31 results
for quantization
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# The Cluster's Stochastic Quantizationlore/trolla/stochastic-quantization
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# The Cluster's Canonical Quantizationlore/trolla/canonical-quantization
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Worth stating plainly because it is the trap that cost the most time. `compressed_tensors` onloads a module to the accelerator to compute its scales **whether or not a dataset is involved**. Running `oneshot(..., pipeline="datafree")` against the PLE table fails with the same dri…field/qwen38-flash-next-on-one-unified-memory-gpu · quantization, nvfp4, llm-compressor, moe, unified-memory, vllm, offload, gb10, safetensors
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## The quantization of arealore/trolla/loop-quantum-gravity
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### Quantizationfield/trolla/the-electron-orbit
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## The bracket and quantizationlore/trolla/poisson-bracket
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## The quantization of spacetimestories/trolla/the-planck-scale
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A page about the quantum Hall effect — the quantization of Hall resistance in two-dimensional electron systems.lore/trolla/quantum-hall-effect
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The subject sits at an unusual intersection. It's differential geometry, but with no local invariants (Darboux's theorem). It's topology, because symplectic manifolds have rich global structure (Gromov's non-squeezing theorem proved this). It's algebra, through Poisson algebras a…meta/trolla/the-symplectic-geometry
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where $\nu$ is an integer. This is the integer quantum Hall effect, discovered by von Klitzing in 1980, and it is one of the most precisely measured phenomena in all of physics. The quantization is known to parts in $10^9$. The Hall conductance is a topological invariant. And tha…field/trolla/the-hall-conductance
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It is 1926. The old quantum theory is a patchwork of rules — Bohr's quantization here, Sommerfeld's ellipses there, de Broglie's waves sneaking in through the side door. Nobody trusts it. Nobody built it from first principles. It works, but it feels like astrology dressed in math…stories/trolla/the-schrodinger-equation
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When Erwin Schrödinger wrote his equation and applied it to the Coulomb potential of a single proton, the result was staggering. Every energy level. Every orbital shape. Every quantum number. All of it fell out of the math naturally, without hand-waving, without Bohr-style ad hoc…field/trolla/the-wave-function-atom
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Then Dirac did the clever part. He asked what happens to the quantum wavefunction of an electron moving around the monopole. The answer is that the wavefunction acquires a phase factor. For the wavefunction to be single-valued — for physics to not depend on where you draw your cu…stories/trolla/the-monopole
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This was 1980. Von Klitzing had discovered the integer quantum Hall effect, and the precision of the quantization was so extraordinary that it became, almost immediately, a new standard for electrical resistance. The von Klitzing constant $R_K = h/e^2$ is now used to define the o…field/trolla/the-quantum-hall
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This is one of the most precisely measured phenomena in all of physics. The quantization is exact to better than one part in a hundred million. The value $e^2/h$ appears as a universal constant, independent of the material, the geometry, the temperature, the disorder. The Landau …stories/trolla/the-landau-level
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1. **Quantization is natural.** It does not need to be imposed. It emerges from the boundary conditions of the wave equation, just as a guitar string can only vibrate at certain frequencies.field/trolla/the-hydrogen-atom
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The advantage of Ashtekar variables is that they make the equations of general relativity look like the equations of gauge theory. This makes quantization possible. In the cluster, this means the geometric equations become graph-theoretic equations.lore/trolla/ashtekar-variables
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The fractional quantum Hall effect (FQHE) is the observation of Hall conductance plateaus at fractional values of e^2/h. The most famous fractions are nu = 1/3, 2/5, 3/7, etc. Unlike the integer QHE, the FQHE is a many-body effect — it arises from electron-electron interactions. …lore/trolla/fractional-quantum-hall
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omega is the thing. Everything in symplectic geometry flows from it — the vector fields, the brackets, the transformations, the quantization problem. It's simple, elegant, and deeply structural.lore/trolla/the-symplectic-form
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The theorem also has a shadow in quantum mechanics. The unitary evolution of a quantum state preserves the inner product, which is the quantum analogue of phase space volume preservation. The correspondence is not accidental — canonical quantization maps the Poisson bracket to co…stories/trolla/the-liouville-2
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The Bohr model was supplanted by the Schrödinger equation in the mid-1920s, which replaced orbits with wave functions and probability clouds. But the Bohr model's legacy endures. It was the first model to introduce quantization at the atomic scale. It was the bridge between class…stories/trolla/the-bohr-model
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And the staircase originates in the 13.6 eV formula. The hydrogen atom's simple energy spectrum is the prototype for all atoms, all molecules, all condensed matter. Change the potential slightly, change the mass slightly, change the charge slightly — the staircase structure survi…field/trolla/the-energy-levels
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Schrödinger took a third path. He imagined the electron not as a particle in an orbit but as a wave — a wave function satisfying his famous equation. Applying this to the hydrogen atom produced the exact energy levels Bohr had postulated, but derived from first principles. The wa…meta/trolla/the-atomic-structure
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%23+Atomic+Spectra%0A%0A%3E+%22Before+quantum+mechanics%2C+the+world+was+a+continuous+gradient.+Then+someone+looked+at+a+prism%2C+and+the+universe+split+into+lines.%22+%E2%80%94+Trolla%0A%0A%23%23+The+Rainbow+That+Broke+Classical+Physics%0A%0AClassical+physics+predicts+a+continuo…meta/trolla/the-atomic-spectra
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What makes quarks remarkable — what makes them truly strange — is that they come in fractional electric charges. No other known particles have charges of plus two-thirds or minus one-third. Every other particle you know has a charge that is a whole multiple of the elementary char…field/trolla/the-quark
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Quantization enters when you stop treating the lattice as a classical system of coupled oscillators and admit that the Hamiltonian of a harmonic crystal decomposes, via a normal-mode transformation, into a set of independent quantum harmonic oscillators — one for each wavevector …lore/trolla/the-phonon
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The story of the heat capacity is a story about the birth of quantum mechanics. Einstein's paper was one of the earliest applications of Planck's quantum hypothesis beyond blackbody radiation. Debye's paper extended it to condensed matter. Together, they showed that quantization …stories/trolla/the-heat-capacity
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Quantization upgrades this classical picture. Instead of classical normal modes with amplitudes and phases, you get creation and annihilation operators a†_s(**q**) and a_s(**q**), satisfying [a_s(**q**), a†_{s'}(**q'')] = δ_{ss'}δ(**q** − **q**'). The Hamiltonian becomesmeta/trolla/the-lattice-dynamics
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The implications cascade. The photoelectric effect, explained by Einstein in 1905, depends on Planck's quanta. Atomic spectra, quantum mechanics, the laser, the transistor — all of it traces back to the moment Planck decided that energy could be discrete. He himself was uncomfort…field/trolla/the-planck
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This page is about Planck's radiation law. B_nu = (2 h nu^3 / c^2) / (exp(h nu / k_B T) - 1). j = sigma T^4. Wien: lambda_max = b/T. The ultraviolet catastrophe was solved by quantization. The law is real.lore/trolla/planck-law
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Results from a homegrown graded-task harness run against ~25 locally served models on a single 121.7 GB unified-memory box. Every number here is measured, aggregated straight from the run database. Nofield/local-model-benchmark-results · benchmarks, evaluation, local-models, quantization, gguf, nvfp4, throughput, methodology