DETERMINISTIC INVERSE-GAP CONTROL-TIME SCALING IN THE BOSE–HUBBARD MODEL
DOI:
https://doi.org/10.60787/tnamp.v25.719Keywords:
Bose–Hubbard model, particle–hole gap, control time, energy–time scaling, Mott insulator, inverse-gap scalingAbstract
Deterministic relationship between the time required to control, localize, or stabilizea quantum state and the energy scale remains a core objective in the Bose- Hubbard model. We derive and numerically validate a deterministic inverse-gap scaling law governing control-time dynamics within the Bose–Hubbard framework. Starting from the particle–hole excitation structure in the Mott- insulating regime, the control time is defined through energy–time reciprocity at a fixed persistence threshold P("τ" _"c" ) = 0.1. Log–log regression confirms an inverse-gap scalingexponent "α≈-1" independent of lattice dimension with determination coefficient "R" ^"2" "≈1.00" , establishing "τ" _"c" "∝" 〖"∆" _"ph" 〗^"-1" . This framework provides a physically motivated energetic time scale in which excitation gaps determine coherence persistence. The results establish a deterministic inverse-gap law arising purely from Hamiltonian many-body structure and provide a testbed for deviations and signatures of macroscopic many-body systems beyond unitary quantum mechanics, motivating future tests against objective collapse models such as Diósi–Penrose.
Downloads
References
Bassi, A., Lochan, K., Satin, S., Singh, T.P. and Ulbricht, H. (2013) 'Models of wave-function collapse, underlying theories, and experimental tests', Reviews of Modern Physics, 85, p. 471.
Bedingham, D.J. and Maroney, O.J.E. (2017) 'Time symmetry in wavefunction collapse models', Physical Review A, 95, p. 042103.
Bloch, I., Dalibard, J. and Nascimbène, S. (2012) 'Quantum simulations with ultracold quantum gases', Nature Physics, 8, p. 267.
Chanda, T. et al. (2025) 'Recent progress on quantum simulations of non-standard Bose–Hubbard models', Reports on Progress in Physics, 88, p. 024401.
Debnath, A., Sahoo, A. and Rakshit, D. (2025) 'Localization from infinitesimal kinetic grading', arXiv:2512.15795. Diósi, L. (1989) 'Models for universal reduction of macroscopic quantum fluctuations', Physical Review A, 40, p. 1165.
Dziarmaga, J. and Mazur, J.M. (2023) 'Tensor network simulation of quantum critical dynamics', arXiv:2302.13347.
Akpojotor et al., Fisher, M.P.A. et al. (1989) 'Boson localization and the superfluid– nsulator transition', Physical Review B, 40, p. 546.
Greiner, M. et al. (2002) 'Collapse and revival of the matter wave field of a Bose–Einstein condensate', Nature, 419, p. 51.
Greiner, M. (2003) Ultracold quantum gases in three-dimensional optical lattice potentials. PhD thesis. LMU Munich.
Gross, C. and Bloch, I. (2017) 'Quantum simulations with ultracold atoms in optical lattices', Science, 357, p. 995.
Ibeh, G.J. and Akpojotor, G.E. (2020) 'Using Dirac's principle of superposition of evolution of time in restoring determinancy in quantum mechanics', Scientia Africana, 19(2), pp. 137-148.
Jaberi, M. and Heydarinasab, F. (2026) 'Ground-state and finite-temperature phase diagrams of the Bose–Hubbard model', Scientific Reports, 16, p. 934.
Łącki, M. and Heyl, M. (2019) 'Dynamical quantum phase transitions in collapse and revival oscillations', Physical Review B, 99, p. 121107(R).
Lewenstein, M. et al. (2007) 'Ultracold atoms in optical lattices: simulating quantum many-body systems', Advances in Physics, 56, p. 243.
Penrose, R. (2019) 'On gravity's role in quantum state reduction', European Physical Journal Plus, 134, p. 139.
Sarkar, S. et al. (2025) 'Exponentially enhanced quantum sensing near many-body phase transitions', Nature Communications, 16, p. 5159.
Schlosshauer, M. (2005) 'Decoherence, the measurement problem, and interpretations of quantum mechanics', Reviews of Modern Physics, 76, p. 1267.
Zurek, W.H. (2003) 'Decoherence and the transition from quantum to classical', Reviews of Modern Physics, 75, p. 715.
Downloads
Published
Issue
Section
License
Copyright (c) 2026 The Transactions of the Nigerian Association of Mathematical Physics
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
