Bound and scattering states of extended Calogero model with an additional PT invariant interaction

Here we discuss two many-particle quantum systems, which are obtained by adding some nonhermitian but PT (i.e. combined parity and time reversal) invariant interaction to the Calogero model with and without confining potential. It is shown that the energy eigenvalues are real for both of these quantum systems. For the case of extended Calogero model with confining potential, we obtain discrete bound states satisfying generalised exclusion statistics. On the other hand, the extended Calogero model without confining term gives rise to scattering states with continuous spectrum. The scattering phase shift for this case is determined through the exchange statistics parameter. We find that, unlike the case of usual Calogero model, the exclusion and exchange statistics parameter differ from each other in the presence of PT invariant interaction.Comment: 7 pages, latex, uses czjphys.cls, contributed to the `1st International Workshop on Pseudo-Hermitian Hamiltonians in Quantum Physics', Prague, June 16-17, 200

Algebraic Bethe ansatz for a quantum integrable derivative nonlinear Schrodinger model

We find that the quantum monodromy matrix associated with a derivative nonlinear Schrodinger (DNLS) model exhibits U(2) or U(1,1) symmetry depending on the sign of the related coupling constant. By using a variant of quantum inverse scattering method which is directly applicable to field theoretical models, we derive all possible commutation relations among the operator valued elements of such monodromy matrix. Thus, we obtain the commutation relation between creation and annihilation operators of quasi-particles associated with DNLS model and find out the $S$-matrix for two-body scattering. We also observe that, for some special values of the coupling constant, there exists an upper bound on the number of quasi-particles which can form a soliton state for the quantum DNLS model.Comment: 17 pages, Latex, minor typos corrected, to be published in Nucl. Phys.

Strong metal–metal coupling in mixed-valent intermediates [Cl(L)Ru(μ-tppz)Ru(L)Cl]+, L = β-diketonato ligands, tppz = 2,3,5,6-tetrakis(2-pyridyl)pyrazine

Five diruthenium(II) complexes [Cl(L)Ru(μ-tppz)Ru(L)Cl] (1–5) containing differently substituted β-diketonato derivatives (1: L = 2,4-pentanedionato; 2: L = 3,5-heptanedionato; 3: L = 2,2,6,6-tetramethyl-3,5-heptanedionato; 4: L = 3-methyl-2,4-pentanedionato; 5: L = 3-ethyl-2,4-pentanedionato) as ancillary ligands (L) were synthesized and studied by spectroelectrochemistry (UV-Vis- NIR, electron paramagnetic resonance (EPR)). X-ray structural characterisation revealed anti (1, 2, 5) or syn (3) configuration as well as non-planarity of the bis-tridentate tppz bridge and strong dπ(RuII) → π*(pyrazine, tppz) back- bonding. The widely separated one-electron oxidation steps, RuIIRuII/RuIIRuIII and RuIIRuIII/RuIIIRuIII, result in large comproportionation constants (Kc) of ≥1010 for the mixed-valent intermediates. The syn-configurated 3n exhibits a particularly high Kc of 1012 for n = 1+, accompanied by density functional theory (DFT)-calculated minimum Ru–N bond lengths for this RuIIRuIII intermediate. The electrogenerated mixed-valent states 1+–5+ exhibit anisotropic EPR spectra at 110 K with average values of 2.304–2.234 and g anisotropies Δg = g1–g3 of 0.82–0.99. Metal-to-metal charge transfer (MMCT) absorptions occur for 1+–5+ in the NIR region at 1660 nm–1750 nm (ε ≈ 2700 dm3 mol−1 cm−1, Δν1/2 ≈ 1800 cm−1). DFT calculations of 1+ and 3+ yield comparable Mulliken spin densities of about 0.60 for the metal ions, corresponding to valence-delocalised situations (Ru2.5)2. Rather large spin densities of about −0.4 were calculated for the tppz bridges in 1+ and 3+. The calculated electronic interaction values (VAB) for 1+–5+ are about 3000 cm−1, comparable to that for the Creutz–Taube ion at 3185 cm−1. The DFT calculations predict that the RuIIIRuIII forms in 12+–52+ prefer a triplet (S = 1) ground state with ΔE (S = 0 − S = 1) [similar]5000 cm−1. One-electron reduction takes place at the tppz bridge which results in species [Cl(L)RuII(μ-tppz˙−)RuII(L)Cl]− (1˙−–3˙−, 5˙−) which exhibit free radical-type EPR signals and NIR transitions typical of the tppz radical anion. The system 4n is distinguished by lability of the Ru–Cl bonds

