arXiv subjects

Junze Zhang

Publications and source records attributed to Junze Zhang.

15 recordsLinked to original sources

arXiv2026

Equivalence of superintegrable Poisson projection chains: magnetic cotangent bundles and spin Calogero-Moser models

We study superintegrable Hamiltonian systems in terms of Poisson projection chains and their (spectral) equivalence. We compare two reduction constructions: (i) the cotangent bundle $T^*(G/A)$, $A=Z_G(γ)$, with the magnetic symplectic form defined by the orbit $G\cdot γ\cong G/A$, and (ii) the left-right Hamiltonian reduction of $T^*G$ that gives spin Calogero-Moser type systems. We prove that the two resulting chains are equivalent on an open set of regular points of principal orbit type: the phase spaces, the intermediate Poisson manifolds and the base spaces are identified compatibly with the projections. In particular, both constructions give the same commuting Hamiltonians.

math-ph↗

arXiv2026

Stratified Superintegrability of Spin Calogero-Moser-Sutherland Systems

We study the Poisson chain of the compact spin Calogero-Moser-Sutherland system obtained by conjugation reduction of $T^*\mathrm{SU}(n)$ at a fixed coadjoint orbit. We give a Horn-type condition ensuring that the spectral torus acts freely on the full fiber over a simple spectrum; for each orbit, the admissible spectra form a nonempty open dense set, and the restricted chain is strongly superintegrable of rank $n-1$ on every orbit-type stratum. We also construct, across certain affine spectral walls, a proper quotient map onto a Hausdorff stratified Poisson space with a finite Whitney stratification. For $\mathrm{SU}(3)$, we compute the free spectral domain and the quotient near two intersecting walls, and a zero-orbit example shows that the analogous quotient need not be Hausdorff on the unrestricted reduced phase space.

math.DG↗

arXiv2026

Microwave Response of the Superconducting Diode Effect in Proximitized Bilayer Graphene Interferometers

Microwave irradiation has emerged as a promising means to tune the superconducting diode effect (SDE) in Josephson junction devices. Previous experimental studies have mainly focused on the adiabatic-driving regime, in which the diode efficiency increases monotonically with microwave power and can approach the ideal value of unity. Beyond this regime, however, the microwave response of the SDE remains largely unexplored experimentally. In this work, we investigate the microwave response of the SDE in bilayer-graphene-based superconducting quantum interference devices (SQUIDs) under a broad range of driving frequencies. We show that increasing the driving frequency changes the response characteristics of the diode efficiency to microwave power--the dependence of the diode efficiency evolves from monotonic enhancement with increasing microwave power in the adiabatic regime to non-monotonic behavior beyond this regime, and ultimately to sign-reversal as well oscillatory characteristics at sufficiently high frequencies. We find that these experimentally observed frequency-dependent power response characteristics of the diode efficiency can be qualitatively captured by simulations based on the resistively shunted junction model using the device current-phase relations extracted from the experiments. These results establish SQUIDs made from bilayer graphene as a versatile platform for studying dynamic properties of superconducting junction devices.

cond-mat.mes-hall↗

arXiv2026

Geometric construction of superintegrable Poisson projection chains via Poisson centralizers

We introduce a geometric framework for constructing superintegrable systems from Poisson centralizers (commutants) in the Lie-Poisson algebra $S(\mathfrak{g})$ of a complex semisimple Lie algebra. Starting from a chain of reductive subgroups, we study the corresponding invariant Poisson subalgebras and their Poisson centers, and formulate superintegrability in terms of a \emph{Poisson projection chain} of affine Poisson varieties. For a maximal torus $T\subset G$, we prove that the inclusions $S(\mathfrak{g})^G\subset S(\mathfrak{g})^T\subset S(\mathfrak{g})$ determine a superintegrable chain and identify the associated quotient maps $\mathfrak{g}\xrightarrow{χ_T}\mathfrak{g}//T\xrightarrowρ\mathfrak{g}//G$. The rank (transcendence degree) computations yield the expected dimension split between commuting Hamiltonians and first integrals, and we describe the corresponding symplectic leaves in the intermediate space. Several examples illustrate how the centralizer generators organize into explicit superintegrable Poisson chains.

math-ph↗

arXiv2026

Poisson Centralisers and Polynomial Superintegrability for Magnetic Geodesic Flows on Reductive Homogeneous Spaces

