arXiv subjects

Yuto Watanabe

Publications and source records attributed to Yuto Watanabe.

At least 19 recordsLinked to original sources

arXiv2026

Weak Convexity and Proximal Bundle Methods for Nonsmooth Policy Optimization in Robust Control

We study policy optimization for discrete-time robust $\mathcal{H}_\infty$ control with static output-feedback, and present the first feasibility-preserving algorithm with a deterministic, non-asymptotic complexity guarantee. This problem naturally leads to a nonsmooth and nonconvex optimization over the set of stabilizing feedback gains. We first establish several structural properties of the $\mathcal{H}_\infty$ cost. In particular, we show that the cost is weakly convex on every convex subset of a sublevel set. For the state-feedback case, we further establish a weak Polyak--{\L}ojasiewicz inequality, which ensures that every stationary point is globally optimal. Building on these properties, we develop a proximal bundle method for $\mathcal{H}_\infty$ policy optimization. The proposed method can be viewed as an implementable approximation of the proximal point method and uses only function value and subgradient information. We show that all iterates remain stabilizing and establish a deterministic non-asymptotic complexity bound of $\mathcal{O}(\max\{\eta^{-4},\epsilon^{-2}\})$ for finding an $(\eta,\epsilon)$-stationary point. Numerical experiments illustrate our theoretical results.

math.OC↗

arXiv2026

Observation of giant nonvolatile magneto-thermal switching in superconductor-ferromagnet hybrids

Magneto-thermal switch is a crucial thermal component which enables heat transfer control by the application of an external magnetic field. Recently, a nonvolatile behavior in magneto-thermal conductivity at zero magnetic field was observed in type-II and phase-separated superconductors owing to magnetic flux pinning nature, leading to an energy-efficient thermal control technology. However, the nonvolatile magneto-thermal switching ratio has been much lower than the volatile one in conventional materials. Here, we demonstrate a giant nonvolatile magneto-thermal switching in ferromagnetic Fe-superconducting Pb hybrids. The dispersion of pure Fe particles realizes increased electron and decreased phonon contributions in the thermal conductivity, which enhances the magneto-thermal switching ratio at the superconducting-to-normal conducting phase transition. Furthermore, in concert with trapped magnetic flux by supercurrent, ferromagnetic moment of Fe breaks the superconductivity of Pb matrix at zero magnetic field, enabling a significantly large nonvolatility even with a slight amount of Fe inclusions. Consequently, the nonvolatile magneto-thermal switching ratio reaches 719% in maximum at the Fe ratio of 8.7 vol%, which is more than twice the previous record value observed in Pb-Sn composites and the volatile one in pure Pb. This work broadens the exploration space and strategy for giant nonvolatile magneto-thermal switching materials.

cond-mat.supr-con↗

arXiv2026

Distinct Roles of Hydrogen in Superconducting and Ferromagnetic Phases of CoZr$_{2}$H$_{x}$

Hydrogenation offers a versatile route to tuning the physical properties of intermetallic compounds. In this study, we synthesized CoZr$_{2}$H$_{x}$ with different hydrogen contents and found that hydrogen is incorporated in two distinct concentration regimes separated by a wide composition gap: a low-concentration hydrogenated superconducting phase ($x$ = 0-0.054) and a high-concentration hydrogenated ferromagnetic phase ($x$ = 2.786). Hydrogen plays fundamentally different roles in the two concentration regimes. In the high hydrogen concentration phase, the Zr-H interactions substantially modify the metallic bands crossing the Fermi level, leading to the emergence of ferromagnetism. In contrast, in the low hydrogen concentration phase, hydrogen behaves as a nonmagnetic impurity without altering the electronic band structure. Despite the nearly identical Debye temperatures across the low-concentration series, the superconducting transition temperature ($T_{\mathrm{c}}$) is progressively suppressed with increasing hydrogen content.The observed $T_{\mathrm{c}}$ suppression is quantitatively described by the Abrikosov-Gor'kov pair-breaking theory, indicating that the superconducting gap of CoZr$_{2}$ is anisotropic or multigap rather than a fully isotropic $s$-wave symmetry.

cond-mat.supr-con↗

arXiv2026

On the Strong Duality in Continuous-time and Discrete-time Linear Quadratic Regulators

