless $(q-1)-$form one. It is also found that the Hodge duality in the bulk naturally becomes two dualities on the brane. The first one is the Hodge duality between a $q-$form zero mode and a $(p-q-1)-$form one, or between a $(q-1)-$form zero mode and a $(p-q)-$form one. The second duality is between two group KK modes: one is an $n-$level massive $q-$form KK mode with mass $m_n$ and an $n-$level massless $(q-1)-$form mode; another is an $n-$level $(p-q)-$form one with the same mass $m_n$ and an $n-$level massless $(p-q-1)-$form mode. Because of the dualities, the effective field theories on the brane for the KK modes of the two dual bulk form fields are physically equivalent.

preprint2015arXiv

#BIS-Hardness for 2-Spin Systems on Bipartite Bounded Degree Graphs in the Tree Nonuniqueness Region

Counting independent sets on bipartite graphs (#BIS) is considered a canonical counting problem of intermediate approximation complexity. It is conjectured that #BIS neither has an FPRAS nor is as hard as #SAT to approximate. We study #BIS in the general framework of two-state spin systems on bipartite graphs. We define two notions, nearly-independent phase-correlated spins and unary symmetry breaking. We prove that it is #BIS-hard to approximate the partition function of any 2-spin system on bipartite graphs supporting these two notions. As a consequence, we classify the complexity of approximating the partition function of antiferromagnetic 2-spin systems on bounded-degree bipartite graphs.

preprint2015arXiv

A Holant Dichotomy: Is the FKT Algorithm Universal?

We prove a complexity dichotomy for complex-weighted Holant problems with an arbitrary set of symmetric constraint functions on Boolean variables. This dichotomy is specifically to answer the question: Is the FKT algorithm under a holographic transformation a \emph{universal} strategy to obtain polynomial-time algorithms for problems over planar graphs that are intractable in general? This dichotomy is a culmination of previous ones, including those for Spin Systems, Holant, and #CSP. A recurring theme has been that a holographic reduction to FKT is a universal strategy. Surprisingly, for planar Holant, we discover new planar tractable problems that are not expressible by a holographic reduction to FKT. In previous work, an important tool was a dichotomy for #CSP^d, which denotes #CSP where every variable appears a multiple of d times. However its proof violates planarity. We prove a dichotomy for planar #CSP^2. We apply this planar #CSP^2 dichotomy in the proof of the planar Holant dichotomy. As a special case of our new planar tractable problems, counting perfect matchings (#PM) over k-uniform hypergraphs is polynomial-time computable when the incidence graph is planar and k >= 5. The same problem is #P-hard when k=3 or k=4, which is also a consequence of our dichotomy. When k=2, it becomes #PM over planar graphs and is tractable again. More generally, over hypergraphs with specified hyperedge sizes and the same planarity assumption, #PM is polynomial-time computable if the greatest common divisor of all hyperedge sizes is at least 5.

preprint2014arXiv

Localization and quasilocalization of spin-$1/2$ fermion field on two-field thick braneworld

Localization of a spin-$1/2$ fermion on the braneworld is an important and interesting problem. It is well known that a five-dimensional free massless fermion $Ψ$ minimally coupled to gravity cannot be localized on the Randall-Sundrum braneworld. In order to trap such a fermion, the coupling between the fermion and bulk scalar fields should be introduced. In this paper, localization and quasilocalization of a bulk fermion on the thick braneworld generated by two scalar fields (a kink scalar $ϕ$ and a dilaton scalar $π$) are investigated. Two types of couplings between the fermion and two scalars are considered. One coupling is the usual Yukawa coupling $-η\barΨϕΨ$ between the fermion and kink scalar, another one is $λ\barΨΓ^{M}\partial_{M}πγ^{5}Ψ$ between the fermion and dilaton scalar. The left-chiral fermion zero mode can be localized on the brane, and both the left- and right-chiral fermion massive Kaluza-Klein modes may be localized or quasilocalized. Hence the four-dimensional massless left-chiral fermion and massive Dirac fermions, whose lifetime is infinite or finite, can be obtained on the brane.

preprint2014arXiv

Localization of $q-$form fields on $AdS_{p+1}$ branes

In this paper, we investigate localization of a free massless $q-$form bulk field on thin and thick $AdS_{p+1}$ branes with codimension one. It is found that the zero mode of the $q-$form field with $q>(p+2)/2$ can be localized on the thin negative tension brane, which is different from the flat brane case given in [JHEP 10 (2012) 060]. For the thick $AdS_{p+1}$ branes, the $q-$form field with $q>(p+2)/2$ also has a localized zero mode under some conditions. Furthermore, we find that there are massive bound KK modes of the $q-$form field, which are localized on this type $p-$branes.