We provide a method for formulating superintegrable magnetic geodesic flows on reductive homogeneous spaces $M=G/A$, with $G$ a compact semisimple Lie group and $A$ a closed subgroup of $G$. In the twisted cotangent bundle $(T^*M,ω_\varepsilon)$, with $ω_\varepsilon=ω_{\mathrm{can}}+\varepsilon\,π^*ω_{\mathrm{KKS}}$ being the canonical plus Kirillov-Kostant-Souriau (KKS) forms, we build two canonical and commuting families of polynomial first integrals: one pulled back from the Lie algebra $\mathfrak{g}$ of $G$ via the magnetic moment map $P$, and one pulled back from a $\mathrm{Ad}(A)$-invariant affine slice of $\mathfrak{m} \cong T_{eA}M$, where $eA$ is the identity of $G/A$. Their common image generates a reduced Poisson algebra obtained from a fiber tensor product, and the natural multiplication map into a Poisson subalgebra of polynomial functions $\mathcal{O}(T^*M) \subset C^\infty(T^*M)$ is Poisson and injective. The center of this fiber tensor product is contained in the Poisson center of the symmetric algebra of $\mathfrak{g}$. In a dense regular locus, the resulting projection chain realises a superintegrable system. As examples, two $\mathrm{SU}(3)$ cases are studied (regular torus and irregular $\mathrm{S}(\mathrm{U}(2)\times \mathrm{U}(1))$ quotients), which illustrate the construction and produce explicit action-angle coordinates.

math-ph↗

arXiv2025

Polynomial Poisson Algebras and Superintegrable Systems from Cartan centralisers of Types $B_3$, $C_3$ and $D_3$

In this work, we construct explicit formulas for the generators of the Cartan centralisers of complex semisimple Lie algebras $B_n,C_n$ and $D_n$, the case $A_n$ being already known \cite{campoamor2023algebraic}. The precise structures for the cases of rank-three simple Lie algebras ($B_3,C_3$ and $D_3$) are provided, and the inclusion relations between the corresponding polynomial Poisson algebras (finitely generated Poisson algebras over $\mathbb{C}[\mathfrak{h}^*]$) are illustrated. We develop the idea of constructing algebraic superintegrable systems and their integrals from the generators of these polynomial Poisson algebras. In particular, we explicitly present the algebraic superintegrable systems corresponding to the Cartan reduction chains $\mathfrak{h} \subset \mathfrak{so}(6,\mathbb{C})$, $\mathfrak{h} \subset \mathfrak{so}(7,\mathbb{C})$, and $\mathfrak{h} \subset \mathfrak{sp}(6,\mathbb{C})$.

math-ph↗

arXiv2025

Subalgebra chains and nuclear physics: Commutant approach and construction of polynomial algebras

In this paper, we review a new approach to study subalgebra chains $\mathfrak{g} \supset \mathfrak{g}'$ in the context of nuclear physics. This approach does not rely on explicit realizations as bosons or differential operators. We rely on the enveloping algebra, the notion of commutant $C_{U(\mathfrak{g})}(\mathfrak{g}^{\prime})$ and $\mathfrak{g}^{\prime}$-invariant polynomials. This approach builds on those $\mathfrak{g}^{\prime}$-invariant polynomials and finding the underlying finitely generated polynomial algebras. Those algebraic structures can then provide further information on sets of labeling operators. Another aspect of this method consists in exploiting the dual space and the symmetric algebra. Being independent of explicit realizations, it endows the algebraic relations with a universal character. We review the chains associated with $\mathfrak{su}(3) \supset \mathfrak{so}(3)$, $\mathfrak{so}(5) \supset \mathfrak{su}(2) \times \mathfrak{u}(1)$, $\mathfrak{su}(4) \supset \mathfrak{su}(2) \times \mathfrak{su}(2)$. Those chains are known as the Elliott, Seniority and Supermultiplet. We also provide new results and insights into the subalgebra chain $\mathfrak{so}(5) \supset \mathfrak{so}(3)$ of the Surfon model. For all chains, we present the related commutant, $\mathfrak{g}^{\prime}$-invariant polynomials and Poisson algebras.

math-ph↗

arXiv2025

Algebraic structures and Hamiltonians from the equivalence classes of 2D conformal algebras

