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arXivOn the canonical threefolds with strictly nef anticanonical divisors H. Uehara 19991231 Any ample Cartier divisor D on a projective variety X is strictly nef (i.e. D.C>0 for any effective curve C on X). In general, the converse statement does not hold. But this is conjectured to be true for anticanonical divisors. The present paper establishes this fact for normal complex projective threefolds with canonical singularities. This result extends several previously known special cases. The proof rests mainly on sophisticated techniques of three dimensional birational geometry developed in the last two decades.
Subject 수학 Source arXiv URL https://arxiv.org/abs/math/9912241view Article Title On the canonical threefolds with strictly nef anticanonical divisorsAuthors H. UeharaAbstract Any ample Cartier divisor D on a projective variety X is strictly nef (i.e. D.C>0 for any effective curve C on X). In general, the converse statement does not hold. But this is conjectured to be true for anticanonical divisors. The present paper establishes this fact for normal complex projective threefolds with canonical singularities. This result extends several previously known special cases. The proof rests mainly on sophisticated techniques of three dimensional birational geometry developed in the last two decades.Is Part Of 19991231 Identifier ISSN: Category math.AGLicense 
arXivMultilevel Quantum Particle as a Few Virtual Qubits Materialization Alexander R. Kessel, Vladimir L. Ermakov 19991231 A conception of virtual quantum information bit  virtual qubit  is introduced. It is shown by means of virtual qubit representation that four states of a single quantum particle is enough for implementation of full set of the gates, which is necessary for creation an arbitrary algorithm for a quantum computer. The physical nature and mutual disposition of four working states is of no significance, if there are suitable selection rules for the particle interaction with the external electromagnetic field pulses.
Subject Source arXiv URL https://arxiv.org/abs/quantph/9912123view Article Title Multilevel Quantum Particle as a Few Virtual Qubits MaterializationAuthors Alexander R. Kessel; Vladimir L. ErmakovAbstract A conception of virtual quantum information bit  virtual qubit  is introduced. It is shown by means of virtual qubit representation that four states of a single quantum particle is enough for implementation of full set of the gates, which is necessary for creation an arbitrary algorithm for a quantum computer. The physical nature and mutual disposition of four working states is of no significance, if there are suitable selection rules for the particle interaction with the external electromagnetic field pulses.Is Part Of Proc. of SPIE Vol. 4061, pp.6878 (2000) 19991231 Identifier ISSN: DOI 10.1117/12.375307Category quantphLicense 
arXivA connected sum formula for the SU(3) Casson invariant Hans U. Boden, Christopher M. Herald 19991231 We provide a formula for the SU(3) Casson invariant for 3manifolds given as the connected sum of two integral homology 3spheres.
Subject 수학 Source arXiv URL https://arxiv.org/abs/math/9912240view Article Title A connected sum formula for the SU(3) Casson invariantAuthors Hans U. Boden; Christopher M. HeraldAbstract We provide a formula for the SU(3) Casson invariant for 3manifolds given as the connected sum of two integral homology 3spheres.Is Part Of J. Diff. Geom. 53 (1999) 443465 19991231 Identifier ISSN: DOI 10.4310/jdg/1214425635Category math.DG math.GTLicense 
arXivSpin correlations in nonlinear optical response: Lightinduced Kondo effect T. V. Shahbazyan, I. E. Perakis, M. E. Raikh... more(3) 19991231 We study the role of spin correlations in nonlinear absorption due to optical transitions from a deep impurity level to states above a Fermi sea. We demonstrate that the Hubbard repulsion between two electrons occupying the impurity state leads to a logarithmic divergence of the thirdorder nonlinear optical susceptibility at the absorption threshold. This divergence is a manifestation of the Kondo physics in the nonlinear optical response of Fermi sea systems. Remarkably, the lightinduced Kondo temperature, which governs the shape of the Kondoabsorption spectrum, can be tuned by varying the intensity and frequency of the pump optical field. We also show that, for offresonant pump excitation, the pumpprobe spectrum exhibits a narrow peak below the linear absorption onset.