preprint2014arXiv

The Complexity of Counting Edge Colorings and a Dichotomy for Some Higher Domain Holant Problems

We show that an effective version of Siegel's Theorem on finiteness of integer solutions and an application of elementary Galois theory are key ingredients in a complexity classification of some Holant problems. These Holant problems, denoted by Holant(f), are defined by a symmetric ternary function f that is invariant under any permutation of the k >= 3 domain elements. We prove that Holant(f) exhibits a complexity dichotomy. This dichotomy holds even when restricted to planar graphs. A special case of this result is that counting edge k-colorings is #P-hard over planar 3-regular graphs for k >= 3. In fact, we prove that counting edge k-colorings is #P-hard over planar r-regular graphs for all k >= r >= 3. The problem is polynomial-time computable in all other parameter settings. The proof of the dichotomy theorem for Holant(f) depends on the fact that a specific polynomial p(x,y) has an explicitly listed finite set of integer solutions, and the determination of the Galois groups of some specific polynomials. In the process, we also encounter the Tutte polynomial, medial graphs, Eulerian partitions, Puiseux series, and a certain lattice condition on the (logarithm of) the roots of polynomials.

preprint2013arXiv

Localization of bulk matter fields, the hierarchy problem and corrections to Coulomb's law on a pure de Sitter thick braneworld

In this paper we investigate the localization and mass spectra of matter fields with spin 0, 1 and 1/2 on a geometric thick brane generated by pure 4D and 5D positive cosmological constants without bulk scalar fields. This model possesses a 4D cosmological constant that can be made as small as one desires without fine-tuning it with the bulk cosmological constant. The RS model is obtained as an analytic continuation of the flat brane limit of this braneworld configuration when the Hubble parameter disappears. Within this inflating braneworld model it is possible to formulate a mechanism for obtaining TeV mass scales from Planck ones by adding a positive thin brane, where the Standard Model fields are trapped, at a distance y_2 from the origin, where the Planck thick brane resides. The brane separation must be of the same order than the inverse thickness parameter of the model in order for the mechanism to generate the desired hierarchy. This result is obtained by imposing the recovery of both the correct 4D gravitational couplings and the actually observed accelerated expansion of the universe in our de Sitter braneworld. Regarding the localization of matter in the purely geometric thick braneworld, for spin 0 massless and massive scalar fields as well as for spin 1 vector fields, the potentials of the Kaluza--Klein (KK) modes in thecorresponding Schroedinger equations are modified Poeschl-Teller potentials, which lead to the localization of the scalar and vector zero modes on the brane as well as to mass gaps in the mass spectra. We also compute the corrections to Coulomb's law coming from massive KK vector modes. For spin 1/2 fermions, we introduce the bulk mass term MF(z)\barΨΨin the action and show that localization of the massless left-chiral fermion zero mode is feasible for two mass functions MF(z) with a finite/infinite number of massive KK bound states.

preprint2013arXiv

Resonances of Kalb-Ramond field on symmetric and asymmetric thick branes

In this paper, we investigate the localization of the Kalb-Ramond field on symmetric and asymmetric thick branes, which are generated by a background scalar field. In order to localize the Kalb-Ramond field, we introduce a coupling with the background scalar field, and find that there exist some Kaluza-Klein resonant modes. For the case of symmetric brane, we seek the resonances by using the relative probability method and transfer matrix method, and obtain the same result for the two methods. For the asymmetric case, we use the transfer matrix method. We find that the number of resonances will decrease with the increase of the asymmetry.

preprint2013arXiv

The Complexity of Planar Boolean #CSP with Complex Weights

We prove a complexity dichotomy theorem for symmetric complex-weighted Boolean #CSP when the constraint graph of the input must be planar. The problems that are #P-hard over general graphs but tractable over planar graphs are precisely those with a holographic reduction to matchgates. This generalizes a theorem of Cai, Lu, and Xia for the case of real weights. We also obtain a dichotomy theorem for a symmetric arity 4 signature with complex weights in the planar Holant framework, which we use in the proof of our #CSP dichotomy. In particular, we reduce the problem of evaluating the Tutte polynomial of a planar graph at the point (3,3) to counting the number of Eulerian orientations over planar 4-regular graphs to show the latter is #P-hard. This strengthens a theorem by Huang and Lu to the planar setting. Our proof techniques combine new ideas with refinements and extensions of existing techniques. These include planar pairings, the recursive unary construction, the anti-gadget technique, and pinning in the Hadamard basis.