The construction of superintegrable systems based on Lie algebras and their universal enveloping algebras has been widely studied over the past decades. However, most constructions rely on explicit differential operator realisations and Marsden-Weinstein reductions. In this paper, we develop an algebraic approach based on the subalgebras of the 2D conformal algebra $\mathfrak{c}(2)$. This allows us to classify the centralisers of the enveloping algebra of the conformal algebra and construct the corresponding Hamiltonians with integrals in algebraic form. It is found that the symmetry algebras underlying these algebraic Hamiltonians are six-dimensional quadratic algebras. The Berezin brackets and commutation relations of the quadratic algebraic structures are closed without relying on explicit realisations or representations. We also give the Casimir invariants of the symmetry algebras. Our approach provides algebraic perspectives for the recent work by Fordy and Huang on the construction of superintegrable systems in the Darboux spaces.

math-ph↗

arXiv2025

Polynomial algebra from the Lie algebra reduction chain $\mathfrak{su}(4) \supset \mathfrak{su}(2) \times \mathfrak{su}(2)$: The supermultiplet model

The supermultiplet model, based on the reduction chain $\mathfrak{su}(4) \supset \mathfrak{su}(2) \times \mathfrak{su}(2)$, is revisited through the lens of commutants within universal enveloping algebras of Lie algebras. From this analysis, a collection of twenty polynomials up to degree nine emerges from the commutant associated with the $\mathfrak{su}(2) \times \mathfrak{su}(2)$ subalgebra. This study is conducted in the Poisson (commutative) framework using the Lie-Poisson bracket associated with the dual of the Lie algebra under consideration. As the main result, we obtain the polynomial Poisson algebra generated by these twenty linearly independent and indecomposable polynomials, with five elements being central. This incorporates polynomial expansions up to degree seventeen in the Lie algebra generators. We further discuss additional algebraic relations among these polynomials, explicitly detailing some of the lower-order ones. As a byproduct of these results, we also show that the recently introduced 'grading method' turns out to be essential for deriving the Poisson bracket relations when the degree of the expansions becomes so high that standard approaches are no longer applicable, due to computational limitations. These findings represent a further step toward the systematic exploration of polynomial algebras relevant to nuclear models.

math-ph↗

arXiv2025

On the construction of polynomial Poisson algebras: a novel grading approach

In this work, we refine recent results on the explicit construction of polynomial algebras associated with commutants of subalgebras in enveloping algebras of Lie algebras by considering an additional grading with respect to the subalgebra. It is shown that such an approach simplifies and systematizes the explicit derivation of the Lie--Poisson brackets of elements in the commutant, and several fundamental properties of the grading are given. The procedure is illustrated by revisiting three relevant reduction chains associated with the rank-two complex simple Lie algebra $\mathfrak{sl}(3,\mathbb{C})$. Specifically, we analyze the reduction chains $\mathfrak{so}(3) \subset \mathfrak{su}(3)$, corresponding to the Elliott model in nuclear physics, the chain $\mathfrak{o}(3) \subset \mathfrak{sl}(3,\mathbb{C})$ associated with the decomposition of the enveloping algebra of $\mathfrak{sl}(3,\mathbb{C})$ as a sum of modules, and the reduction chain $\mathfrak{h} \subset \mathfrak{sl}(3,\mathbb{C})$ connected to the Racah algebra $R(3)$. In addition, a description of the classification of the centralizer with respect to the Cartan subalgebra $\mathfrak{h}$ associated with the classical series $A_n$ in connection with its root system is reconsidered. As an illustration of the procedure, the case of $S(A_3)^\mathfrak{h}$ is considered in detail, which is connected with the rank-two Racah algebra for specific realizations of the generators as vector fields. This case has attracted interest with regard to orthogonal polynomials.

math-ph↗

arXiv2023

On polynomial symmetry algebras underlying superintegrable systems in Darboux spaces

