A Unified Algebraic Approach to Few and Many-Body Correlated Systems

The present article is an extended version of the paper {\it Phys. Rev.} {\bf B 59}, R2490 (1999), where, we have established the equivalence of the Calogero-Sutherland model to decoupled oscillators. Here, we first employ the same approach for finding the eigenstates of a large class of Hamiltonians, dealing with correlated systems. A number of few and many-body interacting models are studied and the relationship between their respective Hilbert spaces, with that of oscillators, is found. This connection is then used to obtain the spectrum generating algebras for these systems and make an algebraic statement about correlated systems. The procedure to generate new solvable interacting models is outlined. We then point out the inadequacies of the present technique and make use of a novel method for solving linear differential equations to diagonalize the Sutherland model and establish a precise connection between this correlated system's wave functions, with those of the free particles on a circle. In the process, we obtain a new expression for the Jack polynomials. In two dimensions, we analyze the Hamiltonian having Laughlin wave function as the ground-state and point out the natural emergence of the underlying linear $W_{1+\infty}$ symmetry in this approach.Comment: 18 pages, Revtex format, To appear in Physical Review

Spatio-temporal dynamics of quantum-well excitons

We investigate the lateral transport of excitons in ZnSe quantum wells by using time-resolved micro-photoluminescence enhanced by the introduction of a solid immersion lens. The spatial and temporal resolutions are 200 nm and 5 ps, respectively. Strong deviation from classical diffusion is observed up to 400 ps. This feature is attributed to the hot-exciton effects, consistent with previous experiments under cw excitation. The coupled transport-relaxation process of hot excitons is modelled by Monte Carlo simulation. We prove that two basic assumptions typically accepted in photoluminescence investigations on excitonic transport, namely (i) the classical diffusion model as well as (ii) the equivalence between the temporal and spatial evolution of the exciton population and of the measured photoluminescence, are not valid for low-temperature experiments.Comment: 8 pages, 6 figure

Measurement of charm production at central rapidity in proton-proton collisions at s=2.76\sqrt{s} = 2.76 TeV

The $p_{\rm T}$-differential production cross sections of the prompt (B feed-down subtracted) charmed mesons D$^0$, D$^+$, and D$^{*+}$ in the rapidity range $|y|<0.5$, and for transverse momentum $1< p_{\rm T} <12$ GeV/$c$, were measured in proton-proton collisions at $\sqrt{s} = 2.76$ TeV with the ALICE detector at the Large Hadron Collider. The analysis exploited the hadronic decays D$^0 \rightarrow$K$\pi$, D$^+ \rightarrow$K$\pi\pi$, D$^{*+} \rightarrow$D$^0\pi$, and their charge conjugates, and was performed on a $L_{\rm int} = 1.1$ nb$^{-1}$ event sample collected in 2011 with a minimum-bias trigger. The total charm production cross section at $\sqrt{s} = 2.76$ TeV and at 7 TeV was evaluated by extrapolating to the full phase space the $p_{\rm T}$-differential production cross sections at $\sqrt{s} = 2.76$ TeV and our previous measurements at $\sqrt{s} = 7$ TeV. The results were compared to existing measurements and to perturbative-QCD calculations. The fraction of cdbar D mesons produced in a vector state was also determined.Comment: 20 pages, 5 captioned figures, 4 tables, authors from page 15, published version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/307

Particle-yield modification in jet-like azimuthal di-hadron correlations in Pb-Pb collisions at sNN\sqrt{s_{\rm NN}} = 2.76 TeV

The yield of charged particles associated with high-$p_{\rm T}$ trigger particles ($8 < p_{\rm T} < 15$ GeV/$c$) is measured with the ALICE detector in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV relative to proton-proton collisions at the same energy. The conditional per-trigger yields are extracted from the narrow jet-like correlation peaks in azimuthal di-hadron correlations. In the 5% most central collisions, we observe that the yield of associated charged particles with transverse momenta $p_{\rm T}> 3$ GeV/$c$ on the away-side drops to about 60% of that observed in pp collisions, while on the near-side a moderate enhancement of 20-30% is found.Comment: 15 pages, 2 captioned figures, 1 table, authors from page 10, published version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/350

