Papers

The hyperbolic mode (HM) refers to a polariton mode in a polar insulator where the dielectric function is negative in some direction of propagation. Within a frequency window the light occupies a greatly expanded region in momentum space. The HM in hexagonal Boron Nitride (hBN) has been under intense study and we consider placing a metal directly on top of hBN and ask whether its physical properties can be strongly affected. While the problem resembles superficially the electron phonon coupling problem, there are important differences. Due to the longitudinal nature of the HM mode the coupling is driven by time dependent charge fluctuations which results in a coupling that strongly increases with the energy difference of the initial and final states. We find a significant frequency and momentum dependence of the self energy which allows us to identify the dimensionless coupling constant $\lambda_0$ that controls this effect. There is a suppression of the quasi-particle weight but it turns out that the leading correction to the velocity renormalization is canceled. We compute the single particle spectral function which shows a side band that can be measured experimentally. The virtual exchange of HM leads to a repulsive interaction which is ineffective to leading order because of the energy dependence. We are motivated to seek pairing by going to second order. Unfortunately we find that the leading contributions exactly cancel. This cancellation is not an accident and we give an explanation of why this cancellation would take place.

The hyperbolic mode (HM) refers to a polariton mode where the dielectric function is negative in some direction of propagation. Within a frequency window the light occupies a greatly expanded region in momentum space. We compute the photon density of states and find that the zero point fluctuation in the RMS electric field can reach $MV/cm$, comparable to the largest field used in pump probe experiments in the THz scale. The HM in hexagonal Boron Nitride (hBN) has been under intense study and we consider placing a material directly on top of or sandwiched between hBN crystals. We consider two examples. First the material is a metal and we calculate the modification of the quasi-particle spectral weight, Fermi velocity and pairing interaction. Next we consider a material that is close to the Mott transition. We find that a substantial shift in the metal-insulator transition is possible, but the effect decays rapidly with distance, so that only a few monolayers are affected. We provide estimates and suggestions for a number of materials of interest.

We identify the limit free energy of all multi-species spin glasses with centered $\pm 1$ spins. The result was previously known only under a convexity assumption on the covariance function of the Hamiltonian. We also obtain a one-species reduction of the formula for balanced multi-species models.

We investigate interaction-induced symmetry breaking in moiré superlattices created by twisting two identical materials where the electronic low-energy degrees of freedom reside in the vicinity of the $M$ points. Based on general symmetry arguments, we identify and classify the possible candidate instabilities that, besides flavor polarized states, also involve a variety of intervalley-coherent (IVC) orders. This complexity is related primarily to the presence of three valleys, instead of the well-studied scenario of two, e.g., in graphene: IVC states can couple all three valleys identically, with a non-trivial sign structure, or even with different magnitudes. We study the energetics using an analytical strong-coupling framework and unrestricted Hartree-Fock applied to the full continuum model, with very good agreement between the two approaches. Interestingly, depending on stacking, IVC instabilities not only appear due to superexchange at moderate bandwidths, but also deep in the strong-coupling regime as a result of deviations from the flat-metric condition. Our work demonstrates that twisted $M$-point materials provide a rich playground for complex correlated physics and highlights differences and similarities to twisted multilayer graphene.

Sycophancy in LLMs is documented across 70+ papers, but expert agreement on construct boundaries remains low (ICC=.184; Ye et al., 2026). The construct fragments because behavioral classification depends on which surface form is privileged. We adopt a materials-science framing: conversation as test specimen under load, LLM-model as material charge, pushback as progressive load, stance-flip as material failure. We characterize this failure across three loading cases (debate n=1000; false-presuppositions n=3400; ethical-setting n=3400; 10-17 material charges per case; 7800 specimens total) using 14 turn-level axis-measurements spanning velocity, damage accumulation, frame-drift, brittleness, and direction stability, plus three speaker-resolved axes from an independent pipeline. The measurements are Hooke-coupled ($\sigma = E \cdot \varepsilon$ analog) and reproduce across loading cases with effects up to $|r_{rb}| = 0.35$ on debate; the sign structure adds a second pattern: the ethical-setting case inverts the velocity and accumulation blocks. Variance composition partitions into two profiles: debate is charge-dominated (brittle-fracture-like: the material grade decides), false-presuppositions and ethical-setting are topic-dominated (creep-like: the load decides); the ratios (2.03 vs 0.13/0.17) are estimator-dependent, for debate even in direction. Cross-judge reliability (GPT-4o vs Haiku 4.5) shows debate scoring is judge-robust (Cohen's $\kappa = 0.88$) while false-presupposition scoring is judge-sensitive ($\kappa = 0.36$) – a caveat single-judge benchmarks must report. This is the methodological move Ye et al.'s diagnosis calls for: a multi-axis characterization that does not depend on which surface form of the construct one privileges.

