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The Kitaev chain is a one-dimensional spinless p-wave superconductor. Its topological phase has a Majorana zero mode at each end of an open chain.

A quadratic fermion Hamiltonian is bilinear in creation and annihilation operators. In a Majorana basis it is determined, up to a constant, by a real antisymmetric matrix.

An open cover of a subset $A$ is a family of open sets whose union contains $A$.

The Sierpiński space is $\{0,1\}$ with open sets $\varnothing$, $\{1\}$, and $\{0,1\}$. Continuous maps $X\to S$ are in bijection with open subsets of $X$ through $g\mapsto g^{-1}(1)$.

A family $\mathcal{T}$ of subsets of a set $X$ is a topology when $\varnothing ,X\in \mathcal{T}$, every union of members of $\mathcal{T}$ belongs to $\mathcal{T}$, and every finite intersection of members of $\mathcal{T}$ belongs to $\mathcal{T}$.

The circle is the subspace $S^1=\{z\in \mathbb{C}:|z|=1\}$, equivalently the quotient of a closed interval obtained by identifying its endpoints.

The unitary group $U(n)$ consists of complex matrices preserving the standard Hermitian inner product.

For loops based at the identity of a topological group, pointwise multiplication and concatenation obey the interchange law and have the same identity. The Eckmann-Hilton argument therefore makes the fundamental group abelian.

For a two-component gapped BdG Hamiltonian constrained to a plane, the winding number counts how many times its coefficient vector encircles the origin as crystal momentum traverses the Brillouin zone.

When pressure and velocity are in quadrature, their instantaneous energy flux oscillates but its period average vanishes.

For $N$ identical sites of spacing $a$ with periodic boundary conditions, translation eigenstates have coefficientsThus $k=2\pi j/(Na)$ modulo the reciprocal-lattice period $2\pi /a$.

The Hills mass is the black-hole mass above which a given star crosses the capture boundary before being tidally disrupted. For a Schwarzschild capture radius $2G{M}_{\mathrm{BH}}/c^2$, it is $c^3{R}_{\ast }^{3/2}/(2G^{3/2}{M}_{\ast }^{1/2})$ with the corresponding tidal-radius convention.

For a star of mass $M_{\ast }$ and radius $R_{\ast }$ near a black hole of mass $M_{\mathrm{BH}}$, the Newtonian tidal disruption radius is $r_t\simeq R_{\ast }(2M_{\mathrm{BH}}/M_{\ast }{)}^{1/3}$ under a peak-to-center tidal-acceleration convention.

The surface density of a disk is its volume density integrated vertically, $\Sigma ={\int }_{-\infty }^{\infty }\rho dz$.

The ideal Diesel cycle consists of reversible adiabatic compression, constant-pressure heat addition, reversible adiabatic expansion, and constant-volume heat rejection.

The ideal Otto cycle has adiabatic compression, constant-volume heat addition, adiabatic expansion, and constant-volume heat rejection. For an ideal gas with compression ratio $r=V_1/V_2$ and specific-heat ratio $\gamma$,

The thermal efficiency of a heat engine is the net work output divided by heat input. For a cycle absorbing $Q_{\mathrm{in}}$ and rejecting the positive amount $Q_{\mathrm{out}}$,

If a relativistic species decouples when the coupled plasma has $g_{\ast s,\mathrm{dec}}$ entropy degrees of freedom, then after the plasma reaches $g_{\ast s}$ degrees of freedom,The ratio follows from separate redshifting of the decoupled species and cosmological entropy conservation in the coupled plasma.

For $u(y)=Uy/h$ between reflecting walls at $y=\pm h$, the flow-induced diffusivity is

The velocity vector of a parametrized curve $\mathbf{r}(t)$ is its tangent vector ${\mathbf{r}}^{\prime }(t)$.