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    Disciplines / Research questions

    Physics

    691 research topics · 2739 questions

    Double-row monodromy matrix3 questions

    1. Commutativity and polynomiality of the Q-operator for the open XXZ spin chain with diagonal boundaries (Vlaar–Weston Conjecture 6.3)

    2. Analytic theory of the rational QQ-system for open spin-ss XXX chains: boundary-induced strings, QQ-function ambiguity, and solution splitting

    3. Correlation-function building blocks for the open XXZ spin-1/2 chain with general integrable boundaries: the overlap factor, form factors of local operators, and the inverse problem without U(1) symmetry

    Double periodicity and quasi-periodicity3 questions

    1. Elliptic eight-vertex model with domain wall boundary conditions: normalization-level identification of the domain wall partition function at generic parameters

    2. Fractal structure of the Fibonacci Ising quasicrystal: uniform multifractality of Lee-Yang zeros and single-fermion spectrum at arbitrary couplings, and the topology of finite-fermion spectra below the interval threshold

    3. Completeness of the Bethe ansatz for the dynamical elliptic (KZB) Bethe algebra and the global geometry of the elliptic Wronski map

    Tetrahedron equation2 questions

    1. Foundations of the state-integral construction of tetrahedron-equation solutions: analytic degeneration and the transpose pentagon hypothesis

    2. Open problems of the tetrahedron duality: anomaly cancellation and the elliptic genus of the (0,2) brane box model, the oblique unit cell, and the reach of the construction

    Four-spin interaction1 questions

    1. Microscopic origin and quantitative strength of the effective four-spin interactions behind molecular-like excitations in frustrated pyrochlore magnets

    Stochastic six-vertex model1 questions

    1. Density profile and limit fluctuations of the stationary measure of the stochastic six-vertex model on a strip

      Open for about 3 years
    Random tilings4 questions

    1. Fluctuations of the uniformly random 3D dimer flow: convergence to the divergence-free projection of white noise

      Open for about 3 years

    2. Kenyon-Okounkov Gaussian free field convergence for uniformly weighted generalized tower graphs: upgrading gradient convergence to the full height field

      Open for about 21 years

    3. Local statistics of random domino tilings of L-shaped Aztec domains: unfrozen connecting paths and correlation kernels at the arctic curve and its cusps

      Open for less than 1 year

    4. Scaling-limit theory for interacting k-tilings of the Aztec diamond: arctic curves, color coupling, and edge fluctuations

      Open for about 3 years
    Topological quantum computation5 questions

    1. Completing a universal fault-tolerant gate set for Majorana braiding on the altermagnet–superconductor heterostructure platform

      Open for about 1 year

    2. Scalable compilation of measurement-only topological gates in Majorana zero-mode arrays

      Open for about 7 years

    3. Making the universal D(S3)D(S_3) topological gate set fault-tolerant: decoders, thresholds, and robust anyon-manipulation protocols under realistic noise including measurement errors

      Open for about 1 year

    4. Experimental and theoretical validation of STT-matrix-based braiding of vortex-hosted Majorana zero modes in two-dimensional topological superconductors

      Open for about 2 years

    5. Leakage-controlled universal gates and a finite-tunneling readout analysis for the diagonal-coset Fibonacci-anyon quantum computer at filling factor 12/5

      Open for about 2 years
    Terahertz waves and their applications2 questions

    1. Fully integrated hybrid photonic terahertz transmitter based on a Kerr microcomb for high-rate sub-THz/THz wireless links

      Open for about 3 years

    2. Absolute output power of fully integrated room-temperature photonic-integrated-circuit terahertz photomixing sources

      Open for about 6 years
    Difficulties faced in terahertz electromagnetic wave transmission research2 questions

    1. Exploiting the molecular absorption effect in terahertz communications: altitude-dependent spectral-window modeling, weather-adaptive VLC/THz cooperation, and closing the physical-layer-security insecure zones

      Open for about 4 years

    2. Water-vapor continuum absorption in the terahertz atmospheric windows: determination of the self and foreign continuum coefficients, their temperature dependence, and the residual window discrepancies

