Quantum Fluctuations in Bose--Einstein Condensates:Microscopic Correlations and Moment Bounds
Abstract
We study higher moments of quantum fluctuations and microscopic correlation energy in the three-dimensional Gross--Pitaevskii regime. For a smooth, compactly supported, nonnegative radial interaction and an N-independent normalized initial condensate wave function in H6, we propagate the third spectral moment of a positive correlated energy along the exact many-body evolution. A uniform initial bound controls the third moment of the depletion number and sixth moments of collective one-particle fluctuations on every compact time interval, independently of N. For a nonzero interaction and a smooth, compactly supported initial condensate, we also identify the excitation-energy measure at scale N2, weighted by the first energy. This limit holds for norm-convergent pure-state families with a uniform bound on the initial third correlated-energy moment. Its positive-energy part is a spectral measure of the relative scattering operator −2Δ+v, multiplied by a time-dependent dressed contact. We compute the radial density and prove strict positivity of the contact for nonzero references with finite kinetic energy and finite mean excitation number. The same evolving states have bounded physical fluctuation moments and excitation-energy moments of order p>1 bounded below by a positive multiple of N2p−2, in the extended spectral sense. Inverse powers of the positive initial energy construct admissible pure and mixed families. For the norm-convergent pure-state class, we determine the scaled interaction-energy moments for 1≤ p<2 and bound the second moment by O(N2). A finite cubic approximation has norm error O(N−3/16) on the energy form domain and O(N−5/4) on a stronger initial domain of its generator.
Related
- Homogeneous attractive Bose-Einstein condensates with repulsive three-body interactions: the two-dimensional case
- Homogeneous attractive Bose-Einstein condensates with repulsive three-body interactions: the one-dimensional case
- Critical surface for two component Bose-Einstein Condensates
- A positive-conservative Fourier optimization method for ground states of Bose--Einstein condensates with higher-order interactions
- Boundary geometry and concentration points for attractive Bose-Einstein condensates with a ring-shaped potential
BibTeX
@misc{chueng2026quantum,
title = {{Quantum Fluctuations in Bose--Einstein Condensates:Microscopic Correlations and Moment Bounds}},
author = {Mauris Chueng and Keheng Zhu and Hexiang Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06367},
eprint = {2610.06367},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06367},
}
RIS
TY - UNPB
TI - Quantum Fluctuations in Bose--Einstein Condensates:Microscopic Correlations and Moment Bounds
AU - Mauris Chueng
AU - Keheng Zhu
AU - Hexiang Wang
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.06367
UR - https://arxiv.org/abs/2610.06367
AB - We study higher moments of quantum fluctuations and microscopic correlation energy in the three-dimensional Gross--Pitaevskii regime. For a smooth, compactly supported, nonnegative radial interaction and an N-independent normalized initial condensate wave function in H^6, we propagate the third spectral moment of a positive correlated energy along the exact many-body evolution. A uniform initial bound controls the third moment of the depletion number and sixth moments of collective one-particle fluctuations on every compact time interval, independently of N. For a nonzero interaction and a smooth, compactly supported initial condensate, we also identify the excitation-energy measure at scale N^2, weighted by the first energy. This limit holds for norm-convergent pure-state families with a uniform bound on the initial third correlated-energy moment. Its positive-energy part is a spectral measure of the relative scattering operator −2Δ+v, multiplied by a time-dependent dressed contact. We compute the radial density and prove strict positivity of the contact for nonzero references with finite kinetic energy and finite mean excitation number. The same evolving states have bounded physical fluctuation moments and excitation-energy moments of order p>1 bounded below by a positive multiple of N^2p−2, in the extended spectral sense. Inverse powers of the positive initial energy construct admissible pure and mixed families. For the norm-convergent pure-state class, we determine the scaled interaction-energy moments for 1≤ p<2 and bound the second moment by O(N^2). A finite cubic approximation has norm error O(N^−3/16) on the energy form domain and O(N^−5/4) on a stronger initial domain of its generator.
ER -