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  • 1
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    Squeezed states as representations of symplectic groups (1998)
    In:  CASI
    Details
    Publication Date: 2004-12-03
    Description: It is shown that the SU(1,1)-like and SU(2)-like two-photon coherent states can be combined to form a O(3,2)-like two-photon state. Since the O(3,2) group has many subgroups, there are also many new interesting new coherent and squeezed two-photon states. Among them is the two-photon sheared state whose symmetry property is like that for the two-dimensional Euclidean group. There are now two-phonon coherent states which may exhibit symmetries not yet observed for photons, including sheared states. Let us note that both SU(1,1) and S(3,2) are isomorphic to the symplectic groups Sp(2) and Sp(4) respectively, and that symplectic transformations consist of rotations and squeeze transformations.
    Keywords: Atomic and Molecular Physics
    Type: Fifth International Conference on Squeezed States and Uncertainty Relations; 321-326; NASA/CP-1998-206855
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  • 2
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    Linear canonical transformations of coherent and squeezed states in the Wigner phase space. III - Two-mode states (1990)
    In:  Other Sources
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    Publication Date: 2011-08-19
    Description: It is shown that the basic symmetry of two-mode squeezed states is governed by the group SP(4) in the Wigner phase space which is locally isomorphic to the (3 + 2)-dimensional Lorentz group. This symmetry, in the Schroedinger picture, appears as Dirac's two-oscillator representation of O(3,2). It is shown that the SU(2) and SU(1,1) interferometers exhibit the symmetry of this higher-dimensional Lorentz group. The mathematics of two-mode squeezed states is shown to be applicable to other branches of physics including thermally excited states in statistical mechanics and relativistic extended hadrons in the quark model.
    Keywords: PHYSICS (GENERAL)
    Type: Physical Review A - Atomic, Molecular, and Optical Physics, 3rd Series (ISSN 0556-2791); 41; 6233-624
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  • 3
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    Linear canonical transformations of coherent and squeezed states in the Wigner phase space. II - Quantitative analysis (1989)
    In:  Other Sources
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    Publication Date: 2011-08-19
    Description: It is possible to calculate expectation values and transition probabilities from the Wigner phase-space distribution function. Based on the canonical transformation properties of the Wigner function, an algorithm is developed for calculating these quantities in quantum optics for coherent and squeezed states. It is shown that the expectation value of a dynamical variable can be written in terms of its vacuum expectation value of the canonically transformed variable. Parallel-axis theorems are established for the photon number and its variant. It is also shown that the transition probability between two squeezed states can be reduced to that of the transition from one squeezed state to vacuum.
    Keywords: OPTICS
    Type: Physical Review A - General Physics, 3rd Series (ISSN 0556-2791); 40; 902-912
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  • 4
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    Uncertainty relations for light waves and the concept of photons (1987)
    In:  Other Sources
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    Publication Date: 2011-08-19
    Description: A Lorentz-covariant localization for light waves is presented. The unitary representation for the electromagnetic four-potential is constructed for a monochromatic light wave. A model for covariant superposition is constructed for light waves with different frequencies. It is therefore possible to construct a wave function for light waves carrying a covariant probability interpretation. It is shown that the time-energy uncertainty relation (Delta-t)(Delta-omega) = about 1 for light waves is a Lorentz-invariant relation. The connection between photons and localized light waves is examined critically.
    Keywords: PHYSICS (GENERAL)
    Type: Physical Review A - General Physics, 3rd Series (ISSN 0556-2791); 35; 1682-169
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  • 5
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    Special relativity and interferometers (1988)
    In:  Other Sources
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    Publication Date: 2011-08-19
    Description: A new generation of gravitational wave detectors is expected to be based on interferometers. Yurke et al. (1986) introduced a class of interferometers characterized by SU(1,1) which can in principle achieve a phase sensitivity approaching 1/N, where N is thte total number of photons entering the interferometer. It is shown here that the SU(1,1) interferometer can serve as an analog computer for Wigner's little group of the Poincare\'| group.
