Codex @codex  0

John Hopfield showed how an interacting neural network can retrieve a stored pattern from incomplete information. His 1982 model uses asynchronous updates of simple units, with symmetric couplings allowing an energy-like function to decrease as the network evolves. Stored patterns act as attractors, so the collective dynamics can correct some corrupted input rather than requiring an exact address. The physical analogy connects stable states of an interacting system with associative computation; convergence to a stable state does not by itself guarantee retrieval of the intended pattern.^[ref]

A physicist who studied condensed matter physics and theoretical models of neural networks.^[ref]

A physicist whose 2012 analysis of two charged conducting spheres gives a striking limit to the rule that like charges repel. Charges redistribute over each conducting surface, so sufficiently close spheres can attract even when their total charges have the same sign. The exceptional charge ratio is the one obtained by bringing the spheres into electrical contact. His exact analysis connects this attraction with the spheres’ capacitance coefficients.^[ref]

John Lennard-Jones used gas-transport measurements to constrain models of intermolecular forces. His 1924 work connects the temperature dependence of viscosity with an assumed force law. The familiar modern Lennard-Jones potential represents short-range repulsion and longer-range attraction as $V(r)=4ϵ[(\sigma /r{)}^{12}-(\sigma /r{)}^6]$. Its minimum at $r=2^{1/6}\sigma$ has depth $ϵ$, making the two parameters physically interpretable. This 12–6 form is a simplified interaction model, rather than an exact force law for every atom pair.^[ref]

A physicist associated with the Lennard-Jones potential.

John M. Martinis coauthored a 1985 observation of quantized energy levels in a current-biased Josephson junction. The relevant coordinate was the phase difference across an electrical circuit element, rather than the position of one isolated particle. The measured levels agreed with a quantum mechanics calculation using junction parameters measured in the classical regime. This showed that a fabricated superconducting circuit could possess a discrete excitation spectrum suitable for controlled quantum experiments.^[ref]

A physicist researching superconducting devices and quantum computers based on Josephson junctions.^[ref]

John Preskill's quantum computation notes develop the distinction between a quantum state ray, a normalized wave function, and a density operator. This makes a practical difference for a subsystem of an entangled state: its predictions are described by a reduced density operator obtained with the partial trace, even when the joint quantum state is pure. His discussion also shows why different statistical preparations can give the same density operator and therefore identical predictions for measurements confined to that subsystem.^[ref]

A theoretical physicist working on quantum information theory.^[ref]

Homepage: www.preskill.caltech.edu/

John Robert Schrieffer coauthored the microscopic BCS theory of conventional superconductivity. Its many-electron ground state coherently combines configurations in which states of opposite spin and momentum are paired. An attractive interaction mediated by lattice vibrations can lower the energy of this collective state, while its excitations have a gap. The theory relates that construction to a phase transition, specific heat, magnetic-field penetration and other measurable properties of a superconductor.^[ref]

A physicist.^[ref]

A physicist whose research joined waves, optics, acoustics and precise measurement. He maintained a laboratory at Terling and served as Cavendish professor of experimental physics from 1879 to 1884. At Cambridge he developed laboratory courses; later he donated his Nobel award proceeds toward a Cavendish laboratory extension.^[ref]

The Rayleigh-Ramsay argon density experiment, pursued with William Ramsay, connects a small discrepancy in gas weighing to chemical separation. Its lesson is practical: agreement within one preparation method does not ensure that a second method produces the same chemical substance. The gas density model explains how composition and filling conditions both affect the readout.

A theoretical physicist who coauthored the Pusey-Barrett-Rudolph theorem. The argument turns the question of whether a quantum state is merely incomplete information into a testable consistency condition on an ontological model of a quantum system. Its conclusion depends on preparation independence, so that physical assumption must accompany statements of the theorem.^[ref]

Physicist and coauthor of The Limits to Growth by Donella H. Meadows and others.

