arXiv subjects

Juan Carlos del Valle

Publications and source records attributed to Juan Carlos del Valle.

5 recordsLinked to original sources

arXiv2026

Time-Dependent Logarithmic Perturbation Theory for Quantum Dynamics: Formulation and Applications

We present a time-dependent extension of logarithmic perturbation theory for nonrelativistic quantum dynamics governed by the Schrödinger equation, in which the logarithm of the wave function is expanded in powers of a coupling constant. The resulting hierarchy of equations defining the perturbative corrections is governed by a gauge-rotated Hamiltonian of the unperturbed system and leads to closed-integral expressions for the time-dependent corrections based on Duhamel's formula. This closed-integral structure of corrections is a hallmark of time-independent logarithmic perturbation theory and is preserved in the present extension. This structure, in particular, provides a computable expression for the instantaneous energy shift. Furthermore, dynamic energy shifts arise naturally within this framework in the form of time-averaged expectation values of pseudopotentials and can be related, for example, to AC Stark shifts and electric polarizabilities. As an illustration, we apply the method to the harmonic oscillator and the hydrogen atom, both driven by a time-dependent laser field. The harmonic oscillator provides a proof of principle for which the exact solution is recovered, while the hydrogen atom illustrates the method applied to atomic systems. Supported by numerical simulations, we demonstrate the applicability to obtain relevant physical observables with high accuracy. The present approach offers a promising alternative for analytical studies of time-dependent multi-photon processes in the perturbative regime.

quant-ph↗

arXiv2026

Atom Addition Formation of Thionylimide (HNSO) on Interstellar Dust Grains: Chemical routes requiring oxygen and nitrogen atom surface diffusion

We investigate the formation of the recently detected HNSO molecule using quantum chemical calculations on ices and astrochemical models in tandem. Our results indicate that HNSO is efficiently produced on grain surfaces through reactions involving atomic oxygen and nitrogen atoms with the radicals NS and SO, forming NSO as a key intermediate. Subsequent hydrogenation of NSO leads to HNSO, with a clear preference for the lowest energy cis conformer, while the trans form is metastable and may be short-lived under typical interstellar conditions. The models predict that solid HNSO can reach abundances comparable to icy OCS, placing it among the major sulfur-bearing species in interstellar ices. Gas-phase abundances, in contrast, remain lower than those of OCS. The implementation of a multibinding scheme in our models clarifies the role of diffusive chemistry in the production of HNSO at early times, improving agreement with observations. These findings suggest that reactions involving diffusing O and N atoms on icy grains contribute significantly to sulfur chemistry and beyond in dense clouds and motivate further searches for molecules containing simultaneously H, N, O and S in other astronomical environments.

astro-ph.GA↗

arXiv2024

Formation of the interstellar sugar precursor, (Z)-1,2-ethenediol, through radical reactions on dust grains

In recent years, the continued detection of complex organic molecules of prebiotic interest has refueled the interest on a panspermic origin of life. The prebiotic molecule glyceraldehyde is proposed to be formed from (Z)-1,2-ethenediol, a molecule recently detected towards the G+0.693-0.027 molecular cloud at the galactic center. In this work, we computationally simulate the formation of (Z)-1,2-ethenediol from vinyl alcohol on the surface of amorphous solid water in a two-step synthesis involving a OH addition and a H abstraction reaction. In total, we considered all reaction possibilities of the 1,1 and 1,2-OH addition to vinyl alcohol followed by H-abstraction or H-addition reactions on the resulting radicals. The combination of these reactions is capable of explaining the formation of (Z)-1,2-ethenediol provided a suprathermal diffusion of OH. We also conclude that our proposed formation pathway is not selective and also yields other abstraction and addition products. Key in our findings is the connection between the adsorption modes of the reactants and intermediates and the stereoselectivity of the reactions.

astro-ph.GA↗

arXiv2024

Second-order exponential splittings in the presence of unbounded and time-dependent operators: construction and convergence

For linear differential equations of the form $u'(t)=[A + B(t)] u(t)$, $t\geq0$, with a possibly unbounded operator $A$, we construct and deduce error bounds for two families of second-order exponential splittings. The role of quadratures when integrating the twice-iterated Duhamel's formula is reformulated: we show that their choice defines the structure of the splitting. Furthermore, the reformulation allows us to consider quadratures based on the Birkhoff interpolation to obtain not only pure-stages splittings but also those containing derivatives of $B(t)$ and commutators of $A$ and $B(t)$. In this approach, the construction and error analysis of the splittings are carried out simultaneously. We discuss the accuracy of the members of the families. Numerical experiments are presented to complement the theoretical consideration.

math.NA↗

arXiv2021

Anharmonic oscillator: a solution

It is shown that for the one-dimensional quantum anharmonic oscillator with potential $V(x)= x^2+g^2 x^4$ the Perturbation Theory (PT) in powers of $g^2$ (weak coupling regime) and the semiclassical expansion in powers of $\hbar$ for energies coincide. It is related to the fact that the dynamics in $x$-space and in $(gx)$-space corresponds to the same energy spectrum with effective coupling constant $\hbar g^2$. Two equations, which govern the dynamics in those two spaces, the Riccati-Bloch (RB) and the Generalized Bloch (GB) equations, respectively, are derived. The PT in $g^2$ for the logarithmic derivative of wave function leads to PT (with polynomial in $x$ coefficients) for the RB equation and to the true semiclassical expansion in powers of $\hbar$ for the GB equation, which corresponds to a loop expansion for the density matrix in the path integral formalism. A 2-parametric interpolation of these two expansions leads to a uniform approximation of the wavefunction in $x$-space with unprecedented accuracy $\sim 10^{-6}$ locally and unprecedented accuracy $\sim 10^{-9}-10^{-10}$ in energy for any $g^2 \geq 0$. A generalization to the radial quartic oscillator is briefly discussed.

quant-ph↗