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  • Articles  (17)
  • American Institute of Physics (AIP)  (17)
  • 2020-2023
  • 2010-2014  (17)
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  • Mathematics  (17)
  • 1
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    Entanglement and the three-dimensionality of the Bloch ball (2014)
    American Institute of Physics (AIP)
    Details
    Publication Date: 2014-12-17
    Description: We consider a very natural generalization of quantum theory by letting the dimension of the Bloch ball be not necessarily three. We analyze bipartite state spaces where each of the components has a d -dimensional Euclidean ball as state space. In addition to this, we impose two very natural assumptions: the continuity and reversibility of dynamics and the possibility of characterizing bipartite states by local measurements. We classify all these bipartite state spaces and prove that, except for the quantum two-qubit state space, none of them contains entangled states. Equivalently, in any of these non-quantum theories, interacting dynamics is impossible. This result reveals that “existence of entanglement” is the requirement with minimal logical content which singles out quantum theory from our family of theories.
    Print ISSN: 0022-2488
    Electronic ISSN: 1089-7658
    Topics: Mathematics , Physics
    Published by American Institute of Physics (AIP)
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  • 2
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    Riemann–Hilbert problem approach for two-dimensional flow inverse scatteringa) (2014)
    American Institute of Physics (AIP)
    Details
    Publication Date: 2014-10-07
    Description: We consider inverse scattering for the time-harmonic wave equation with first-order perturbation in two dimensions. This problem arises in particular in the acoustic tomography of moving fluid. We consider linearized and nonlinearized reconstruction algorithms for this problem of inverse scattering. Our nonlinearized reconstruction algorithm is based on the non-local Riemann–Hilbert problem approach. Comparisons with preceding results are given.
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    Electronic ISSN: 1089-7658
    Topics: Mathematics , Physics
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  • 3
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    Coherent state transforms and the Mackey-Stone-Von Neumann theorem (2014)
    American Institute of Physics (AIP)
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    Publication Date: 2014-10-07
    Description: Mackey showed that for a compact Lie group K , the pair ( K , C   0 ( K )) has a unique non-trivial irreducible covariant pair of representations. We study the relevance of this result to the unitary equivalence of quantizations for an infinite-dimensional family of K × K invariant polarizations on T * K . The Kähler polarizations in the family are generated by (complex) time-τ Hamiltonian flows applied to the (Schrödinger) vertical real polarization. The unitary equivalence of the corresponding quantizations of T * K is then studied by considering covariant pairs of representations of K defined by geometric prequantization and of representations of C   0 ( K ) defined via Heisenberg time-(−τ) evolution followed by time-(+τ) geometric-quantization-induced evolution. We show that in the semiclassical and large imaginary time limits, the unitary transform whose existence is guaranteed by Mackey's theorem can be approximated by composition of the time-(+τ) geometric-quantization-induced evolution with the time-(−τ) evolution associated with the momentum space [W. D. Kirwin and S. Wu, “Momentum space for compact Lie groups and the Peter-Weyl theorem ” (unpublished)] quantization of the Hamiltonian function generating the flow. In the case of quadratic Hamiltonians, this asymptotic result is exact and unitary equivalence between quantizations is achieved by identifying the Heisenberg imaginary time evolution with heat operator evolution, in accordance with the coherent state transform of Hall.
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    Electronic ISSN: 1089-7658
    Topics: Mathematics , Physics
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  • 4
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    Yang-Mills like instantons in eight and seven dimensions (2014)
    American Institute of Physics (AIP)
    Details
    Publication Date: 2014-10-10
    Description: We consider a gauge theory in which a nonassociative Moufang loop takes the place of a structure group. We construct Belavin-Polyakov-Schwartz-Tyupkin (BPST) and t’Hooft like instanton solutions of the gauge theory in seven and eight dimensions.
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    Electronic ISSN: 1089-7658
    Topics: Mathematics , Physics
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  • 5
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    Riemann–Hilbert problem approach for two-dimensional flow inverse scatteringa) (2014)
    American Institute of Physics (AIP)
    Details
    Publication Date: 2014-10-10
    Description: We consider inverse scattering for the time-harmonic wave equation with first-order perturbation in two dimensions. This problem arises in particular in the acoustic tomography of moving fluid. We consider linearized and nonlinearized reconstruction algorithms for this problem of inverse scattering. Our nonlinearized reconstruction algorithm is based on the non-local Riemann–Hilbert problem approach. Comparisons with preceding results are given.
