This paper is concerned with the modeling and analysis of quantum dissipation phenomena in the Schrödinger picture. More precisely, we do investigate in detail a dissipative, nonlinear Schrödinger equation somehow accounting for quantum Fokker-Planck effects, and how it is drastically reduced to a simpler logarithmic equation via a nonlinear gauge transformation in such a way that the physics underlying both problems keeps unaltered. From a mathematical viewpoint, this allows for a more achievable analysis regarding the local wellposedness of the initial-boundary value problem. This simplification requires the performance of the polar (modulus-argument) decomposition of the wavefunction, which is rigorously attained (for the first time to the best of our knowledge) under quite reasonable assumptions.

A nonlinear Schrödinger equation describing how a quantum particle interacts with its surrounding reservoir is derived from the Wigner–Fokker–Planck equation (WFPE) via stochastic (Nelsonian) mechanical techniques. This model can be reduced just to a logarithmic Schrödinger equation through a suitable gauge transformation that allows one to explore its steady state dynamics and makes its mathematical and numerical analysis more tractable. The transient behavior of the standard deviation from the mean position associated with its solutions is also studied numerically and compared with that stemming from the WFPE.

The United Nations 2030 agenda includes quality university education, highlighting the importance of writing competence, as a basic skill for the dissemination of sustainable knowledge. However, there is little evidence of the factors that predict effective written communication to support such quality. Among these factors, the literature highlights motivation and writing metacognition, as well as the adequate structuring of the academic and/or scientific genre. The main novelty of the present research is the study of the relationships between the mentioned factors, measured with validated instruments. To this end, content analysis is first applied to determine the rhetorical moves of argumentative essays written by a sample of 72 university students. Secondly, the correlations between each of the rhetorical moves, metacognition and argumentative writing self-efficacy are calculated. The relationships are studied in depth, applying step-by-step linear regression models. Finally, the dependence of the results, observed with respect to unmeasured factors, is contrasted by means of a confirmatory analysis based on structural equations. The analyses show that it is the practical ability to express rhetorical moves—Conclusion and Bibliographic References—which predicts a students’ writing metacognition. Moreover, the minor relationship that argumentative self-efficacy shows with the expression of rhetorical moves, compared to writing metacognition, point to the need to consider another motivational dimension that is driving the learning of the argumentative essay at university level, a hypothesis that is confirmed with the structural equations model. These, and other findings, allow for the establishment of a series of educational quality criteria for the empowerment of written argumentation in academic and scientific contexts.

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Keywords: Quantum open system Dissipative quantum mechanics Madelung decomposition of the wavefunction Schrödinger-Langevin operator Kostin equation Quantum Fokker-Planck equation Caldeira-Leggett master equationIn this paper we make it mathematically rigorous the formulation of the following quantum Schrödinger-Langevin nonlinear operator for the wavefunctionin bounded domains via its mild interpretation. The a priori ambiguity caused by the presence of the multi-valued potential λS ψ , proportional to the argument of the complexvalued wavefunctionis circumvented by subtracting its positional expectation value,as motivated in the original derivation (Kostin, 1972 [45]). The problem to be solved in order to find S ψ is mostly deduced from the modulus-argument decomposition of ψ and dealt with much like in Guerrero et al. (2010) [37]. Hereh is the (reduced) Planck constant, m is the particle mass, λ is a friction coefficient, n ψ = |ψ| 2 is the local probability density, J ψ =h m Im(ψ∇ x ψ) denotes the electric current density, and Θh is a general operator (eventually nonlinear) that only depends upon the macroscopic observables n ψ and J ψ . In this framework, we show local well-posedness of the initial-boundary value problem associated with the Schrödinger-Langevin operator A QSL in bounded domains. In particular, all of our results apply to the analysis of the well-known Kostin equation derived in Kostin (1972) [45] and of the Schrödinger-Langevin equation with Poisson coupling and enthalpy dependence (Jüngel et al., 2002 [41]).