Permutation Invariant Algebras, a Fock Space Realization and the Calogero Model

We study permutation invariant oscillator algebras and their Fock space representations using three equivalent techniques, i.e. (i) a normally ordered expansion in creation and annihilation operators, (ii) the action of annihilation operators on monomial states in Fock space and (iii) Gram matrices of inner products in Fock space. We separately discuss permutation invariant algebras which possess hermitean number operators and permutation invariant algebras which possess non-hermitean number operators. The results of a general analysis are applied to the S_M extended Heisenberg algebra, underlying the M-body Calogero model. Particular attention is devoted to the analysis of Gram matrices for the Calogero model. We discuss their structure, eigenvalues and eigenstates. We obtain a general condition for positivity of eigenvalues, meaning that all norms of states in Fock space are positive if this condition is satisfied. We find a universal critical point at which the reduction of the physical degrees of freedom occurs. We construct dual operators, leading to the ordinary Heisenberg algebra of free Bose oscillators. From the Fock-space point of view, we briefly discuss the existence of mapping from the Calogero oscillators to the free Bose oscillators and vice versa.Comment: 40 pages, Latex, no figures, accepted in EPJ

Interacting families of Calogero-type particles and SU(1,1) algebra

We study a one-dimensional model with F interacting families of Calogero-type particles. The model includes harmonic, two-body and three-body interactions. We emphasize the universal SU(1,1) structure of the model. We show how SU(1,1) generators for the whole system are composed of SU(1,1) generators of arbitrary subsystems. We find the exact eigenenergies corresponding to a class of the exact eigenstates of the F-family model. By imposing the conditions for the absence of the three-body interaction, we find certain relations between the coupling constants. Finally, we establish some relations of equivalence between two systems containing F families of Calogero-type particles.Comment: 16 pages, no figures, to be published in Mod.Phys.Lett.

Spectroscopy of orbital ordering in La0.5Sr1.5MnO4 : A many-body cluster calculation

We have studied the orbital ordering (OO) in La0.5Sr1.5MnO4 and its soft x-ray resonant diffraction spectroscopic signature at the Mn L2, L3 edges. We have modelled the system in second quantization as a small planar cluster consisting of a central Mn atom, with the first neighbouring shells of oxygen and Mn atoms. For the effective Hamiltonian we consider Slater-Koster parameters, charge transfer and electron correlation energies obtained from previous measurements on manganites. We calculate the OO as a function of oxygen distortion and spin correlation used as adjustable parameters. Their contribution as a function of temperature is clearly distinguished with a good spectroscopic agreement.Comment: 5 pages 3 figure

Exclusion statistics,operator algebras and Fock space representations

We study exclusion statistics within the second quantized approach. We consider operator algebras with positive definite Fock space and restrict them in a such a way that certain state vectors in Fock space are forbidden ab initio.We describe three characteristic examples of such exclusion, namely exclusion on the base space which is characterized by states with specific constraint on quantum numbers belonging to base space M (e.g. Calogero-Sutherland type of exclusion statistics), exclusion in the single-oscillator Fock space, where some states in single oscillator Fock space are forbidden (e.g. the Gentile realization of exclusion statistics) and a combination of these two exclusions (e.g. Green's realization of para-Fermi statistics). For these types of exclusions we discuss extended Haldane statistics parameters g, recently introduced by two of us in Mod.Phys.Lett.A 11, 3081 (1996), and associated counting rules. Within these three types of exclusions in Fock space the original Haldane exclusion statistics cannot be realized.Comment: Latex,31 pages,no figures,to appear in J.Phys.A : Math.Ge

Autonomous object harvesting using synchronized optoelectronic microrobots

Optoelectronic tweezer-driven microrobots (OETdMs) are a versatile micromanipulation technology based on the application of light induced dielectrophoresis to move small dielectric structures (microrobots) across a photoconductive substrate. The microrobots in turn can be used to exert forces on secondary objects and carry out a wide range of micromanipulation operations, including collecting, transporting and depositing microscopic cargos. In contrast to alternative (direct) micromanipulation techniques, OETdMs are relatively gentle, making them particularly well suited to interacting with sensitive objects such as biological cells. However, at present such systems are used exclusively under manual control by a human operator. This limits the capacity for simultaneous control of multiple microrobots, reducing both experimental throughput and the possibility of cooperative multi-robot operations. In this article, we describe an approach to automated targeting and path planning to enable open-loop control of multiple microrobots. We demonstrate the performance of the method in practice, using microrobots to simultaneously collect, transport and deposit silica microspheres. Using computational simulations based on real microscopic image data, we investigate the capacity of microrobots to collect target cells from within a dissociated tissue culture. Our results indicate the feasibility of using OETdMs to autonomously carry out micromanipulation tasks within complex, unstructured environments

Mapping of Dietary Interventions Beneficial in the Prevention of Secondary Health Conditions in Spinal Cord Injured Population: A Systematic Review.

OBJECTIVES Individuals with spinal cord injury are at risk of secondary health conditions (SHC) that develop as a consequence of autonomic dysfunction, prolonged oxidative stress and inflammation, and physical inactivity coupled with inadequate energy and nutritional intake. SHC can be debilitating and even life-threatening, and its prevention remains one of the major challenges in the continuum of medical care of aging SCI population. An unhealthy diet is a major driver of inflammation, oxidative stress, and unfavourable metabolic status and may be a practical preventive target to tackle increased SHC risk post-injury. AIMS To provide a catalogue of dietary interventions beneficial in prevention of SHC among individuals with SCI by conducting a systematic review of the literature on dietary interventions and dietary supplementation in promoting health and well-being after the injury. In addition, we aimed to provide a summary of observational studies exploring the association between habitual diet (macro- and micronutrients intake and dietary patterns) and health patterns following the injury. METHOD This review was registered at PROSPERO (University of York) with registration number CRD42022373773. Four medical databases (EMBASE.com, MEDLINE [Ovid], Cochrane CENTRAL, and Web of Science Core Collection) and Google Scholar were searched from inception until 11th July 2022. Studies were included if they were clinical trials or observational studies conducted in adult individuals with SCI and provided information of interest. Based on strength of the study design and risk of bias assessment (using the NIH tool), we classified studies from Level 1 (most reliable studies) to Level 4 (least reliable studies). RESULTS Of 12,313 unique citations, 47 articles (based on 43 original studies) comprising 32 interventional (22 RCTs, 3 NRCT, and 7 pre-post studies) and 11 observational studies (2 cohort studies, 2 case-control, 1 post-intervention follow-up study, and 6 cross-sectional studies) were included in the present systematic review. Twenty studies (46.5%) were classified as Level 1 or 2, indicating high/moderate methodological quality. Based on those studies, dietary strategies including high protein diet, intermittent fasting, balanced diet in combination with physical conditioning and electrical stimulation, and dietary supplementation including alpha-lipoic acid, creatine, vitamin D, and cranberry-derived supplements and probiotics were mapped as the most promising in prevention of SHC among individuals with SCI. CONCLUSIONS To develop timely and effective preventive strategies targeting major SHC (e.g., cardiometabolic diseases, urinary tract infections) in SCI, further research is warranted to confirm the effectiveness of dietary strategies/interventions identified through the current systematic review of the literature