Yang-Baxter equation in spin chains with long range interactions

We consider the $su(n)$ spin chains with long range interactions and the spin generalization of the Calogero-Sutherland models. We show that their properties derive from a transfer matrix obeying the Yang-Baxter equation. We obtain the expression of the conserved quantities and we diagonalize them.Comment: Saclay-t93/00

On the exactly solvable pairing models for bosons

We propose the new exactly solvable model for bosons corresponding to the attractive pairing interaction. Using the electrostatic analogy, the solution of this model in thermodynamic limit is found. The transition from the superfluid phase with the Bose condensate and the Bogoliubov - type spectrum of excitations in the weak coupling regime to the incompressible phase with the gap in the excitation spectrum in the strong coupling regime is observed.Comment: 19 page

Momentum distribution of a freely expanding Lieb-Liniger gas

We numerically study free expansion of a few Lieb-Liniger bosons, which are initially in the ground state of an infinitely deep hard-wall trap. Numerical calculation is carried out by employing a standard Fourier transform, as follows from the Fermi-Bose transformation for a time-dependent Lieb-Liniger gas. We study the evolution of the momentum distribution, the real-space single-particle density, and the occupancies of natural orbitals. Our numerical calculation allows us to explore the behavior of these observables in the transient regime of the expansion, where they are non-trivially affected by the particle interactions. We derive analytically (by using the stationary phase approximation) the formula which connects the asymptotic shape of the momentum distribution and the initial state. For sufficiently large times the momentum distribution coincides (up to a simple scaling transformation) with the shape of the real-space single-particle density (the expansion is asymptotically ballistic). Our analytical and numerical results are in good agreement.Comment: small changes; references correcte

Agricultural management and plant selection interactively affect rhizosphere microbial community structure and nitrogen cycling.

BACKGROUND:Rhizosphere microbial communities are key regulators of plant performance, yet few studies have assessed the impact of different management approaches on the rhizosphere microbiomes of major crops. Rhizosphere microbial communities are shaped by interactions between agricultural management and host selection processes, but studies often consider these factors individually rather than in combination. We tested the impacts of management (M) and rhizosphere effects (R) on microbial community structure and co-occurrence networks of maize roots collected from long-term conventionally and organically managed maize-tomato agroecosystems. We also explored the interaction between these factors (M × R) and how it impacts rhizosphere microbial diversity and composition, differential abundance, indicator taxa, co-occurrence network structure, and microbial nitrogen-cycling processes. RESULTS:Host selection processes moderate the influence of agricultural management on rhizosphere microbial communities, although bacteria and fungi respond differently to plant selection and agricultural management. We found that plants recruit management-system-specific taxa and shift N-cycling pathways in the rhizosphere, distinguishing this soil compartment from bulk soil. Rhizosphere microbiomes from conventional and organic systems were more similar in diversity and network structure than communities from their respective bulk soils, and community composition was affected by both M and R effects. In contrast, fungal community composition was affected only by management, and network structure only by plant selection. Quantification of six nitrogen-cycling genes (nifH, amoA [bacterial and archaeal], nirK, nrfA, and nosZ) revealed that only nosZ abundance was affected by management and was higher in the organic system. CONCLUSIONS:Plant selection interacts with conventional and organic management practices to shape rhizosphere microbial community composition, co-occurrence patterns, and at least one nitrogen-cycling process. Reframing research priorities to better understand adaptive plant-microbe feedbacks and include roots as a significant moderating influence of management outcomes could help guide plant-oriented strategies to improve productivity and agroecosystem sustainability