Novel multi-band quantum soliton states for a derivative nonlinear Schrodinger model

We show that localized N-body soliton states exist for a quantum integrable derivative nonlinear Schrodinger model for several non-overlapping ranges (called bands) of the coupling constant \eta. The number of such distinct bands is given by Euler's \phi-function which appears in the context of number theory. The ranges of \eta within each band can also be determined completely using concepts from number theory such as Farey sequences and continued fractions. We observe that N-body soliton states appearing within each band can have both positive and negative momentum. Moreover, for all bands lying in the region \eta > 0, soliton states with positive momentum have positive binding energy (called bound states), while the states with negative momentum have negative binding energy (anti-bound states).Comment: LaTeX, 20 pages including 2 figure

Jost solutions and quantum conserved quantities of an integrable derivative nonlinear Schrodinger model

We study differential and integral relations for the quantum Jost solutions associated with an integrable derivative nonlinear Schrodinger (DNLS) model. By using commutation relations between such Jost solutions and the basic field operators of DNLS model, we explicitly construct first few quantum conserved quantities of this system including its Hamiltonian. It turns out that this quantum Hamiltonian has a new kind of coupling constant which is quite different from the classical one. This modified coupling constant plays a crucial role in our comparison between the results of algebraic and coordinate Bethe ansatz for the case of DNLS model. We also find out the range of modified coupling constant for which the quantum $N$-soliton state of DNLS model has a positive binding energy.Comment: 36 pages, latex, two references added, to be published in Nucl. Phys.

Prevalence of anaemia and associated factors among Oraon females of North 24 Parganas, West Bengal, India

Low haemoglobin level or anaemia is a health problem worldwide especially in developing countries like India. Anaemia is generally higher among indigenous groups compared to general population globally and females are specifically more prone to anaemia. However, studies are inadequate on indigenous groups of India. The aims of the study are to determine the prevalence of anaemia among the female Oraons of North 24 Parganas and to study the association between anaemia and concomitants like socio-demographic and food habit variables. Data have been collected on demographic, socio-economic and food habit variables using well-tested questionnaire from 309 Oraon females living in rural and urban areas of North 24 Parganas, West Bengal. Haemoglobin data were collected using standard instrument and technique. Descriptive statistics and binary logistic regression were used to analyze the data using SPSS version 16.0. Females of rural and urban areas were mostly married and non-literate, employed as labourers and had sedentary occupations. Majority of them consume fruits and vegetables but less animal protein and dairy product. Around 80% of the females were anaemic, irrespective of their habitat, socio-economic status and food habits. Anaemic status was associated with insufficient intake of animal protein, which is significantly associated with the anaemia status of the females in the present study

Differences in Selected Health Traits between Occupational Groups among Oraons of Jalpaiguri District, West Bengal

Occupational health deals with diseases or injuries caused due to work. Different types of work cause different types of ill-effect on health and may cause changes in health traits; empirical studies on the issues are scanty. The present study aims to investigate the differences in selected health traits between two occupational groups of the same ethnic origin. Cross-sectional data collected on 357 adult Oraon labourers engaged in two different occupations, namely, agriculture and brickfield in Jalpaiguri district, West Bengal, of which are 62 male and 43 female agricultural labourers and 136 male and 116 female brickfield labourers. Data consists of anthropometric measurements, blood pressure, and haemoglobin traits. Health status assessed in terms of BMI, systolic and diastolic blood pressure, and haemoglobin level following standard cut-off values. Mean values of both the occupational groups show similar trends in case of selected anthropometric and health traits. Individuals are ecto-mesomorphic irrespective of sex and occupation. Majority of individuals of either sex of both the occupational groups are underweight but hypertensive. In anthropological data, the trend of mean values is important than mere statistical significance. Data indicates that both the occupational groups have similar health condition, maybe due to their heavy manual activity