Living cells utilize condensates to spatially concentrate molecules in response to dynamic signals. For instance, nuclear condensates respond to oscillations in transcription factor levels in the nucleoplasm, including those involved in repairing multiple DNA breaks. To understand how oscillating signals affect condensates, we analyze a theoretical model using numerical simulations and analytical theory. While passive dynamics would drive all molecules into a single condensate, we find that sufficiently fast oscillations stabilize multiple droplets, allowing control of their sizes. We thus reveal a new behavior of chemically active droplets, which could be exploited in synthetic applications.

Owing to rapid recent progress, ultracold atomic lattice systems for simulating topological phases are now at a pivotal stage, evolving from established paradigms into increasingly versatile and programmable quantum simulators. In this review, we survey recent experimental advances across four major classes of platforms: optical lattices, including optical lattices with laser-assisted tunneling and optical Raman lattices; synthetic lattices in momentum or internal-state space; Floquet-engineered lattices; and optical tweezer arrays, all of which offer distinct capabilities for realizing and probing topological matter. For each class, we highlight representative experimental breakthroughs, the topological models that have been realized, and the advanced detection and characterization techniques employed, emphasizing how these complementary approaches collectively expand the frontier of quantum simulation. We also discuss emerging directions in strongly correlated and nonequilibrium topological phases, and conclude with an outlook on future prospects.

We investigate magnetotransport in a van der Waals heterostructure composed of monolayer graphene and the insulating helical antiferromagnet nickel iodide (NiI$_2$). While NiI$_2$ is highly resistive and thus poorly suited for direct transport measurements, we demonstrate that magnetotransport in an adjacent graphene layer provides an electrical readout of magnetic-state-dependent interfacial behavior. Most notably, first-harmonic longitudinal magnetoresistance under in-plane magnetic fields exhibits large, anisotropic low-field peaks that are absent from a monolayer graphene/h-BN control device and are suppressed above the multiferroic transition temperature of NiI$_2$. Temperature-dependent harmonic measurements provide complementary evidence: the second-harmonic resistance shows the clearest nonlinear contrast relative to the control device, while the third harmonic contains a larger generic nonlinear and thermal background that is nevertheless modified in the heterostructure. These results demonstrate that graphene-based transport measurements offer a sensitive, non-invasive probe of magnetic phase behavior in electrically insulating van der Waals magnets, opening routes toward spintronic devices based on insulating vdW multiferroics.

Quadrupolar excitons in van der Waals heterostructures - quantum superpositions of anti-aligned dipolar excitons - offer a novel platform to explore exotic many-body physics, with applications to quantum sensing and photonic devices. Yet their internal structure, symmetry, and real-space localisation remain largely unknown. Here, we reveal the atomic-scale structure of quadrupolar excitons in twisted WSe2/WS2/WSe2 trilayers by solving the Bethe-Salpeter equation within a large-scale atomistic framework. We discover that large atomic relaxations at small twist angles give rise to two distinct quadrupolar excitons trapped at moiré lattice sites, differing in the in-plane symmetry of the electron density about the hole: one azimuthally symmetric, with the density maximal at the hole, and one threefold symmetric, with a node at the hole. Moiré trapping, neglected in commonly used models of quadrupolar exciton formation, is critical to their many-exciton phases. Without moiré trapping, quadrupolar excitons transition into anti-parallel dipolar excitons on a bipartite square lattice, while with trapping, the same dipoles are confined to a triangular lattice and experience geometric frustration. Our study uncovers the highly non-trivial nature of quadrupolar excitons, with direct implications for simulating frustrated quantum magnetism in a fully tunable excitonic platform.