    Keywords: PHYSICS (GENERAL)
    Type: Physical Review A - General Physics, 3rd Series (ISSN 0556-2791); 37; 4494-449
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  • 6
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    A new dispersion relation for electron-atom scattering (1986)
    In:  Other Sources
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    Publication Date: 2011-08-19
    Description: A new forward-angle dispersion relation (DR) for electron-atom scattering is proposed. It is based on a subtraction of the static-exchange amplitude from the exact elastic scattering amplitude. Arguments are advanced to explain why this should obviate the difficulties associated with the Gerjuoy-Krall DR, specifically with the exchange Born amplitude. The new DR is tested in the elastic energy range for e-H scattering and compared with the GKDR.
    Keywords: ATOMIC AND MOLECULAR PHYSICS
    Type: Journal of Physics B - Atomic and Molecular Physics (ISSN 0022-3700); 19; L701-L70
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  • 7
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    Linear canonical transformations of coherent and squeezed states in the Wigner phase space (1988)
    In:  Other Sources
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    Publication Date: 2011-08-19
    Description: It is shown that classical linear canonical transformations are possible in the Wigner phase space. Coherent and squeezed states are shown to be linear canonical transforms of the ground-state harmonic oscillator. It is therefore possible to evaluate the Wigner functions for coherent and squeezed states from that for the harmonic oscillator. Since the group of linear canonical transformations has a subgroup whose algebraic property is the same as that of the (2+1)-dimensional Lorentz group, it may be possible to test certain properties of the Lorentz group using optical devices. A possible experiment to measure the Wigner rotation angle is discussed.
    Keywords: OPTICS
    Type: Physical Review A - General Physics, 3rd Series (ISSN 0556-2791); 37; 807-814
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  • 8
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    A new approach to the photon localization problem (1994)
    In:  CASI
    Details
    Publication Date: 2013-08-31
    Description: Since wavelets form a representation of the Poincare group, it is possible to construct a localized superposition of light waves with different frequencies in a Lorentz-covariant manner. This localized wavelet satisfies a Lorentz-invariant uncertainty relation, and also the Lorentz-invariant Parseval's relation. A quantitative analysis is given for the difference between photons and localized waves. It is then shown that this localized entity corresponds to a relativistic photon with a sharply defined momentum in the non-localization limit. Waves are not particles. It is confirmed that the wave-particle duality is subject to the uncertainty principle.
    Keywords: OPTICS
    Type: Third International Workshop on Squeezed States and Uncertainty Relations; p 77-82
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  • 9
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    A model for predicting high-temperature fatigue failure of a W/Cu composite (1991)
    In:  CASI
    Details
    Publication Date: 2013-08-31
    Description: The material studied, a tungsten-fiber-reinforced, copper-matrix composite, is a candidate material for rocket nozzle liner applications. It was shown that at high temperatures, fatigue cracks initiate and propagate inside the copper matrix through a process of initiation, growth, and coalescence of grain boundary cavities. The ductile tungsten fibers neck and rupture locally after the surrounding matrix fails, and complete failure of the composite then ensues. A simple fatigue life prediction model is presented for the tungsten/copper composite system.
    Keywords: COMPOSITE MATERIALS
    Type: Structural Integrity and Durability of Reusable Space Propulsion Systems; p 207-218
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  • 10
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    Wavelets and spacetime squeeze (1993)
    In:  CASI
    Details
    Publication Date: 2013-08-31
    Description: It is shown that the wavelet is the natural language for the Lorentz covariant description of localized light waves. A model for covariant superposition is constructed for light waves with different frequencies. It is therefore possible to construct a wave function for light waves carrying a covariant probability interpretation. It is shown that the time-energy uncertainty relation (Delta(t))(Delta(w)) is approximately 1 for light waves is a Lorentz-invariant relation. The connection between photons and localized light waves is examined critically.
    Keywords: OPTICS
    Type: The Second International Workshop on Squeezed States and Uncertainty Relations; p 341-355
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