This paper revisits the strong duality in the linear quadratic regulator (LQR) for continuous-time and discrete-time systems, and explores its interconnection with typical assumptions and the uniqueness of primal-dual solutions. Using a linear operator $\Psi$, we formulate a common nonconvex LQR problem that captures both time domains. We then derive its Lagrange dual problem and establish the strong duality via a rank-constrained tight semidefinite program (SDP) relaxation. Further, we show that the primal-dual optimal solutions to the SDP relaxation, after dropping the rank constraint, recover the classical algebraic Riccati equations and optimal feedback gains in a constructive manner. The dual derivation and strong duality analysis rely on mild standard assumptions and exploit the properties of the linear operator and its adjoint, revealing a structural symmetry between the two time domains.

math.OC↗

arXiv2026

Revealing nonvolatile behaviors in magneto-thermal switching using microstructure-controlled superconducting composites

Thermal conductivity in a conductor changes by the application of an external magnetic field, which functions as a magneto-thermal switch. For superconductors, a large magneto-thermal switching can occur through a superconducting-to-normal conducting phase transition due to the change in the electron contribution in thermal conductivity. Arima et al. recently reported a nonvolatile nature of the magneto-thermal switching for superconducting solders, which consist of phase-separated Sn and Pb domains. Although they clarified that magnetic flux trapping is required to induce the nonvolatile magneto-thermal switching, a rule for such material design is still unclear. Here, we investigate the microstructure dependence of magneto-thermal switching in superconducting Sn/Pb multilayered composites, which are created by an accumulative roll bonding method. The thickness of each layer, that is the scale of microstructure, can be systematically controlled by the repetition number of roll bonding while the whole sample size and average composition are unchanged. We find that, as the formation of micro-scaled Sn domains proceeds by increasing the repetition number, a nonvolatility in the magneto-thermal conductivity gradually appears in correlation with the remanent magnetization. This study directly confirms that the inclusions with a size comparable to or less than the magnetic vortex in superconducting matrix is essential for magnetic flux trapping, enabling the nonvolatile magneto-thermal switching in superconducting composites.

cond-mat.supr-con↗

arXiv2026

Policy Optimization of Mixed H2/H-infinity Control: Benign Nonconvexity and Global Optimality

Mixed H2/H-infinity control balances performance and robustness by minimizing an H2 cost bound subject to an H-infinity constraint. However, classical Riccati/LMI solutions offer limited insight into the nonconvex optimization landscape and do not readily scale to large-scale or data-driven settings. In this paper, we revisit mixed H2/H-infinity control from a modern policy optimization viewpoint, including the general two-channel and single-channel cases. One central result is that both cases enjoy a benign nonconvex structure: every stationary point is globally optimal. We characterize the H-infinity-constrained feasible set, which is open, path-connected, with boundary given exactly by policies saturating the H-infinity constraint. We also show that the mixed objective is real analytic in the interior with explicit gradient formulas. Our key analysis builds on an Extended Convex Lifting (ECL) framework that bridges nonconvex policy optimization and convex reformulations. The ECL constructions rely on non-strict Riccati inequalities that allow us to characterize global optimality. These insights reveal hidden convexity in mixed H2/H-infinity control and facilitate the design of scalable policy iteration methods in large-scale settings.

math.OC↗

arXiv2026

Gradient Dominance in the Linear Quadratic Regulator: A Unified Analysis for Continuous-Time and Discrete-Time Systems

Despite its nonconvexity, policy optimization for the Linear Quadratic Regulator (LQR) admits a favorable structural property known as gradient dominance, which facilitates linear convergence of policy gradient methods to the globally optimal gain. While gradient dominance has been extensively studied, continuous-time and discrete-time LQRs have largely been analyzed separately, relying on slightly different assumptions, proof strategies, and resulting guarantees. In this paper, we present a unified gradient dominance property for both continuous-time and discrete-time LQRs under mild stabilizability and detectability assumptions. Our analysis is based on a convex reformulation derived from a common Lyapunov inequality representation and a unified change-of-variables procedure. This convex-lifting perspective yields a single proof framework applicable to both time models. The unified treatment clarifies how differences between continuous-time and discrete-time dynamics influence theoretical guarantees and reveals a deeper structural symmetry between the two formulations. Numerical examples illustrate and support the theoretical findings.

math.OC↗

arXiv2026

Enhanced $T_\mathrm{c}$ in eutectic high-entropy alloy superconductors Hf-Nb-Sc-Ti-Zr

