arXiv subjects

Fabricio de Souza Luiz

Publications and source records attributed to Fabricio de Souza Luiz.

2 recordsLinked to original sources

arXiv2026

Orbit-resolved spectra and dynamical accessibility in multi-register covering Hamiltonians

Which part of a Hamiltonian spectrum is relevant when the initial state and interpolation preserve multiple symmetries? We study this question for a multi-register encoding of fixed-cardinality Set Cover. Register permutations and incidence automorphisms define a joint action whose orbits are unlabelled candidate covers, with an exact hopping Hamiltonian on the orbit quotient. We distinguish the symmetry-fixed space from the generally smaller common invariant cyclic envelope generated by the initial state and endpoint Hamiltonians; a prescribed trajectory may span less still. We prove a sector-resolved Schur-complement bound on cover-measurement probability that includes the kinetic floor induced by sector projection. For a retained-walk linear path, a general hopping-cancellation point makes the spectrum exactly orbit-resolved. Multiplicity outside the fixed sector is then dynamically dark, while transverse dark crossings satisfy a separate stability theorem. On even cycles the fixed-sector excitation gap at cancellation equals $λ(n-1)/(2n-1)$ despite global multiplicity closure. Separately, for the same instances, we construct a distinct Johnson--Metropolis parent path on the injective hard-core space, from a Dicke state to a Gibbs-amplitude state. Its cover-failure probability is $O(n^{-5})$ and its cyclic-envelope gap is at least $1024\,n^{-13}$ uniformly along the path, yielding a conditional polynomial adiabatic runtime in an abstract Hamiltonian-access model. We claim no quantum speedup; the result is a protocol-dependent separation of global, symmetry-fixed, cyclic-envelope, and tracked spectra.

quant-ph↗

arXiv2026

Stochastic dynamics from maximum entropy in action space

We develop an information-theoretic formulation of stochastic dynamics in which the fundamental stochastic variable is the total action connecting spacetime points, rather than individual paths. By maximizing Shannon entropy over a joint distribution of actions and endpoints, subject to normalization and a constraint on the mean action, we obtain a Boltzmann-like distribution in action space. This framework reproduces the standard Brownian propagator in the nonrelativistic limit and naturally extends to relativistic regimes, where the Wiener construction fails to preserve Lorentz covariance. The approach bypasses functional integration over paths, makes the role of entropic degeneracy explicit through an action-space density of states, and provides a transparent connection between the principle of least action and statistical inference. We derive the density of states explicitly using large deviation theory, showing that it takes a Gaussian form centered at the minimal action, and rigorously justify the saddle-point approximation in the diffusive regime. The Markovian property of the resulting propagator is verified to hold via the Chapman--Kolmogorov equation, following from the additivity of the minimal action for free-particle dynamics. In the diffusive regime, the resulting dynamics are governed by a competition between extremization of the action and entropic effects, which can be interpreted in terms of an effective action free energy. Our results establish an unified, covariant, and information-based foundation for classical and relativistic stochastic processes.

cond-mat.stat-mech↗