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| Quantum Many-Body Problem | |
|---|---|
| Name | Quantum Many-Body Problem |
| Field | Theoretical physics |
| Notable | Albert Einstein, Erwin Schrödinger, Paul Dirac, Wolfgang Pauli |
| Related | Richard Feynman, Lev Landau, John Bardeen, Philip W. Anderson |
Quantum Many-Body Problem The Quantum Many-Body Problem is the challenge of predicting collective quantum behavior of large assemblies of interacting particles; it spans contexts from condensed matter to nuclear and atomic systems. It connects foundational work by Albert Einstein, Erwin Schrödinger, Paul Dirac, and Wolfgang Pauli to contemporary research involving Richard Feynman, Lev Landau, John Bardeen, and Philip W. Anderson, and underpins phenomena studied at institutions such as CERN, Bell Labs, MIT, Caltech, Stanford University.
The problem arises when extending single-particle quantum frameworks developed by Erwin Schrödinger, Paul Dirac, and Werner Heisenberg to many-body systems where interactions studied by Niels Bohr and Enrico Fermi generate emergent properties. Historically motivated by experiments at Bell Labs and theoretical advances at Landau Institute and Princeton University, it unites ideas from Richard Feynman's path integrals, Julian Schwinger's operator methods, and Lev Landau's quasiparticles. Applications range across research at Max Planck Society, IBM Research, Los Alamos National Laboratory, Argonne National Laboratory, and Lawrence Berkeley National Laboratory.
Formulations begin with an N-body Hamiltonian of particles introduced by Erwin Schrödinger and formalized by Paul Dirac; common models include the Hubbard model inspired by studies at Bell Labs, the Heisenberg model connected to Werner Heisenberg's magnetism work, and the BCS theory developed by John Bardeen, Leon Cooper, and Robert Schrieffer. The full Hilbert space grows exponentially as noted in analyses by Richard Feynman and David Bohm, requiring second quantization techniques from Pascual Jordan and Paul Dirac and Green's function methods formalized by Julian Schwinger and Leo Kadanoff. Boundary conditions and symmetries draw on group-theoretic tools used by Hermann Weyl and Eugene Wigner, while effective field theories connect to work at CERN and Brookhaven National Laboratory.
Perturbative approaches trace to Freeman Dyson and Richard Feynman's diagrammatics, while mean-field theories follow Lev Landau and Pierre-Gilles de Gennes strategies verified in Bell Labs experiments. Variational techniques invoke the Rayleigh–Ritz principle associated with Erwin Schrödinger and computational ansätze like Hartree–Fock used in Lawrence Livermore National Laboratory and Oak Ridge National Laboratory. Renormalization group methods by Kenneth Wilson link to critical phenomena analyzed at Landau Institute and Princeton University, and bosonization and conformal field theory leverage contributions from Alexander Zamolodchikov and John Cardy. Strongly correlated regimes invoke ideas of Philip W. Anderson, John Hubbard, and Andrey Kolmogorov-related complexity perspectives explored at Institute for Advanced Study.
Collective effects include superconductivity described by BCS theory and observed by John Bardeen, Leon Cooper, Robert Schrieffer and explored at Bell Labs, superfluidity linked to Lev Landau's two-fluid model and measured at CERN cryogenic facilities, magnetism via Heisenberg model and experiments at Los Alamos National Laboratory, and the fractional quantum Hall effect discovered by researchers affiliated with Princeton University, Bell Labs, and Columbia University. Other phenomena such as Mott insulators, Kondo effect investigated by Jun Kondo, and topological phases connected to Michael Berry and F. Duncan M. Haldane have driven work at Harvard University, Yale University, University of Cambridge, and Imperial College London.
Numerical renormalization group and density matrix renormalization group (DMRG) techniques trace to Kenneth Wilson and Steven R. White and are implemented on platforms from IBM Research to Google Quantum AI. Quantum Monte Carlo methods influenced by Nicholas Metropolis and John von Neumann address stochastic sampling challenges and are run at Argonne National Laboratory and NVIDIA-supported centers. Tensor network ansätze relate to Guifre Vidal and Frank Verstraete’s work at Massachusetts Institute of Technology and University of Vienna, while dynamical mean-field theory (DMFT) was developed by researchers linked to École Polytechnique and Rutgers University. Emerging quantum computing algorithms from Peter Shor and Lov Grover are tested on hardware by IBM, Google, Rigetti Computing, and IonQ.
Cold-atom simulators pioneered by groups at MIT, Harvard University, and University of Innsbruck exploit Bose–Einstein condensates first produced in labs guided by Eric Cornell and Carl Wieman, and Wolfgang Ketterle. Electron spectroscopy techniques such as angle-resolved photoemission spectroscopy (ARPES) are routinely used at Stanford Linear Accelerator Center and Brookhaven National Laboratory to probe electronic structure underlying many-body effects. Neutron scattering experiments at Oak Ridge National Laboratory and Institut Laue–Langevin examine magnetic correlations, while scanning tunneling microscopy advances at IBM Research and Max Planck Institute for Solid State Research resolve local density of states relevant to superconductivity and charge order.
Key open problems include a rigorous characterization of high-temperature superconductivity pursued at Columbia University, Stanford University, and Princeton University, non-equilibrium dynamics studied by groups at Caltech and Max Planck Institute for the Physics of Complex Systems, quantum thermalization and many-body localization investigated by teams at Harvard University and ETH Zurich, and entanglement scaling laws explored at Perimeter Institute and Institute for Advanced Study. Cross-disciplinary efforts involve quantum simulation pilots at Google Quantum AI and IBM, materials discovery using machine learning from Google DeepMind and Microsoft Research, and foundational issues tied to quantum information theory advanced at University of Oxford and Yale University.
Category:Quantum physics