OpenStem

@openstem · Joined Jul 2026

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Flashcards12 cards

What does it mean for light to be polarized?1 / 12

Light is a transverse electromagnetic wave — its electric field oscillates perpendicular to the direction of travel. In unpolarized light (e.g. sunlight), the field oscillates in every direction perpendicular to propagation, randomly and rapidly. Polarized light has its electric field confined to a single, fixed plane.

Physics

Physics · L4 · Polarization & Diffraction

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Flashcards8 cards

State the Biot–Savart law for the field of a current element.1 / 8

dB = (μ₀/4π) · I dL × r̂ / r², where I dL is a current element, r̂ points from the element to the field point, and r is the distance between them. The total field is the vector sum (integral) of contributions from every element along the wire.

Physics

Physics · L4 · Magnetism — Biot–Savart & Ampere's Law

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Flashcards8 cards

State Kirchhoff's current law (KCL).1 / 8

The sum of currents entering a node equals the sum of currents leaving it — charge cannot accumulate at a node in a steady circuit. It is a direct statement of conservation of charge.

Physics

Physics · L4 · DC Circuits — Kirchhoff's Laws & RC Transients

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State the ideal gas law and identify each symbol.1 / 8

PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the universal gas constant (8.314 J/(mol·K)), and T is absolute temperature (in kelvin).

Physics

Physics · L4 · Kinetic Theory of Gases

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Flashcards8 cards

State Newton's law of universal gravitation.1 / 8

F = Gm₁m₂/r², directed along the line joining the two masses, always attractive. G = 6.674 × 10⁻¹¹ N·m²/kg² is the universal gravitational constant.

Physics

Physics · L4 · Gravitation & Orbital Mechanics

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Define mechanical stress and give its SI unit.1 / 8

Stress σ = F/A, the force per unit cross-sectional area applied to a material. SI unit: Pa (pascal, N/m²) — the same unit as pressure, since both describe force distributed over area.

Physics

Physics · L4 · Elasticity — Stress, Strain & Young's Modulus

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What determines the speed of sound in a medium, in general terms?1 / 8

v = √(elastic property / density) — for a gas, roughly v = √(γRT/M) for an ideal gas (γ ratio of specific heats). Sound travels faster in stiffer, less dense media: faster in solids than liquids, faster in liquids than gases.

Physics

Physics · L4 · Sound Waves & the Doppler Effect

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Flashcards8 cards

State Fourier's law of heat conduction through a slab of thickness L, area A, and thermal conductivity k.1 / 8

The rate of heat flow: Q/t = kA(ΔT)/L, where ΔT is the temperature difference across the slab. Heat flows from hot to cold, at a rate proportional to the conductivity, area, and temperature gradient, and inversely proportional to thickness.

Physics

Physics · L4 · Heat Transfer — Conduction, Convection & Radiation

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Flashcards8 cards

Define capacitance and state its defining formula.1 / 8

C = Q/V, the ratio of stored charge to the potential difference across the capacitor. It is a geometric property of the conductor pair (and any dielectric between them) — independent of Q and V individually. SI unit: farad (F = C/V).

Physics

Physics · L4 · Capacitance & Dielectrics

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Flashcards5 cards

What mathematical structure does quantum mechanics assign to the state space of a physical system?1 / 5

A separable complex Hilbert space ℋ. Pure states are represented by unit rays (equivalence classes of vectors differing by a phase), or equivalently by rank-1 projection operators (density matrices |ψ⟩⟨ψ|).

Physics

Physics · L5 · Formal Quantum Mechanics

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Define the canonical partition function Z for a system in thermal contact with a reservoir at temperature T.1 / 5

Z is a sum over all microstates i with energy Eᵢ:

Physics

Physics · L5 · Statistical Mechanics

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Flashcards10 cards

State Bloch's theorem for an electron in a periodic crystal potential U(r).1 / 10

If U(r + a) = U(r) for every lattice vector a, the energy eigenstates take the form

Physics

Physics · L5 · Condensed Matter Physics

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Flashcards10 cards

What is n-type doping, and how does it introduce extra carriers?1 / 10

A pentavalent (Group V) impurity such as phosphorus or arsenic substitutes for a host atom (e.g. silicon, Group IV). Four of its five valence electrons form covalent bonds with neighbours; the fifth is only weakly bound to the donor ion, occupying a shallow donor level just below the conduction band edge. At room temperature it is thermally ionised into the conduction band, donating a free electron — the majority carrier in n-type material.