Cryogenic hydrogen isotope fuel layers with high structural integrity and atomic-scale smoothness are prerequisites for symmetric implosion and ignition in inertial confinement fusion (ICF). Using deuterium (D$_2$) as model fuel, we perform large-scale molecular dynamics simulations with a Feynman-Hibbs corrected Silvera-Goldman potential to describe nuclear quantum effects at low temperatures, systematically investigating D$_2$ crystallization inside spherical ablator capsules. By varying substrate lattice constant from 3.1 angstrom to 3.9 angstrom, we demonstrate that lattice matching dictates the transition from coherent epitaxial growth to polycrystalline formation, establishing it as the primary design principle for high-performance targets. When the substrate lattice closely matches the equilibrium hexagonal-close-packed (HCP) spacing of cryogenic D$_2$ (approximately 3.5 angstrom), D$_2$ forms coherent layer-by-layer epitaxial growth consistent with Ostwald's stepwise nucleation theory, yielding HCP-dominated near-single crystals with minimal dislocations and ultra-smooth inner surfaces. In contrast, large lattice mismatch destabilizes coherent growth and causes island-like growth, producing polycrystalline structures with mixed HCP/FCC phases, elevated defects, and greatly increased surface roughness. Radial stress analysis shows that interfacial stress from mismatch localizes within 2-3 molecular layers near the interface, triggering subsequent defect-mediated growth. These findings highlight substrate lattice matching in regulating confined solid growth and crystallization quality, establish it as a key principle for ablator inner-surface engineering in ICF cryogenic targets, and offer atomic guidance for growing high-quality single-crystal deuterium-tritium (DT) fuel layers with optimal smoothness.

We investigate the real-space vortex structure of a flat-band superconductor described by the attractive Hubbard model on the Mielke checkerboard lattice. Using a momentum-space mean-field analysis, we derive a closed-form expression for the coherence length in terms of the quantum metric of the Bloch states and a particle-hole-symmetric pair density. Self-consistent Bogoliubov-de Gennes calculations on a finite disk confirm this prediction across a wide range of fillings and interaction strengths. The coherence length is minimized at half filling, diverges toward both band edges as the pair density vanishes, and depends only logarithmically on the interaction strength. These features differ qualitatively from the conventional BCS picture, which relies on a well-defined Fermi surface and a kinetic mechanism for pair transport. Instead, the vortex-core size is governed by a geometric pair mass arising from virtual interband processes encoded in the quantum metric. Our results establish the vortex core as a direct real-space manifestation of flat-band quantum geometry.

HfO$_{2}$-based ferroelectrics are essential for the next generation of CMOS-compatible memory and logic devices, yet their performance is governed by a complex interplay between oxygen vacancies, dopants, and structural defects that remains an active area of investigation. These defects shape the function-critical dynamic phenomena, such as polar phase stabilization, wake-up, fatigue, and imprint. In this Perspective, we review the limitations of established high-resolution structural characterization techniques and propose atom probe tomography (APT) as a powerful tool for the three-dimensional (3D), atomic-scale mapping of all constituent species in hafnia-based ferroelectric systems. By resolving individual dopants, vacancy clustering, and interfacial segregation, APT can facilitate a quantitative understanding of defect-property relations in hafnia-based ferroelectrics. We discuss current experimental challenges for APT application to ferroelectric oxides, demonstrate a proof-of-concept of atomic-scale reconstruction in a hafnia-based device stack, and highlight the potential of APT to guide the development of ferroelectric structures with enhanced reliability and performance.

We introduce a geometric decomposition of the hard-sphere partition function. Using a close-packing-inspired geometric bound on the available insertion volume, made rigorous when a corresponding local density certificate is available, we establish a reference upper bound $Q^\ast$ on the configurational integral. Factoring this upper bound out of the statistical geometric partition function found by Speedy yields a new form for the $d$-dimensional partition function, $Q(N,V,T)=Q^\ast \exp(-N \mathcal{J})$, where $\mathcal{J}$ depends strictly on the boundary-to-volume ratio of the voids and the close-packing density. Overall, this work provides an exact reformulation of hard-sphere thermodynamics, thus deepening our statistical geometric understanding of hard spheres.

