Flexible scheme to truncate the hierarchy of pure states

The hierarchy of pure states (HOPS) is a wavefunction-based method which can be used for numerically modeling open quantum systems. Formally, HOPS recovers the exact system dynamics for an infinite depth of the hierarchy. However, truncation of the hierarchy is required to numerically implement HOPS. We want to choose a 'good' truncation method, where by 'good' we mean that it is numerically feasible to check convergence of the results. For the truncation approximation used in previous applications of HOPS, convergence checks are numerically challenging. In this work we demonstrate the application of the '$n$-particle approximation' ($n$PA) to HOPS. We also introduce a new approximation, which we call the '$n$-mode approximation' ($n$MA). We then explore the convergence of these truncation approximations with respect to the number of equations required in the hierarchy. We show that truncation approximations can be used in combination to achieve convergence in two exemplary problems: absorption and energy transfer of molecular aggregates.Comment: 8 pages, 3 figure

The Quantum Super Yangian and Casimir Operators of Uq(gl(M∣N))U_q(gl(M|N))

The quantum super Yangian $Y_q(gl(M|N))$ associated with the Perk - Schultz solution of the Yang - Baxter equation is introduced. Its structural properties are investigated, in particular, an extensive study of its central algebra is carried out. A $Z_2$ graded associative algebra epimorphism $Y_q(gl(M|N))--> U_q(gl(M|N))$ is established and constructed explicitly. Images of the central elements of the quantum super Yangian under this epimorphism yield the Casimir operators of the quantum supergroup $U_q(gl(M|N))$ constructed in an earlier publication.Comment: 10 pages in plain LaTe

Probing the birth of fast rotating magnetars through high-energy neutrinos

We investigate the high-energy neutrino emission expected from newly born magnetars surrounded by their stellar ejecta. Protons might be accelerated up to 0.1-100 EeV energies possibly by, e.g., the wave dissipation in the winds, leading to hadronic interactions in the stellar ejecta. The resulting PeV-EeV neutrinos can be detected by IceCube/KM3Net with a typical peak time scale of a few days after the birth of magnetars, making the characteristic soft-hard-soft behavior. Detections would be important as a clue to the formation mechanism of magnetars, although there are ambiguities coming from uncertainties of several parameters such as velocity of the ejecta. Non-detections would also lead to useful constraints on the scenario.Comment: 5 pages, 3 figures, accepted for publication in PR