• Journal of the Korean Mathematical Society
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• v.61 no.1
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• pp.91-107
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• 2024

We determine the N → ∞ asymptotics of the expected value of entanglement entropy for pure states in H_1,N ⊗ H_2,N, where H_1,N and H_2,N are the spaces of holomorphic sections of the N-th tensor powers of hermitian ample line bundles on compact complex manifolds.

• Journal of the Korean Physical Society
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• v.73 no.10
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• pp.1596-1602
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• 2018

We suggest that the dark matter in the universe has quantum entanglement if the dark matter is a Bose-Einstein condensation of ultra-light scalar particles. In this theory, any two regions of a galaxy are quantum entangled due to the quantum nature of the condensate. We calculate the entanglement entropy of a typical galactic halo, which turns out to be at least O(ln(M/m)), where M is the mass of the halo and m is the mass of a dark matter particle. The entanglement can be inferred from the rotation curves of the galaxy or the interference patterns of the dark matter density.

• Journal of the Korean Physical Society
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• v.73 no.10
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• pp.1420-1430
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• 2018

We investigate an entangled system, which is analogous to a composite system of a black hole and Hawking radiation. If Hawking radiation is well approximated by an outgoing particle generated from pair creation around the black hole, such a pair creation increases the total number of states. There should be a unitary mechanism to reduce the number of states inside the horizon for black hole evaporation. Because the infalling antiparticle has negative energy, as long as the infalling antiparticle finds its partner such that the two particles form a separable state, one can trace out such a zero energy system by maintaining unitarity. In this paper, based on some toy model calculations, we show that such a unitary tracing-out process is only possible before the Page time while it is impossible after the Page time. Hence, after the Page time, if we assume that the process is unitary and the Hawking pair forms a separable state, the internal number of states will monotonically increase, which is supported by the Almheiri-Marolf-Polchinski-Sully (AMPS) argument. In addition, the Hawking particles cannot generate randomness of the entire system; hence, the entanglement entropy cannot reach its maximum. Based on these results, we modify the correct form of the Page curve for the remnant picture. The most important conclusion is this: if we assume unitarity, semi-classical quantum field theory, and general relativity, then the black hole should violate the Bekenstein-Hawking entropy bound around the Page time at the latest; hence, the infinite production arguments for remnants might be applied for semi-classical black holes, which seems very problematic.

• The Bulletin of The Korean Astronomical Society
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• v.42 no.2
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• pp.55.5-56
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• 2017

Galaxy dynamics probes weak gravity at accelerations below the de Sitter scale of acceleration adS = cH, where c is the velocity of light and H is the Hubble parameter. Low and high redshift galaxies hereby offer a novel probe of weak gravity in an evolving cosmology, satisfying H(z) = H0(1 + A(6z + 12z^2 +12z^3+ 6z^4+ (6/5)z^5)/(1 + z) with baryonic matter content A sans tension to H0 in surveys of the Local Universe. Galaxy rotation curves show anomalous galaxy dynamics in weak gravity aN < adS across a transition radius r beyond about 5 kpc for galaxy mass of 1e11 solar mass. where aN is the Newtonian acceleration based on baryonic matter content. We identify this behavior with a holographic origin of inertia from entanglement entropy, that introduces a C0 onset across aN=adS with asymptotic behavior described by a Milgrom parameter satisfying a0=omega/(2pi), where omega=sqrt(1-q)H is a fundamental eigenfrequency of the cosmological horizon. Extending an earlier confrontation with data covering 0.003 < aN/adS < 1 at redshift z about zero in Lellie et al. (2016), the modest anomalous behavior in the Genzel et al. sample at redshifts 0.854 < z <2.282 is found to be mostly due to clustering 0.36 < aN/adS < 1 close to the C0 onset to weak gravity and an increase of up to 65% in a0.

• Bulletin of the Korean Chemical Society
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• v.24 no.6
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• pp.864-880
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• 2003

A unified picture for magnetism, superconductivity, quantum optics and other properties of molecule-based materials has been presented on the basis of effective model Hamiltonians, where necessary parameter values have been determined by the first principle calculations of cluster models and/or band models. These properties of the matetials are qualitatively discussed on the basis of the spin and pseudo-spin Hamiltonian models, where several quantum operators are expressed by spin variables under the two level approximation. As an example, ab initio broken-symmetry DFT calculations are performed for cyclic magnetic ring constructed of 34 hydrogen atoms in order to obtain effective exchange integrals in the spin Hamiltonian model. The natural orbital analysis of the DFT solution was performed to obtain symmetry-adapted molecular orbitals and their occupation numbers. Several chemical indices such as information entropy and unpaired electron density were calculated on the basis of the occupation numbers to elucidate the spin and pair correlations, and bonding characteristic (kinetic correlation) of this mesoscopic magnetic ring. Both classical and quantum effects for spin alignments and singlet spin-pair formations are discussed on the basis of the true spin Hamiltonian model in detail. Quantum effects are also discussed in the case of superconductivity, atom optics and quantum optics based on the pseudo spin Hamiltonian models. The coherent and squeezed states of spins, atoms and quantum field are discussed to obtain a unified picture for correlation, coherence and decoherence in future materials. Implications of theoretical results are examined in relation to recent experiments on molecule-based materials and molecular design of future molecular soft materials in the intersection area between molecular and biomolecular materials.