Papers

A system evolving unitarily does not dephase or thermalize by definition. Yet, if one considers a part of a unitary system, situation is different. Here we analyze an isolated set of coupled qubits taking one qubit at a time as a subsystem, and writing self-consistently a weak-coupling master equation for it. Weakly anharmonic oscillators and ideal qubits (two-level systems) demonstrate dephasing, i.e. the diagonal elements of the density matrix reach a steady-state in the long-time limit, and the off-diagonal elements of ideal qubits decay exponentially. For the linear coupling between the qubits, only the degenerate ones interact, and the system does not reach thermal distribution. However, non-linearity, in our analysis in form of three-wave mixing, ensures a thermal distribution in the long time limit, where the temperature is determined uniquely by the energy in the initial non-thermal state. Finally, we present a potential experimental scheme based on a superconducting quantum circuit.

We report the structural and optical properties of nanoscale Sr2IrO4 freestanding thin-films fabricated using a water-soluble Sr3Al2O6 layer. The coherent lattice structure, phonon modes, two-magnon Raman scattering, and optical absorption spectra of the Sr2IrO4 nanomembrane are analogous to those of the layered iridate epitaxial thin-films and single crystals. Remarkably, the formation of 3-unit-cell-thick SrIrO3 and interfacial composite layers alleviates antiphase boundaries at the Sr2IrO4/Sr3Al2O6 interface, resulting in structurally-robust nanomembranes. Our experimental results show that this freestanding thin-film approach of layered oxides can provide techniques for tuning or realizing unprecedented states beyond conventional thin-film methods, suggesting a pathway in achieving flexible layered-oxide electronics.

Barium zirconate titanate, Ba(Zr$_x$Ti$_{1-x}$)O$_3$ (BZT), is a leading lead-free candidate for high-performance electronic components due to its highly tunable ferroelectric-to-relaxor transition. In this study, we employ molecular dynamics simulations to investigate the effects of local chemical clustering on the structural and functional properties of BZT in both ferroelectric (x = 0.2) and relaxor (x = 0.4) regimes. Crucially, we demonstrate that Zr clustering induces a significant enhancement of local polarization across both compositions. Rather than a purely volume-driven effect, this enhancement is fundamentally governed by a spatial redistribution of local structural phases (rhombohedral, orthorhombic, and tetragonal); Zr segregation forms larger, continuous Ti-rich regions that expand highly polar rhombohedral domains and foster cooperative dipolar alignment. This cooperative coupling thermally stabilizes the local polar order, systematically elevating the Curie, maximum permittivity, and Burns temperatures. Focusing on the relaxor composition (x = 0.4), chemical segregation promotes the formation of resilient, swirling polar topological textures,categorized into vortices circulating around Zr-rich clusters and interstitial vortices localized within the Ti-rich matrix. These topological structures act as effective pinning barriers against polarization reversal, driving pronounced electrical hardening with elevated coercive fields. Ultimately, these findings establish a quantitative link between nanoscale compositional heterogeneity, polar domain topology, and macroscopic performance, providing a robust framework for engineering lead-free perovskites via local chemical order control.

We investigate the proximity-induced spin-orbit coupling (SOC) in graphene on transition-metal dichalcogenide (TMD) heterostructures using a tight-binding approach. The tight-binding parameters of an effective 4-band model describing the low-energy physics of the graphene layer are extracted as a function of twist angle, material composition (MoS${}_2$, MoSe${}_2$, WS${}_2$, WSe${}_2$), band alignment, and charge-transfer dipole. We investigate the effect of a charge-transfer dipole induced on the chalcogen layer closest to graphene, which is typically neglected in tight-binding models but included in ab initio calculations through charge redistribution. In addition, we explore the influence of variations in the band alignment. We find that the spin-valley and Rashba spin-orbit coupling energies as well as the so-called Rashba phase, governing the orientation of momentum-space spin textures, show a strong dependence on the twist angle and electrostatic tuning. Our results suggest that variations in band alignment and charge redistribution contribute to the spread of spin-orbit parameters reported in the literature.