We review three different approaches to polynomial symmetry algebras underlying superintegrable systems in Darboux spaces. The first method consists of using deformed oscillator algebra to obtain finite-dimensional representations of quadratic algebras. This allow one to gain information on the spectrum of the superintegrable systems. The second method has similarities with the induced module construction approach in the context of Lie algebras and can be used to construct infinite dimensional representations of the symmetry algebras. Explicit construction of these representations is a non-trivial task due to the non-linearity of the polynomial algebras. This method allows the construction of states of the superintegrable systems beyond the reach of separation of variables. As a result, we are able to construct a large number of states in terms of Airy, Bessel and Whittaker functions which would be difficult to obtain in other ways. We also discuss the third approach which is based on the notion of commutants of subalgebras in the enveloping algebra of a Poisson algebra or a Lie algebra. This allows us to discover new superintegrable models in the Darboux spaces and to construct their integrals and symmetry algebras via polynomials in the enveloping algebras.

math-ph↗

arXiv2023

Infinite dimensional representations of cubic and quintic algebras and special functions

Finite and Infinite-dimensional representations of symmetry algebras play a significant role in determining the spectral properties of physical Hamiltonians. In this paper, we introduce and apply a practical method to construct infinite dimensional representations of certain polynomial algebras which appear in the context of quantum superintegrable systems. Explicit construction of these representations is a non-trivial task due to the non-linearity of the polynomial algebras. Our method has similarities with the induced module construction approach in the context of Lie algebras and allows the construction of states of the superintegrable systems beyond the reach of separation of variables. Our main focus is the representations of the polynomial algebras underlying superintegrable systems in 2D Darboux spaces. We are able to construct a large number of states in terms of complicated expressions of Airy, Bessel and Whittaker functions which would be difficult to obtain in other ways.

math-ph↗

arXiv2023

Algebraic approach and exact solutions of superintegrable systems in 2D Darboux spaces

Superintegrable systems in 2D Darboux spaces were classified and it was found that there exist 12 distinct classes of superintegrable systems with quadratic integrals of motion (and quadratic symmetry algebras generated by the integrals) in the Darboux spaces. In this paper, we obtain exact solutions via purely algebraic means for the energies of all the 12 existing classes of superintegrable systems in four different 2D Darboux spaces. This is achieved by constructing the deformed oscillator realization and finite-dimensional irreducible representation of the underlying quadratic symmetry algebra generated by quadratic integrals respectively for each of the 12 superintegrable systems. We also introduce generic cubic and quintic algebras, generated respectively by linear and quadratic integrals and linear and cubic integrals, and obtain their Casimir operators and deformed oscillator realizations. As examples of applications, we present three classes of new superintegrable systems with cubic symmetry algebras in 2D Darboux spaces.

nlin.SI↗

arXiv2022

Avoiding the "Great Filter": An Assessment of Climate Change Solutions and Combinations for Effective Implementation

Climate change is the long-term shift in global weather patterns, largely caused by anthropogenic activity of greenhouse gas emissions. Global climate temperatures have unmistakably risen and naturally occurring climate variability alone cannot account for this trend. Human activities are estimated to have caused about 1.0 degree C of global warming above the pre-industrial baseline and if left unchecked, will continue to drastically damage the Earth and its inhabitants. Globally, natural disasters and subsequent economic losses have become increasingly impactful because of climate change. Both wildlife ecosystems and human habitats have been negatively impacted, from rising sea levels to alarming frequency of severe weather events around the world. Attempts towards alleviating the effects of global warming have often been at odds and remain divided among a multitude of strategies, reducing the overall effectiveness of these efforts. It is evident that collaborative action is required for avoiding the most severe consequences of climate change. This paper evaluates the main strategies (industrial/energy, political, economic, agricultural, atmospheric, geological, coastal, and social) towards both mitigating and adapting to climate change. As well, it provides an optimal combination of seven solutions which can be implemented simultaneously, working in tandem to limit and otherwise accommodate the harmful effects of climate change. Previous legislation and deployment techniques are also discussed as guides for future endeavors.

physics.soc-ph↗

arXiv2022

Complex structures on stratified Lie algebras

This paper investigates some properties of complex structures on Lie algebras. In particular, we focus on $\textit{nilpotent}$ $\textit{complex structures}$ that are characterized by a suitable $J$-invariant ascending or descending central series $\mathfrak{d}^j$ and $\mathfrak{d}_j$ respectively. In this article, we introduce a new descending series $\mathfrak{p}_j$ and use it to give proof of a new characterization of nilpotent complex structures. We examine also whether nilpotent complex structures on stratified Lie algebras preserve the strata. We find that there exists a $J$-invariant stratification on a step $2$ nilpotent Lie algebra with a complex structure.

math.DG↗