published_or_final_version / Physics / Master / Master of Philosophy

A critical survey of the present state of the quantum statistical theory of thermal conductivity is given. Recently several attempts have been made to extend Kubo's treatment of electrical conduction to other irreversible transport processes in -which the interaction between the driving system and the system of interest is not precisely known. No completely satisfactory solution of the problems involved is contained in the literature. In this thesis, a detailed derivation of a Kubo-type formula for thermal conductivity is given, using essentially the concepts and methods of Nakajima and Mori, with no pretense that it settles the problem completely. Some general remarks are made on the evaluation of a Kubo-type expression, in particular, the use of Van Hove's master equations and the reduction of the usual N-particle formula to a single particle formula. An explicit calculation of thermal conductivity is made for the simple model of elastic electron scattering by randomly distributed, spherically symmetric impurities. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

We study properties of super-KMS functionals on ℤ₂ graded von Neumann algebras. We prove that if a normal self-adjoint functional ω is weakly super-KMS, then the uniquely defined by the polar decomposition of ω positive functional |ω| is KMS. We construct a graded representation of any von Neumann algebra with a normal self-adjoint super-KMS functional on it as an algebra of bounded operators on a Hilbert space. The grading of the algebra of operators that we obtain is induced from a natural orthogonal decomposition of the Hilbert space. In our construction we have to use the weak super-KMS property and the implications we have derived from it. We present a generalization of the Tomita — Takesaki theorem to the case of (not necessarily positive) self-adjoint normal faithful functionals. We show that for every such functional ω there is a canonically defined *-automorphism group (the analog of the modular group) and a canonical ℤ₂ grading of the algebra, commuting with the automorphism group. The functional ω is weakly super-KMS with respect to them. Furthermore, the canonical automorphism group and ℤ₂ grading are the unique pair of a σ-weakly continuous one-parameter *-automorphism group and a ℤ₂ grading, commuting with each other, with respect to which ω is super-KMS. / Ph. D.

A quantum channel is a mapping which sends density matrices to density matrices. The estimation of quantum channels is of great importance to the field of quantum information. In this thesis two topics related to estimation of quantum channels are investigated. The first of these is the upper bound of Sarovar and Milburn (2006) on the Fisher information obtainable by measuring the output of a channel. Two questions raised by Sarovar and Milburn about their bound are answered. A Riemannian metric on the space of quantum states is introduced, related to the construction of the Sarovar and Milburn bound. Its properties are characterized. The second topic investigated is the estimation of unitary channels. The situation is considered in which an experimenter has several non-identical unitary channels that have the same parameter. It is shown that it is possible to improve estimation using the channels together, analogous to the case of identical unitary channels. Also, a new method of phase estimation is given based on a method sketched by Kitaev (1996). Unlike other phase estimation procedures which perform similarly, this procedure requires only very basic experimental resources.

by Sanjoy K. Mitter, Stephen K. Young. / Bibliography: p. 10. / "January 1979." / Supported by NSF Grant ENG76-02860 NSF Grant ENG77-28444

Long-term storage of quantum information has diverse applications in quantum information science. This work presents an experimental realization of quantum memories with lifetimes greater then 0.1 s. The memories are based on cold rubidium atoms confined in one-dimensional optical lattices. First realization of lattice-based quantum memory and entanglement between a light field and a spin wave is presented in Chapter II. Chapter III describes two different methods (two-photon and magnetic) of compensation for inhomogeneous differential light shifts between the memory levels due to optical trapping potentials, and demonstration of entanglement between a telecom-band light field and a light-shift compensated memory qubit. Highly excited Rydberg atoms present a unique platform for study of strongly correlated systems and quantum information, because of their enormous dipole moments and consequent strong, long-range interactions. In the experiment described in Chapter IV single collective Rydberg excitations are created in a cold atomic gas. After a variable storage period the excitations are converted into light. As the principal quantum number n of the Rydberg level is increased beyond ~ 70, no more than a single excitation is retrieved from the entire mesoscopic ensemble of atoms. In Chapter V, by spatially selective conversion of the spin wave into a light field, we demonstrate that Rydberg-level interactions create long-range correlations of collective atomic excitations. These results hold promise for studies of dynamics and disorder in many-body systems with tunable interactions and for scalable quantum information networks. Chapter VI presents initial observations of coherent many-body Rabi oscillations between the ground level and a Rydberg level using several hundred cold rubidium atoms. The strongly pronounced oscillations indicate a nearly complete excitation blockade of the entire mesoscopic ensemble by a single excited atom.