Stepwise Crystallization: Illustrative Examples of the Use of Metalloligands Cu-6(mna)(6)](6-) and (Ag-6(Hmna)(2)(mna)(4)](4-) (H(2)mna=2-Mercapto Nicotinic Acid) in the Formation of Heterometallic Two- and Three-Dimensional Assemblies with brucite, pcu, and sql Topologies

Three new inorganic coordination polymers, {Mn(H2O)(6)]-Mn-2(H2O)(6)](Cu-6(mna)(6)]center dot 6H(2)O}, 1, {Mn-4(OH)(2)(H2O)(10)] (Cu-6(mna)6]center dot 8H(2)O}, 2, and {Mn-2(H2O)(5)]Ag-6(Hmna)(2)(mna)(4)]center dot 20H(2)O}, 3, have been synthesized at room temperature through a sequential crystallization route. In addition, we have also prepared and characterized the molecular precursor Cu-6(Hmna)(6)]. Compounds 1 and 3 have a two-dimensional structure, whereas 2 has a three-dimensional structure. The formation of 2 has been achieved by minor modification in the synthetic composition, suggesting the subtle relationship between the reactant composition and the structure. The hexanudear copper and silver duster cores have Cu center dot center dot center dot Cu and Ag center dot center dot center dot Ag distances close to the sum of the van der Waals radii of Cu1+ and Ag1+, respectively. The connectivity between Cu-6(mna)(6)](6-) cluster units and Mn2+ ions gives rise to a brucite related layer in 1 and a pcu-net in 2. The Ag-6(Hmna)(2)(mna)(4)](4-) cluster in 3, on the other hand, forms a sql-net with Mn2+. Compound 1 exhibits an interesting and reversible hydrochromic behavior, changing from pale yellow to red, on heating at 70 degrees C or treatment under a vacuum. Electron paramagnetic resonance studies indicate no change in the valence states, suggesting the color change could be due to changes in the coordination environment only. The magnetic studies indicate weak antiferromagnetic behavior. Proton conductivity studies indicate moderate proton migrations in 1 and 3. The present study dearly establishes sequential crystallization as an important pathway for the synthesis of heterometallic coordination polymers

Stabilization of the Anionic Metalloligand, Ag-6(mna)(6)](6-) (H(2)mna=2-Mercapto Nicotinic Acid), in cor, alpha-Po, and sql Nets Employing Alkaline Earth Metal Ions: Synthesis, Structure, and Nitroaromatics Sensing Behavior

Three new heterometallic metal organic frameworks, {Ca-6(H2O)(18)]Ag-6(mna)(6)](2)}center dotAg-6(Hmna)(6)]center dot 20H(2)O], 1, {Sr-3(H2O)(10)]Ag-6(mna)(6)]center dot 12H(2)O}, 2, and {Ba-3(H2O)(10)]Ag-6(mna)(6)]center dot 8H(2)O}, 3, have been synthesized following hard-soft acids-bases principle. Compounds 1 and 2 have three-dimensional structures with cor and pcu (alpha-Po) topology, whereas compound 3 has a two-dimensional sql topology. Smaller calcium and strontium ions form a simple dimer (Ca2/Sr2, 1/2) and tetramer units (Sr4, 2), whereas the larger barium ion forms infinite Ba-O-Ba chains. The presence of the electron-rich mna ligand in all the compounds paved the way for the detection of electron-deficient hazardous nitroaromatics employing photoluminescence quenching methods. The luminescence intensities of the compounds are strongly quenched by picric acid, p-nitro phenol, and 2-nitro toluene at low concentration, which indicates that these compounds are excellent materials for the detection of these nitroaromatics in solution