      Open for about 13 years
    Can solar energy replace traditional energy sources?4 questions

    1. Integrated system-level feasibility of a global PV-dominated electricity transition under full embodied-energy and material burdens

      Open for about 16 years

    2. Minimum extended-boundary EROI for sustaining a complex modern society and the dynamic net-energy viability of the renewable energy transition

      Open for about 17 years

    3. Determining the minimum societal energy return on investment (EROI): the sustainable cut-off for net-energy-constrained solar resource accounting and the implications of falling below it

      Open for about 17 years

    4. Genuine substitution of fossil generation by intermittent renewables in European electricity systems: empirical assessment across the generation, capacity and demand perspectives and the fossil backup requirement

      Open for about 8 years
    Extrasolar planetary systems: searching for distant worlds4 questions

    1. The unseen planetary system of Fomalhaut: identifying the planets that sculpt its debris disk after Fomalhaut b proved to be a transient dust cloud

      Open for about 21 years

    2. The Formation Pathway of the HR 8799 Wide-Orbit Planetary System: Core Accretion versus Gravitational Instability

      Open for about 17 years

    3. Establishing the habitability of Hycean worlds and validating their atmospheric biosignatures

      Open for about 5 years

    4. How rare is the Solar System's architecture: the intrinsic occurrence rate of inner-depleted planetary systems with cold giant planets

      Open for about 11 years
    Exploring nucleon structure3 questions

    1. The x→1x\to1 limit of the proton d/ud/u parton distribution ratio and the valence-quark dynamics it discriminates

      Open for about 53 years

    2. Process-independent observability of the gauge-invariant canonical orbital angular momentum in the nucleon spin decomposition

      Open for about 13 years

    3. Scheme-independent quark-gluon decomposition of the nucleon mass in QCD and the physical role of the trace anomaly

      Open for about 31 years
    Can gradient methods be used to solve the Dirac equation?6 questions

    1. Convergence of the power-iteration and parameter-tuning scheme for self-consistent bound states of the Schrödinger and Dirac equations

      Open for about 5 years

    2. Variational collapse in gradient-based minimization of the Dirac equation: a general selection mechanism for positive-energy eigenstates

      Open for about 40 years

    3. Rigorous error analysis of the Dirac-sVQA splitting variational quantum algorithm for the nonlinear Dirac equation

      Open for less than 1 year

    4. Fully discrete convergence analysis of normalized-gradient-flow and min-max schemes for stationary states of nonlinear Dirac operators

      Open for about 6 years

    5. Rigorous error analysis, temporal sampling complexity, and long-time mass conservation for physics-informed neural network solvers of the time-dependent Dirac equation

      Open for about 4 years

    6. Conditioning versus preconditioning for gradient-based Dirac solvers in lattice QCD: net time-to-solution advantage at physical quark masses, production volumes, and many right-hand sides

      Open for about 18 years
    Iron-based high-temperature superconductivity and its mechanism2 questions

    1. Origin of the pairing glue in iron-based superconductors

      Open for about 18 years

    2. Origin of the magnetic pairing glue in iron-based superconductors: itinerant spin fluctuations or local-moment physics

      Open for about 18 years
    Nuclear isomers and possible gamma-ray lasers5 questions

    1. Experimental validation of a current-driven thin-film 229^{229}Th vacuum-ultraviolet nuclear light source

      Open for about 3 years

    2. Stimulated de-excitation of the 186m^{186m}Re nuclear isomer in laser-produced plasma: reproducibility, mechanism, and the hypothesized second isomeric state in 186^{186}Re

      Open for about 8 years

    3. Optical-range nuclear gamma-ray laser on the 229Th isomer transition: population inversion and stimulated-emission gain in a doped solid

      Open for about 15 years

    4. Existence and charge-state-modulated decay of the conjectured isomer above the 8+ state in 92Zr

      Open for about 1 year

    5. Undemonstrated experimental program of the multi-photon stimulated graser: net gamma-ray amplification from laser-plasma gamma flashes with intense supplied photon fields

