Classical Dynamics Generated by Long-Range Interactions for Lattice Fermions and Quantum Spins
arXiv:2009.05315 · doi:10.1016/j.jmaa.2020.124434
Abstract
We study the macroscopic dynamical properties of fermion and quantum-spin systems with long-range, or mean-field, interactions. The results obtained are far beyond previous ones and require the development of a mathematical framework to accommodate the macroscopic long-range dynamics, which corresponds to an intricate combination of classical and short-range quantum dynamics. In this paper we focus on the classical part of the long-range, or mean-field, macroscopic dynamics, but we already introduce the full framework. The quantum part of the macroscopic dynamics is studied in a subsequent paper. We show that the classical part of the macroscopic dynamics results from self-consistency equations within the (quantum) state space. As is usual, the classical dynamics is driven by Liouville's equation.
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References in corpus (24)
- On the Mean Field and Classical Limits of Quantum Mechanics
- Mean-field Evolution of Fermionic Systems
- Justification of c-Number Substitutions in Bosonic Hamiltonians
- Equilibrium Statistical Mechanics of Fermion Lattice Systems
- Mean field evolution of fermions with Coulomb interaction
- Mean-Field Dynamics of Fermions with Relativistic Dispersion
- Kinetic Energy Estimates for the Accuracy of the Time-Dependent Hartree-Fock Approximation with Coulomb Interaction
- Accuracy of the time-dependent Hartree-Fock approximation for uncorrelated initial states
- Density Functional Theory versus the Hartree Fock Method: Comparative Assessment
- Feller Evolution Systems: Generators and Approximation
- Lieb-Robinson Bounds for Multi-Commutators and Applications to Response Theory
- Concentration of cylindrical Wigner measures
- Macroscopic quantum phenomena from the large N perspective
- Non-cooperative Equilibria of Fermi Systems With Long Range Interactions
- Quasi-Classical Dynamics
- Effect of a Locally Repulsive Interaction on s-wave Superconductors
- Derivation of the time dependent Gross-Pitaevskii equation for a class of non purely positive potentials
- Free energy density for mean field perturbation of states of a one-dimensional spin chain
- Quantum Dynamics Generated by Long-Range Interactions for Lattice Fermions and Quantum Spins
- Macroscopic Dynamics of the Strong-Coupling BCS-Hubbard Model
- On well-posedness and uniqueness for general hierarchy equations of Gross-Pitaevskii and Hartree type
- Classical Dynamics from Self-Consistency Equations in Quantum Mechanics -- Extended Version
- Entanglement of Classical and Quantum Short-Range Dynamics in Mean-Field Systems
- Long time behaviour of interacting particles through a vibrating medium: comparison between the N-particle systems and the natural kinetic equation dynamics
Cited by in corpus (4)
- Quantum Dynamics Generated by Long-Range Interactions for Lattice Fermions and Quantum Spins
- Macroscopic Dynamics of the Strong-Coupling BCS-Hubbard Model
- Classical Dynamics from Self-Consistency Equations in Quantum Mechanics -- Extended Version
- Entanglement of Classical and Quantum Short-Range Dynamics in Mean-Field Systems