method

quantum dynamics

Theoretical framework for simulating time evolution of quantum systems, used here to model reactions.
21 related articles

Description

Quantum dynamics is the theoretical framework for describing how quantum systems evolve over time. It provides the mathematical tools to simulate the time-dependent behavior of particles, fields, and interacting many-body systems, from simple two-level atoms to complex chemical reactions. In practice, quantum dynamics is used to model processes like molecular vibrations, electron transfer, and photochemical reactions, where classical mechanics fails to capture quantum effects such as superposition, tunneling, and coherence. By solving the time-dependent Schrödinger equation or using approximations like path integrals, researchers can predict reaction rates, spectra, and dynamical properties that are otherwise inaccessible.

History

The foundations were laid by Erwin Schrödinger in 1926 with his wave equation, and later extended by Paul Dirac and Richard Feynman with path integral formulations. Practical computational methods emerged in the mid-20th century with the advent of digital computers.

How it works

The core equation is the time-dependent Schrödinger equation, iℏ∂ψ/∂t = Hψ, where H is the Hamiltonian operator representing the system's total energy. Solving this equation yields the wavefunction ψ(t), from which observable properties can be extracted. For complex systems, exact solutions are rare, so approximations are used: the Born-Oppenheimer approximation separates nuclear and electronic motion, while methods like time-dependent density functional theory (TDDFT) or quantum master equations handle larger systems. These approaches propagate the quantum state in small time steps, often using numerical integration techniques on powerful computers.

In practice

Quantum dynamics simulations are used in computational chemistry to design catalysts, in materials science to predict charge transport, and in photovoltaics to understand energy conversion processes.

Fun fact

Quantum dynamics simulations of photosynthesis have revealed that coherence between electronic states may enhance energy transfer efficiency, a phenomenon still debated in the field.