      Open for about 2 years
    Exploring the origin of the pseudogap in copper oxide high-temperature superconductors3 questions

    1. Mutual relationship and common origin of the cuprate pseudogap and strange metal: testing the Mott-Slater localization / van-Hove-singularity coincidence scenario

      Open for about 37 years

    2. Mechanism of the non-monotonic temperature dependence of the cuprate normal-state pseudogap and of its spectral correspondence with incommensurate charge ordering in transition-metal dichalcogenides

      Open for about 18 years

    3. Nature of the quantum criticality at the pseudogap end point of hole-doped cuprate superconductors

      Open for about 27 years
    Gauge hierarchy problem in unified field theory8 questions

    1. Is the electroweak hierarchy problem a physical problem? Scheme-independent naturalness from the distance to the electroweak critical surface

      Open for about 45 years

    2. Threshold naturalness of the Higgs mass-squared: protective ultraviolet structures for the coexistence of the electroweak scale with high mass scales

      Open for about 12 years

    3. Radiative and dynamical stability of scalar-tensor (equivalence-principle) solutions to the gauge hierarchy problem

      Open for about 18 years

    4. Landscape and anthropic inputs for the weak-scale hierarchy: the Higgs-VEV and Yukawa distributions and the weak-to-weakless habitable-universe ratio

      Open for about 5809 years

    5. Consistent quantization of internal fermionic (particle-ghost) symmetry as a solution to the gauge hierarchy problem

      Open for about 12 years

    6. High-scale attraction at ultraviolet fixed points: can a large anomalous mass dimension in asymptotically safe gravity explain the gauge hierarchy?

      Open for about 14 years

    7. Does renormalization-group consistency enforce strong supercooling in classically scale-invariant extensions of the Standard Model?

      Open for about 6 years

    8. Completing the physical-tuning account of Higgs naturalness: the UV-tuned region, its origin in a UV completion, robustness of the Wilsonian flow, and observable tests

      Open for about 4 years
    Turbulence: models and computations10 questions

    1. Closure of the Reynolds-averaged Navier–Stokes equations via constitutive relations or transport equations for the velocity-fluctuation fields

      Open for about 130 years

    2. Well-posedness of the exterior turbulent flow boundary-value problem for RANS equations with two-equation turbulence models

      Open for about 5 years

    3. Existence of weak solutions for the Jiang–Layton corrected eddy-viscosity turbulence model with an anisotropic time-derivative term

      Open for about 11 years

    4. How much domain knowledge must be embedded in machine-learned subgrid-scale closures for large-eddy simulation: invariance, cross-regime generalization, and computational cost

      Open for about 7 years

    5. Quantifying the turbulent potential model's cost advantage over full Reynolds-stress closures and completing stress-transport model evaluation in complex flowfields

      Open for about 27 years

    6. Weak uniqueness of mean outputs and dual stability for weak solutions of the Navier–Stokes equations in turbulent flow

      Open for about 21 years

    7. Physically consistent subgrid-scale models for large-eddy simulation: significance, compatibility, and realizability of model constraints

      Open for about 10 years

    8. Guaranteed computability of high-Reynolds-number turbulent-flow outputs: the missing rigorous theory of dual (adjoint) stability

      Open for about 22 years

    9. Systematic predictive and computational assessment of stress-transport turbulence closures versus two-equation eddy-viscosity models in complex flows

      Open for about 19 years

    10. Open problems in the mathematical theory of the NS-TKE and k-epsilon turbulence models: uniqueness, energy balance, and the realistic unbounded-eddy-viscosity regime

      Open for about 12 years
    Turbulent reactive flows9 questions

    1. Regime-general turbulence–chemistry interaction closures for large-eddy simulation of premixed turbulent combustion

      Open for about 19 years

    2. Turbulent flame speeds of non-equidiffusive (Le≠1Le \neq 1) mixtures: a generalized scaling with Markstein/Lewis-number effects, the mechanism of stretch-affected local extinction, and a diffusivity-aware combustion regime diagram