Physics

Physics · L5 · Condensed Matter Physics — Doping & the p–n Junction

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Flashcards10 cards

What are the two classes of fundamental fermions in the Standard Model, and what distinguishes them?1 / 10

Quarks and leptons. Quarks carry color charge and participate in the strong interaction (in addition to the electroweak); leptons carry no color charge and interact only electroweakly. Both are spin-½ fermions.

Physics

Physics · L5 · Particle Physics

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Name the four fundamental force carriers (gauge bosons) of the Standard Model and the interaction each mediates.1 / 9

Photon (γ) — electromagnetism. Gluon (g) — strong interaction. W± and Z⁰ bosons — weak interaction. (Gravity has no confirmed Standard Model carrier; the hypothesized graviton lies outside the SM.)

Physics

Physics · L5 · Particle Physics

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Flashcards11 cards

What is meant by 'sensitive dependence on initial conditions' (the butterfly effect)?1 / 11

Two trajectories starting arbitrarily close together in phase space diverge exponentially in time, so that after a finite time the systems are effectively uncorrelated. Formally, |δx(t)| ≈ |δx(0)| e^(λt) with λ > 0 (the Lyapunov exponent). This makes long-term prediction impossible even though the governing equations are fully deterministic — the term comes from the notion that a butterfly's wingbeat could, in principle, alter the trajectory of a distant weather system weeks later.

Physics

Physics · L5 · Nonlinear Dynamics & Chaos

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Flashcards8 cards

What is a Poincaré section, and why is it a useful tool for analyzing chaotic flows?1 / 8

A Poincaré section reduces a continuous flow in an n-dimensional phase space to a discrete map on an (n−1)-dimensional surface, by recording the state each time the trajectory crosses a chosen surface transversally (e.g. z = z₀ with ż > 0). A periodic orbit becomes a single fixed point (or finite set of points) on the section; a strange attractor appears as a self-similar fractal pattern of points. It converts an intractable continuous problem into a discrete map that is far easier to visualize and analyze.

Physics

Physics · L5 · Chaos: Routes, Measures & Applications

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Flashcards10 cards

Define the electromagnetic field tensor F^μν in terms of the four-potential A^μ.1 / 10

F^μν is the antisymmetrized four-gradient of the four-potential A^μ = (φ/c, A). Because it is built from a curl-like operation on A^μ, it is automatically antisymmetric: F^μν = −F^νμ.

Physics

Physics · L5 · Covariant Electrodynamics

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Flashcards8 cards

Define the four-potential A^μ and give the SI expressions for E and B in terms of φ and A.1 / 8

The scalar potential φ and vector potential A combine into one four-vector. From them: E = −∇φ − ∂A/∂t and B = ∇×A. These are exactly the relations that make F^μν = ∂^μA^ν − ∂^νA^μ reproduce the correct E and B.

Physics

Physics · L5 · Covariant Electrodynamics — Four-Potential, Gauge, and Field Mixing

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Flashcards10 cards

What is an order parameter, and what does it mean physically?1 / 10

A quantity that is exactly zero in the disordered (symmetric) phase and nonzero in the ordered phase, serving as a measure of how much the phase transition's symmetry has been spontaneously broken. Example: the magnetization M of a ferromagnet is zero above the Curie temperature and nonzero below it.

Physics

Physics · L5 · Phase Transitions & Critical Phenomena

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Flashcards9 cards

Define the critical exponent β and state the scaling law it appears in.1 / 9

β governs how the order parameter vanishes as T approaches T_c from below:

Physics

Physics · L5 · Phase Transitions & Critical Phenomena

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Flashcards10 cards

In quantum field theory, what is treated as the fundamental physical object — the particle or the field?1 / 10

The field. A quantum field φ̂(x) is defined at every point of spacetime; what we call a 'particle' is not a fundamental entity but a quantized excitation (a normal mode) of the underlying field. This is the reverse of non-relativistic QM, where a fixed number of particles is promoted to have wavefunctions.

