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Xiaowen Zhu

Publications and source records attributed to Xiaowen Zhu.

14 recordsLinked to original sources

Geometric bulk-edge correspondence for $\mathbb{Z}_2$-topological insulators

Fermionic time-reversal-invariant insulators in two dimensions--class AII in the Kitaev table--come in two topological phases. These phases are characterized by a $\mathbb{Z}_2$-valued invariant, the Fu-Kane-Mele index. We prove a geometric bulk-edge correspondence for curved interfaces: if two such insulators occupy complementary regions separated by a curved boundary, then the $\mathbb{Z}_2$ edge index of the interface system is the product, modulo two, of the difference of the two bulk $\mathbb{Z}_2$ indices and a geometric intersection number associated with the boundary and the measurement region. The argument is a $\mathbb{Z}_2$ analogue of the curved-interface connection formula proved for Hall insulators in \cite{DZ24}.

math-ph↗

Potential-Guided Flow Matching for Vision-Language-Action Policy Improvement

Large vision-language-action (VLA) policies are increasingly trained as conditional generative models over action chunks. Yet deployment produces mixed-quality experience-successful demonstrations, partial completions, recoverable mistakes, and failures-that is difficult to use with standard imitation. Full behavior cloning (BC) imitates failures, filtered BC discards useful sub-trajectories, and offline reinforcement learning adds a large critic. We introduce ForesightFlow, a self-guided flow-matching policy that augments each generated action chunk with a learned success-potential trajectory. The same flow proposes and scores candidate actions, enabling best-of-$K$ inference without an external critic. The key issue is that policy improvement and value calibration require different supervision: advantage weighting should emphasize high-quality actions, but applying the same weights to potential coordinates suppresses failure gradients and creates overconfident scores. We address this with decoupled advantage-weighted flow matching, applying exponentiated advantage weights only to action velocities while training potential velocities uniformly. We further derive a one-step boundary estimator for conditional flow matching, allowing advantage computation with a single stop-gradient forward pass. Across five BEHAVIOR-1K simulation tasks and five real-world bimanual tasks, ForesightFlow improves over imitation baselines, matches the strongest separate-critic baseline in simulation success, improves real-world success, and reduces training compute by $38\%$. Ablations show that decoupling prevents value hallucination, the one-step estimator preserves candidate-ranking fidelity, and self-guided sampling improves long-horizon execution.

cs.RO↗

Edge spectrum for truncated $\mathbb{Z}_2$-insulators

Fermionic time-reversal-invariant insulators in two dimensions -- class AII in the Kitaev table -- come in two different topological phases. These are characterized by a $\mathbb{Z}_2$-index: the Fu-Kane-Mele index. We prove that if two such insulators with different indices occupy regions containing arbitrarily large balls, then the spectrum of the resulting operator fills the bulk spectral gap. Our argument follows a proof by contradiction developed in an earlier work by two of the authors for quantum Hall systems. It boils down to showing that the $\mathbb{Z}_2$-index can be computed only from bulk information in sufficiently large balls. This is achieved via a result of independent interest: a local trace formula for the $\mathbb{Z}_2$-index.

math-ph↗

Absolutely continuous spectrum for truncated topological insulators

We show that if a topological insulator is truncated along a curve that separates the plane in two sufficiently large regions, then the edge system admits absolutely continuous spectrum. Our approach combines a recent version of the bulk-edge correspondence along curves that separates geometry and intrinsic conductance [DZ24], with a result about absolutely continuous spectrum for straight edges [BW22].

math-ph↗

Dynamical Localization for the Singular Anderson Model in $\mathbb{Z}^d$

We prove that once one has the ingredients of a ``single-energy multiscale analysis (MSA) result'' on the $\mathbb{Z}^d$ lattice, several spectral and dynamical localization results can be derived, the most prominent being strong dynamical localization (SDL). In particular, given the recent progress at the bottom of the spectrum for the $\mathbb{Z}^2$ and $\mathbb{Z}^3$ cases with Bernoulli single site probability distribution, our results imply SDL in these regimes.

math-ph↗

The bulk-edge correspondence for curved interfaces

The bulk-edge correspondence is a condensed matter theorem that relates the conductance of a Hall insulator in a half-plane to that of its (straight) boundary. In this work, we extend this result to domains with curved boundaries. Under mild geometric assumptions, we prove that the edge conductance of a topological insulator sample is an integer multiple of its Hall conductance. This integer counts the algebraic number of times that the interface (suitably oriented) enters the measurement set. This result provides a rigorous proof of a well-known experimental observation: arbitrarily truncated topological insulators support edge currents, regardless of the shape of their boundary.