      Open for about 11 years

    3. Characterizing turbulence within a premixed turbulent flame brush: separating intrinsic turbulence from reactant-product intermittency and mean-velocity-jump effects

      Open for about 17 years

    4. A posteriori assessment of the flamelet regime diagram for non-premixed turbulent combustion LES: self-consistency of flamelet-model solutions and explicit-versus-implicit filtering

      Open for about 9 years

    5. Turbulent diffusion of chemically reacting admixtures beyond first-order, constant-density assumptions: predictive theory for the effective turbulent chemical time and the turbulent diffusion coefficient at finite Reynolds and Damköhler numbers

      Open for about 11 years

    6. Quantifying the statistical-independence factorization in assumed-PDF turbulence–chemistry closures for non-equilibrium reacting flows

      Open for about 8 years

    7. A posteriori validation of sub-filter variance and unsteady NO-transport closures for predictive LES of NOx in gas-turbine combustors

      Open for about 18 years

    8. Predictive turbulence-chemistry interaction modeling of MILD combustion: closing the CO and OH prediction gap in jet-in-hot-coflow flames

      Open for about 14 years

    9. Closure of the zone-conditioned moment and PDF transport equations in the thin-reaction-zone framework for turbulent reacting flows at low Damköhler number

      Open for about 6 years
    Elliptic RR matrix2 questions

    1. Rigorous proof or refutation of the Yang–Baxter equation for the elliptic R-matrix of the XX spin chain in a staggered magnetic field

      Open for about 2 years

    2. Quantum integrability of the BC_n elliptic XYZ long-range spin chain

      Open for about 1 year
    Elliptic parameters k,λ,qk,\lambda,q1 questions

    1. Monotonicity of the elliptic nome q(t)q(t) in discrete heat kernel expansions in the quadrant

      Open for about 2 years
    Elliptic modulus kk and complementary modulus k′k'4 questions

    1. Unproved arithmetic of Broadhurst's level-48 class invariants at discriminants N ≡ 3 (mod 8): the Chowla–Selberg unit λ and mod-64-signature generation of the Hilbert class field

    2. Riffaut's conjecture: no singular modulus of degree at least 3 is a root of a rational trinomial (unconditional status)

    3. Multiplicatively dependent triples of singular moduli: the Bilu–Gun–Tron classification conjecture

    4. Integrality of singular values of the generalized lambda function Λk=W[k,2,1]\Lambda_k=W_{[k,2,1]} in the excluded regime δ=gcd⁡(k,N)>1\delta=\gcd(k,N)>1 with 3∣δ3\mid\delta or N/δN/\delta a prime power

    Elliptic curves2 questions

    1. Infinitely many non-jumping specializations for arbitrary nonisotrivial elliptic curves over Q(T)\mathbb{Q}(T)

    2. Universal (all-tuples) Schanuel-type conjecture for elliptic and quasi-elliptic functions: prove or refute the semi-elliptic conjecture and its sigma-refinement

    Ferroelectric model in external fields2 questions

    1. Extending the analytical Landau–Khalatnikov theory of ferroelectric switching to first-order transitions, low fields, and quantitative KAI correspondence

      Open for about 13 years

    2. Explicit solution of the six-vertex-model Bethe-ansatz integral equations in arbitrary external electric fields

    Perfect matching2 questions

    1. A controlled coarse-grained theory of classical dimers and the quantum dimer phase diagram on the Ammann-Beenker quasiperiodic tiling

      Open for about 5 years

    2. Existence of perfect matchings for weakly consistent dimer models on surfaces with or without boundary

      Open for about 2 years
    Complete elliptic integrals K,K′K,K'1 questions

    1. Complete the algebraic theory of modular-form integration kernels for elliptic Feynman integrals: algorithmic seed construction and equivalence with elliptic multiple polylogarithms

    Theory and experiments on the non-Gaussianity of the microwave background radiation spectrum6 questions

    1. Non-Gaussianity of primordial isocurvature perturbations: detection-level observational determination and the model-to-bispectrum mapping

