“The dynamics become effectively Haar-random well before the system can ergodically explore the physically accessible Hilbert space.”

“The paper proposes local approximations to the global Minkowski Hamiltonian in quantum field theory (QFT) motivated by the operator-algebraic property of nuclearity.”

“The paper derives bilinear tau forms of the canonically quantized Painlevé equations, relating them to those previously obtained from the $\mathbb{C}^2/\mathbb{Z}_2$ blowup relations.”

“The paper presents a computer algebra package for efficiently computing Poisson brackets and reconstructing constraint algebras.”

“The authors report an experimentally accessible protocol for directly measuring the mixed-state topological invariant.”

“The eigenfunctions admit an expansion with universal coefficients so that the dependence on the twist $a$ is hidden only in these ground state eigenfunctions, and we suggest a general formula that allows one to construct these eigenfunctions from non-symmetric Macdonald polynomials.”

“A novel contribution arises that is proportional to the phase derivative of the levels broadening.”

“The paper introduces Energy-Aware Bayesian-CBFs (EB-CBFs) that construct conservative energy-based barriers directly from the Hamiltonian and vector-field posteriors, yielding safety filters that minimally modify a nominal controller while providing probabilistic energy safety guarantees.”

“The paper derives a generalized Heisenberg-Robertson uncertainty inequality valid across all spectral regimes.”

“In cases V and VI, the Hamiltonian analysis yields 8 degrees of freedom, while only 6 and 5 modes are visible at linear order in perturbations, respectively. This indicates that additional modes are strongly coupled on cosmological backgrounds.”

“All models are exactly-solvable, admit algebraic forms for the Hamiltonian and integrals, have polynomial eigenfunctions, hidden algebraic structure, and possess a polynomial algebra of integrals.”

“The paper establishes asymptotically tight lower and upper bounds on the over-thresholds and shows that for infinitely many instances of m the two bounds coincide.”

“The framework can accommodate Hamiltonian mechanics, enabling dynamical modeling.”

“N/A - Based on the provided information, there are no quotes.”

“The paper discusses two correspondences: one based on Hamiltonian reduction and its quantum counterpart, and another involving non-trivial dualities like Fourier and Legendre transforms.”

“The paper demonstrates that as few as three qubits per plaquette is sufficient to reach per-mille level precision on predictions for observables.”

“”

“”

“The paper shows how to construct statistical mechanical models for stabilizer circuits subject to independent Pauli errors, by mapping logical equivalence class probabilities of errors to partition functions using the spacetime subsystem code formalism.”

“The approach reduces each embedding solve to a deterministic ground-state eigenvalue problem in the reduced space, and reduces the cost of the EH solution by orders of magnitude.”

“The research focuses on microwave-driven Josephson circuits.”

“The study focuses on macroscopic quantum states and quantum phase transitions for a system of N three-level atoms.”

“Without the full text, it's impossible to provide a specific quote. However, a relevant quote would likely discuss the Hamiltonian used to model the interactions or the observed magnetic behavior.”

“The study focuses on O(1) oracle-query quantum state preparation.”

“The article's focus is on optimal certification of constant-local Hamiltonians.”