math-ph↗

Magnetic response of twisted bilayer graphene

In this article, we analyse the Bistritzer--MacDonald (BM) model (also known as the continuum model) of twisted bilayer graphene (TBG) with an additional external magnetic field. We provide an explicit semiclassical asymptotic expansion of the density of states (DOS) in the limit of strong magnetic fields. The explicit expansion of the DOS enables us to study magnetic response properties such as magnetic oscillations which includes Shubnikov-de Haas and de Haas-van Alphen oscillations as well as the integer quantum Hall effect. In particular, we elucidate the role played by different types of interlayer tunnelings ($AA^{\prime}$/$BB^{\prime}$ vs. $AB^{\prime}$/$BA^{\prime}$) in the study of the DOS, and magnetic properties.

math-ph↗

Spectral theory of twisted bilayer graphene in a magnetic field

In this article we study the Bistritzer-MacDonald (BM) model with external magnetic field. We study the spectral properties of the Hamiltonian in an external magnetic field with a particular emphasis on the flat band of the chiral model at magic angles. Our analysis includes different types of interlayer tunneling potentials, the so-called chiral and anti-chiral limits. One novelty of our article is that we show that using a magnetic field one can discriminate between flat bands of different multiplicities, as they lead to different Chern numbers in the presence of magnetic fields, while for zero magnetic field their Chern numbers always coincide.

math-ph↗

Topological edge spectrum along curved interfaces

We prove that that if the boundary of a topological insulator divides the plane in two regions containing arbitrarily large balls, then it acts as a conductor. Conversely, we show that topological insulators that fit within strips do not need to admit conducting boundary modes.

math-ph↗

Anderson Localization for Schrödinger Operators with Monotone Potentials over Circle Homeomorphisms

In this paper, we prove pure point spectrum for a large class of Schrödinger operators over circle maps with conditions on the rotation number going beyond the Diophantine. More specifically, we develop the scheme to obtain pure point spectrum for Schrödinger operators with monotone bi-Lipschitz potentials over orientation-preserving circle homeomorphisms with Diophantine or weakly Liouville rotation number. The localization is uniform when the coupling constant is large enough.

math-ph↗

High-frequency structure design and RF stability analysis of a 4-vane radio frequency quadrupole with pi-mode stabilizer loops

Compact accelerator-based neutron source facilities are garnering attention and play an important and expanding role in material and engineering sciences, as well as in neutron science education and training. Neutrons are produced by bombarding a low-energy proton beam onto a beryllium or lithium target. In such an accelerator-based neutron source, a radio frequency quadrupole (RFQ) is usually utilized to accelerate a high-intensity proton beam to a few MeV. This study mainly covers the high-frequency structure design optimizations of a 4-vane RFQ with pi-mode stabilizer loops (PISLs) and its RF stability analysis. A 176 MHz RFQ accelerator is designed to operate at a 10% duty factor and could accelerate an 80 mA proton beam from 65 keV to 2.5 MeV within a length of 5.3 m. The adoption of PISLs ensures high RF stability, eases the operation of the accelerator, and implies less stringent alignment and machining tolerances.

physics.acc-ph↗

Coupled multiphysics analysis of a 4-vane RFQ accelerator under high power operation

The radiofrequency resonant four-quadrant mechanical structure of a 4-vane Radio Frequency Quadrupole (RFQ) has a high quality factor and narrow bandwidth, resulting in high sensitivity to frequency detuning caused by thermal expansion under high power operation, so minimization of frequency errors and affording dynamic tuning are very important design issues. Here we describe an optimization approach to figure out a suitable cooling design for a 4-vane RFQ in steady state. Besides, we investigate how the accelerator responds in transient thermal analysis that could help to guide commissioning and reduce frequency detuning. Multiphysics analysis utilized with CST and ANSYS for a recently developed 176 MHz 4-vane RFQ is taken as an example. This RFQ will dissipate 211 kW when reaching an inter-vane voltage of 80 kV, which is required for an acceleration of an 80-mA proton from 65 keV to 2.5 MeV in 5.3 meters.

physics.acc-ph↗

Localization for random CMV matrices

We prove Anderson localization (AL) and dynamical localization in expectation (EDL, also known as strong dynamical localization) for random CMV matrices for arbitrary distribution of i.i.d. Verblunsky coefficients.

math-ph↗

Large deviations of the Lyapunov exponent and localization for the 1D Anderson model

The proof of Anderson localization for the 1D Anderson model with arbitrary (e.g. Bernoulli) disorder, originally given by Carmona-Klein-Martinelli in 1987, is based in part on the multi-scale analysis. Later, in the 90s, it was realized that for one-dimensional models with positive Lyapunov exponents some parts of multi-scale analysis can be replaced by considerations involving subharmonicity and large deviation estimates for the corresponding cocycle, leading to nonperturbative proofs for 1D quasiperiodic models. In this paper we present a short proof along these lines, for the Anderson model. To prove dynamical localization we also develop a uniform version of Craig-Simon's bound that works in high generality and may be of independent interest.

math-ph↗