In this work we analyze correlations of X-ray photoelectron and diffraction spectra, and dielectric properties of hafnia-zirconia nanoparticles (the chemical compositions Hf0.4Zr0.6O2 and Hf0.6Zr0.4O2, and the average size of 7.5 nm) prepared by the solid-state organo-nitrate synthesis and annealed in air. The phase state of the nanoparticles, determined by the X-ray diffraction spectroscopy, is the coexistence of the nonpolar monoclinic (42 - 76 mass %) and orthorhombic (56 - 24 mass %) phases. Concentration of the oxygen vacancies was estimated from the X-ray photoelectron spectroscopy. The increase in the intensity of the dielectric permittivity maximum observed near 350 - 450 K in a PVDF matrix with embedded Hf0.4Zr0.6O2 nanoparticles can be related with an increase in oxygen vacancy concentration. Theoretical calculations, based on Landau-Ginzburg-Devonshire theory, explain the increase of the dielectric permittivity in Hf0.4Zr0.6O2 nanoparticles compared to Hf0.6Zr0.4O2 nanoparticles.

Transforming textile fibres into sensors can facilitate continuous physiological monitoring for improving human healthcare. Coating fibres with electronic conductors can help detect physiological stimuli but their sensitivity scales with thickness and often lowers the fibre mechanical flexibility. Proton conductors are potential alternatives; however, they suffer from fragile physical interfaces, and sluggish kinetics. Here, we report a bio-templated, scalable strategy to create superprotonic interfaces using natural silk fibres. We exploit ordered nanofibrils on silk fibres to selectively grow continuous metal-organic framework (MOF) nanostrips. This patterned, ca. $10\,\mu\mathrm{m}$-diameter fibre-structure provides low-defect interfacial pathways for ultrafast proton transport, yielding conductivities up to 40 $S\,cm^{-1}$ - two orders of magnitude above the state of the art - with millisecond response and high mechanical robustness. The individual micro-thread sensors facilitate respiratory monitoring with a mean bias of 0.01 breaths $min^{-1}$ in volunteer testing, unaffected by human movement and readily capture breathing signature in high-flow oxygen therapy devices. We integrate arrays of micro-thread sensors in textiles and exploit deep learning to demonstrate high-resolution spatiotemporal humidity mapping in dynamic flow-fields and resolve asymmetric respiratory patterns that elude conventional single-point detectors. Our results should have broad-ranging implications, e.g. in wearable health monitoring, bioelectronics, and human-machine interfaces.

Spin-orbit-coupled $d^1$ double perovskites exhibit a rich interplay of spin, orbital, and quadrupolar degrees of freedom (DOF), giving rise to competing magnetic and multipolar phases. Although quantum mean-field theories predict many exotic phases, their stability against thermal fluctuations and reproducibility within a classical framework remain an open question. Here, we surpass the mean-field limitations by deploying large-scale classical Monte Carlo simulations on the projected $j=3/2$ manifold of the FCC lattice, allowing complex ordering patterns to emerge spontaneously without preassigned magnetic symmetries. Our thermodynamic mapping reveals that thermal fluctuations melt the intermediate-temperature quadrupolar phase over part of the phase diagram, while it survives intact elsewhere. Crucially, by systematically isolating the boundary between classical and quantum stability, we demonstrate that while the four-sublattice antiferromagnetic and ferromagnetic (FM) phases are robustly classical, the coplanar canted FM[110] state completely destabilizes. This identifies the FM[110] phase as an intrinsically quantum state born out of quantum fluctuations. Our results demonstrate that the dominant magnetic phases are robust within a classical description, where the essential physics of the system is captured by weakly entangled, short-range correlated DOF and highlight the role of thermal fluctuations in determining the stability of different types of magnetic and quadrupolar order.

We apply a finite-state geometric formulation based on Bargmann invariants to a two-band Weyl Hamiltonian and the one-dimensional Kitaev model of a p-wave superconductor. For the Weyl system, a symmetry-antisymmetrized third-order Bargmann combination selects the chirality-sensitive component of the local pseudospin geometry and extends to a two-band lattice Weyl model. For the Kitaev chain, a normalized ratio involving a third-order Bargmann invariant and a second-order overlap factor removes the dependence on an intermediate state and reproduces the $Z_2$ distinction between its two gapped phases. We further construct a fourth-order loop connecting localized Majorana edge-mode profiles with finite-energy BdG states and an alternating fourth-order loop involving opposite Weyl pseudospin sectors. These constructions illustrate how suitable Bargmann combinations can probe chirality-sensitive, topological, and higher-order geometric information directly through quantum-state overlaps, providing an alternative state-based route without requiring a continuous description of the underlying state-space geometry.

