Replacement of an early Rab-regulated membrane identity by a later one, exemplified by Rab5 loss and Rab7 acquisition during endosome maturation.

A Rab-family regulator associated with early endosomal membrane domains.

Active Rab5 recruits partners that organize early endosomes and membrane fusion. Replacement of Rab5-associated identity by Rab7-associated identity helps connect early uptake with later degradative trafficking, rather than requiring each endosome to retain one permanent molecular label. ^[ref]

A Rab-family regulator associated with late endosomal and degradative trafficking.

Its effectors help connect late endosomes to movement, targeting and fusion with degradative compartments. The transition from Rab5 to Rab7 illustrates maturation of membrane identity; a static marker image captures a state rather than the whole trafficking history. ^[ref]

Rab11a is a Rab GTPase associated with recycling membrane traffic. It helps organize the return or redistribution of internalized components and contributes to polarized delivery in several cell types. Its effectors connect nucleotide state to targeting and motor systems. A recycled receptor can regain surface availability without being synthesized again, illustrating how trafficking changes cellular responsiveness on short timescales. ^[ref]

Rab8a is a Rab GTPase involved in delivery toward the cell surface and ciliary membrane organization. Rabin8 activates it through nucleotide exchange, linking upstream signals to effector recruitment. Its membrane location and nucleotide state together help determine productive interactions. A fluorescent Rab8a spot therefore reports localization without automatically specifying whether the switch is active or transport is proceeding. ^[ref]

A transverse confinement eigenstate that defines a threshold for propagation along a narrow conductor. Above that threshold, its longitudinal dispersion supplies an incident channel from each reservoir. spin can label separate channels; an unresolved spin-degenerate mode contributes twice the single-spin spin-resolved conductance quantum. This physical use of mode is unrelated to the most probable value of a probability distribution.

For exchange $J>0$, the Jordan–Wigner transformation gives a band ${ϵ}_k=h-J\cos k$. At zero temperature, negative-energy states form a filled interval $|k|<\arccos (h/J)$. Since each fermion decreases total magnetization by one, the thermodynamic magnetization per site is $1/2-\arccos (h/J)/\pi$. It saturates at $1/2$ for $h\ge J$. A finite ring instead has discrete level crossings and parity-dependent momentum grids.

Suppression of tunnelling because adding or removing a discrete island charge costs more energy than the accessible transport and thermal energy window. Weak junction coupling and small island capacitance make it observable.

A biased double-barrier structure whose intermediate quasi-bound levels control transmission from reservoirs. Bias-dependent alignment can produce negative differential resistance when a resonance moves out of the available injection window.

At energy equal to a finite rectangular barrier height, the stationary interior Schrödinger equation has a linear solution $\psi =bx+c$. Its probability current can be nonzero: $J=(\hslash /m)\mathrm{Im}(c^{\ast }b)$. Setting the interior classical kinetic energy to zero does not set the transmitted quantum flux to zero.

Transport by successive real charge-state changes across weak tunnel barriers. Charge electrochemical potentials must enter the source-drain bias window; outside it sequential transport is Coulomb blocked. Higher-order virtual cotunnelling is a distinct process.

Finite lifetime of an island state due to tunnelling into leads gives an energy-width scale of order $\hslash \Gamma$. The numerical factor depends on whether $\Gamma$ denotes a population decay rate, an amplitude decay rate or a sum of partial rates.

A bosonic state with Gaussian phase-space characteristic function, specified by its first and second optical quadrature moments. Vacuum, coherent states, optical squeezed vacuum and thermal states are examples. Gaussian here describes phase-space statistics, not a Gaussian optical pulse envelope.

A particle incident below a semi-infinite step has a unit-modulus quantum reflection amplitude but a nontrivial phase. Continuity of the oscillating and evanescent solutions yields the displayed coefficient, for the incident phase origin at the interface. Its decaying exterior wave has zero net probability current. The phase depends on the chosen scattering convention; the unit reflection probability does not.

A quantum reflection amplitude is the complex ratio of the outgoing reflected wave to the incident wave in a chosen scattering convention. In one reflected channel with the same exterior speed, the reflection probability is $|r{|}^2$. Its phase affects interference even when its modulus is one; shifting the reference plane changes that phase.

When the free angular-momentum phases all recur at the driving period, successive identical kicks add coherently. For the full revival $\hslash T/(2I)=2\pi$ and an initial zero-angular-momentum state, the kinetic energy after $N$ kicks is ${\hslash }^2{\eta }^2{N}^2/(4I)$. This ballistic law is specific to the stated resonance and boundary conditions.

Pair production creates a particle and its antiparticle while conserving energy, momentum and relevant charges. For an electron–Positron pair, the available invariant energy must at least supply their combined rest mass, with additional kinetic energy and other final-state requirements included.

A single free photon in empty flat spacetime cannot produce just that pair: its four-momentum has zero invariant mass, while the massive pair has a positive invariant mass. A second photon or another participant, such as a nucleus taking recoil, can satisfy the full kinematics. The pair's charges cancel globally, but each outgoing particle can leave its own detector track. A laboratory-frame photon energy threshold therefore depends on the complete reaction, not only on writing twice the electron rest energy.