2013/04/23 by Nima Lashkari · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Boson #Density matrix #Eigenvalues and eigenvectors #Hamiltonian (control theory) #Hermitian matrix #Hilbert space #Mathematical physics #Mathematics #Observable #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum entanglement #Quantum field theory #Quantum many-body systems #Quantum mechanics #Random matrix #Scrambling #Statistical physics #Thermodynamic limit #hep-th #quant-ph
paper · pdf · doi:10.1007/s00220-014-2263-y
published as Comm. in Math. Phys. 333, 3 (2015), 1199
arxiv created 2013/04/23 · openalex publication_date 2015/01/02 · arxiv updated 2015/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
It has been recently shown that small subsystems of finite quantum systems generically equilibrate. We extend these results to infinite-dimensional Hilbert spaces of field theories and matrix models. We consider a quench setup, where initial states are chosen from a microcanonical ensemble of finite energy in free theory, and then evolve with an arbitrary non-perturbative Hamiltonian. Given a dynamical assumption on the expectation value of particle number density, we prove that small subsystems reach equilibrium at the level of quantum wave-function, and with respect to all observables. The picture that emerges is that at higher energies, larger subsystems can reach equilibrium. For bosonic fields on a lattice, in the limit of large number of bosons per site, all subsystem smaller than half equilibrate. In the Hermitian matrix model, by contrast, this occurs in the limit of large energy per matrix element, emphasizing the importance of the O(N2) energy scale for the fast scrambling conjecture. Applying our techniques to continuum field theories on compact spaces, we show that the density matrix of small momentum-space observables equilibrate. Finally, we discuss the connection with scrambling, and provide a sufficient condition for a time-independent Hamiltonian to be a scrambler in terms of the entanglement entropy of its energy eigenstates.