Subject Source arXiv URL https://arxiv.org/abs/condmat/9912495view Article Title Spin correlations in nonlinear optical response: Lightinduced Kondo effectAuthors T. V. Shahbazyan; I. E. Perakis; M. E. RaikhAbstract We study the role of spin correlations in nonlinear absorption due to optical transitions from a deep impurity level to states above a Fermi sea. We demonstrate that the Hubbard repulsion between two electrons occupying the impurity state leads to a logarithmic divergence of the thirdorder nonlinear optical susceptibility at the absorption threshold. This divergence is a manifestation of the Kondo physics in the nonlinear optical response of Fermi sea systems. Remarkably, the lightinduced Kondo temperature, which governs the shape of the Kondoabsorption spectrum, can be tuned by varying the intensity and frequency of the pump optical field. We also show that, for offresonant pump excitation, the pumpprobe spectrum exhibits a narrow peak below the linear absorption onset.Is Part Of Phys. Rev. Lett. 84, 5896 (2000) 19991231 Identifier ISSN: DOI 10.1103/PhysRevLett.84.5896Category condmatLicense 
arXivOxygen isotope effect on the inplane penetration depth in underdoped La_{2x}Sr_{x}CuO_{4} single crystals J. Hofer, K. Conder, T. Sasagawa, ... more(7) 19991231 We report measurements of the oxygen isotope effect (OIE) on the inplane penetration depth \lambda_{ab}(0) in underdoped La_{2x}Sr_{x}CuO_{4} single crystals. A highly sensitive magnetic torque sensor with a resolution of \Delta \tau ~ 10^{12} Nm was used for the magnetic measurements on microcrystals with a mass of ~ 10 microg. The OIE on \lambda_{ab}^{2}(0) is found to be 10(2)% for x = 0.080 and 8(1)% for x = 0.086. It arises mainly from the oxygen mass dependence of the inplane effective mass m_{ab}*. The present results suggest that lattice vibrations are important for the occurrence of high temperature superconductivity.
Subject Source arXiv URL https://arxiv.org/abs/condmat/9912493view Article Title Oxygen isotope effect on the inplane penetration depth in underdoped La_{2x}Sr_{x}CuO_{4} single crystalsAuthors J. Hofer; K. Conder; T. Sasagawa; Guomeng Zhao; M. Willemin; H. Keller; K. KishioAbstract We report measurements of the oxygen isotope effect (OIE) on the inplane penetration depth \lambda_{ab}(0) in underdoped La_{2x}Sr_{x}CuO_{4} single crystals. A highly sensitive magnetic torque sensor with a resolution of \Delta \tau ~ 10^{12} Nm was used for the magnetic measurements on microcrystals with a mass of ~ 10 microg. The OIE on \lambda_{ab}^{2}(0) is found to be 10(2)% for x = 0.080 and 8(1)% for x = 0.086. It arises mainly from the oxygen mass dependence of the inplane effective mass m_{ab}*. The present results suggest that lattice vibrations are important for the occurrence of high temperature superconductivity.Is Part Of 19991231 Identifier ISSN: DOI 10.1103/PhysRevLett.84.4192Category condmat.suprconLicense 
arXivStatistics of Turbulence from SpectralLine Data Cubes A. Lazarian 19991231 Emission in spectral lines can provide unique information on interstellar turbulence. Doppler shifts due to supersonic motions contain information on turbulent velocity field which is otherwise difficult to measure. However, the problem of separation of velocity and density fluctuations is far from being trivial. Using atomic hydrogen (HI) as a test case, I review techniques applicable to emission line studies with the emphasis on those that can provide information on the underlying power spectra of velocity and density. I show that recently developed mathematical machinery is promising for the purpose. Its application to HI shows that in cold neutral hydrogen the velocity fluctuations dominate the small scale structures observed in spectralline data cubes and this result is very important for the interpretation of observational data, including the identification of clouds. Velocity fluctuations are shown to dominate the formation of small scale structures that can be erroneously identified as diffuse clouds. One may argue that the HI data is consistent with the GoldreichShridhar picture of magnetohydrodynamic turbulence, but the cascade from the scales of several kpc that this interpretation involves does not fit well in the current paradigm of energy injection. The issue whether magnetic field does make the turbulence anisotropic is still open, but if this is the case, I show that studies of emission lines can provide a reliable way of determining magnetic field direction. I discuss various techniques for studying interstellar turbulence using emission lines, e.g. spectral correlation functions, genus statistics and principal component analysis.
