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1. Stochastic quantisation of Yang–Mills–Higgs in 3D

   https://doi.org/10.1007/s00222-024-01264-2  

   Chandra, Ajay; Chevyrev, Ilya; Hairer, Martin; Shen, Hao (August 2024, Inventiones mathematicae)

   Abstract We define a state space and a Markov process associated to the stochastic quantisation equation of Yang–Mills–Higgs (YMH) theories. The state space$$\mathcal{S}$$ $S$is a nonlinear metric space of distributions, elements of which can be used as initial conditions for the (deterministic and stochastic) YMH flow with good continuity properties. Using gauge covariance of the deterministic YMH flow, we extend gauge equivalence ∼ to$$\mathcal{S}$$ $S$and thus define a quotient space of “gauge orbits”$$\mathfrak {O}$$ $O$. We use the theory of regularity structures to prove local in time solutions to the renormalised stochastic YMH flow. Moreover, by leveraging symmetry arguments in the small noise limit, we show that there is a unique choice of renormalisation counterterms such that these solutions are gauge covariant in law. This allows us to define a canonical Markov process on$$\mathfrak {O}$$ $O$(up to a potential finite time blow-up) associated to the stochastic YMH flow. 

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2. Connecting physics to systems with modular spin-circuits

   https://doi.org/10.1038/s44306-024-00059-8  

   Selcuk, Kemal; Bunaiyan, Saleh; Singh, Nihal Sanjay; Sayed, Shehrin; Ganguly, Samiran; Finocchio, Giovanni; Datta, Supriyo; Camsari, Kerem Y (December 2024, npj Spintronics)

   Abstract An emerging paradigm in modern electronics is that of CMOS+$${\mathsf{X}}$$ $X$requiring the integration of standard CMOS technology with novel materials and technologies denoted by$${\mathsf{X}}$$ $X$. In this context, a crucial challenge is to develop accurate circuit models for$${\mathsf{X}}$$ $X$that are compatible with standard models for CMOS-based circuits and systems. In this perspective, we present physics-based, experimentally benchmarked modular circuit models that can be used to evaluate a class of CMOS+$${\mathsf{X}}$$ $X$systems, where$${\mathsf{X}}$$ $X$denotes magnetic and spintronic materials and phenomena. This class of materials is particularly challenging because they go beyond conventional charge-based phenomena and involve the spin degree of freedom which involves non-trivial quantum effects. Starting from density matrices—the central quantity in quantum transport—using well-defined approximations, it is possible to obtain spin-circuits that generalize ordinary circuit theory to 4-component currents and voltages (1 for charge and 3 for spin). With step-by-step examples that progressively become more complex, we illustrate how the spin-circuit approach can be used to start from the physics of magnetism and spintronics to enable accurate system-level evaluations. We believe the core approach can be extended to include other quantum degrees of freedom like valley and pseudospins starting from corresponding density matrices. 

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3. Leveraging Hamiltonian simulation techniques to compile operations on bosonic devices

   https://doi.org/10.1088/1751-8121/adb5df  

   Kang, Christopher; Soley, Micheline B; Crane, Eleanor; Girvin, Steven M; Wiebe, Nathan (April 2025, Journal of Physics A: Mathematical and Theoretical)

   Abstract Circuit quantum electrodynamics enables the combined use of qubits and oscillator modes. Despite a variety of available gate sets, many hybrid qubit-boson (i.e. qubit-oscillator) operations are realizable only through optimal control theory, which is oftentimes intractable and uninterpretable. We introduce an analytic approach with rigorously proven error bounds for realizing specific classes of operations via two matrix product formulas commonly used in Hamiltonian simulation, the Lie–Trotter–Suzuki and Baker–Campbell–Hausdorff product formulas. We show how this technique can be used to realize a number of operations of interest, including polynomials of annihilation and creation operators, namely $\left(a{)}^p\right(a^{†}{)}^q$for integer $p,q$. We show examples of this paradigm including obtaining universal control within a subspace of the entire Fock space of an oscillator, state preparation of a fixed photon number in the cavity, simulation of the Jaynes–Cummings Hamiltonian, and simulation of the Hong-Ou-Mandel effect. This work demonstrates how techniques from Hamiltonian simulation can be applied to better control hybrid qubit-boson devices. 