Physics

Physics · L5 · Quantum Field Theory

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Flashcards11 cards

What does the Feynman propagator represent physically?1 / 11

The amplitude for a field excitation (a particle) created at one spacetime point y to be found — propagated, possibly faster than the naive classical light-cone picture suggests, but causally consistent overall — and annihilated at another spacetime point x. It is the fundamental building block from which all scattering amplitudes are assembled.

Physics

Physics · L5 · Quantum Field Theory

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Flashcards8 cards

State the first-order energy correction in time-independent perturbation theory for H = H₀ + λH'.1 / 8

E_n^(1) = ⟨n⁽⁰⁾|H'|n⁽⁰⁾⟩, the expectation value of the perturbation in the unperturbed eigenstate. It is simply the diagonal matrix element — no summation over other states is needed at first order.

Physics

Physics · L5 · Perturbation Theory & Scattering

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Flashcards7 cards

What key assumption underlies the FLRW metric, and what does it imply about the universe's large-scale structure?1 / 7

The cosmological principle: on large enough scales, the universe is homogeneous (the same everywhere) and isotropic (the same in every direction). This forces spacetime's spatial geometry to be one of constant curvature, described by a single time-dependent scale factor a(t) and a curvature constant k.

Physics

Physics · L5 · Cosmology — Friedmann Equations & the Expanding Universe

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What are the two defining experimental signatures of superconductivity?1 / 7

(1) Zero DC electrical resistance below a critical temperature T_c — persistent currents have been observed to flow essentially undiminished for years. (2) The Meissner effect — a superconductor actively expels magnetic field from its interior, not merely a consequence of zero resistance (a perfect conductor alone would only trap flux, not expel it).

Physics

Physics · L5 · Superconductivity — BCS Theory & the Meissner Effect

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Flashcards7 cards

What is a qubit, and how does its state space differ from a classical bit?1 / 7

A qubit is a two-level quantum system whose state is a normalised superposition |ψ⟩ = α|0⟩ + β|1⟩, with |α|² + |β|² = 1, in contrast to a classical bit which is always definitely 0 or 1. The continuum of possible superpositions (and, for mixed states, the full Bloch sphere) gives a qubit vastly richer state space than a classical bit.

Physics

Physics · L5 · Quantum Information — Entanglement & Bell's Theorem

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Flashcards7 cards

Distinguish a global symmetry from a local (gauge) symmetry.1 / 7

A global symmetry transforms fields by the same fixed amount everywhere in spacetime, e.g. ψ → e^(iα)ψ for constant α. A local (gauge) symmetry allows the transformation parameter to vary from point to point, α(x), and demanding invariance under this much larger symmetry group forces the introduction of a compensating gauge field.

Physics

Physics · L5 · Gauge Theories & the Higgs Mechanism

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Flashcards7 cards

What defines a plasma as a distinct state of matter, beyond simply being an ionised gas?1 / 7

A plasma is a quasi-neutral ionised gas exhibiting collective behaviour — charged particles interact with the self-consistent electromagnetic fields generated by the whole ensemble, not just via individual nearby collisions. This collective, long-range electromagnetic coupling is what distinguishes plasma dynamics from an ordinary neutral gas.

Physics

Physics · L5 · Plasma Physics — Debye Shielding & Plasma Oscillations

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Flashcards6 cards

State Feynman's central postulate of the path integral formulation.1 / 6

The quantum amplitude for a particle to go from point A to point B is a sum over every possible path connecting them, each path weighted by e^(iS[path]/ℏ), where S is the classical action of that path. Unlike classical mechanics, which picks out one extremal path, quantum mechanics sums the contributions of literally all paths, however wild.

Physics

Physics · L5 · The Path Integral Formulation of Quantum Mechanics

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