The present investigation into the superconducting properties of eutectic high-entropy alloy (HEA) Hf-Nb-Sc-Ti-Zr systems reveals an enhanced superconducting critical temperature ($T_\mathrm{c}$) in body-centered cubic (bcc) phases compared to typical quinary bcc HEAs. In Hf$_{10}$Nb$_{25}$Sc$_{25}$Ti$_{20}$Zr$_{20}$, Hf$_{5}$Nb$_{45}$Sc$_{20}$Ti$_{15}$Zr$_{15}$, and Hf$_{5}$Nb$_{45}$Sc$_{10}$Ti$_{5}$Zr$_{35}$ systems, which span a broad range of valence electron concentration per atom, lattice strain and the presence of partial or absent eutectic phases are characteristic features at lower annealing temperatures. The eutectic regions expand rapidly following annealing at 600$^{\circ}$C in all systems. The $T_\mathrm{c}$ of each system increases markedly with rising annealing temperatures from 400$^{\circ}$C to 600$^{\circ}$C, reaching a maximum value of 9.93 K in the Hf$_{5}$Nb$_{45}$Sc$_{10}$Ti$_{5}$Zr$_{35}$ sample annealed at 800$^{\circ}$C. Nearly all samples can be classified as strong-coupling superconductors. The sample annealed at 500$^{\circ}$C in the Hf$_{5}$Nb$_{45}$Sc$_{10}$Ti$_{5}$Zr$_{35}$ system exhibits a critical current density ($J_\mathrm{c}$) exceeding the practical threshold of 10$^{5}$ A/cm$^{2}$ up to approximately 4 T at 4.2 K and 6 T at 2 K. The elevated $J_\mathrm{c}$ is attributed to significant lattice strain and phase instability. The underlying mechanism for the enhanced $T_\mathrm{c}$ in Hf-Nb-Sc-Ti-Zr systems is examined through specific heat data analysis, suggesting that the expansion of the eutectic regions induced by thermal annealing plays a pivotal role.

cond-mat.supr-con↗

arXiv2026

Insight into high-entropy effect in body-centered cubic superconducting alloys

We have characterized the superconducting critical temperature ($T_\mathrm{c}$), the Debye temperature ($\theta_\mathrm{D}$), the electronic specific heat coefficient, and the Vickers microhardness of HfNbTiVZr, NbTiZr, HfNbTi, HfNbZr, and HfNbTa, all possessing a body-centered cubic (bcc) structure. By compiling a comparable dataset for other equiatomic quinary bcc high-entropy alloy (HEA) superconductors, we have examined the validity of the hypothesis regarding the high-entropy effect in bcc HEA superconductors, as proposed in our previous work. This hypothesis attributes the observed negative correlation between the electron-phonon coupling constant ($\lambda_\mathrm{e-p}$) and $\theta_\mathrm{D}$ to a reduced phonon lifetime at higher $\theta_\mathrm{D}$, arising from the uncertainty principle in highly disordered quinary alloys. However, a pronounced change in this negative correlation is not evident in equiatomic ternary alloys with a lower degree of atomic disorder, thereby providing limited support for the hypothesis. Alternatively, by assembling the full dataset of bcc alloys spanning binary through senary systems, we have identified a universal negative correlation between $\lambda_\mathrm{e-p}$ and $\theta_{D}$. This result would be useful for the materials design of bcc superconducting alloys. We further propose that the Vickers microhardness offers an alternative means to evaluate $\theta_{D}$ and may serve as a rapid screening metric for identifying bcc alloys with desired properties.

cond-mat.supr-con↗

arXiv2025

Policy Optimization in Robust Control: Weak Convexity and Subgradient Methods

Robust control seeks stabilizing policies that perform reliably under adversarial disturbances, with $\mathcal{H}_\infty$ control as a classical formulation. It is known that policy optimization of robust $\mathcal{H}_\infty$ control naturally lead to nonsmooth and nonconvex problems. This paper builds on recent advances in nonsmooth optimization to analyze discrete-time static output-feedback $\mathcal{H}_\infty$ control. We show that the $\mathcal{H}_\infty$ cost is weakly convex over any convex subset of a sublevel set. This structural property allows us to establish the first non-asymptotic deterministic convergence rate for the subgradient method under suitable assumptions. In addition, we prove a weak Polyak-{\L}ojasiewicz (PL) inequality in the state-feedback case, implying that all stationary points are globally optimal. We finally present a few numerical examples to validate the theoretical results.