Much has been studied on Floquet engineering in Rashba nanowire model regarding topological superconductivity hosting Majorana $0$- and anomalous $\pi$-modes, here we theoretically investigate the possible emergence of finite momentum Fulde-Ferrell (FF) superconducting state in quasi-energy of the above model under the periodic modulation of in-plane and out-of-plane magnetic fields while the static limit does not host a FF ground state. We demonstrate controllable switching between Floquet Majorana $0$- and $\pi$-modes via reversal of the supercurrent direction, revealing pronounced nonreciprocal supercurrent signatures which is a manifestation of the FF pairing. We validate the onset of FF pairing following a self-consistent mean-field analysis where externally applied supercurrent facilitates nonreciprocal signatures in quasi-energy spectra. The above findings directly indicates to the intriguing phenomenon of superconducting diode effect (SDE). The drive amplitude serves as a parameter to regulate the diode efficiency with chemical potential. Our study thus reveals a rich interplay between Floquet topological superconductivity and finite-momentum FF pairing, providing a tunable way to switch between different Floquet Majorana modes and realize the SDE with high efficiency.

We investigate the persistence properties during phase ordering in the two-dimensional ($d=2$) Ising model evolving under competing nonconserved spin-flip and conserved spin-exchange dynamics by means of Monte Carlo simulations at zero temperature. We examine three distinct persistence probabilities: (i) the total persistence probability, defined as the probability that a lattice site has never experienced a change in the sign of the spin residing there; (ii) the spin-flip persistence probability, which exclusively measures the fraction of sites that have never undergone a spin-flip event; and (iii) the composite persistence probability, defined as the fraction of sites that have experienced neither a spin-flip nor a spin-exchange event. In the asymptotic regime, both the total and spin-flip persistence probabilities exhibit identical power-law decay, irrespective of the relative occurrence probability of the spin-flip move $p_r$. The corresponding persistence exponent $\theta_i \approx 0.225$, is found to be consistent with the value reported for systems evolving purely under nonconserved dynamics. We further demonstrate that both persistence measures satisfy the scaling relation $d-d_f^i=\theta_i/\alpha_i$, where $d_f^i$ is the fractal dimension of the corresponding persistence lattice and $\alpha_i\approx 1/2$ characterizes the asymptotic power-law growth of spatially correlated regions of non-persistent spins. In contrast, although the composite persistence probability also exhibits asymptotic power-law decay, both the corresponding persistence exponent $\theta_{\rm c}$ and the fractal dimension $d_f^{\rm c}$ of the persistence lattice show strong dependence on $p_r$. Combined with the presence of a universal growth exponent $\alpha_{\rm c}\approx 1/2$, this leads to the breakdown of the scaling relation among the characteristic exponents for the composite persistence.

We study noisy identical Kuramoto-Sakaguchi oscillators with phase lag $\alpha\in[0,\pi/2)$, where $\alpha>0$ induces nonreciprocal interactions. Numerical phase diagrams in the $(\sigma, \alpha)$ plane in fully-connected graphs, formed by long-range weights tuned by $\sigma$ on $d$-dimensional lattices, reveal a critical phase lag $\alpha_c$, below which spontaneous synchronization occurs. This critical phase lag decreases monotonically with $\sigma$. We characterize the critical behavior analytically using the dynamical renormalization group theory.

Non-Hermitian systems host unconventional topological phenomena, while real-space spectral calculations in three dimensions remain computationally challenging. Here, we develop a tensor-network framework that combines a quantics-based matrix-product-operator representation of large real-space tight-binding Hamiltonians with a non-Hermitian kernel polynomial method. The Hermitized spectral problem is retained within the compact tensor-network representation, enabling real-space spectral function calculations for systems exceeding one billion lattice sites. Using this approach, we investigate a three-dimensional non-Hermitian higher-order topological insulator and resolve its corner-mode spectral response on a billion-site lattice, demonstrating the scalability and computational reach of the method. By tuning the gain–loss strength, we identify distinct in-gap corner-mode features in the weak- and strong-gain–loss regimes. Our results establish a scalable tensor-network framework for real-space spectral calculations in exceptionally large non-Hermitian lattice systems.