Inspired by the recent progress in the simulation of tight-binding Hamiltonians on large lattices using tensor networks, we introduce a systematic matrix product operator (MPO) construction for single-particle Hamiltonians on recursively structured lattices. Taking advantage of this recursive structure, we encode the lattice geometry in a finite-state automaton and, adapting ideas from Abelian-symmetric tensor networks, obtain an exact and analytical MPO representation of the Hamiltonian, where the number of tensors grows logarithmically with the system size and the bond dimension is set by the number of automaton states. Several examples demonstrate the generality of the framework: regular lattices, fractals, Cayley trees, hyperbolic lattices, and one- and two-dimensional Fibonacci quasicrystals. Combined with the kernel polynomial method, these MPO representations enable large-scale calculations of spectral properties without explicitly constructing the full Hamiltonian. This provides a unified route to the exploration of electronic properties across a broad class of lattices at exponentially large system sizes.

Iontronic devices that replicate physiological processes will improve energy efficiency to support artificial-intelligence architectures. Energy storage and conversion devices, however, display disordered interfacial and bulk configurations that conventional impedance spectroscopy cannot resolve. Here, we show that the onset of frequency dispersion in the impedance of an electrolytic cell with non-uniformly charged electrodes takes place at approximately twice the resonator natural frequency, independently of whether the cell is driven by oscillating charges or voltage differences, and remains valid for both overlapping and non-overlapping double layers. In addition to characterizing energy storage devices, these universal findings apply to devices interfaced with biomaterials.

Generally the mobility in the Cahn-Hilliard equation may depend on the order parameter; this was evident already from the original derivation. However, explicit introduction of such dependence results in tremendous calculation difficulties, so the constant mobility approximation was commonly used. On the other hand, in several cases this dependence appeared to be crucial, so more realistic expressions were applied, usually positive powers or polynomials; still, for such dependencies only approximate and/or numerical solution exist. We consider 'reciprocal' linear and quadratic dependencies of mobility on the order parameter; for these dependencies exact traveling wave solutions are obtained. Even more, in a limited interval of the parameters reciprocal quadratic mobilities are rather good approximations to polynomial mobilities.

We characterise the approach to nonequilibrium steady state in nested resetting processes by deriving accumulation times for the system, which quantify the effective first-passage time for the local establishment of steady state. For equal resetting rates, we obtain closed-form expressions showing that relaxation propagates as a wavefront with a delay that increases linearly along the resetting chain. We then extend this analysis to heterogeneous resetting rates, deriving exact steady-state distributions, spatial moments and accumulation times for both degenerate and non-degenerate resetting rates. We show that relaxation to steady state is ultimately governed by the minimum resetting rate in the system and, in degenerate systems, its multiplicity. These results provide a comprehensive analytical description of first-passage to nonequilibrium steady state in hierarchically coupled stochastic resetting systems, with potential applications to relaxation and transport processes in biological systems.

We revisit the long-standing problem of the anyon gas. We study the solvable near-bosonic limit of a large number of anyons $N$ at fixed $N/k$, where $1/k$ characterizes the statistical interaction. In this limit, the ground state is a crystal with order $N/k$ lattice sites. The statistical interactions, mediated by a long-range gauge field, are completely screened within the crystalline phase. The resulting state is a conventional crystal without superfluidity. We characterize this anyon crystal by determining its unit-cell size, ground-state energy, acoustic excitations, angular momentum crossings, and other properties. Our results indicate a quantum phase transition between the crystal at $k>k_c$ and a superfluid at $k<k_c$, with a critical value $k_c\simeq2\text{--}5$. These results imply that an anyon gas with only statistical interactions is not necessarily a superfluid, contrary to common lore. We also present a detailed analysis of the renormalization-group evolution of anyon–anyon interactions, identifying many new potential fixed points and elucidating finite-size effects.