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Related articles · 21

Quantum Physics2026-08-132 minarXiv:2608.13041express
Quantum Computer Simulates Turbulence for the First Time
When a fluid flows around an obstacle, it spawns vortices and shock waves. Describing their behavior means solving a nonlinear equation in which the flow velocity depends on itself. Classical supercomputers spend days on this, while quantum computers have barely been used: their native language is linear operations, but fluids are inherently nonlinear.
Quantum Physics2026-08-101 minarXiv:2608.09850express
Quantum systems and threads of memory
A drop of ink in a glass of water spreads in intricate swirls. Similarly, a quantum particle exchanging energy with its environment changes its state in a complex and entangled manner. Describing this dance between particle and environment has long baffled scientists.
Statistical Mech2026-07-192 minarXiv:2607.17072express
Chemistry Under the Metronome
A kitchen mixer runs at a single speed, but start jabbing the button and the mixture whips up differently. Chemical reactions behave much the same way when the rates of their individual steps are not constant but pulse over time.
Quantum Physics2026-06-272 minarXiv:2606.28660express
Cosmology2026-06-182 minarXiv:2606.20036express
Dark Energy from the Depths of the Atomic Nucleus
The universe is expanding at an accelerating rate, like dough that keeps rising faster even though the yeast ran out long ago. For twenty years, astronomers have been searching for the cause and call it dark energy. But what it is remains a mystery. New work proposes an unexpected source: the vacuum inside the atomic nucleus.
Math Physics2026-06-172 minarXiv:2606.19014express
The Political System as a Galaxy: A Quantum-Mechanical Model of Public Opinion
You can think of a political system as a vast galaxy — a gravitationally bound system of stars, gas, and dust. In this analogy, parties are the stars, radiating the light of public activity, while their supporters are dark matter, the invisible substance that emits no electromagnetic radiation but whose mass holds the whole structure…
HEP Phenomenology2026-06-101 minarXiv:2606.12404express
How Neutrinos Get Entangled in Stellar Cores
In the scorching heart of a dying star, an invisible stream is born — a neutrino gas. The particles race through matter almost without stopping, but when their density is enormous, they start to feel each other. Old calculations described this as a jostle in a crowd: each shove changes direction, but no connection arises between passersby.
How to Find the Perfect Nudge for a Complex System
An orchestra plays without a conductor, and you hear the tempo speeding up and slowing down. All you have is a recording of the sound, not the score. Can you tell from that recording which string to pluck to make the whole orchestra play more steadily?
Galaxies2026-05-312 minarXiv:2606.01496express
Why quasars flicker differently than we thought
A candle flame in a draft dances: now it flares up, now it almost goes out. Quasars behave much the same way — supermassive black holes in the centers of distant galaxies, surrounded by a scorching disk of infalling matter. Only they flicker not over seconds, but over months and years.
Quantum Gases2026-05-221 minarXiv:2605.23881express
Time Crystals: Eternal Ticking Clocks Made of Atoms
A time crystal resembles an eternal clock: its atoms spontaneously perform rhythmic movements. In ordinary clocks, a pendulum is driven by a spring or battery, but here the motion arises without an energy supply — the system simply returns to its initial state at regular intervals. This idea was proposed by Frank Wilczek in 2012.
HEP Theory2026-05-071 minarXiv:2605.06985express
Quantum Chaos on a Glowing Sphere
On the surface of a tiny sphere live two invisible fields, like two kinds of ripples on a soap bubble. These fields don't just oscillate on their own: they constantly influence each other, like musicians playing in unison. In a new study, physicists derived exact equations that describe how this ripple changes over time, heats up, and descends into chaos.
Nuclear Theory2026-03-271 minarXiv:2603.26881express
Nuclear Reactions on a Quantum Computer
When two atomic nuclei collide, the outcome depends on their energy and the angle at which the fragments fly apart. Typically, such calculations demand enormous computing power, and accuracy hits a wall due to approximations.
General Relativity2026-03-212 minarXiv:2603.20747express
How the Universe's Clocks Set the Pace of Time
In everyday life, time flows on its own, like a river past its banks. But in quantum gravity, things are different: time does not flow; it emerges from relations between objects, like a pattern in a carpet that is only visible when viewed from a certain spot.
Quantum Physics2026-02-162 minarXiv:2602.14437express
Magnetic Resonance for Electrons
Electrons in a conductor behave like a crowd on an escalator: each one moves on its own, but together they create a flow. If you make them circle around a ring, their angular momentum (a measure of rotation) can couple to a magnetic field, like gears in a clock.
Quantum Physics2026-02-051 minarXiv:2602.05223express
A Quantum Cat in a Beam of Light
Light trapped in a tiny cavity is like a pendulum that gets pushed harder and harder. At first, it swings smoothly and predictably, like an ordinary clock. But if you push it hard enough, the motion becomes strange: the pendulum seems to be in two extreme positions at once.
Statistical Mech2026-02-031 minarXiv:2602.03764express
Quantum Bath: How Noise Does Work
A pot on a stove receives heat, but not work: the gas under the lid just heats up. But what if the stove is not ordinary, but quantum? Then heat and work can arrive simultaneously, like from an engine that also heats. In a new study, exactly this case is described: a classical system (say, a pendulum or a small mirror) bathes in a quantum environment.
HEP Theory2026-01-051 minarXiv:2601.02331express
Particles Play Shy in an Expanding Universe
The expansion of the universe is like a dance floor stretching wider. For decades, physicists assumed that more stretching would spawn more particles, like the floor spontaneously generating new dancers. But those models ignored an obvious fact: dancers sometimes link arms. When particles interact, new simulations reveal, they actually suppress creation.
Quantum Physics2025-10-301 minarXiv:2510.26295express
Quantum Predator-Prey Games
In nature, everything is cyclical: hares multiplied — foxes thrived — hares ran out — foxes died off — and the cycle repeated. This 'predator-prey' model was invented a century ago, and it works everywhere: from chemistry to economics. Physicists have now brought this storyline to the atomic stage.
Quantum Physics2025-10-131 minarXiv:2510.11679express
Hourglass of Entropy: How Cold Atoms Keep Time
In the lab, time usually ticks on the wall: hands, digits, a frequency standard. But for the Universe, there are no external clocks. The Wheeler–DeWitt equation, the main law of quantum gravity, contains no time at all, and all fundamental theories lack an inbuilt arrow of time.
A Translator That Hears Who Controls Whom
Picture a translator at a meeting where everyone speaks an unfamiliar language. They don't know the words, but they notice: when one person raises their voice, another starts nodding a minute later. At first it seems like coincidence, but over time the translator learns to understand who influences whom.