Subject Source arXiv URL https://arxiv.org/abs/astroph/0001001view Article Title Statistics of Turbulence from SpectralLine Data CubesAuthors A. LazarianAbstract Emission in spectral lines can provide unique information on interstellar turbulence. Doppler shifts due to supersonic motions contain information on turbulent velocity field which is otherwise difficult to measure. However, the problem of separation of velocity and density fluctuations is far from being trivial. Using atomic hydrogen (HI) as a test case, I review techniques applicable to emission line studies with the emphasis on those that can provide information on the underlying power spectra of velocity and density. I show that recently developed mathematical machinery is promising for the purpose. Its application to HI shows that in cold neutral hydrogen the velocity fluctuations dominate the small scale structures observed in spectralline data cubes and this result is very important for the interpretation of observational data, including the identification of clouds. Velocity fluctuations are shown to dominate the formation of small scale structures that can be erroneously identified as diffuse clouds. One may argue that the HI data is consistent with the GoldreichShridhar picture of magnetohydrodynamic turbulence, but the cascade from the scales of several kpc that this interpretation involves does not fit well in the current paradigm of energy injection. The issue whether magnetic field does make the turbulence anisotropic is still open, but if this is the case, I show that studies of emission lines can provide a reliable way of determining magnetic field direction. I discuss various techniques for studying interstellar turbulence using emission lines, e.g. spectral correlation functions, genus statistics and principal component analysis.Is Part Of 19991231 Identifier ISSN: Category astroph condmat.statmech physics.aoph physics.fludyn physics.plasmph physics.spacephLicense 
arXivCompactification, Geometry and Duality: N=2 Paul S. Aspinwall 19991231 These are notes based on lectures given at TASI99. We review the geometry of the moduli space of N=2 theories in four dimensions from the point of view of superstring compactification. The cases of a type IIA or type IIB string compactified on a CalabiYau threefold and the heterotic string compactified on K3xT2 are each considered in detail. We pay specific attention to the differences between N=2 theories and N>2 theories. The moduli spaces of vector multiplets and the moduli spaces of hypermultiplets are reviewed. In the case of hypermultiplets this review is limited by the poor state of our current understanding. Some peculiarities such as ``mixed instantons'' and the nonexistence of a universal hypermultiplet are discussed.
Subject Source arXiv URL https://arxiv.org/abs/hepth/0001001view Article Title Compactification, Geometry and Duality: N=2Authors Paul S. AspinwallAbstract These are notes based on lectures given at TASI99. We review the geometry of the moduli space of N=2 theories in four dimensions from the point of view of superstring compactification. The cases of a type IIA or type IIB string compactified on a CalabiYau threefold and the heterotic string compactified on K3xT2 are each considered in detail. We pay specific attention to the differences between N=2 theories and N>2 theories. The moduli spaces of vector multiplets and the moduli spaces of hypermultiplets are reviewed. In the case of hypermultiplets this review is limited by the poor state of our current understanding. Some peculiarities such as ``mixed instantons'' and the nonexistence of a universal hypermultiplet are discussed.Is Part Of 19991231 Identifier ISSN: Category hepthLicense 
arXivCorrections to the Abelian BornInfeld Action Arising from Noncommutative Geometry L. Cornalba 19991231 In a recent paper Seiberg and Witten have argued that the full action describing the dynamics of coincident branes in the weak coupling regime is invariant under a specific field redefinition, which replaces the group of ordinary gauge transformations with the one of noncommutative gauge theory. This paper represents a first step towards the classification of invariant actions, in the simpler setting of the abelian single brane theory. In particular we consider a simplified model, in which the group of noncommutative gauge transformations is replaced with the group of symplectic diffeomorphisms of the brane world volume. We carefully define what we mean, in this context, by invariant actions, and rederive the known invariance of the BornInfeld volume form. With the aid of a simple algebraic tool, which is a generalization of the Poisson bracket on the brane world volume, we are then able to describe invariant actions with an arbitrary number of derivatives.
