Physics:Quantum many-body problem: Difference between revisions
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{{Short description|Problem of describing interacting systems with many quantum particles}} | {{Short description|Problem of describing interacting systems with many quantum particles}} | ||
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|image=[[File:Quantum_many_body_problem_yellow.png|430px|Many interacting particles generate a rapidly growing quantum state space.]] | |image=[[File:Quantum_many_body_problem_yellow.png|430px|Many interacting particles generate a rapidly growing quantum state space.]] | ||
|text=The | |text=The quantum many-body problem is a Book I topic in the Quantum Collection. It is the challenge of describing systems made of many interacting quantum particles, where the size of the Hilbert space grows rapidly with particle number. Exact solutions are rare, so the field uses approximations, effective theories, numerical methods, and emergent collective descriptions. The problem appears in atoms, nuclei, solids, quantum fluids, plasmas, and quantum information. It explains why simple microscopic rules can produce phases, quasiparticles, correlations, and complex macroscopic behavior. | ||
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== State-space growth == | == State-space growth == | ||
For a single particle, a wavefunction may be described over ordinary space. For many particles, the wavefunction depends on all particle coordinates and internal degrees of freedom. The number of amplitudes needed to represent the state can grow exponentially. | For a single particle, a wavefunction may be described over ordinary space. For many particles, the wavefunction depends on all particle coordinates and internal degrees of freedom. The number of amplitudes needed to represent the state can grow exponentially. | ||
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== See also == | == See also == | ||
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== References == | == References == | ||
Latest revision as of 23:02, 23 May 2026
The quantum many-body problem is a Book I topic in the Quantum Collection. It is the challenge of describing systems made of many interacting quantum particles, where the size of the Hilbert space grows rapidly with particle number. Exact solutions are rare, so the field uses approximations, effective theories, numerical methods, and emergent collective descriptions. The problem appears in atoms, nuclei, solids, quantum fluids, plasmas, and quantum information. It explains why simple microscopic rules can produce phases, quasiparticles, correlations, and complex macroscopic behavior.
State-space growth
For a single particle, a wavefunction may be described over ordinary space. For many particles, the wavefunction depends on all particle coordinates and internal degrees of freedom. The number of amplitudes needed to represent the state can grow exponentially.
This growth makes approximation methods central. Mean-field theory, perturbation theory, density functional theory, tensor networks, Monte Carlo methods, and effective models are all ways to reduce or reorganize the complexity.
Collective behavior
Many-body systems often display properties not obvious from individual particles alone. Examples include superconductivity, spin liquids, Fermi liquids, and topological phases.
The many-body problem is therefore both a technical challenge and a source of new physical phenomena.
See also
Table of contents (217 articles)
Index
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References
Source attribution: Physics:Quantum many-body problem