21 research outputs found
Ehrenfest breakdown of the mean-field dynamics of Bose gases
The mean-field dynamics of a Bose gas is shown to break down at time where is the Lyapunov exponent of the mean-field
theory, is the number of bosons, and is a system-dependent constant.
The breakdown time is essentially the Ehrenfest time that
characterizes the breakdown of the correspondence between classical and quantum
dynamics. This breakdown can be well described by the quantum fidelity defined
for reduced density matrices. Our results are obtained with the formalism in
particle-number phase space and are illustrated with a triple-well model. The
logarithmic quantum-classical correspondence time may be verified
experimentally with Bose-Einstein condensates.Comment: 6 pages, 4 figure
Entanglement Features of Random Neural Network Quantum States
Restricted Boltzmann machines (RBMs) are a class of neural networks that have
been successfully employed as a variational ansatz for quantum many-body wave
functions. Here, we develop an analytic method to study quantum many-body spin
states encoded by random RBMs with independent and identically distributed
complex Gaussian weights. By mapping the computation of ensemble-averaged
quantities to statistical mechanics models, we are able to investigate the
parameter space of the RBM ensemble in the thermodynamic limit. We discover
qualitatively distinct wave functions by varying RBM parameters, which
correspond to distinct phases in the equivalent statistical mechanics model.
Notably, there is a regime in which the typical RBM states have near-maximal
entanglement entropy in the thermodynamic limit, similar to that of Haar-random
states. However, these states generically exhibit nonergodic behavior in the
Ising basis, and do not form quantum state designs, making them distinguishable
from Haar-random states.Comment: 22 pages, 13 figures, close to published versio
Deep Quantum Geometry of Matrices
We employ machine learning techniques to provide accurate variational wave functions for matrix quantum mechanics, with multiple bosonic and fermionic matrices. The variational quantum Monte Carlo method is implemented with deep generative flows to search for gauge-invariant low-energy states. The ground state (and also long-lived metastable states) of an SU(N) matrix quantum mechanics with three bosonic matrices, and also its supersymmetric “mini-BMN” extension, are studied as a function of coupling and N. Known semiclassical fuzzy sphere states are recovered, and the collapse of these geometries in more strongly quantum regimes is probed using the variational wave function. We then describe a factorization of the quantum mechanical Hilbert space that corresponds to a spatial partition of the emergent geometry. Under this partition, the fuzzy sphere states show a boundary-law entanglement entropy in the large N limit