Non-classical non-Gaussian state of a mechanical resonator via selectively incoherent damping in three-mode optomechanical systems

We theoretically propose a scheme for the generation of a non-classical single-mode motional state of a mechanical resonator (MR) in the three-mode optomechanical systems, in which two optical modes of the cavities are linearly coupled to each other and one mechanical mode of the MR is optomechanically coupled to the two optical modes with the same coupling strength simultaneously. One cavity is driven by a coherent laser light. By properly tuning the frequency of the weak driving field, we obtain engineered Liouvillian superoperator via engineering the selective interaction Hamiltonian confined to the Fock subspaces. In this case, the motional state of the MR can be prepared into a non-Gaussian state, which possesses the sub-Poisson statistics although its Wigner function is positive.Comment: 6 pages, 5 figure

The Follow-up Report of MRI After Transforaminal Endoscopic Surgery of Lumbar Disc Herniation with Spinal Stenosis

Objective: To observe the imaging changes of MRI in the responsible disc area after modifed TESSYS foraminal scopy in pa-tients with lumbar disc herniation (LDH), and to explore the postoperative repair time of the responsible disc area, so as to provide imaging reference for the rehabilitation plan of the patients. Materials: To investigate the VAS score and MRI imaging of patients with lumbar disc herniation and spinal stenosis after transforaminal endoscopic surgery, which to lay the foundation for the rehabilitation plan. Methods: Ten patients with lumbar disc herniation (L4/5, L5/S1) with spinal stenosis were collected and followed up by MRI and the VAS score on 1 week, 1 month, 4 months and 6 months after transforaminal endoscopic surgery. Results: The VAS score were signifcantly lower than those before operation (P 0.05) on 1 month and 6 months after operation. The high signal could be seen around the intervertebral foramen and nerve roots on the operation site on 1 week, 1 month and 4 months after operation Which disappeared at 6 months after operation. Con-clusion: The symptoms of low back and leg pain in patients with lumbar disc herniation and spinal canal stenosis disappeared after 1 month, while the infammatory reaction symptoms of intervertebral foramen and nerve root were disappeared on 6 months

On q-deformed infinite-dimensional n-algebra

The $q$-deformation of the infinite-dimensional $n$-algebra is investigated. Based on the structure of the $q$-deformed Virasoro-Witt algebra, we derive a nontrivial $q$-deformed Virasoro-Witt $n$-algebra which is nothing but a sh-$n$-Lie algebra. Furthermore in terms of the pseud-differential operators on the quantum plane, we construct the (co)sine $n$-algebra and the $q$-deformed $SDiff(T^2)$ $n$-algebra. We prove that they are the sh-$n$-Lie algebras for the case of even $n$. An explicit physical realization of the (co)sine $n$-algebra is given.Comment: 22 page

Fine root morphology and growth in response to nitrogen addition through drip fertigation in a Populus × euramericana “Guariento” plantation over multiple years

International audienceAbstractKey messageNitrogen addition through drip fertigation to a poplar plantation (Populus × euramericana“Guariento”) promoted fine root growth only in the early period. The relationship between root growth and soil N content was positive in the first 2 years, but became negative in the third year when the soil N availability had substantially increased.ContextNitrogen (N) deficiency is common in forest soils, and N addition is sometimes applied in the case of intensive plantations. There is a need to better document the impact of N addition through the high-efficiency fertilization technique on fine root morphology and growth, given their importance for the uptake of nutrients and for tree growth.AimsWe aimed to quantitatively investigate the responses of fine roots in morphology and growth to N addition through surface drip fertigation over multiple years in a Populus × euramericana “Guariento” plantation.MethodsA field experiment that included four drip fertigation treatments with N addition levels (0, 60, 120, and 180 kg N ha−1 year−1) was conducted for three successive years. A coring method was used to sample soils and quantify the root morphological traits and soil N content along 0–60-cm profiles.ResultsThe root biomass density, length, surface area, specific length, and tissue density were significantly higher in the N addition treatments than those in the control after the first year, but the positive effect decreased in the second year. In the third year, root biomass in the N addition treatments was even lower by 11–39% than that in the control. The relationship between root growth and soil N content was also positive in the first 2 years and negative in the third year.ConclusionN addition promoted fine root growth mainly in the shallow soil and in the early period of experiment. The relationship between root growth and soil N content became negative in the third year when the soil N availability had substantially increased. It is suggested that fine roots adjust their growth and morphology in response to N availability varying along the soil profile and with the fertilization duration