preprint2012arXiv

Deformed brane with finite extra dimension

We construct a deformed brane solution generated by a double-kink scalar field and a dilaton scalar field. In this brane scenario the extra dimension is finite, which is due to the introduction of the dilaton field with special form. The finity of the extra dimension will result in the localization of the zero mode for the vector fields. While the localization of the Kalb-Ramond fields {depends} on the coupling to the dilaton. For the fermion fields, {with different values of the dilaton-fermion coupling constant}, there are three types of the effective potential for the fermion KK modes. Moreover, we investigate the effect of the deformation of the brane on the localization, and find that the number of the resonances will increase with the distances of the two sub-branes.

preprint2012arXiv

Domain Wall Brane in Eddington Inspired Born-Infeld Gravity

Recently, inspired by Eddington's theory, an alternative gravity called Eddington-inspired Born-Infeld gravity was proposed by Ba$\tilde{\text{n}}$ados and Ferreira. It is equivalent to Einstein's general relativity in vacuum, but deviates from it when matter is included. Interestingly, it seems that the cosmological singularities are prevented in this theory. Based on the new theory, we investigate a thick brane model with a scalar field presenting in the five-dimensional background. A domain wall solution is obtained, and further, we find that at low energy the four-dimensional Einstein gravity is recovered on the brane. Moreover, the stability of gravitational perturbations is ensured in this model.

preprint2012arXiv

Gravity Localization and Effective Newtonian Potential for Bent Thick Branes

In this letter, we first investigate the gravity localization and mass spectrum of gravity KK modes on de Sitter and Anti-de Sitter thick branes. Then, the effective Newtonian gravitational potentials for these bent branes are discussed by the two typical examples. The corrections of the Newtonian potential turns out to be $ΔU(r)\sim 1/r^{2}$ at small $r$ for both cases. These corrections are very different from that of the Randall-Sundrum brane model $ΔU(r)\sim 1/r^{3}$.

preprint2012arXiv

Inapproximability After Uniqueness Phase Transition in Two-Spin Systems

A two-state spin system is specified by a 2 x 2 matrix A = {A_{0,0} A_{0,1}, A_{1,0} A_{1,1}} = {β1, 1 γ} where β, γ\ge 0. Given an input graph G=(V,E), the partition function Z_A(G) of a system is defined as Z_A(G) = \sum_{σ: V -> {0,1}} \prod_{(u,v) \in E} A_{σ(u), σ(v)} We prove inapproximability results for the partition function in the region specified by the non-uniqueness condition from phase transition for the Gibbs measure. More specifically, assuming NP \ne RP, for any fixed β, γin the unit square, there is no randomized polynomial-time algorithm that approximates Z_A(G) for d-regular graphs G with relative error ε= 10^{-4}, if d = Ω(Δ(β,γ)), where Δ(β,γ) > 1/(1-βγ) is the uniqueness threshold. Up to a constant factor, this hardness result confirms the conjecture that the uniqueness phase transition coincides with the transition from computational tractability to intractability for Z_A(G). We also show a matching inapproximability result for a region of parameters β, γoutside the unit square, and all our results generalize to partition functions with an external field.

preprint2012arXiv

Thermodynamic Geometry of black hole in the deformed Horava-Lifshitz gravity

We investigate the thermodynamic geometry and phase transition of Kehagias-Sfetsos black hole in the deformed Horava-Lifshitz gravity with coupling constant $λ=1$. The phase transition in black hole thermodynamics is thought to be associated with the divergence of the capacities. And the structures of these divergent points are studied. We also find that the thermodynamic curvature produced by the Ruppeiner metric is positive definite for all $r_+ > r_-$ and is divergence at $η_2=0$ corresponded to the divergent points of $C_Φ$ and $C_T$. These results suggest that the microstructure of the black hole has an effective repulsive interaction, which is very similar to the ideal gas of fermions. These may shine some light on the microstructure of the black hole.

preprint2012arXiv

Thick branes with a nonminimally coupled bulk-scalar field

In this paper, we investigate thick branes with a nonminimally coupled background scalar field, whose solution is a single-kink or a double-kink. The effects of the nonminimal coupling constant $ξ$ on the structure of the thick branes and the localization of gravity, fermions, scalars and vectors are discussed. It is shown that each brane will split into two sub-branes as increasing the nonminimal coupling constant $ξ$. By investigating the tensor perturbation equations of gravity and the general covariant Dirac equation of fermions, we find that both the gravity zero mode and left-chiral fermion zero mode are localized at the center of the single-kink branes and localized between the two sub-branes generated by the double-kink, which indicates that the constant $ξ$ does not effect the localization of these zero modes. However, the zero mode of scalars is localized on each sub-brane (for both single-kink and double-kink branes) when $ξ$ is larger than its critical value $ξ_0$. The effects of the nonminimal coupling constant $ξ$ on the resonances of gravity and fermions with finite lifetime on the branes are also discussed.

