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Sebastian Weiss - One of the best experts on this subject based on the ideXlab platform.
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scalar field probes of power law space time singularities
Journal of High Energy Physics, 2006Co-Authors: Matthias Blau, Denis Frank, Sebastian WeissAbstract:We analyse the effective potential of the scalar wave equation near generic space-time singularities of power-law type (Szekeres-Iyer metrics) and show that the effective potential exhibits a universal and scale invariant leading inverse square behaviour ~ x−2 in the ``tortoise coordinate'' x provided that the metrics satisfy the strict Dominant Energy Condition (DEC). This result parallels that obtained in [1] for probes consisting of families of massless particles (null geodesic deviation, a.k.a. the Penrose Limit). The detailed properties of the scalar wave operator depend sensitively on the Numerical Coefficient of the x−2-term, and as one application we show that timelike singularities satisfying the DEC are quantum mechanically singular in the sense of the Horowitz-Marolf (essential self-adjointness) criterion. We also comment on some related issues like the near-singularity behaviour of the scalar fields permitted by the Friedrichs extension.
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scalar field probes of power law space time singularities
arXiv: High Energy Physics - Theory, 2006Co-Authors: Matthias Blau, Denis Frank, Sebastian WeissAbstract:We analyse the effective potential of the scalar wave equation near generic space-time singularities of power-law type (Szekeres-Iyer metrics) and show that the effective potential exhibits a universal and scale invariant leading x^{-2} inverse square behaviour in the ``tortoise coordinate'' x provided that the metrics satisfy the strict Dominant Energy Condition (DEC). This result parallels that obtained in hep-th/0403252 for probes consisting of families of massless particles (null geodesic deviation, a.k.a. the Penrose Limit). The detailed properties of the scalar wave operator depend sensitively on the Numerical Coefficient of the x^{-2}-term, and as one application we show that timelike singularities satisfying the DEC are quantum mechanically singular in the sense of the Horowitz-Marolf (essential self-adjointness) criterion. We also comment on some related issues like the near-singularity behaviour of the scalar fields permitted by the Friedrichs extension.
Lowell S Brown - One of the best experts on this subject based on the ideXlab platform.
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charged particle motion in a highly ionized plasma
Physics Reports, 2005Co-Authors: Lowell S Brown, Dean L Preston, Robert L SingletonAbstract:Abstract A recently introduced method utilizing dimensional continuation is employed to compute the energy loss rate for a non-relativistic particle moving through a highly ionized plasma. No restriction is made on the charge, mass, or speed of this particle. It is, however, assumed that the plasma is not strongly coupled in the sense that the dimensionless plasma coupling parameter g = e 2 κ D / 4 π T is small, where κ D is the Debye wave number of the plasma. To leading and next-to-leading order in this coupling, d E / d x is of the generic form g 2 ln [ Cg 2 ] . The precise Numerical Coefficient out in front of the logarithm is well known. We compute the constant C under the logarithm exactly for arbitrary particle speeds. Our exact results differ from approximations given in the literature. The differences are in the range of 20% for cases relevant to inertial confinement fusion experiments. The same method is also employed to compute the rate of momentum loss for a projectile moving in a plasma, and the rate at which two plasmas at different temperatures come into thermal equilibrium. Again these calculations are done precisely to the order given above. The loss rates of energy and momentum uniquely define a Fokker–Planck equation that describes particle motion in the plasma. The Coefficients determined in this way are thus well-defined, contain no arbitrary parameters or cutoffs, and are accurate to the order described. This Fokker–Planck equation describes the straggling—the spreading in the longitudinal position of a group of particles with a common initial velocity and position—and the transverse diffusion of a beam of particles. It should be emphasized that our work does not involve a model, but rather it is a precisely defined evaluation of the leading terms in a well-defined perturbation theory.
