arXiv subjects

Sirui Yu

Publications and source records attributed to Sirui Yu.

7 recordsLinked to original sources

arXiv2026

Coulomb interaction unlocks Majorana-mediated electron teleportation between Quantum dots

We investigate quantum transport in a hybrid system composed of two quantum dots (QDs) coupled through a pair of spatially separated Majorana zero modes (MZMs) with negligible coupling energy. We focus on nonlocal correlations mediated by the MZMs, particularly the role of Coulomb interaction U between the QDs and the Majorana wire. Using the numerically exact fermionic dissipation equation of motion (DEOM) method, we compute both the transient current and the current-current cross-correlation noise spectrum. In the non-interacting case (U=0), destructive interference between the degenerate normal tunneling and anomalous tunneling channels suppresses electron teleportation between the dots. Introducing a finite Coulomb interaction $U$ lifts this channel degeneracy, enabling strong nonlocal correlations and inter-dot electron teleportation. This effect manifests as a robust signal in the cross-correlation noise spectrum, which is significantly stronger than that induced by a finite Majorana coupling energy $\varepsilon_{M}$. Our findings propose Coulomb interaction as an efficient and experimentally accessible control parameter for generating and detecting Majorana-mediated nonlocal transport in the topologically relevant long-wire limit ($\varepsilon_{M}\rightarrow0$).

cond-mat.mes-hall↗

arXiv2025

Differential calculus on bigraded spaces and Koszul duality

Let $\mathbb R^{m|n}$ be the usual superspace. The algebra of functions on it is Koszul, but its Koszul dual is not graded commutative, and in particular not the algebra of functions on $\mathbb R^{n|m}$. This contrasts with the two extreme cases, in which the polynomial and exterior algebras are Koszul dual. We remedy this discrepancy by realizing the algebra $\mathcal{O}(\mathbb{R}^{m|n})$ as the algebra of a bigraded space, and its Koszul dual, in the bigraded sense, is then also the algebra of a bigraded space. We then show that the differential calculus structures on these two spaces are isomorphic via Koszul duality. As an application, in the second half of the paper, we study Poisson structures on these spaces and show that for quadratic bigraded Poisson structures, Koszul duality also identifies the corresponding differential calculus structures on the Poisson (co)homology groups of these two spaces. Moreover, if the Poisson structures are unimodular, then the associated Batalin-Vilkovisky algebras on the Poisson cohomology groups are also isomorphic.

math.RA↗

arXiv2025

Phase-controlled quantum transport signatures in a quantum dot-Majorana hybrid ring system

We investigate the quantum transport in a hybrid ring system consisting of a quantum dot (QD) coupled to two Majorana bound states (MBSs) hosted in a topological superconducting nanowire, threaded by a magnetic flux. Utilizing the dissipaton equation-of-motion approach, we demonstrate that the differential conductance shows periodic behavior and its periodicity depends on both the QD energy level and the MBS overlapping. A zero-bias peak (ZBP) emerges as a result of the balance between normal and anomalous tunneling processes, associated with the presence of a single MBS. Beyond the phase-dependent periodic behavior, the shot noise exhibits voltage-dependent transitions between sub-Poissonian ($F = 0.5$), Poissonian ($F = 1$), and super-Poissonian ($F > 1$) regimes. Strikingly, we find a giant Fano factor ($F\gg1$) emerging at the balance point, accompanied by a peak in the shot noise. This distinctive feature may serve as a supplementary signature for MBS detection. However, both ZBP in the differential conductance and shot noise peak are degraded by thermal effects.

cond-mat.mes-hall↗

arXiv2024

Majorana qubit readout by a point-contact detector under finite bias voltages

In this work we revisit the problem of a Majorana box qubit (MBQ) readout by a point-contact (PC) detector. The logic states of the MBQ are associated with the combined fermion parities of the MBQ and its tunnel-coupled quantum dot, which is measured by a PC detector. Beyond the existing studies on limiting bias voltage regimes, we analyze the steady-state current and the current power spectrum across all bias voltages. Our results indicate that the MBQ readout via the parity-dependent detector current is effective only at low bias voltage regime and requires the dot energy level to be off-resonance with the Majorana qubit. In contrast, the current power spectrum allows MBQ readout through the parity-dependent Rabi oscillation peak signals for arbitrary bias voltages, without restrictions on the dot energy level. Particularly, with focus on the MBQ measurement visibility, we analyze the peak-to-pedestal ratio for each characteristic peak (associated with each logic state of the qubit) and the signal-to-noise ratio of the two peaks. By examining these two metrics, we identify the optimal bias voltage window for the PC detector at low temperature limit.

cond-mat.mes-hall↗

arXiv2023

Quantization of the minimal nilpotent orbits and the quantum Hikita conjecture

We show that the specialized quantum D-module of the equivariant quantum cohomology ring of the minimal resolution of an ADE singularity is isomorphic to the D-module of graded traces on the minimal nilpotent orbit in the Lie algebra of the same type. This generalizes a recent result of Shlykov [Hikita conjecture for the minimal nilpotent orbit, to appear in Proc. AMS, https://doi.org/10.1090/proc/15281] and hence verifies in this case the quantum version of Hikita's conjecture, proposed by Kamnitzer, McBreen and Proudfoot [The quantum Hikita conjecture, Advances in Mathematics 390 (2021) 107947]. We also show analogous isomorphisms for singularities of BCFG type.

math.RT↗

arXiv2021

Batalin-Vilkovisky algebra structure on Poisson manifolds with diagonalizable modular symmetry

We study the ``twisted" Poincar\'e duality of smooth Poisson manifolds, and show that, if the modular vector field is diagonalizable, then there is a mixed complex associated to the Poisson complex, which, combining with the twisted Poincar\'e duality, gives a Batalin-Vilkovisky algebra structure on the Poisson cohomology. This generalizes the previous results obtained by Xu for unimodular Poisson manifolds. We also show that the Batalin-Vilkovisky algebra structure is preserved under Kontsevich's deformation quantization, and in the case of polynomial algebras it is also preserved by Koszul duality.

math.DG↗

arXiv2017

Derived categories and Calabi-Yau algebras

We study the derived equivalence of Calabi-Yau algebras and show that, for two derived Morita equivalent algebras, if one is Calabi-Yau, then so is the other. Keywords: Derived equivalence, Calabi-Yau algebra

math.RA↗