The bulk photovoltaic effect in non-centrosymmetric materials provides an alternative mechanism for the conversion of light into a current response compared to p-n junctions. Among its various contributions, the shift current is particularly attractive because it is governed by the geometric properties of electronic wavefunctions and can generate large photocurrents in low-dimensional materials. Here, we investigate the evolution of the shift current response in mono-, bi-, and trilayer H-MoS2, as well as in twisted moiré bilayers and trilayers. To describe large moiré supercells we develop a Slater-Koster tight-binding model parametrized from first-principles calculations. The resulting electronic structures and shift-current responses are compared with density functional theory calculations and Wannier-interpolated results to verify the accuracy of the approach. The model accurately reproduces the electronic structure near the band edges and captures the main spectral features of the shift current conductivity. We show that twisting breaks the crystal symmetry and activates additional conductivity tensor components that are forbidden in untwisted structures, leading to new tunable in-plane photocurrent components. Analysis of the shift distance reveals a direct connection between the twist-induced modification of the electronic wavefunctions and the increase of the nonlinear response. Our results establish the twist angle as an effective parameter for engineering shift current generation in multilayer transition-metal dichalcogenide base systems and demonstrate that tight-binding approaches provide a practical route for exploring nonlinear optical phenomena in large-scale moiré materials beyond the limits of conventional first-principles calculations.

Pyroelectric energy conversion offers a route for harvesting time-dependent thermalfluctuations that are abundant in natural and technological environments. Twodimensional ferroelectrics are particularly attractive for this purpose because reduced dimensionality enables ultrathin, mechanically compliant device architectures. Here, we demonstrate direct nanoscale pyroelectric characterization of an out-of-plane van der Waals nanogenerator based on CuInP2S6 (CIPS) encapsulated between few-layer graphene electrodes. A scanning thermal microscopy (SThM) probe is employed as a localized nanoscale heat source while the electrically generated response is measured in situ through the device electrodes. Harmonic detection isolates the pyroelectric signal from parasitic first-harmonic electromechanical contributions, while finite-element thermal modeling combined with probe calibration enables direct determination of the local pyroelectric coefficient from the measured electrical response. Beyond quantitative characterization, the spatially resolved measurements directly identify electrically inactive regions associated with device defects, revealing local performance-limiting features that remain hidden in conventional spatially averaged pyroelectric measurements. The presented approach establishes a versatile platform for quantitative nanoscale pyroelectric characterization and the optimization of van der Waals pyroelectric devices.

Information criteria such as WAIC and WBIC extend model selection to singular learning machines, but they are usually derived for equilibrium posteriors. We formulate a finite-time analogue of WBIC by replacing the equilibrium posterior with an effective ensemble generated by learning dynamics under a resource constraint. When this ensemble admits an analytic effective potential, singular learning theory yields a resource-dependent real log canonical threshold. The resulting estimator gives a computable thermodynamic contribution to time-bounded MDL and identifies the finite-time singular complexity relevant to the structural information measured by epiplexity.

Quantum oscillations provide a fundamental probe of electronic structure in magnetic fields, revealing the Fermi surface topology in metals, and/or the quasiparticle properties even in the insulating regimes. Here we study quantum oscillations in minimal models of high-angular-momentum (HAM) band inversion for both a chiral two-band model and a time-reversal-invariant four-band model. In the former case, finite oscillations can appear at the hybridized Chern-insulating regime due to thermal-activated excitations. In the latter case, interference between the two time-reversal-related blocks drives a strong deviation from the Lifshitz-Kosevich form, producing a non-monotonic temperature dependence of the oscillation amplitude and characteristic suppression temperatures whose number follows the angular momentum $l$. These results identify experimentally accessible signatures of HAM band inversion and provide a framework for other discrete-symmetry-related hybridizations and excitonic pairings.

The propulsion of active colloids is governed by their symmetry and shape, yet a systematic investigation of how small geometric effects influence the locomotion of anisotropic active colloids is lacking. In this paper, we study the effect of a cone shape by combining high-resolution two-photon polymerization 3D printing with AC electric field experiments to study anisotropic Janus micro swimmers. We fabricate a series of Janus colloids with different shapes, ranging from a sphere to a hemisphere with a cone-protrusion, but containing similar hemispherical gold-coatings. Under an applied alternating current (AC) electric field, all particles exhibit active, ballistic motion. We find a shape and size dependence on the propulsion velocity, with the spherical Janus particle moving fastest, followed by a small cone and a large cone protrusion, while surprisingly a printed sphere with a flat side moves slowest. In addition, a reversal in the direction of motion for all shapes was triggered, a phenomenon governed by a transition from induced-charge electrophoresis (ICEP) at low frequencies to self-dielectrophoresis (sDEP) at high frequencies. We reveal a distinct shape influence, with the large cone-protrusion increasing their velocity in the sDEP regime. Our results provide insight into the link between active particle geometry and their propulsion velocity that are important for understanding biological micro swimmers and designing optimized microrobots.