math.OC↗

arXiv2025

Uniaxial negative thermal expansion in a weak-itinerant-ferromagnetic phase of CoZr$_{2}$H$_{3.49}$

We discovered unique uniaxial negative thermal expansion (NTE) behavior for a weak-itinerant-ferromagnetic phase of CoZr$_{2}$H$_{3.49}$. CoZr$_{2}$ is known as a superconductor exhibiting uniaxial NTE along the $c$-axis, which is called anomalous thermal expansion (ATE). Additionally, CoZr$_{2}$ is also known as a well-absorbent of hydrogen, and hydrogen insertion raises weak-itinerant ferromagnetism instead of superconductivity. However, the influence of hydrogen insertion on ATE behavior in this system is still unclear. To investigate it, we performed powder synchrotron X-ray diffraction (SXRD) for CoZr$_{2}$H$_{3.49}$. Through Arrott plots analysis, we determined the Curie temperature ($T_{\mathrm{C}}$) to be 139 K, and the Rhodes-Wohlfarth ratio was estimated to be 3.49, which clearly exceeds 1, suggesting the itinerancy of emerging ferromagnetism. Temperature dependencies of lattice constants $a$ and $c$ were extracted from powder SXRD analyses, and we revealed that lattice constant $c$ exhibited NTE behavior below $T_{\mathrm{C}}$. The uniaxial NTE behavior along the $c$-axis can be understood by sharpening an antibonding Co3$dz^{2}$ partial density of states near the Fermi level, linked to the expansion of a one-dimensional Co-Co chain running parallel to the $c$-axis.

cond-mat.mtrl-sci↗

arXiv2025

Thermal rectification in jointless Pb solid wire

Thermal rectification is observed in jointless Pb wires at temperatures near the superconducting transition of Pb under magnetic fields. Using different magnetic-field (H) response of temperature dependence of thermal conductivity (\k{appa}-T) under H parallel to J and H perpendicular to J where J is heat flow, we fabricated a jointless thermal diode. Thermal rectification is observed with the thermal rectification ratio (TRR) of 1.5 and the difference in \k{appa} of 330 W m-1 K-1 at T = 5.11 K under H = 400 Oe for a Pb wire with a 50%-bent (H perpendicular to J) and 50%-straight (H parallel to J) structure. The peak temperature of TRR can be tuned by the strength of applied magnetic field. By changing bent ratio to 40%-bent, a higher TRR exceeding 2 was observed. The Pb-jointless thermal diode will be a useful material for thermal management at cryogenic temperatures.

cond-mat.supr-con↗

arXiv2025

Huge anisotropic magneto-thermal switching in high-purity polycrystalline compensated metals

Magneto-thermal transport is a promising physical property for thermal management applications. Magneto-thermal switching enables active control of heat flows, and a high switching ratio is desirable for improving performance. Here, we report on the observation of a huge magneto-thermal switching (MTS) effect in high-purity (5N) Pb polycrystalline wires, where magnetic fields perpendicular to the heat current direction are applied at low temperatures. At T = 3 K and B = 0.1 T, the measured thermal conductivity (\k{appa}) of the Pb wire is about 2500 W m-1 K-1 but is reduced to ~150 and ~5 W m-1 K-1 at B = 1 and 9 T, respectively. This strong suppression is attributed to magnetoresistance in compensated metals. Although the huge magnetoresistance has been studied in single crystals with field along the selected orbitals, our results demonstrate that a huge MTS can similarly be realized even in flexible polycrystalline wires. This finding highlights the practical potential of magneto-thermal control in low-temperature thermal management, including applications in space environments where temperatures are around 3 K.

cond-mat.mtrl-sci↗

arXiv2025

Semidefinite Programming Duality in Infinite-Horizon Linear Quadratic Differential Games

Semidefinite programs (SDPs) play a crucial role in control theory, traditionally as a computational tool. Beyond computation, the duality theory in convex optimization also provides valuable analytical insights and new proofs of classical results in control. In this work, we extend this analytical use of SDPs to study the infinite-horizon linear-quadratic (LQ) differential game in continuous time. Under standard assumptions, we introduce a new SDP-based primal-dual approach to establish the saddle point characterized by linear static policies in LQ games. For this, we leverage the Gramian representation technique, which elegantly transforms linear quadratic control problems into tractable convex programs. We also extend this duality-based proof to the $\mathcal{H}_\infty$ suboptimal control problem. To our knowledge, this work provides the first primal-dual analysis using Gramian representations for the LQ game and $\mathcal{H}_\infty$ control beyond LQ optimal control and $\mathcal{H}_\infty$ analysis.