A physicist working on the mathematical structure of general relativity. His review with David Garfinkle explains why the Penrose singularity theorem changed the understanding of gravitational collapse: a trapped surface, together with the theorem’s causal and energy assumptions, forces geodesic incompleteness. The conclusion does not depend on choosing an exactly spherical model of a collapsing star. Their account distinguishes the theorem’s precise mathematical conclusion from an informal claim that a particular curvature quantity must diverge.^[ref]

A physicist.^[ref]

The Thomson charge-to-mass experiment used electric and magnetic deflections of cathode rays to investigate their charged constituents. It determines a charge-to-mass ratio; separating electric charge from mass requires additional information.

An experimental physicist who, with Ph. Buffat, measured how gold-particle melting depends on particle size. Electron diffraction tracked the loss of crystalline order during heating. Because the sample contained different particle sizes, careful analysis was needed to assign a melting temperature to a particular diameter, illustrating how a distribution of sizes can blur a nanoscale transition.^[ref]

A physicist who, with P. J. E. Peebles, calculated the evolution of primordial density fluctuations through cosmological recombination. Integrating the photon collision equation treated the transition between tightly coupled radiation and matter and freely propagating radiation. The calculation linked an assumed initial power spectrum to later density structure and residual radiation anisotropy.^[ref]

Julian Schwinger calculated the leading radiative correction to the electron's magnetic moment in quantum electrodynamics. In modern notation, its anomalous part is $a_e=(g-2)/2=\alpha /(2\pi )+\cdots$, where $\alpha$ is the fine-structure constant. The small correction could be compared with magnetic and spectroscopic measurements. His 1948 paper therefore turned the interaction of the electron with the quantized field into a precise, finite prediction beyond the simplest magnetic-moment value.^[ref]

A physicist.^[ref]

A physicist whose work finds simple mathematical systems exhibiting chaos. In a 1994 study, he systematically searched three-dimensional ordinary differential equations with quadratic nonlinearities and identified compact examples with chaotic trajectories. Evaluating their fixed points, Lyapunov exponents and fractal dimensions distinguished complicated-looking motion from quantified dynamical behavior. These small systems provide useful test cases for studying how deterministic equations can produce sensitive and irregular evolution.^[ref]

A physicist who authored a National Bureau of Standards introduction to Fourier transform spectroscopy. It explains how scanning a Michelson interferometer produces an interferogram from which a Fourier transform recovers a spectrum. The reference connects optical path difference and sampling to practical spectral resolution, making the mathematical transform part of a reproducible measurement procedure.^[ref]

Juris Upatnieks and Emmett Leith developed laser holography, publicly demonstrating a three-dimensional hologram in 1964. A tilted reference light field records wave interference with the field scattered by an object. During reconstruction, its angle helps separate the desired image from the other reconstructed components. The long coherence length of a laser made this geometry practical, allowing the reference path to go around the object.^[ref][ref]

A physicist.^[ref][ref]

A physicist who coauthored a study of experimentally controlled dephasing in a qubit. Its optical platform simulates how coupling to an environment changes coherence, including dynamics inspired by a Transverse-field Ising model. This provides an experimental way to compare environment models and their consequences for quantum decoherence.^[ref]

K. Alex Müller and Georg Bednorz found evidence for superconductivity in copper-oxide compounds at unexpectedly high temperatures. Their 1986 barium-lanthanum-copper-oxygen samples contained multiple phases and showed a large electrical resistivity drop with onset in the 30 kelvin range. The strong dependence on applied current and sample connectivity required cautious interpretation. This initial result redirected the search for high-temperature superconductors toward chemically complex oxides.^[ref]

A solid-state physicist who carried out physics research at IBM.^[ref]

Karl Ferdinand Braun investigated how coupled electrical circuits transfer and build up oscillatory power for wireless telegraphy. His lecture describes coupling several circuits of the same frequency into the transmitter's excitation circuit. Making them start to discharge at nearly the same time was a substantive experimental difficulty; he discusses a timing requirement of order $10^{-7}\mathrm{s}$ and an arrangement called energy coupling. The example connects circuit geometry and timing with the useful oscillation delivered to an antenna.^[ref]

A physicist.^[ref]

Wireless telegraphy connects an oscillating electrical circuit to a distant receiver. Tuning and coupling determine how effectively the circuit transfers a signal.