Foundations

An ideal spinless one-dimensional p-wave pairing chain has a gapped topological phase with boundary Majorana modes for nonzero pairing and |μ|<2|t| in the uniform nearest-neighbour model.

Will, Cochran and collaborators reported signatures of non-equilibrium topological order in a periodically driven quantum-processor experiment published 10 September 2025.

Liu, Sau and Das Sarma's 2018 nanowire calculations show how trivial Andreev bound states can generate local zero-bias peaks resembling topological Majorana signals.

The Boltzmann equation evolves a dilute one-particle distribution with streaming, force and collision terms.

ETH proposes that suitable local-observable matrix elements in many chaotic energy eigenstates have thermal structure, allowing narrow-energy isolated preparations to approach thermal local expectations.

For perturbation H′(t)=−f(t)B, the retarded response of A is χ_AB(t)=(i/ħ)θ(t)⟨[A(t),B(0)]⟩ in an equilibrium reference state.

Expanding a diffeomorphism-invariant gravitational action in curvature and derivatives organizes low-energy quantum corrections without claiming a complete short-distance theory.

String theory organizes extended-object states and includes a massless spin-two excitation in appropriate constructions; loop approaches quantize geometric variables with spin-network/holonomy methods; asymptotic safety seeks a suitable ultraviolet renormalization-group fixed point.

The 2017 Marletto–Vedral proposal links entanglement between two masses to nonclassical mediation under explicit subsystem and locality assumptions.

For constant-density incompressible flow, averaging u=U+u′ adds the Reynolds stress R_ij=⟨u′_iu′_j⟩ to the mean momentum equation.

DNS aims to resolve the dynamically relevant viscous scales of a specified flow; LES filters resolved scales and models subfilter stress.

A nonlinear polarization drives new frequency components.

In a lossless scalar narrowband Kerr envelope convention, i∂_zA=−D∂²_tA+δ|A|²A represents second-order dispersion and self-phase modulation.

Yee FDTD staggers electric/magnetic fields in space and time to approximate Maxwell curl evolution.

For a vector measurand Y=f(X), propagating a joint input distribution retains output dependence and non-Gaussian shape.

For a nonsingular m-variate Gaussian assigned distribution with mean y and known covariance U, (Y−y)ᵀU⁻¹(Y−y)≤χ²_(m,p) gives probability p.

Monte Carlo draws from the joint input model and evaluates all outputs from each common draw.

Under an assigned distribution g_Y for a measurand and a specification interval[T_L,T_U], the conformity probability is∫_(T_L)^(T_U)g_Y(y)dy.

For an upper specification limit T and assigned Y|data∼N(y,u²), accepting only y≤T−zu ensures Pr(Y>T|data)≤1−Φ(z) under that model.

Specific risk concerns an item given its measurement information.

For a causal linear time-invariant sensor with specified initial state, output is the convolution of input with impulse response plus noise.

A normalized frequency-domain Tikhonov inverse G=H*/(|H|²+λ²|L|²) suppresses ill-conditioned frequencies instead of dividing by an arbitrarily small H.

For N observations of one stationary process with covariance C_ij, Var(mean)=N⁻²Σ_ijC_ij.

A calibration likelihood can treat reference values x_i as latent uncertain quantities, with measured standards r_i and instrument indications y_i modelled jointly around x_i and f(x_i,θ).

Calibration parameters are identifiable only when distinct parameter values lead to distinguishable predictions for the available design and reference information.

A posterior predictive distribution integrates p(y_new|θ) over p(θ|data), retaining parameter uncertainty under the declared model.

For ν independent repetitions of a specified parameter-encoding state/channel, a locally unbiased estimator obeys Var(θ̂)≥1/(νF_Q) when the regularity assumptions apply.

Squeezing lowers noise in one optical quadrature while increasing conjugate noise.

Jia, Xu and collaborators reported quantum noise below a stated free-mass standard quantum limit by up to 3 dB with broadband sensitivity improvement using frequency-dependent squeezing.

Optical transition standards on the CIPM list are secondary representations of the second; their improved instrument performance does not itself change the SI definition.