Paramagnetic ruthenium-biimidazole derivatives [(acac)<SUB>2</SUB>Ru<SUP>III</SUP>(LH<SUB>n</SUB>)]<SUP>m</SUP>, n/m = 2/+, 1/0, 0/-. Synthesis, structures, solution properties and anion receptor features in solution state

The paramagnetic ruthenium-biimidazole complexes [(acac)2RuIII(LH-)] (1 = red-brown), [(acac)2RuIII(LH2)](ClO4) (2 = pink) and Bu4N[(acac)2RuIII(L2-)] (3 = greenish yellow) comprising of monodeprotonated, neutral and bideprotonated states of the coordinated biimidazole ligand (LHn, n = 1, 2, 0), respectively, have been isolated (acac- = acetylacetonate). Single-crystal X-ray diffraction of 1 reveals that the asymmetric unit consists of three independent molecules: A-C, where molecule A corresponds to complex 1 and the other two molecules B and C co-exist as a hydrogen bonded dimeric unit perhaps between the cationic 2+ and anionic 3-. The packing diagram further reveals that the molecule A in the crystal of 1 also forms a hydrogen bonded dimer with the neighbouring another unit of molecule A. The formation of [(acac)2RuIII(LH2)](ClO4) (2) has also been authenticated independently by its single-crystal X-ray structure. The packing diagram of 2 shows multiple hydrogen bonds between the N-H protons of coordinated LH2 and the counter ClO4-. Paramagnetic complexes show 1H NMR spectra over a wide range of chemical shift, δ (ppm), +10 to -35 in CDCl3. One-electron paramagnetic 1-3 (μ /B.M. ∼1.9) exhibit distinct rhombic-EPR spectra with relatively large g anisotropic factors: &lt;g&gt; 2.136-2.156 and Δ g 0.65-0.77, typical for distorted octahedral ruthenium(III) complexes. The complexes 1-3 are inter-convertible as a function of pH. The pKa1 and pKa2 of 6.8 and 11, respectively, for 2 are estimated by monitoring the pH dependent spectral changes. The Ru(III)-Ru(IV) couple near 1.25 V vs. SCE remains almost invariant in 1-3 whereas the corresponding Ru(III)-Ru(II) couple varies appreciably in the range of -0.52 to -0.85 V vs. SCE based on the protonated-deprotonated states of the coordinated biimidazole ligand. Compounds 1-3 exhibit one weak ligand to metal charge transfer (LMCT) transition near 500 nm and intense intraligand transitions in the higher energy UV region. The spectrophotometric titrations of 2 with the TBA (TBA = tetrabutylammonium) salts of a wide variety of anions, F-, Cl-, Br-, I-, HSO4-, OAc-, H2PO4- in CH3CN reveal that the possible hydrogen bonds between the N-H protons of LH2 in 2 and Cl- or Br- or I- or HSO4- or H2PO4- anion are rather weak or negligible. However, in presence of excess H2PO4- anion, the molar ratio of 2 to H2PO4- being 1:4, simple liberation of one N-H proton of the coordinated LH2 in 2 has been taken place which in effect yields 1 and H3PO4. On the contrary, the spectrophotometric titrations of 1:1 molar solution of 2 and OAc- or F- anion suggest the initial formation of hydrogen bonds between the N-H protons of LH2 in 2 and the anion with the calculated log K value of 5.92 or 4.7, respectively, which eventually leads to the transfer of one of the N-H protons of LH2 in 2 to the anion, resulting in 1 and HOAc or HF. On addition of excess OAc- to the above solution of 1 (molar ratio of OAc- to 1, 4:1), further hydrogen bonding between the N-H proton of LH- in 1 and OAc- occurs but without the abstraction of the N-H proton of LH-. However, excess F- anion concentration (molar ratio of anion to 1, 5:1) facilitates the removal of the remaining N-H proton of LH- in 1 which in turn yields 3 incorporating the bideprotonated form L2-