Generating experimentally relevant amorphous structures via melt-quench molecular dynamics is prohibitively expensive at the first-principles level. Universal machine-learning interatomic potentials (uMLIPs) could accelerate such simulations, but their reliability under non-equilibrium conditions remains unclear. Here, we examine eight leading uMLIPs for generating amorphous IrO2, using this electrocatalytically relevant oxide as a diagnostic case. Under the conventional melt-quench protocol, all models yield unphysically expanded structures with densities of 1-4 g/cm3, far below the ab initio molecular dynamics (AIMD) reference value of 10.04 g/cm3. Comparisons against ab initio references show that accurate energies and forces alone do not ensure stable NPT dynamics; correct energy-volume responses and pressure predictions are also essential. We identify two practical remedies: pressure-targeted fine-tuning and a revised NVT-quench/NPT-equilibration protocol that avoids unphysical volume expansion without additional ab initio training data. Both recover IrO2 densities and local structures consistent with AIMD. Across 30 chemically diverse materials, the volume-expansion failure proves general, and the revised protocol substantially improves density predictions, reducing the AIMD-referenced MAE from 2.46 to 0.35 g/cm3. This work establishes practical validation criteria and simulation strategies for robust uMLIP-driven amorphous structure generation.

Predicting the initiation and propagation of cracks in heterogeneous wellbore systems under complex in-situ conditions remains challenging. We present a hybrid phase-field fracture framework to model crack growth in heterogeneous wellbore systems with weak interfaces. The framework is first validated against benchmark problems with available analytical and numerical solutions. Subsequently, numerical experiments are conducted to isolate the effects of interface strength and casing eccentricity on crack growth. The results show that casing eccentricity strongly influences both the pressure at crack initiation and the resulting crack paths, reducing the crack initiation pressure by up to 30% relative to the concentric configuration. For the examples considered here, beyond a critical eccentricity threshold of 50%, localized shear stresses drive the nucleation of inclined cracks in the rock formation in addition to radial cracking – a failure mode absent in concentric configurations. For sufficiently weak interfaces (i.e., interfaces with 30% of the toughness of the surrounding bulk material), radially propagating cracks in the cement sheath are deflected along the interface rather than penetrating into the rock formation. This deflection delays stress relaxation within the sheath, promotes the nucleation of additional radial cracks, and increases the risk of sustained casing pressure and wellbore failure. Finally, a three-dimensional simulation reveals depth-dependent crack nucleation, stress-shadow effects that suppress full-depth crack growth, and crack coalescence along the cement-rock interface – phenomena that are fundamentally inaccessible under plane-strain assumptions – demonstrating the applicability of the framework to realistic heterogeneous wellbore systems.

Thermodynamic Uncertainty Relations (TURs) impose universal bounds linking current precision to entropy production in nonequilibrium systems. While general bounds like the Proesmans–Van den Broeck (PV) relation provide a broad framework, they often remain loose for processes characterized by renewal events. In this work, we derive a generalized entropic bound for current fluctuations in renewal-reward processes. By utilizing a rigorous variance decomposition within the framework of renewal-reward theory, we obtain a model-independent bound that is not only rigorous but tighter than the standard PV relation. Notably, in the linear-response regime, our bound correctly scales with the renewal rate and identifies a precision penalty arising from cycle-length fluctuations. These results provide a physically informative constraint on the precision of run-and-tumble-type dynamics and highlight the universal limits of transport in complex stochastic walkers.

The non-stationary longitudinal Josephson effect in bilayer systems with pairing of spatially separated electrons and holes is investigated. The tunneling current between two (right and left) weakly coupled electron-hole condensates is analyzed in the presence of an external voltage applied along the layers. Two limiting regimes are considered: the high-density regime, where pairing occurs in momentum space similarly to conventional superconductors, and the low-density regime corresponding to a Bose-Einstein condensate of spatially indirect excitons. Using the tunneling Hamiltonian approach, expressions for the quasiparticle, superconducting and interference contributions to the tunneling current are derived. It is shown that in the high-density limit the quasiparticle and interference currents vanish at zero temperature below a threshold voltage determined by the energy gap, so that only the supercurrent remains. In contrast, in the low-density regime the gapless spectrum of collective excitations leads to finite dissipative contributions even at zero temperature, resulting in damping of Josephson oscillations. For spatially separated tunneling barriers with distance exceeding the coherence length, phase jumps occur at each barrier, resulting in voltage oscillations across the electron and hole barriers and a non-sinusoidal current-phase relation governed by the critical currents of the two barriers.