Motivated by two-dimensional bilayer systems we numerically study an anti-ferromagnetic spin-$1/2$ Heisenberg model on the honeycomb lattice with a nearest-neighbour exchange coupling $J_1$, and a next-nearest-neighbour exchange coupling $J_2'$ for the B sublattice sites only. Using infinite Projected Entangled-Pair States (iPEPS), variational uniform matrix-product states on cylinders, and exact diagonalization, we find an extended symmetric regime $0.4\lesssim J'_2/J_1\lesssim0.6$, in which local observables show no magnetic, valence-bond, or chiral spin order. At $J'_2/J_1=0.5$, the PEPS correlation length grows systematically with bond dimension, and an inverse-correlation-length extrapolation favors a vanishing limit. We also find that various observables scale algebraically with the finite bond-dimension-induced correlation length, which points to a gapless spin liquid ground state. We propose a $\mathbb{Z}_2$ Dirac spin liquid parton state, with Dirac points that are protected by translation, time-reversal and three-fold rotation symmetry, as a promising candidate state to explain the numerical results. We also discuss the possibility that the symmetric ground state is a featureless, short-range entangled state with a small gap.

Whether a nonequilibrium quantum-critical steady state can be described by an effective temperature remains an open question. We address it in a voltage-biased electronic Lipkin–Meshkov–Glick model, a minimal driven-dissipative model of a collective spin coupled to metallic leads. A controlled large-$N$ treatment reveals an overdamped open quantum-critical regime distinct from the closed model. The surrounding quantum critical fan, organized by temperature and voltage, is explored and fluctuations are found to be governed by an effective temperature $T_{\rm eff}$. At strong bias, the transition becomes first-order through a tricritical point. Remarkably, the same $T_{\rm eff}$ governs the strongly driven regime, but now varies across the entire order-parameter landscape. The steady state is therefore selected by a non-Boltzmann rule, shifting the first-order transition away from the equal-depth point of a deterministic potential. Driven criticality thus remains organized by an effective temperature while revealing non-thermal state selection.

We introduce and develop Functional Dimensional Regularization (FDR), a novel functional renormalization group (RG) framework that extends the principles of dimensional regularization beyond the perturbative $\varepsilon$-expansion. The key insight is to define the FDR beta functions, valid in any continuous dimension $d$ and characterized by threshold functions, as a sum over all critical dimensions of the corresponding scheme-independent beta functions computed in DR. We demonstrate that this formalism exhibits all the hallmarks of a fully-fledged functional RG. Within the local potential approximation, we perform a general fixed point analysis, recovering the $\varepsilon$-expansion for all multi-critical models and establishing a direct connection to functional scaling solutions, spike plots, and eigen-perturbation spectra. Extending the framework to the second order of the derivative expansion, we compute the critical exponents for the Ising universality class in $d=3$, providing estimates for the anomalous dimension $\eta$ and RG spectrum that converge rapidly and show favorable agreement with state-of-the-art results. We present a detailed comparison with non-perturbative and proper-time RG approaches, highlighting structural similarities and key differences. In particular, we introduce a “distillation” procedure that allows one to systematically derive the FDR flow from any other one-loop-exact RG scheme. Our results establish FDR as a self-contained and competitive RG framework that combines the technical simplicity of dimensional regularization with the versatility of the functional approach.

Nanophotonic cavities provide strong atom-photon coupling in a compact, directly fiber-coupled geometry, while a reconfigurable array of $^{171}$Yb atoms combines high-fidelity gates with a metastable qubit state coupled directly to a telecom-band transition, making the two a natural interface between neutral-atom quantum processors and telecom quantum networks. Here, we realize strong atom-cavity coupling on the ${}^{3}\mathrm{P}_0 \leftrightarrow {}^{3}\mathrm{D}_1$ transition of ${}^{171}\mathrm{Yb}$, establishing, to our knowledge, the first neutral-atom cavity-QED system to reach the single-atom strong-coupling regime on a telecom-band atomic transition. Reflection spectroscopy of a single-sided cavity yields a single-atom internal cooperativity of $C_{\mathrm{in}}=5.6(1.0)$ and collective coupling following $\sqrt{N}$ scaling up to $N=5$ atoms, with homogeneous coupling at antinodes over $\sim$200 $\mathrm{\mu}$m along the nanofiber. Thermal tuning of a fiber Bragg grating provides in situ control of the cavity outcoupling rate over two orders of magnitude from the undercoupled to the overcoupled regime, relevant for various atom-cavity protocols. We confirm compatibility with reconfigurable atom arrays by demonstrating 99.95(6)% imaging fidelity and trap lifetimes comparable to free-space array, at 1 $\mathrm{\mu}$m from the nanofiber axis. Moreover, the diameter-engineered antireflection design of the nanofiber enables tweezer-based atom transport across the nanofiber with no measurable loss or heating at 4.5 $\mathrm{\mu}$m above the nanofiber, supporting a two-layer architecture for the nanofiber-integrated atom array. From the demonstrated atom-cavity coupling, atom capacity, and cavity mode profile, we project time-multiplexed remote atom-atom entanglement generation at 40 kHz, with prospects for further scaling through technical enhancements and channel multiplexing.

