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

High-temperature deformation behavior of a gamma TiAl alloy-microstructural evolution and mechanisms

The present investigation was carried out in the context of the internal-variable theory of inelastic deformation and the dynamic-materials model (DMM), to shed light on the high-temperature deformation mechanisms in TiAl. A series of load-relaxation tests and tensile tests were conducted on a fine-grained duplex gamma TiAl alloy at temperatures ranging from 800 degreesC to 1050 degreesC. Results of the load-relaxation tests, in which the deformation took place at an infinitesimal level (epsilon congruent to 0.05), showed that the deformation behavior of the alloy was well described by the sum of dislocation-glide and dislocation-climb processes. To investigate the deformation behavior of the fine-grained duplex gamma TiAl alloy at a finite strain level, processing maps were constructed on the basis of a DMM. For this purpose, compression tests were carried out at temperatures ranging from 800 degreesC to 1250 degreesC using strain rates ranging from 10 to 10(-4)/s. Two domains were identified and characterized in the processing maps obtained at finite strain levels (0.2 and 0.6). One domain was found in the region of 980 degreesC and 10(-3)/s with a peak efficiency (maximum efficiency of power dissipation) of 48 pct and was identified as a domain of dynamic recrystallization (DRx) from microstructural observations. Another domain with a peak efficiency of 64 pct was located in the region of 1250 degreesC and 10(-4)/s and was considered to be a domain of superplasticity.ope

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

Track D Social Science, Human Rights and Political Science

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/138414/1/jia218442.pd

Search for leptophobic Z ' bosons decaying into four-lepton final states in proton-proton collisions at root s=8 TeV

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Search for black holes and other new phenomena in high-multiplicity final states in proton-proton collisions at root s=13 TeV

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Search for heavy resonances decaying into a vector boson and a Higgs boson in final states with charged leptons, neutrinos, and b quarks

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Search for high-mass diphoton resonances in proton-proton collisions at 13 TeV and combination with 8 TeV search

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Measurements of differential production cross sections for a Z boson in association with jets in pp collisions at root s=8 TeV

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