preprint2011arXiv

Bulk matter fields on two-field thick branes

In this paper we obtain a new solution of a brane made up of a scalar field coupled to a dilaton. There is a unique parameter $b$ in the solution, which decides the distribution of the energy density and will effect the localization of bulk matter fields. For free vector fields, we find that the zero mode can be localized on the brane. And for vector fields coupled with the dilaton via $\text{e}^{τπ}F_{MN}F^{MN}$, the condition for localizing the zero mode is $τ\geq-\sqrt{b/3}$ with $0<b\leq1$, or $τ>-1/\sqrt{3b}$ with $b>1$, which includes the case $τ=0$. While the zero mode for free Kalb-Ramond fields can not be localized on the brane, if only we introduce a coupling between the Kalb-Ramond fields and the dilaton via $\text{e}^{ζπ}H_{MNL}H^{MNL}$. When the coupling constant satisfies $ζ>1/\sqrt{3b}$ with $b\geq1$ or $ζ>\frac{2-b}{\sqrt{3b}}$ with $0<b<1$, the zero mode for the KR fields can be localized on the brane. For spin half fermion fields, we consider the coupling $η\barΨ\text{e}^{λπ}ϕΨ$ between the fermions and the background scalars with positive Yukawa coupling $η$. The effective potentials for both chiral fermions have three types of shapes decided by the relation between the dilaton-fermion coupling constant $λ$ and the parameter $b$. For $λ\leq-1/\sqrt{3b}$, the zero mode of left-chiral fermion can be localized on the brane. While for $λ>-1/\sqrt{3b}$ with $b>1$ or $-1/\sqrt{3b}<λ<-\sqrt{b/3}$ with $0<b\leq1$, the zero mode for left-chiral fermion also can be localized.

preprint2011arXiv

Fermion Resonances on a Thick Brane with a Piecewise Warp Factor

In this paper, we mainly investigate the problems of resonances of massive KK fermions on a single scalar constructed thick brane with a piecewise warp factor matching smoothly. The distance between two boundaries and the other parameters are determined by one free parameter through three junction conditions. For the generalized Yukawa coupling $η\barΨϕ^{k}Ψ$ with odd $k=1,3,5,...$, the mass eigenvalue $m$, width $Γ$, lifetime $τ$, and maximal probability $P_{max}$ of fermion resonances are obtained. Our numerical calculations show that the brane without internal structure also favors the appearance of resonant states for both left- and right-handed fermions. The scalar-fermion coupling and the thickness of the brane influence the resonant behaviors of the massive KK fermions.

preprint2011arXiv

Localization of Bulk Matters on a Thick Anti-de Sitter Brane

In this paper, we investigate the localization and the mass spectra of gravity and various bulk matter fields on a thick anti-de Sitter (AdS) brane, by presenting the mass-independent potentials of the Kaluza-Klein (KK) modes in the corresponding Schrödinger equations. For gravity, the potential of the KK modes tends to infinity at the boundaries of the extra dimension, which leads to an infinite number of the bound KK modes. Although the gravity zero mode cannot be localized on the AdS brane, the massive modes are trapped on the brane. The scalar perturbations of the thick AdS brane have been analyzed, and the brane is stable under the scalar perturbations. For spin-0 scalar fields and spin-1 vector fields, the potentials of the KK modes also tend to infinity at the boundaries of the extra dimension, and the characteristic of the localization is the same as the case of gravity. For spin-1/2 fermions, by introducing the usual Yukawa coupling $η\barΨϕΨ$ with the positive coupling constant $η$, the four-dimensional massless left-chiral fermion and massive Dirac fermions are obtained on the AdS thick brane.

preprint2011arXiv

Relationship between High-Energy Absorption Cross Section and Strong Gravitational Lensing for Black Hole

In this paper, we obtain a relation between the high-energy absorption cross section and the strong gravitational lensing for a static and spherically symmetric black hole. It provides us a possible way to measure the high-energy absorption cross section for a black hole from strong gravitational lensing through astronomical observation. More importantly, it allows us to compute the total energy emission rate for high-energy particles emitted from the black hole acting as a gravitational lens. It could tell us the range of the frequency, among which the black hole emits the most of its energy and the gravitational waves are most likely to be observed. We also apply it to the Janis-Newman-Winicour solution. The results suggest that we can test the cosmic censorship hypothesis through the observation of gravitational lensing by the weakly naked singularities acting as gravitational lenses.