Previous studies of network dynamics have suggested that heterogeneity among nodes inhibits stability, at odds with the ubiquity of inherently heterogeneous natural and engineered systems. Here, we show that this conclusion arises from model reductions introduced for mathematical tractability and breaks down when nodal dynamics are higher-dimensional, yielding non-Hermitian Jacobians. In such systems, including neural, power-grid, and material networks, nodal heterogeneity can instead enhance stability, even when parameters are randomly disordered. Non-Hermiticity also underlies the stabilizing effects of network heterogeneity, which can arise even in one-dimensional nodal dynamics through nonreciprocal interactions, as shown for ecological networks. Our framework reveals disorder not as a liability but as a general resource for stabilizing complex systems.

We present a theoretical study of the Rabi and Ramsey coherence time of Majorana-based qubits formed by double $N$-site quantum-dot artificial Kitaev chains, following the recent experimental realization arXiv:2607.09511. We generalize the qubit to two chains of arbitrary length and compare the Rabi and Ramsey oscillations of the four-dot and six-dot qubits, simulated with realistic disorder for three sets of parameters: small and large superconducting gaps, and the experimental parameters. We find that, in the pristine limit, the Rabi oscillation is independent of the chain length, whereas the Ramsey oscillation of the six-dot qubit suffers from larger leakage, because the third site suppresses the unwanted energy splitting away from the sweet spot but at the same time makes the deliberate splitting difficult to achieve, which requires a larger detuning that could excite the bulk. In reality with disorder, neither coherence time improves universally with the chain length. The Rabi coherence is set by the competition of three dephasing channels, and the additional dots pay off only if the fluctuation of the interchain tunneling is suppressed; the Ramsey coherence is set by the fluctuation of the energy splitting during the $\sigma_z$ rotation, which for the four-dot qubit is fixed by the sweet-spot disorder alone and does not depend on the mean splitting, whereas for the six-dot qubit the detuning that generates the splitting adds a fluctuation growing with the splitting itself, so the additional dots pay off only for small splittings. This implies that a longer chain is thus a better quantum memory but not necessarily a better qubit under manipulation. Although topological protection is expected in a longer Kitaev chain qubit, observing it in the current Rabi and Ramsey measurement protocols remains an experimental challenge.

Radiative capture in a non-relativistic system can become non-perturbative even when the underlying transition interaction is weak. We demonstrate this mechanism in a simple quantum-mechanical two-channel model with a systematic power counting, where strong mixing between scattering and bound states develops in a narrow region around a finite momentum $k_0$, leading to a perturbative violation of unitarity. In this regime, the enhanced contributions factorize, reducing the dynamics to a free scattering state interacting through a strong local coupling. Under RG evolution in the factorization scale, this local interaction approaches a unitary fixed point, analogous to that of systems with an anomalously large scattering length. This motivates an EFT organized around the finite-momentum surface $|\mathbf{k}|=k_0$, describing fermions at unitarity with a linear dispersion relation. The resummation resulting from the EFT restores unitarity and provides a systematic expansion for both elastic scattering and radiative capture.

We present bulk-primary operator-product coefficients for every Virasoro minimal model with an $E_6$, $E_7$, or $E_8$ modular invariant. Dividing by a universal product of chiral generalized-minimal-model OPE coefficients reduces the conformal bootstrap problem to a finite algebraic problem governed by root-of-unity quantum-group $6j$ symbols. The exceptional factors of the OPE coefficients can be chosen independent of the second Kac indices $s$, and their dependence on the central charge reduces to finitely many reference cases and explicit phases. A finite computer-assisted calculation yields candidate algebraic $s=1$ seed data and high-precision numerical evidence for existence and uniqueness modulo primary-field signs. We prove that exact existence and uniqueness for these seeds imply the corresponding result for all Kac labels within the genus-zero bulk locality and crossing equations; the finite seed step remains uncertified. The three families require $18$, $32$, and $107$ representative reduced OPE coefficients for $E_6$, $E_7$, and $E_8$, respectively. We provide reconstruction conventions and coefficient tables for both unitary and nonunitary models. Our calculation assumes only Virasoro symmetry, bulk locality (permutation symmetry) and OPE associativity (crossing equations).