Revisiting Absorbing Phase Transition in Energy Exchange Models

A recent study of conserved Manna model, with both discrete and continuous variable, indicates that absorbing phase transitions therein belong to the directed percolation (DP) universality class. In this context we revisit critical behaviour in energy exchange models with a threshold. Contrary to the previous claims [PRE 83, 061130 (2011), arXiv:1102.1631], our results indicate that both the maximal and minimal versions of this model belong to the DP class.Comment: 8 pages, 7 eps figure

Heterodi- (Fe, Pd/Pt) and heterotrimetallic (Fe2, Pd) complexes derived from 4-(ferrocenylmethyl)-N-(2-methoxyethyl)-3,5-diphenylpyrazole as potential antitumoral agents

The study of the reactivity of the pyrazole derivative 1-[MeO-(CH2)2]-3,5-Ph2-4-(CH2Fc) (C3N2) (1, Fc = ferrocenyl) with Na2[PdCl4], Pd(OAc)2, and [MCl2(dmso)2] (M = Pd or Pt,dmso = dimethyl sulfoxide) has allowed us to isolate trans-[Pd{κ-N-(1-{MeO(CH2)2}-3,5-Ph2-4-{CH2Fc} {C3N2})}2Cl2] (2), [Pd{κ2-C,N(1-{MeO(CH2)2}-3-{C6H4}-5-Ph-{C3N2})}{κ-N-(1-{MeO(CH2)2}-3,5-Ph2-4-{CH2Fc} {C3N2})}Cl] (3), [Pd{κ2-C,N(1-{MeO(CH2)2}-3-{C6H4}-4-{CH2Fc}-5-Ph-{C3N2})}Cl-(PPh3)] (4), and the trans (5) and cis (6) isomers of [Pt{κ-N-(1-{MeO(CH2)2}-3,5-Ph24-{CH2Fc} {C3N2})}Cl2(dmso)]. Compound 1 acts as a N (in 2, 5, and 6) or (C,N) donor ligand (in 4) and shows both binding modes in 3. The cytotoxic assessment of 1 6 against MCF7, MDA-MB231 (breast), and HCT-116 (colon) cancer cell lines reveal that (1) 1 is more potent than 1-[MeO(CH2)2]-3,5-Ph2-(C3HN2) (V), (2) 2 6 have cytotoxic activity, (3) 2 and 3 are less active than 4 6, and (4) 6 is the most potent compound against the three cancer cell lines

Constructing Exactly Solvable Pseudo-hermitian Many-particle Quantum Systems by Isospectral Deformation

A class of non-Dirac-hermitian many-particle quantum systems admitting entirely real spectra and unitary time-evolution is presented. These quantum models are isospectral with Dirac-hermitian systems and are exactly solvable. The general method involves a realization of the basic canonical commutation relations defining the quantum system in terms of operators those are hermitian with respect to a pre-determined positive definite metric in the Hilbert space. Appropriate combinations of these operators result in a large number of pseudo-hermitian quantum systems admitting entirely real spectra and unitary time evolution. Examples of a pseudo-hermitian rational Calogero model and XXZ spin-chain are considered.Comment: To appear in the Special Issue PHHQP 2010, International Journal of Theoretical Physics; 16 pages, LateX, no figur

An explicit realization of fractional statistics in one dimension

An explicit realization of anyons is provided, using the three-body Calogero model. The fact that in the coupling domain, $-1/4<g<0$, the angular spectrum can have a band structure, leads to the manifestation of the desired phase in the wave function, under the exchange of the paticles. Concurrently, the momentum corresponding to the angular variable is quantized, exactly akin to the relative angular momentum quantization in two dimensional anyonic systemComment: 12 page

Inequivalent quantization of the rational Calogero model with a Coulomb type interaction

We consider the inequivalent quantizations of a $N$-body rational Calogero model with a Coulomb type interaction. It is shown that for certain range of the coupling constants, this system admits a one-parameter family of self-adjoint extensions. We analyze both the bound and scattering state sectors and find novel solutions of this model. We also find the ladder operators for this system, with which the previously known solutions can be constructed.Comment: 15 pages, 3 figures, revtex4, typos corrected, to appear in EPJ