arXiv subjects

Matheus V. Scherer

Publications and source records attributed to Matheus V. Scherer.

3 recordsLinked to original sources

arXiv2026

Semiclassical entanglement entropy for spin-field interaction

We study a general bipartite quantum system consisting of a spin interacting with a bosonic field, with the initial state prepared as the product of a spin coherent state and a canonical coherent state. Our goal is to develop a semiclassical framework to describe the entanglement dynamics between these two subsystems. Using appropriate approximations, we derive a semiclassical expression for the entanglement entropy that depends exclusively on the trajectories of the underlying classical description. By analytically extending the classical phase space into the complex domain, we identify additional complex trajectories that significantly improve the accuracy of the semiclassical description. The inclusion of these complex trajectories allows us to capture the entanglement dynamics with remarkable precision, even well beyond the Ehrenfest time. The approach is illustrated with a representative example, where the role of real and complex trajectories in reproducing the quantum entanglement entropy is explicitly demonstrated.

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arXiv2024

Testing trajectory-based determinism via time probability distributions

It is notorious that quantum mechanics cannot predict well-defined values for all physical quantities. Less well-known, however, is the fact that quantum mechanics is unable to furnish -- without additional assumptions -- probabilistic predictions even in emblematic scenarios such as the double-slit experiment. In contrast, trajectory-equipped theories naturally have more predictive power. This work formalizes the aforementioned assertions and illustrates them through three case studies: (i) free particle, (ii) free fall under a uniform gravitational field, and (iii) the double-slit experiment. Specifically, we introduce a prescription for constructing an arrival-time probability distribution within generic trajectory-equipped theories and then derive a conditional probability distribution that is unreachable by quantum mechanics. Our results can, in principle, be tested experimentally, thereby assessing the validity of trajectory-based determinism without the need for experiments involving the direct measurement of arrival time.

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arXiv2021

Entanglement dynamics of spins using a few complex trajectories

In this work, we consider two spins initially prepared in a product of coherent states and study their entanglement dynamics due to a general interacting Hamiltonian. We adopt an approach that allowed the derivation of a semiclassical formula for the linear entropy of the reduced density operator, assumed as an entanglement quantifier. The resulting expression depends on sets of four trajectories, originated from the underlying classical description, and having mutually connected final phase-space points. Such classical elements, which are capable to reproduce the quantum entanglement even for long values of propagation time, arise when we assume a proper analytical continuation of the classical phase space onto a complex domain. We apply this theory to a particular physical system, showing that taking into account only a few sets of complex trajectories is enough to get an excellent agreement between the semiclassical linear entropy of the reduced density operator and its quantum counterpart.

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