We propose a realization of the Kitaev honeycomb Hamiltonian – an archetypal spin-liquid model – in a superconducting metamaterial. The architecture consists of Cooper-pair boxes coupled through depleted semiconductor–superconductor heterostructures that do not require spin–orbit coupling. The Cooper-pair boxes encode effective spin degrees of freedom, while normal and anomalous virtual propagation through the heterostructures mediate bond-directional interactions. Two key control parameters are an out-of-plane magnetic flux and the semiconductor Fermi energy. The former controls interference and distinguishes the bond directions, while tuning the latter close to the bottom of the band gives rise to an emergent Nambu-exchange symmetry that enforces the required bond directionality. Through numerical calculations, we identify an operating regime with controlled corrections, with associated energy and length scales within experimental reach. These results establish a route toward equilibrium quantum spin liquids in engineered superconducting networks.

Fast, high-fidelity qubit initialization is a key primitive for scalable quantum information processing, but conventional reset protocols either require long relaxation times or discard information contained in continuous measurement records. We demonstrate an adaptive measurement-based reset protocol for superconducting qubits that uses Bayesian inference to update the qubit-state estimate after each readout and dynamically adjust the feedback threshold. Unlike fixed-threshold or repeat-until-success (RUS) protocols, the method utilizes the full analog measurement history, enabling the reset decision to become progressively more conservative as confidence in ground-state preparation increases. Implemented with real-time FPGA-based feedback on a dispersively readout transmon qubit, the protocol achieves a ground-state initialization fidelity of $99.44\pm0.04\%$ after a small number of reset rounds. We further compare adaptive reset with RUS strategies in multi-qubit experiments and show that adaptive thresholding provides deterministic reset duration while maintaining a five-qubit simultaneous-reset fidelity of $98.78 \pm 0.19\%$. These results establish Bayesian adaptive thresholding as a practical and scalable route to fast qubit reset in superconducting quantum processors.

We formulate an exact theory for a 2-band superconductor with inter-orbital pairing and band Hatsugai-Kohmoto (HK) interactions. We apply this theory to a Chern dartboard insulator and compute the pair susceptibility and pair correlations analytically. We find that in the insulating phase previously predicted by BCS theory (small pairing strength $g$, chemical potential $\mu$ in the gap), the HK interaction can induce superconductivity, and possibly a Chern dartboard superconductor, by lifting the doubly-occupied band and making it cross the chemical potential. From this HK-induced superconductor, we notice that in a significant parameter range (HK interaction strength $U = 1$, $\mu = 0.5$), an insulator-superconductor-insulator re-entrant transition exists. We isolate the re-entrance to a conflation between HK interactions and inter-orbital pairings.

Quantum simulators are beginning to prepare long-sought phases of matter that remain difficult to realize cleanly in materials. Yet identifying such phases remains a major challenge when their defining properties are inherently non-local and cannot be captured by conventional local measurements. Here we establish multiple-quantum coherences (MQCs) as phase-sensitive diagnostics for gapped $\mathbb{Z}_2$ quantum spin liquids. Focusing on the extended toric code and using large-scale quantum Monte Carlo simulations, we build a direct correspondence between the elementary anyonic excitations and the weights of different MQC sectors. MQCs thereby reveal anyon condensation across the phase transitions through characteristic signatures that remain robust against fluctuations that obscure conventional diagnostics. Subsystem-resolved MQCs further provide a bipartite entanglement witness that distinguishes a classical loop gas from a quantum-coherent closed-loops gas. We develop and benchmark a practical protocol to extract MQCs based on the return fidelity of adiabatic round trips, and show that local coherence measurements retain experimentally accessible signatures of the phase transitions. Our results establish MQCs as a practical diagnostic for the excitations, phase structure and global constraints of quantum spin liquids.