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charged particle motion in a highly ionized plasma
arXiv: Plasma Physics, 2005Co-Authors: Lowell S Brown, Dean L Preston, Robert L SingletonAbstract:A recently introduced method utilizing dimensional continuation is employed to compute the energy loss rate for a non-relativistic particle moving through a highly ionized plasma. No restriction is made on the charge, mass, or speed of this particle. It is, however, assumed that the plasma is not strongly coupled in the sense that the dimensionless plasma coupling parameter g=e^2\kappa_D/ 4\pi T is small, where \kappa_D is the Debye wave number of the plasma. To leading and next-to-leading order in this coupling, dE/dx is of the generic form g^2 \ln[C g^2]. The precise Numerical Coefficient out in front of the logarithm is well known. We compute the constant C under the logarithm exactly for arbitrary particle speeds. Our exact results differ from approximations given in the literature. The differences are in the range of 20% for cases relevant to inertial confinement fusion experiments. The same method is also employed to compute the rate of momentum loss for a projectile moving in a plasma, and the rate at which two plasmas at different temperatures come into thermal equilibrium. Again these calculations are done precisely to the order given above. The loss rates of energy and momentum uniquely define a Fokker-Planck equation that describes particle motion in the plasma. The Coefficients determined in this way are thus well-defined, contain no arbitrary parameters or cutoffs, and are accurate to the order described. This Fokker-Planck equation describes the longitudinal straggling and the transverse diffusion of a beam of particles. It should be emphasized that our work does not involve a model, but rather it is a precisely defined evaluation of the leading terms in a well-defined perturbation theory.
Matthias Blau - One of the best experts on this subject based on the ideXlab platform.
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scalar field probes of power law space time singularities
Journal of High Energy Physics, 2006Co-Authors: Matthias Blau, Denis Frank, Sebastian WeissAbstract:We analyse the effective potential of the scalar wave equation near generic space-time singularities of power-law type (Szekeres-Iyer metrics) and show that the effective potential exhibits a universal and scale invariant leading inverse square behaviour ~ x−2 in the ``tortoise coordinate'' x provided that the metrics satisfy the strict Dominant Energy Condition (DEC). This result parallels that obtained in [1] for probes consisting of families of massless particles (null geodesic deviation, a.k.a. the Penrose Limit). The detailed properties of the scalar wave operator depend sensitively on the Numerical Coefficient of the x−2-term, and as one application we show that timelike singularities satisfying the DEC are quantum mechanically singular in the sense of the Horowitz-Marolf (essential self-adjointness) criterion. We also comment on some related issues like the near-singularity behaviour of the scalar fields permitted by the Friedrichs extension.
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scalar field probes of power law space time singularities
arXiv: High Energy Physics - Theory, 2006Co-Authors: Matthias Blau, Denis Frank, Sebastian WeissAbstract:We analyse the effective potential of the scalar wave equation near generic space-time singularities of power-law type (Szekeres-Iyer metrics) and show that the effective potential exhibits a universal and scale invariant leading x^{-2} inverse square behaviour in the ``tortoise coordinate'' x provided that the metrics satisfy the strict Dominant Energy Condition (DEC). This result parallels that obtained in hep-th/0403252 for probes consisting of families of massless particles (null geodesic deviation, a.k.a. the Penrose Limit). The detailed properties of the scalar wave operator depend sensitively on the Numerical Coefficient of the x^{-2}-term, and as one application we show that timelike singularities satisfying the DEC are quantum mechanically singular in the sense of the Horowitz-Marolf (essential self-adjointness) criterion. We also comment on some related issues like the near-singularity behaviour of the scalar fields permitted by the Friedrichs extension.
Denis Frank - One of the best experts on this subject based on the ideXlab platform.
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scalar field probes of power law space time singularities
Journal of High Energy Physics, 2006Co-Authors: Matthias Blau, Denis Frank, Sebastian WeissAbstract:We analyse the effective potential of the scalar wave equation near generic space-time singularities of power-law type (Szekeres-Iyer metrics) and show that the effective potential exhibits a universal and scale invariant leading inverse square behaviour ~ x−2 in the ``tortoise coordinate'' x provided that the metrics satisfy the strict Dominant Energy Condition (DEC). This result parallels that obtained in [1] for probes consisting of families of massless particles (null geodesic deviation, a.k.a. the Penrose Limit). The detailed properties of the scalar wave operator depend sensitively on the Numerical Coefficient of the x−2-term, and as one application we show that timelike singularities satisfying the DEC are quantum mechanically singular in the sense of the Horowitz-Marolf (essential self-adjointness) criterion. We also comment on some related issues like the near-singularity behaviour of the scalar fields permitted by the Friedrichs extension.