      Open for about 18 years

    2. Robust inference of the primordial trispectrum from patch-to-patch variation of observed non-Gaussianity

      Open for about 13 years

    3. The post-inflationary CMB bispectrum of metric f(R)f(R) gravity: full second-order transfer, templates, and observational confrontation

      Open for about 16 years

    4. Observational status of the predicted large equilateral/orthogonal non-Gaussianity in the two-field DBI inflation model of Nozari and Asadi (2016)

      Open for about 10 years

    5. Testing scale-dependent primordial non-Gaussianity as the origin of the large-scale CMB anomalies: a joint bispectrum and power-modulation analysis beyond the Sachs-Wolfe approximation

      Open for about 11 years

    6. Physical origin of the spherical-harmonic phase non-Gaussianities detected in cleaned Planck and WMAP CMB temperature maps

      Open for about 6 years
    Experimental and theoretical studies of tensor modes in the microwave background radiation7 questions

    1. Observationally discriminating the chiral gravitational-wave background of spectator axion-SU(2) inflation from the vacuum background: completing the CMB and laser-interferometer program

      Open for about 9 years

    2. Can multi-field inflation produce a testably large tensor tilt for LiteBIRD: realistic model building and robust forecasts

      Open for about 2 years

    3. Foreground-robust inference of the tensor-to-scalar ratio with CMB-S4: residual-bias control, non-oracle debiasing, spatially adaptive component separation, and multi-pipeline validation for defensible primordial B-mode claims

      Open for about 1 year

    4. CMB BB-mode constraints on causal primordial gravitational-wave sources beyond the white-noise k3k^3 template

      Open for less than 1 year

    5. Completing the gravitational-wave prediction for inflationary gauge-field sourcing: post-inflationary magnetic fields, reheating transitions, tensor non-Gaussianity, and renormalization

      Open for less than 1 year

    6. Robust end-to-end test of the single-field inflationary tensor consistency relation across CMB and laser-interferometer scales

      Open for about 12 years

    7. Polarized foreground complexity and the robustness of CMB tensor-to-scalar-ratio constraints to foreground model mis-specification

      Open for about 10 years
    Differential and Integral Identities3 questions

    1. Differential Galois group of the level-three cubic-theta differential field over Ramanujan's differential field

    2. Riemann-Xi integral for the second error-function transformation, exact evaluations of its confluent-hypergeometric integrals, and the Delta/Nabla parity reversal (open questions of Dixit-Roy-Zaharescu)

    3. Wan's first conjecture on moments of products of complete elliptic integrals: settling ∫01(2K2−4EK+3E2−K′E′) dx=0\int_0^1 (2K^2-4EK+3E^2-K'E')\,dx=0 and determining the five remaining open even moments

    Lattice-Boltzmann Simulation of Fluid Flow and Heat Transfer at Micro-Nano Scale5 questions

    1. Generalizing the linearized double-distribution thermal lattice Boltzmann method: coupled shear–thermal noncontinuum flows, stable full-form equilibria, and complex geometries

      Open for about 11 years

    2. Parameter-free thermal lattice Boltzmann boundary treatment for rarefied gas microflow: maintaining accuracy beyond the first-order slip regime (Kn around 0.1 and above) at large Eckert and Prandtl numbers

      Open for about 19 years

    3. Kinetic lattice Boltzmann modeling of rarefied gas flow and heat transfer in the transition regime (Kn≳0.1\mathrm{Kn}\gtrsim0.1): Knudsen-layer resolution, parameter-independent kinetic boundary conditions, and tractable discrete-velocity sets

      Open for about 14 years

    4. General validated effective-property models and the single-phase validity limit for nanofluid microchannel heat-transfer prediction

      Open for about 21 years

    5. Effect of non-unity momentum and thermal accommodation coefficients on slip flow and heat transfer in an asymmetrically heated microchannel simulated by the thermal lattice Boltzmann method

      Open for about 5 years
    Phase Change Heat Transfer in Micro-Nano Channels5 questions

    1. Experimental validation of slope- and curvature-dependent disjoining pressure in microchannel thin-film evaporation

      Open for about 13 years

    2. Predictive design framework for subcooled flow boiling in microchannels with chemically patterned (wettability-patterned) surfaces