We study the edge spectrum of two-dimensional lattice Hamiltonians and magnetic Schrödinger operators in a mobility gap, an energy interval in which the bulk spectrum is potentially localized rather than necessarily absent. Under suitable localization and boundary assumptions, we prove that a constant nonzero bulk topological index implies that the entire interval belongs to the absolutely continuous spectrum of the corresponding half-space operator. The absolutely continuous spectral multiplicity is bounded below by the absolute value of the index at almost every energy in the interval. The first version of the auxiliary-space cut construction in Section 2.3 was generated using ChatGPT 6.

Can primordial cosmological correlations originate from statistical fluctuations of an early-universe thermal system? We connect grand-canonical thermodynamics, stochastic transport, and gauge-invariant cosmological perturbations for a charged fluid at finite chemical potential. Energy-charge susceptibilities determine curvature, charge-isocurvature, and cross-correlation amplitudes, while transport sets when each mode leaves equilibrium. For an isolated, adiabatic conformal plasma with conserved charge-to-entropy ratio and power-law diffusion, diffusive freeze-out yields the universal spectrum $\mathcal P_S(k)\propto k^3$, with $n_{\rm iso}=4$, while equal-time local-equilibrium curvature-isocurvature covariance vanishes in the conformal source basis. Thus neither finite chemical potential nor replacing Hubble crossing by diffusion crossing alone yields approximate scale invariance. We evade this obstruction with an open subsystem of massless Dirac fermions during a sourced quasi-de Sitter phase. There, grand-canonical energy cumulants generate a nearly scale-invariant red curvature spectrum. A benchmark gives $\mathcal P_{\zeta_X}(k_\star)=2.10\times10^{-9}$ and $n_s(k_\star)=0.9649$, stays within $0.30%$ of the fitted power law over $0.002\leq k/k_\star\leq4$, and predicts weak negative running and small positive intrinsic non-Gaussianity from higher-order cumulants, $f_{\rm NL}(k_\star)\simeq0.106$ and $g_{\rm NL}(k_\star)\simeq0.0158$. With a two-helicity vacuum tensor spectrum, the tensor-to-scalar ratio is $r_{t/s}(k_\star)=1.82\times10^{-4}$. This isolates the limitation of isolated conformal thermal seeding and the open-system ingredient needed to overcome it. Thermal energy-charge fluctuations thus provide a calculable source of realistic scalar correlations, while reservoir dynamics, equilibration, and later curvature-isocurvature transfer must come from a microscopic model.

In classical systems, rugged potential energy landscapes provide a transparent mechanism for the celebrated Mpemba effect, in which hotter initial states cool down faster. This picture generally does not survive in quantum systems. Here we show how to design a quantum energy landscape with local dissipation leading to an Mpemba effect with parametrically separated timescales. Our approach uses Stark localization to design an energy landscape and localized incoherent hopping as cooling mechanism. The hops are triggered by rare "detection" events whose rate grows with energy, allowing hotter states to cool faster and producing super-exponentially separated cooling rates for localized initial states. We further show that the effect is dramatically enhanced by collective hopping of bound pairs in the presence of attractive on-site interactions. These findings have clear experimental signatures accessible in present-day setups.

The collective coordinate dynamics of antiferromagnetic and ferrimagnetic textures emerges as a geodesic equation governed by the quantum geometry of the CP$^1$ state associated with the Néel vector, rendering an effective Riemannian gravity and a Lorentz force in the texture motion. This unveils a physical scenario fundamentally distinct from the Thiele equation widely used for ferromagnetic textures, which is inertialess without any gravity analogy. Applying our framework to an optically driven ultrafast antiferromagnetic domain wall, we can explain the helicity-dependent asymmetric motion observed experimentally and predict a vibrantly breathing wall width.

The magnon Kerr effect is a nonlinear phenomenon that occurs universally in any ferromagnet with finite magnetic anisotropy. It manifests itself as a magnon population-dependent change in the magnon dispersion relation. Here, we derive the Hamiltonian for the magnon Kerr effect for a thin film with uniaxial anisotropy. We consider the external field, parallel, perpendicular, and at an intermediate angle to the anisotropy axis, and determine the Kerr coefficient in each case. We show how the nonlinearity scales for different magnetic materials as a function of magnon frequency and magnetic sample volume. Moreover, we derive the equations of motion for a hybrid cavity-magnon system with such thin-film magnon Kerr nonlinearity, to obtain populations of photons and magnons, and scattering matrix terms for the microwave transmission of the cavity, relevant for experimental observations.