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scalar field probes of power law space time singularities
arXiv: High Energy Physics - Theory, 2006Co-Authors: Matthias Blau, Denis Frank, Sebastian WeissAbstract:We analyse the effective potential of the scalar wave equation near generic space-time singularities of power-law type (Szekeres-Iyer metrics) and show that the effective potential exhibits a universal and scale invariant leading x^{-2} inverse square behaviour in the ``tortoise coordinate'' x provided that the metrics satisfy the strict Dominant Energy Condition (DEC). This result parallels that obtained in hep-th/0403252 for probes consisting of families of massless particles (null geodesic deviation, a.k.a. the Penrose Limit). The detailed properties of the scalar wave operator depend sensitively on the Numerical Coefficient of the x^{-2}-term, and as one application we show that timelike singularities satisfying the DEC are quantum mechanically singular in the sense of the Horowitz-Marolf (essential self-adjointness) criterion. We also comment on some related issues like the near-singularity behaviour of the scalar fields permitted by the Friedrichs extension.
Robert L Singleton - One of the best experts on this subject based on the ideXlab platform.
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charged particle motion in a highly ionized plasma
Physics Reports, 2005Co-Authors: Lowell S Brown, Dean L Preston, Robert L SingletonAbstract:Abstract A recently introduced method utilizing dimensional continuation is employed to compute the energy loss rate for a non-relativistic particle moving through a highly ionized plasma. No restriction is made on the charge, mass, or speed of this particle. It is, however, assumed that the plasma is not strongly coupled in the sense that the dimensionless plasma coupling parameter g = e 2 κ D / 4 π T is small, where κ D is the Debye wave number of the plasma. To leading and next-to-leading order in this coupling, d E / d x is of the generic form g 2 ln [ Cg 2 ] . The precise Numerical Coefficient out in front of the logarithm is well known. We compute the constant C under the logarithm exactly for arbitrary particle speeds. Our exact results differ from approximations given in the literature. The differences are in the range of 20% for cases relevant to inertial confinement fusion experiments. The same method is also employed to compute the rate of momentum loss for a projectile moving in a plasma, and the rate at which two plasmas at different temperatures come into thermal equilibrium. Again these calculations are done precisely to the order given above. The loss rates of energy and momentum uniquely define a Fokker–Planck equation that describes particle motion in the plasma. The Coefficients determined in this way are thus well-defined, contain no arbitrary parameters or cutoffs, and are accurate to the order described. This Fokker–Planck equation describes the straggling—the spreading in the longitudinal position of a group of particles with a common initial velocity and position—and the transverse diffusion of a beam of particles. It should be emphasized that our work does not involve a model, but rather it is a precisely defined evaluation of the leading terms in a well-defined perturbation theory.
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charged particle motion in a highly ionized plasma
arXiv: Plasma Physics, 2005Co-Authors: Lowell S Brown, Dean L Preston, Robert L SingletonAbstract:A recently introduced method utilizing dimensional continuation is employed to compute the energy loss rate for a non-relativistic particle moving through a highly ionized plasma. No restriction is made on the charge, mass, or speed of this particle. It is, however, assumed that the plasma is not strongly coupled in the sense that the dimensionless plasma coupling parameter g=e^2\kappa_D/ 4\pi T is small, where \kappa_D is the Debye wave number of the plasma. To leading and next-to-leading order in this coupling, dE/dx is of the generic form g^2 \ln[C g^2]. The precise Numerical Coefficient out in front of the logarithm is well known. We compute the constant C under the logarithm exactly for arbitrary particle speeds. Our exact results differ from approximations given in the literature. The differences are in the range of 20% for cases relevant to inertial confinement fusion experiments. The same method is also employed to compute the rate of momentum loss for a projectile moving in a plasma, and the rate at which two plasmas at different temperatures come into thermal equilibrium. Again these calculations are done precisely to the order given above. The loss rates of energy and momentum uniquely define a Fokker-Planck equation that describes particle motion in the plasma. The Coefficients determined in this way are thus well-defined, contain no arbitrary parameters or cutoffs, and are accurate to the order described. This Fokker-Planck equation describes the longitudinal straggling and the transverse diffusion of a beam of particles. It should be emphasized that our work does not involve a model, but rather it is a precisely defined evaluation of the leading terms in a well-defined perturbation theory.