      Open for about 7 years

    3. Quantitative synchronization criteria for flow boiling in parallel microchannels: coupling-coefficient thresholds, design mapping, measurement, and validated actuation

      Open for about 6 years

    4. Critical heat flux limits of constructally optimized two-phase microchannel heat sinks

      Open for about 6 years

    5. Evaporation-driven instability mechanism, thresholds, and predictive modelling for a meniscus in a heated flat micro-channel

      Open for about 15 years
    Liquid Transport in Micro-Nano Channels1 questions

    1. Microscopic origin of low-frequency 1/f-type current noise in nanoscale ion transport and its control by channel material and surface properties

      Open for about 54 years
    Influence of Dimension on Properties of Strongly Correlated Electron Systems3 questions

    1. Microscopic origin of the thickness-driven electronic evolution in SrRuO3/LaAlO3 superlattices (bad metal - weak localization - metal-insulator transition - strong 2D localization)

      Open for about 13 years

    2. Microscopic nature of the quantum criticality at the thickness-driven Mott transition in SrVO3 quantum wells: order parameter, emergent phases, and microscopic theory

      Open for about 9 years

    3. Dimensional crossover of weakly coupled Hubbard chains: charge-gap closing, spinon-confinement dynamics, and the ordering threshold beyond the quantum Monte Carlo window

      Open for about 13 years
    Why have about 40 Λ\Lambda hypernuclei been found experimentally, but only one Σ\Sigma hypernucleus?5 questions

    1. Quark–quark hyperfine interactions and their medium modification in the Friedberg–Lee soliton model of nuclear matter and hypernuclei

      Open for about 12 years

    2. The unsettled Sigma (and Lambda) single-particle potentials in dense matter: constraining sign, isospin dependence, and momentum dependence from chiral EFT and hyperon directed flow

      Open for about 48 years

    3. Sigma-minus admixture in the Λ10^{10}_{\Lambda}Li hypernucleus and the production mechanism of neutron-rich Λ\Lambda hypernuclei in the 10B(π−,K+)^{10}\mathrm{B}(\pi^-,K^+) reaction

      Open for about 21 years

    4. Completing the SU(3) chiral hyperon-nucleon interaction at N²LO: YNN three-baryon forces, charge-symmetry breaking, convergence, and empirical constraints

      Open for about 7 years

    5. Determining the interior radial shape and central repulsion of the Σ⁻-nucleus optical potential from Coulomb-assisted Σ⁻ bound states

      Open for about 17 years
    Why is spacetime four-dimensional?6 questions

    1. Is the (3+1)-dimensional nature of the universe a thermodynamic necessity: robustness of the Helmholtz-free-energy selection and freezing of three spatial dimensions

      Open for about 10 years

    2. Can the two assumptions of Deser's classical D = 4 selection argument — completeness of the second-order gravitational action and uniqueness of the stable vacuum — be derived from deeper principles rather than postulated?

      Open for about 6 years

    3. Microscopic foundation and quantitative predictions of the Afshordi–Stojkovic evolving-dimensions worldsheet model

      Open for about 12 years

    4. Dynamical foundations of the Machian integral formulation of Einstein's equations and the selection of 3+1 spacetime dimensions

      Open for about 14 years

    5. Reduction of the four-principle axiomatic basis for observed 3+1 spacetime dimensionality

      Open for about 21 years

    6. Dominant late-time phase and the emergence of commutative (3+1)-dimensional expanding spacetime in the Lorentzian type IIB matrix model

      Open for about 13 years
    Why can't strict many-body wave function calculations produce a superconducting state, while simple BCS mean-field calculations can?2 questions

    1. Quantitative convergence and error control of particle-number-projected BCS wavefunctions versus exact many-body solutions for pairing correlations

      Open for about 12 years

    2. d-wave superconductivity in the hole-doped two-dimensional Hubbard model: establishing the low-temperature, sign-problem-blocked regime by controlled computation and quantum simulation

      Open for about 39 years

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