Related papers: Optimal Semiclassical Regularity of Projection Operators and Strong Weyl Law

Optimal Semiclassical Regularity of Projection Operators and Strong Weyl Law

URL: http://arxiv.org/abs/2302.04816v3
Date: Wed, 1 Nov 2023 10:52:52 GMT
Title: Optimal Semiclassical Regularity of Projection Operators and Strong Weyl Law
Authors: Laurent Lafleche
Abstract summary: We prove that projection operators converge to characteristic functions of the phase space. This can be interpreted as a semiclassical on the size of commutators in Schatten norms.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
Abstract: Projection operators arise naturally as one-particle density operators associated to Slater determinants in fields such as quantum mechanics and the study of determinantal processes. In the context of the semiclassical approximation of quantum mechanics, projection operators can be seen as the analogue of characteristic functions of subsets of the phase space, which are discontinuous functions. We prove that projection operators indeed converge to characteristic functions of the phase space and that in terms of quantum Sobolev spaces, they exhibit the same maximal regularity as characteristic functions. This can be interpreted as a semiclassical asymptotic on the size of commutators in Schatten norms. Our study answers a question raised in [J. Chong, L. Lafleche, C. Saffirio, arXiv:2103.10946 [math.AP]] about the possibility of having projection operators as initial data. It also gives a strong convergence result in Sobolev spaces for the Weyl law in phase space.

Related papers

Quantum Random Walks and Quantum Oscillator in an Infinite-Dimensional Phase Space [45.9982965995401]
We consider quantum random walks in an infinite-dimensional phase space constructed using Weyl representation of the coordinate and momentum operators. We find conditions for their strong continuity and establish properties of their generators.
arXiv Detail & Related papers (2024-06-15T17:39:32Z)
A relativistic statistical field theory on a discretized Minkowski lattice with quantum-like observables [0.0]
A relativistic statistical field theory is constructed for a fluctuating complex-valued scalar field on a discretized Minkowski lattice. A Hilbert space of observables is then constructed from functionals of the fluctuating complex-valued scalar field with an inner product defined in terms of expectation values of the functionals. A bosonic Fock space is then constructed from the Hilbert space and creation and operators that act on the Fock space are defined.
arXiv Detail & Related papers (2024-05-30T16:41:25Z)
Matter relative to quantum hypersurfaces [44.99833362998488]
We extend the Page-Wootters formalism to quantum field theory. By treating hypersurfaces as quantum reference frames, we extend quantum frame transformations to changes between classical and nonclassical hypersurfaces.
arXiv Detail & Related papers (2023-08-24T16:39:00Z)
Semiclassical approximation of the Wigner function for the canonical ensemble [0.0]
Weyl-Wigner representation of quantum mechanics allows one to map the density operator in a function in phase space. We approximate this quantum phase space representation of the canonical density operator for general temperatures. A numerical scheme which allows us to apply the approximation for a broad class of systems is also developed.
arXiv Detail & Related papers (2023-07-31T12:44:23Z)
Computationally Efficient PAC RL in POMDPs with Latent Determinism and Conditional Embeddings [97.12538243736705]
We study reinforcement learning with function approximation for large-scale Partially Observable Decision Processes (POMDPs) Our algorithm provably scales to large-scale POMDPs.
arXiv Detail & Related papers (2022-06-24T05:13:35Z)
Energy transitions driven by phase space reflection operators [0.0]
Phase space reflection operators lie at the core of the Wigner-Weyl representation of density operators and observables. In their active role as unitary operators, they generate transitions between pairs of eigenstates specified by Wigner functions. It is shown here how the improved approximation of the spectral Wigner functions in terms of Airy functions resolves the singularity.
arXiv Detail & Related papers (2022-01-05T20:46:00Z)
Entanglement dynamics of spins using a few complex trajectories [77.34726150561087]
We consider two spins initially prepared in a product of coherent states and study their entanglement dynamics. We adopt an approach that allowed the derivation of a semiclassical formula for the linear entropy of the reduced density operator.
arXiv Detail & Related papers (2021-08-13T01:44:24Z)
Models of zero-range interaction for the bosonic trimer at unitarity [91.3755431537592]
We present the construction of quantum Hamiltonians for a three-body system consisting of identical bosons mutually coupled by a two-body interaction of zero range. For a large part of the presentation, infinite scattering length will be considered.
arXiv Detail & Related papers (2020-06-03T17:54:43Z)
Emergence of classical behavior in the early universe [68.8204255655161]
Three notions are often assumed to be essentially equivalent, representing different facets of the same phenomenon. We analyze them in general Friedmann-Lemaitre- Robertson-Walker space-times through the lens of geometric structures on the classical phase space. The analysis shows that: (i) inflation does not play an essential role; classical behavior can emerge much more generally; (ii) the three notions are conceptually distinct; classicality can emerge in one sense but not in another.
arXiv Detail & Related papers (2020-04-22T16:38:25Z)
Probing nonclassicality with matrices of phase-space distributions [0.0]
We devise a method to certify nonclassical features via correlations of phase-space distributions. Our approach complements and extends recent results that were based on Chebyshev's inequality.
arXiv Detail & Related papers (2020-03-24T18:00:02Z)

This list is automatically generated from the titles and abstracts of the papers in this site.