math.OC↗

arXiv2025

Revisiting Strong Duality, Hidden Convexity, and Gradient Dominance in the Linear Quadratic Regulator

The Linear Quadratic Regulator (LQR) is a cornerstone of optimal control theory, widely studied in both model-based and model-free approaches. Despite its well-established nature, certain foundational aspects remain subtle. In this paper, we revisit three key properties of policy optimization in LQR: (i) strong duality in the nonconvex policy optimization formulation, (ii) the gradient dominance property, examining when it holds and when it fails, and (iii) the global optimality of linear static policies. Using primal-dual analysis and convex reformulation, we refine and clarify existing results by leveraging Riccati equations/inequalities, semidefinite programming (SDP) duality, and a recent framework of Extended Convex Lifting (\texttt{ECL}). Our analysis confirms that LQR 1) behaves almost like a convex problem (e.g., strong duality) under the standard assumptions of stabilizability and detectability and 2) exhibits strong convexity-like properties (e.g., gradient dominance) under slightly stronger conditions. In particular, we establish a broader characterization under which gradient dominance holds using \texttt{ECL} and the notion of Cauchy directions. By clarifying and refining these theoretical insights, we hope this work contributes to a deeper understanding of LQR and may inspire further developments beyond LQR.

math.OC↗

arXiv2025

Stark difference in the in-plane anomalous Hall response in Zintl compounds EuA2Sb2 (A = Zn, Cd) thin films

Recent observation of the in-plane anomalous Hall effect in magnetic Weyl semimetal EuCd2Sb2 has drawn attention to out-of-plane orbital magnetization induced by an in-plane field component. Here we study EuZn2Sb2, a sister compound of EuCd2Sb2, to demonstrate sensitive changes of the in-plane anomalous Hall effect on the band modulation. The Hall resistivity measured with rotating the magnetic field within the (001) principal plane of EuZn2Sb2 films exhibits a clear three-fold component corresponding to the in-plane anomalous Hall effect, which is distinct from the two-fold component of the planar Hall effect. The in-plane anomalous Hall effect of EuZn2Sb2 is highly contrasting to EuCd2Sb2, especially in terms of its opposite sign and field dependence, which can be explained by model calculations with different band inversion parameters. Our results pave the way for systematically controlling the in-plane anomalous Hall effect and orbital magnetization through elaborate band engineering.

cond-mat.mtrl-sci↗

arXiv2024

Distinct topological Hall responses in CeCu$_2$-type EuZn$_2$ and EuCd$_2$ films

Rare earth intermetallic compounds crystallized in AlB$_2$-type and its low-symmetry derivative CeCu$_2$-type structures potentially host diverse frustrated magnetic structures and rich magnetotransport phenomena. We report the film growth of CeCu$_2$-type EuZn$_2$ by molecular beam epitaxy and the observation of topological Hall responses highly contrastive to isostructural EuCd$_2$. While their magnetization curves are rather similar, the topological Hall effect observed in EuZn$_2$ is simpler, with the only one component enhanced at the magnetic transition field. EuZn$_2$ may be a unique system for studying the magnetic domain boundary effect on topological Hall responses among the CeCu$_2$-type rare-earth intermetallic compounds.

cond-mat.mtrl-sci↗

arXiv2024

Investigation of superconducting gap of high-entropy telluride AgInSnPbBiTe5

We performed transverse-field muon spin relaxation/rotation (TF-{\mu}SR) on a high-entropy-type (HE-type) superconductor AgInSnPbBiTe5. The emergence of bulk superconducting states was confirmed from magnetic susceptibility, specific heat, and {\mu}SR. The superconducting gap 2{\Delta}(0) estimated from {\mu}SR was clearly larger than that expected from conventional weak-coupling phonon-mediated model, suggesting the strong-coupling nature of superconductivity. In addition, a long penetration depth of 3.21(7) {\mu}m was obtained. The strong-coupling nature of superconductivity and the long penetration depth are similar to the trends observed in the other HE-type superconductors (HE alloys and transition-metal zirconides), which may be universal feature of HE-type superconductors.

cond-mat.supr-con↗