Mott insulators are materials in which strong correlations among the electrons induce an unconventional insulating state. Rich interplay between the structural, magnetic, and electronic degrees of freedom resulting from the electron correlation can lead to unusual complexity of Mott materials on the atomic scale, such as microscopically heterogeneous phases or local structural correlations that deviate significantly from the average structure. Such behavior must be studied by suitable experimental techniques, i.e. "local probes", that are sensitive to this local behavior rather than just the bulk, average properties. In this thesis, I will present results from our studies of multiple families of Mott insulators using two such local probes: muon spin relaxation (muSR), a probe of local magnetism; and pair distribution function (PDF) analysis of x-ray and neutron total scattering, a probe of local atomic structure. In addition, I will present the development of magnetic pair distribution function analysis, a novel method for studying local magnetic correlations that is highly complementary to the muSR and atomic PDF techniques. We used muSR to study the phase transition from Mott insulator to metal in two archetypal Mott insulating systems: RENiO₃ (RE = rare earth element) and V₂O₃. In both of these systems, the Mott insulating state can be suppressed by tuning a nonthermal parameter, resulting in a "quantum" phase transition at zero temperature from the Mott insulating state to a metallic state. In RENiO₃, this occurs through variation of the rare-earth element in the chemical composition; in V₂O₃, through the application of hydrostatic pressure. Our results show that the metallic and Mott insulating states unexpectedly coexist in phase-separated regions across a large portion of parameter space near the Mott quantum phase transition and that the magnitude of the ordered antiferromagnetic moment remains constant across the phase diagram until it is abruptly destroyed at the quantum phase transition. Taken together, these findings point unambiguously to a first-order quantum phase transition in these systems. We also conducted x-ray and neutron PDF experiments, which suggest that the distinct atomic structures associated with the insulating and metallic phases similarly coexist near the quantum phase transition. These results have significant implications for our understanding of the Mott metal-insulator quantum phase transition in real materials. The second part of this thesis centers on the derivation and development of the magnetic pair distribution function (mPDF) technique and its application to the antiferromagnetic Mott insulator MnO. The atomic PDF method involves Fourier transforming the x-ray or neutron total scattering intensity from reciprocal space into real space to directly reveal the local atomic correlations in a material, which may deviate significantly from the average crystallographic structure of that material. Likewise, the mPDF method involves Fourier transforming the magnetic neutron total scattering intensity to probe the local correlations of magnetic moments in the material, which may exist on short length scales even when the material has no long-range magnetic order. After deriving the fundamental mPDF equations and providing a proof-of-principle by recovering the known magnetic structure of antiferromagnetic MnO, we used this technique to investigate the short-range magnetic correlations that persist well into the paramagnetic phase of MnO. By combining the mPDF measurements with ab initio calculations of the spin-spin correlation function in paramagnetic MnO, we were able to quantitatively account for the observed mPDF. We also used the mPDF data to evaluate competing ab initio theories, thereby resolving some longstanding questions about the magnetic exchange interactions in MnO.

Bibliography: leaves 143-146 / vii, 147 leaves ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Mathematical Physics, 1986

Thesis (Ph. D.)--University of Adelaide, Dept. of Mathematical Physics, 1986. / Includes bibliographical references (leaves 143-146).

Orientador: Amir Ordacgi Caldeira / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin / Made available in DSpace on 2018-08-04T01:41:57Z (GMT). No. of bitstreams: 1 Oliveira_ThiagoRodriguesde_M.pdf: 7229972 bytes, checksum: df8825145d26326f700bc04d2d767b90 (MD5) Previous issue date: 2004 / Resumo: Não informado / Abstract: Not informed. / Mestrado / Física Estatística / Mestre em Física