    Print ISSN: 0022-2488
    Electronic ISSN: 1089-7658
    Topics: Mathematics , Physics
    Published by American Institute of Physics (AIP)
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  • 6
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    Coherent state transforms and the Mackey-Stone-Von Neumann theorem (2014)
    American Institute of Physics (AIP)
    Details
    Publication Date: 2014-10-10
    Description: Mackey showed that for a compact Lie group K , the pair ( K , C   0 ( K )) has a unique non-trivial irreducible covariant pair of representations. We study the relevance of this result to the unitary equivalence of quantizations for an infinite-dimensional family of K × K invariant polarizations on T * K . The Kähler polarizations in the family are generated by (complex) time-τ Hamiltonian flows applied to the (Schrödinger) vertical real polarization. The unitary equivalence of the corresponding quantizations of T * K is then studied by considering covariant pairs of representations of K defined by geometric prequantization and of representations of C   0 ( K ) defined via Heisenberg time-(−τ) evolution followed by time-(+τ) geometric-quantization-induced evolution. We show that in the semiclassical and large imaginary time limits, the unitary transform whose existence is guaranteed by Mackey's theorem can be approximated by composition of the time-(+τ) geometric-quantization-induced evolution with the time-(−τ) evolution associated with the momentum space [W. D. Kirwin and S. Wu, “Momentum space for compact Lie groups and the Peter-Weyl theorem ” (unpublished)] quantization of the Hamiltonian function generating the flow. In the case of quadratic Hamiltonians, this asymptotic result is exact and unitary equivalence between quantizations is achieved by identifying the Heisenberg imaginary time evolution with heat operator evolution, in accordance with the coherent state transform of Hall.
    Print ISSN: 0022-2488
    Electronic ISSN: 1089-7658
    Topics: Mathematics , Physics
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  • 7
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    Characteristic decomposition of compressible Euler equations for a non-ideal gas in two-dimensions (2014)
    American Institute of Physics (AIP)
    Details
    Publication Date: 2014-10-10
    Description: We consider a two-dimensional compressible Euler system for a non-ideal gas, and use the characteristic decomposition to establish that any pseudo-steady isentropic irrotational flow, adjacent to a constant state, must be a simple wave. Further, the constancy of the entropy and vorticity along the pseudo-flow characteristics extends the foregoing conclusion to full Euler system. An attention is drawn to the fact that the result is also applicable to the shallow water system as it bears a close structural resemblance with the system under study. These results are generalization of the well-known theorem on reducible equations by Courant and Friedrichs [Supersonic Flow and Shock Waves (Springer-Verlag, New York, 1999)] and a recent result on compressible Euler system for an ideal gas by Li et al. [“Simple waves and a characteristic decomposition of the two-dimensional compressible Euler equations ,” Commun. Math. Phys.267, 1–12 (2006)]
    Print ISSN: 0022-2488
    Electronic ISSN: 1089-7658
    Topics: Mathematics , Physics
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  • 8
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    Construction of conformally invariant higher spin operators using transvector algebras (2014)
    American Institute of Physics (AIP)
    Details
    Publication Date: 2014-10-29
    Description: This paper deals with a systematic construction of higher spin operators, defined as conformally invariant differential operators acting on functions on flat space R m with values in an arbitrary half-integer irreducible representation for the spin group. To be more precise, the higher spin version of the Dirac operator and associated twistor operators will be constructed as generators of a transvector algebra, hereby generalising the well-known fact that the classical Dirac operator on R m and its symbol generate the orthosymplectic Lie superalgebra osp ( 1 , 2 ) . To do so, we will use the extremal projection operator and its relation to transvector algebras. In the second part of the article, the conformal invariance of the constructed higher spin operators will be proven explicitly.
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    Electronic ISSN: 1089-7658
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  • 9
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    Characteristic decomposition of compressible Euler equations for a non-ideal gas in two-dimensions (2014)
    American Institute of Physics (AIP)
    Details
    Publication Date: 2014-09-26
    Description: We consider a two-dimensional compressible Euler system for a non-ideal gas, and use the characteristic decomposition to establish that any pseudo-steady isentropic irrotational flow, adjacent to a constant state, must be a simple wave. Further, the constancy of the entropy and vorticity along the pseudo-flow characteristics extends the foregoing conclusion to full Euler system. An attention is drawn to the fact that the result is also applicable to the shallow water system as it bears a close structural resemblance with the system under study. These results are generalization of the well-known theorem on reducible equations by Courant and Friedrichs [Supersonic Flow and Shock Waves (Springer-Verlag, New York, 1999)] and a recent result on compressible Euler system for an ideal gas by Li et al. [“Simple waves and a characteristic decomposition of the two-dimensional compressible Euler equations ,” Commun. Math. Phys.267, 1–12 (2006)]
    Print ISSN: 0022-2488
    Electronic ISSN: 1089-7658
    Topics: Mathematics , Physics
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  • 10
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    Global solutions of certain plasma fluid models in three-dimension (2014)
    American Institute of Physics (AIP)
    Details
    Publication Date: 2014-12-18
    Description: We consider several dispersive time-reversible plasma fluid models in 3 dimensions: the Euler-Poisson 2-fluid model, the relativistic Euler–Maxwell 1-fluid model, and the relativistic Euler–Maxwell 2-fluid model. In all of these models, we prove global stability of the constant background solutions, in the sense that small, smooth, and irrotational perturbations lead to smooth global solutions that decay as t → ∞.
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    Electronic ISSN: 1089-7658
    Topics: Mathematics , Physics
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