preprint2010arXiv

Bulk Matters on a GRS-Inspired Braneworld

In this paper we investigate the localization and mass spectra of bulk matter fields on a Gergory-Rubakov-Sibiryakov-inspired braneworld. In this braneworld model, there are one thick brane located at the origin of the extra dimension and two thin branes at two sides. For spin 1/2 fermions coupled with the background scalar $ϕ$ via $η\barΨϕ^pΨ$ with $p$ a positive odd integer, the zero mode of left-hand fermions can be localized on the thick brane for finite distance of the two thin branes, and there exist some massive bound modes and resonance modes. The resonances correspond to the quasi-localized massive fermions. For free massless spin 0 scalars, the zero mode can not be localized on the thick brane when the two thin branes are located finitely. While for a massive scalar $Φ$ coupled with itself and the background scalar field $ϕ$, in order to get a localized zero mode on the thick brane, a fine-tuning relation should be introduced. Some massive bound modes and resonances also will appear. For spin 1 vectors, there is no bound KK mode because the effective potential felt by vectors vanishes outside the two thin branes. We also investigate the physics when the distance of the two thin branes tends to infinity.

preprint2010arXiv

Charged Spinning Black Holes as Particle Accelerators

It has recently been pointed out that the spinning Kerr black hole with maximal spin could act as a particle collider with arbitrarily high center-of-mass energy. In this paper, we will extend the result to the charged spinning black hole, the Kerr-Newman black hole. The center-of-mass energy of collision for two uncharged particles falling freely from rest at infinity depends not only on the spin $a$ but also on the charge $Q$ of the black hole. We find that an unlimited center-of-mass energy can be approached with the conditions: (1) the collision takes place at the horizon of an extremal black hole; (2) one of the colliding particles has critical angular momentum; (3) the spin $a$ of the extremal black hole satisfies $\frac{1}{\sqrt{3}}\leq \frac{a}{M}\leq 1$, where $M$ is the mass of the Kerr-Newman black hole. The third condition implies that to obtain an arbitrarily high energy, the extremal Kerr-Newman black hole must have a large value of spin, which is a significant difference between the Kerr and Kerr-Newman black holes. Furthermore, we also show that, for a near-extremal black hole, there always exists a finite upper bound for center-of-mass energy, which decreases with the increase of the charge $Q$.

preprint2010arXiv

Localization of Matters on Anti-de Sitter Thick Branes

By presenting the mass-independent potentials of the Kaluza-Klein (KK) modes in the corresponding Schrödinger equations, we investigate the localization and mass spectra of various bulk matter fields on an AdS thick brane. For a spin 0 scalar $Φ$ coupled with itself and the domain-wall-forming field $ϕ$ via a coupling potential $V=(λϕ^{2}-u^{2})Φ^{2}+τΦ^{4}$, the localization and spectrum are decided by a critical coupling constant $λ_{0}$. When $λ>λ_0$, the potential of the scalar KK modes in the corresponding Schrödinger equation tends to infinite when far away from the brane, which results in that there exist infinite discrete scalar bound KK states, and the massless modes could be trapped on the AdS brane by fine-tuning of parameters. When $λ<λ_0$, the potential of the scalar KK modes tends to negative infinite when far away from the brane, hence there does not exist any scalar bound KK state. For a spin 1 vector, the situation is same like the scalar with a coupling constant $λ>λ_0$, but the zero mode can not be localized on the brane. For a spin 1/2 fermion, we introduce the usual Yukawa coupling $η\barΨϕΨ$, and find that the localization of the fermion is decided by a critical coupling constant $η_0$. For $η> η_0$, the four-dimensional massless left chiral fermion and massive Dirac fermions consisted of the pairs of coupled left-hand and right-hand KK modes could be localized on the AdS brane, and the massive Dirac fermions have a set of discrete mass spectrum. While for the case $0<η< η_{0}$, no four-dimensional Dirac fermion can be localized on the AdS brane.

preprint2010arXiv

Topological aspects in a two component Bose condensed system in neutron star

By making use of Duan-Ge's decomposition theory of gauge potential and the Duan's topological current theory proposed by Prof. Duan Yi-Shi, we study a two component superfluid Bose condensed system, which is supposed being realized in the interior of neutron stars in the form of a coexistent neutron superfluid and protonic superconductor. We propose that this system possesses vortex lines. The topological charge of the vortex lines are characterized by the Hopf indices and the Brower degrees of $ϕ$-mapping.