The acoustic flexural (phonon) modes of low-dimensional materials should show a quadratic dispersion close to the Brillouin zone center. Any departure from this behavior in Density Functional Theory calculations is typically associated with a breaking of the rotational invariance, with few methods available to correct it. In this work, we reexamine this issue based on a reciprocal-space imposition of this condition, with corrections on the zone-center IFCs and their first and second derivatives with respect to the phonon wavevector. We propose two correction schemes for the short-range part of the interatomic force constants, one based on the Moore-Penrose pseudoinverse, that we implement in the ABINIT software package, and one based on the straight modification of the on-site antisymmetric part of the first-order derivative of the dynamical matrix with respect to the wavevector. We investigate the impact of imposing rotational invariance for different system dimensionalities and pseudopotentials. Finally, we discuss rotational invariance in the context of long-range electrostatics contribution to the IFCs. We observe that the usual treatment of electrostatics is by construction not rotationally invariant. This is found especially critical when correcting the second derivatives of the IFCs.

The well-known Curzon-Ahlborn (CA) engine [Am. J. Phys. 43, 22 (1975)] runs in finite time and yields a finite power output. In order to recover the standard Carnot cycle from the CA model, the limit of quasi-static operation has to be concurrent with the reversible limit, a condition strangely missing from the CA model. We augment this model by specifying the duration of the isothermal process as a monotonic decreasing function of the temperature difference between the working substance and the reservoir. As an illustration, we analyze the machine's operation in the low-dissipation (LD) regime in which the entropy production in each isothermal branch is inversely proportional to the duration of the process. The modified model, while retaining the optimal features of the CA model, also yields explicit expressions for the optimal durations of isothermal processes. We compare the optimal cycle periods of the present model and the LD model, and show their agreement in the linear response regime.

This chapter reviews the foundations of entropy and their extensions to complex systems. We first discuss the relation between Boltzmann's formula, multiplicity, coarse-graining, and Shannon entropy, before introducing generalized entropies such as Rényi, Tsallis, and Burg entropy. We then examine Maxwell–Boltzmann, Bose–Einstein, and Fermi–Dirac statistics, structure-forming systems, sample-space reducing processes, Pólya urns, and nonlinear dynamics. Axiomatic approaches are presented through the Shannon–Khinchin axioms, Tempesta group-composability, Hanel–Thurner asymptotic scaling, Shore–Johnson consistency axioms, and Lieb–Yngvason axioms. Finally, we discuss calibration invariance, Hanel–Thurner–Gell-Mann duality between linear and escort averages, and Kolmogorov–Nagumo averages, showing how the same distribution can arise from different entropies, constraints, or dynamics. These results emphasize that the choice of entropy should be guided by the structure and physical properties of the system.

Fault-tolerant quantum computing fundamentally relies on the accurate characterization of circuit-level noise to optimize decoding algorithms. However, extracting complex multi-body error correlations remains challenging. Contemporary greedy inference algorithms can suffer from statistical distortion, discarding true physical mechanisms while introducing many unphysical false positives. Here, we introduce the Correlation-Analysis-based Hypergraph Reconstruction (CAHR) algorithm, a globally consistent framework to invert experimental syndrome statistics directly into discrete physical hypergraphs. By coupling exact algebraic correlation equations with a top-down concurrent-pruning strategy, CAHR recovers the fault topology without false positives for both $d=5$ rotated surface codes and dense 8-body 2D color codes in our benchmark settings. Furthermore, we show that exact continuous parameter extraction in dense codes is limited by a variance cascade, where absolute statistical variance accumulates linearly from high- to low-degree mechanisms. This motivates a two-stage inference paradigm: utilizing CAHR to extract the fault topology, followed by continuous probability optimization. This provides a practical approach for characterizing and decoding highly correlated noise in realistic quantum hardware.