Current induced domain wall dynamics in the presence of spin orbit torques

Current induced domain wall (DW) motion in perpendicularly magnetized nanostripes in the presence of spin orbit torques is studied. We show using micromagnetic simulations that the direction of the current induced DW motion and the associated DW velocity depend on the relative values of the field like torque (FLT) and the Slonczewski like torques (SLT). The results are well explained by a collective coordinate model which is used to draw a phase diagram of the DW dynamics as a function of the FLT and the SLT. We show that a large increase in the DW velocity can be reached by a proper tuning of both torques.Comment: 9 pages, 3 figure

sl_2 Gaudin model with Jordanian twist

sl_2 Gaudin model with Jordanian twist is studied. This system can be obtained as the semiclassical limit of the XXX spin chain deformed by the Jordanian twist. The appropriate creation operators that yield the Bethe states of the Gaudin model and consequently its spectrum are defined. Their commutation relations with the generators of the corresponding loop algebra as well as with the generating function of integrals of motion are given. The inner products and norms of Bethe states and the relation to the solutions of the Knizhnik-Zamolodchikov equations are discussed.Comment: 22 pages; corrected typo

Characterizing and correcting the proper motion bias of the bright Gaia EDR3 sources

In this paper we characterize magnitude-dependent systematics in the proper motions of the Gaia EDR3 catalog and provide a prescription for their removal. The reference frame of bright stars (G<13) in EDR3 is known to rotate with respect to extragalactic objects, but this rotation has proven difficult to characterize and correct. We employ a sample of binary stars and a sample of open cluster members to characterize this proper motion bias as a magnitude-dependent spin of the reference frame. We show that the bias varies with G magnitude, reaching up to 80 {\mu}as/yr for sources in the range G = 11 - 13, several times the formal EDR3 proper motion uncertainties. We also show evidence for an additional dependence on the color of the source, with a magnitude up to 10 {\mu}as/yr. However, a color correction proportional to the effective wavenumber is unsatisfactory for very red or very blue stars and we do not recommend its use. We provide a recipe for a magnitude-dependent correction to align the proper motion of the Gaia EDR3 sources brighter than G=13 with the International Celestial Reference Frame

Diagonalization of an Integrable Discretization of the Repulsive Delta Bose Gas on the Circle

We introduce an integrable lattice discretization of the quantum system of n bosonic particles on a ring interacting pairwise via repulsive delta potentials. The corresponding (finite-dimensional) spectral problem of the integrable lattice model is solved by means of the Bethe Ansatz method. The resulting eigenfunctions turn out to be given by specializations of the Hall-Littlewood polynomials. In the continuum limit the solution of the repulsive delta Bose gas due to Lieb and Liniger is recovered, including the orthogonality of the Bethe wave functions first proved by Dorlas (extending previous work of C.N. Yang and C.P. Yang).Comment: 25 pages, LaTe

Attempted Bethe ansatz solution for one-dimensional directed polymers in random media

We study the statistical properties of one-dimensional directed polymers in a short-range random potential by mapping the replicated problem to a many body quantum boson system with attractive interactions. We find the full set of eigenvalues and eigenfunctions of the many-body system and perform the summation over the entire spectrum of excited states. The analytic continuation of the obtained exact expression for the replica partition function from integer to non-integer replica parameter N turns out to be ambiguous. Performing the analytic continuation simply by assuming that the parameter N can take arbitrary complex values, and going to the thermodynamic limit of the original directed polymer problem, we obtain the explicit universal expression for the probability distribution function of free energy fluctuations.Comment: 32 pages, 1 figur

Magnetic anomalies in Nd6Co(1.67)Si3: Surprising first order transitions in the low-temperature isothermal magnetization

We present the results of magnetic measurements on Nd6Co(1.67)Si3, a compound recently reported to crystallize in a hexagonal structure (space group P6_3/m) and to undergo long range magnetic ordering below 84 K. The results reveal that the magnetism of this compound is quite complex with additional magnetic anomalies near 50 and 20 K. There are qualitative changes in the isothermal magnetization behavior with the variation of temperature. Notably, there is a field-induced spin reorientation as the temperature is lowered below 20 K. A finding we stress is that this transition is discontinuous for 1.8K in the virgin curve, but the first order character appears only after a field-cycling for a narrow higher temperature range near 5 K. Thus, this compound serves as an example for the stabilisation of first-order transition induced by magnetic-field-cycling. The issues of 'Phase co-existence' and 'meta-stability' after a field-cycling at low temperatures in this compound are also addressed