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4. Planar chemical reaction systems with algebraic and non-algebraic limit cycles

   https://doi.org/10.1007/s00285-025-02221-0  

   Craciun, Gheorghe; Erban, Radek (May 2025, Journal of Mathematical Biology)

   Abstract The Hilbert numberH(n) is defined as the maximum number of limit cycles of a planar autonomous system of ordinary differential equations (ODEs) with right-hand sides containing polynomials of degree at most$$n \in {{\mathbb {N}}}$$ $n\in N$. The dynamics of chemical reaction systems with two chemical species can be (under mass-action kinetics) described by such planar autonomous ODEs, wherenis equal to the maximum order of the chemical reactions in the system. Analogues of the Hilbert number H(n) for three different classes of chemical reaction systems are investigated: (i) chemical systems with reactions up to then-th order; (ii) systems with up ton-molecular chemical reactions; and (iii) weakly reversible chemical reaction networks. In each case (i), (ii) and (iii), the question on the number of limit cycles is considered. Lower bounds on the modified Hilbert numbers are provided for both algebraic and non-algebraic limit cycles. Furthermore, given a general algebraic curve$$h(x,y)=0$$ $h(x,y)=0$of degree$$n_h \in {{\mathbb {N}}}$$ $n_h\in N$and containing one or more ovals in the positive quadrant, a chemical system is constructed which has the oval(s) as its stable algebraic limit cycle(s). The ODEs describing the dynamics of the constructed chemical system contain polynomials of degree at most$$n=2\,n_h+1.$$ $n=2n_h+1.$Considering$$n_h \ge 4,$$ $n_h\ge 4,$the algebraic curve$$h(x,y)=0$$ $h(x,y)=0$can contain multiple closed components with the maximum number of ovals given by Harnack’s curve theorem as$$1+(n_h-1)(n_h-2)/2$$ $1+(n_h-1)(n_h-2)/2$, which is equal to 4 for$$n_h=4.$$ $n_h=4.$Algebraic curve$$h(x,y)=0$$ $h(x,y)=0$with$$n_h=4$$ $n_h=4$and the maximum number of four ovals is used to construct a chemical system which has four stable algebraic limit cycles. 

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5. Statistical (n,$$\gamma $$) cross section model comparison for short-lived nuclei

   https://doi.org/10.1140/epja/s10050-023-00920-0  

   Lewis, R.; Couture, A.; Liddick, S. N.; Spyrou, A.; Bleuel, D. L.; Campo, L. Crespo; Crider, B. P.; Dombos, A. C.; Guttormsen, M.; Kawano, T.; et al (March 2023, The European Physical Journal A)

   Abstract Neutron-capture cross sections of neutron-rich nuclei are calculated using a Hauser–Feshbach model when direct experimental cross sections cannot be obtained. A number of codes to perform these calculations exist, and each makes different assumptions about the underlying nuclear physics. We investigated the systematic uncertainty associated with the choice of Hauser-Feshbach code used to calculate the neutron-capture cross section of a short-lived nucleus. The neutron-capture cross section for$$^{73}\hbox {Zn}$$ ${}^{73}\text{Zn}$(n,$$\gamma $$ $\gamma$)$$^{74}\hbox {Zn}$$ ${}^{74}\text{Zn}$was calculated using three Hauser-Feshbach statistical model codes: TALYS, CoH, and EMPIRE. The calculation was first performed without any changes to the default settings in each code. Then an experimentally obtained nuclear level density (NLD) and$$\gamma $$ $\gamma$-ray strength function ($$\gamma \hbox {SF}$$ $\gamma \text{SF}$) were included. Finally, the nuclear structure information was made consistent across the codes. The neutron-capture cross sections obtained from the three codes are in good agreement after including the experimentally obtained NLD and$$\gamma \hbox {SF}$$ $\gamma \text{SF}$, accounting for differences in the underlying nuclear reaction models, and enforcing consistent approximations for unknown nuclear data. It is possible to use consistent inputs and nuclear physics to reduce the differences in the calculated neutron-capture cross section from different Hauser-Feshbach codes. However, ensuring the treatment of the input of experimental data and other nuclear physics are similar across multiple codes requires a careful investigation. For this reason, more complete documentation of the inputs and physics chosen is important. 

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