Subject Source arXiv URL https://arxiv.org/abs/hepth/9912293view Article Title Corrections to the Abelian BornInfeld Action Arising from Noncommutative GeometryAuthors L. CornalbaAbstract In a recent paper Seiberg and Witten have argued that the full action describing the dynamics of coincident branes in the weak coupling regime is invariant under a specific field redefinition, which replaces the group of ordinary gauge transformations with the one of noncommutative gauge theory. This paper represents a first step towards the classification of invariant actions, in the simpler setting of the abelian single brane theory. In particular we consider a simplified model, in which the group of noncommutative gauge transformations is replaced with the group of symplectic diffeomorphisms of the brane world volume. We carefully define what we mean, in this context, by invariant actions, and rederive the known invariance of the BornInfeld volume form. With the aid of a simple algebraic tool, which is a generalization of the Poisson bracket on the brane world volume, we are then able to describe invariant actions with an arbitrary number of derivatives.Is Part Of JHEP 0009 (2000) 017 19991231 Identifier ISSN: DOI 10.1088/11266708/2000/09/017Category hepthLicense 
arXivLax pairs, Painlev\'e properties and exact solutions of the alogero Kortewegde Vries equation and a new (2+1)dimensional equation SongJu Yu, Kouichi Toda 19991231 We prove the existence of a Lax pair for the Calogero Kortewegde Vries (CKdV) equation. Moreover, we modify the T operator in the the Lax pair of the CKdV equation, in the search of a (2+1)dimensional case and thereby propose a new equation in (2+1) dimensions. We named this the (2+1)dimensional CKdV equation. We show that the CKdV equation as well as the (2+1)dimensional CKdV equation are integrable in the sense that they possess the Painlev\'e property. Some exact solutions are also constructed.
Subject 수학 Source arXiv URL https://arxiv.org/abs/math/0001188view Article Title Lax pairs, Painlev\'e properties and exact solutions of the alogero Kortewegde Vries equation and a new (2+1)dimensional equationAuthors SongJu Yu; Kouichi TodaAbstract We prove the existence of a Lax pair for the Calogero Kortewegde Vries (CKdV) equation. Moreover, we modify the T operator in the the Lax pair of the CKdV equation, in the search of a (2+1)dimensional case and thereby propose a new equation in (2+1) dimensions. We named this the (2+1)dimensional CKdV equation. We show that the CKdV equation as well as the (2+1)dimensional CKdV equation are integrable in the sense that they possess the Painlev\'e property. Some exact solutions are also constructed.Is Part Of J. Nonlinear Math. Phys. 7 (2000), no. 1, 113 19991231 Identifier ISSN: DOI 10.2991/jnmp.2000.7.1.1Category math.AP nlin.SILicense 
arXivThe Deepest Spectrum of the Universe? Constraints on the Lyman Continuum Background at High Redshift Andrew J. Bunker, Francine R. Marleau, James R. Graham... more(3) 19991231 We describe an ongoing experiment to search for the metagalactic Lymancontinuum background at z~23. We are obtaining one of the deepest optical spectra ever, using LRIS/KeckII to search for the fluorescent Lyalpha emission from optically thick HI clouds. The null results of our pilot study (Bunker, Marleau & Graham 1998) placed a 3sigma upper bound on the mean intensity of the ionizing background of J_{nu 0} < 2E21 erg/s/cm^2/Hz/sr at z~3. This constraint was more than two orders of magnitude more stringent than any previously published direct limit. Our results excluded the possibility that decaying relic neutrinos are responsible for the metagalactic radiation field. We have recently greatly extended our search, obtaining a 16hour spectrum which is sensitive to UV background fluxes ~1E21 erg/s/cm^2/Hz/sr (z~2.3 at 3sigma, assuming the HI clouds are ~10arcsec in extent). We describe how the results of this study can be used to constrain the quasar luminosity function and the contribution of highredshift starforming galaxies to the ambient ionizing background.
Subject Source arXiv URL https://arxiv.org/abs/astroph/9912565view Article Title The Deepest Spectrum of the Universe? Constraints on the Lyman Continuum Background at High RedshiftAuthors Andrew J. Bunker; Francine R. Marleau; James R. GrahamAbstract We describe an ongoing experiment to search for the metagalactic Lymancontinuum background at z~23. We are obtaining one of the deepest optical spectra ever, using LRIS/KeckII to search for the fluorescent Lyalpha emission from optically thick HI clouds. The null results of our pilot study (Bunker, Marleau & Graham 1998) placed a 3sigma upper bound on the mean intensity of the ionizing background of J_{nu 0} < 2E21 erg/s/cm^2/Hz/sr at z~3. This constraint was more than two orders of magnitude more stringent than any previously published direct limit. Our results excluded the possibility that decaying relic neutrinos are responsible for the metagalactic radiation field. We have recently greatly extended our search, obtaining a 16hour spectrum which is sensitive to UV background fluxes ~1E21 erg/s/cm^2/Hz/sr (z~2.3 at 3sigma, assuming the HI clouds are ~10arcsec in extent). We describe how the results of this study can be used to constrain the quasar luminosity function and the contribution of highredshift starforming galaxies to the ambient ionizing background.Is Part Of 19991231 Identifier ISSN: Category astrophLicense