arXiv subjects

Takashi Okamura

Publications and source records attributed to Takashi Okamura.

49 records · Page 3Linked to original sources

arXiv2004

Noncommutative Quantum Mechanics and Seiberg-Witten Map

In order to overcome ambiguity problem on identification of mathematical objects in noncommutative theory with physical observables, quantum mechanical system coupled to the NC U(1) gauge field in the noncommutative space is reformulated by making use of the unitarized Seiberg-Witten map, and applied to the Aharonov-Bohm and Hall effects of the NC U(1) gauge field. Retaining terms only up to linear order in the NC parameter θ, we find that the AB topological phase and the Hall conductivity have both the same formulas as those of the ordinary commutative space with no θ-dependence.

hep-th↗

arXiv2003

Hall effect in Noncommutative spaces

In order to investigate whether space coordinates are intrinsically noncommutative, we make use of the Hall effect on the two-dimensional plane. We calculate the Hall conductivity in such a way that the noncommutative U(1) gauge invariance is manifest. We find that the noncommutativity parameter theta does not appear in the Hall conductivity itself, but the particle number density of electron depends on theta. We point out that the peak of particle number density differs from that of the charge density.

hep-th↗

arXiv2002

Hall Effect on Noncommutative Phase Space

When phase space coordinates are noncommutative, especially including arbitrarily noncommutative momenta, the Hall effect is reinvestigated. A minimally gauge-invariant coupling of electromagnetic field is introduced by making use of Faddeev-Jackiw formulation for unconstrained and constrained systems. We find that the parameter of noncommutative momenta makes an important contribution to the Hall conductivity.

hep-th↗

arXiv2002

Noncommutative Hall Effect

When coordinates are noncommutative, the Hall effect is reinvestigated. The Hall conductivity is expressed with noncommutative parameters, so that in the commutative limit it tends to the conventional result.

hep-th↗

arXiv2002

Wigner's Formulation of Noncommutative Quantum Mechanics

When we have noncommutativity among coordinates (or conjugate momenta), we consider Wigner's formulation of quantum mechanics, including a new derivation of path integral formula. We also propose the Moyal star product based on the Dirac bracket in constrained systems.

hep-th↗

arXiv2000

A Comment on Non-Archimedean Character of Quantum Buoyancy

In a gedankenexperiment about the generalized second law (GSL) of black hole thermodynamics, the buoyant force by black hole atmosphere (the acceleration radiation) plays an important role, and then it is significant to understand the nature of the buoyant force. Recently, Bekenstein criticizes that the fluid approximation of the acceleration radiation which is often used in the estimation of the buoyant force is invalid for the case that the size of the target is much less than a typical wavelength of the acceleration radiation, due to the diffractive effect of wave scattering. In this letter, we argue that even if it is correct that we should calculate the buoyant force as a wave scattering process, its implication in the GSL strongly depends on whether there exists any massless scalar field, that is, S-wave scattering. By reconsidering the diffractive effect by S-wave scattering, we show that if some massless scalar field exists, then the GSL can hold without invoking a new physics, such as an entropy bound for matter.

gr-qc↗

arXiv2000

Entropy for Asymptotically AdS_3 Black Holes

We propose that Strominger's method to derive the BTZ black hole entropy is in fact applicable to other asymptotically AdS_3 black holes and gives the correct functional form of entropies. We discuss various solutions in the Einstein-Maxwell theory, dilaton gravity, Einstein-scalar theories, and Einstein-Maxwell-dilaton theory. In some cases, solutions approach AdS_3 asymptotically, but their entropies do not have the form of Cardy's formula. However, it turns out that they are actually not "asymptotically $AdS_3$" solutions. On the other hand, for truly asymptotically AdS_3 solutions, their entropies have the form of Cardy's formula. In this sense, all known solutions are consistent with our proposal.

hep-th↗

arXiv2000

Three-Dimensional Gravity with Conformal Scalar and Asymptotic Virasoro Algebra

Strominger has derived the Bekenstein-Hawking entropy of the BTZ black hole using asymptotic Virasoro algebra. We apply Strominger's method to a black hole solution found by Martinez and Zanelli (MZ). This is a solution of three-dimensional gravity with a conformal scalar field. The solution is not $AdS_3$, but it is asymptotically $AdS_3$; therefore, it has the asymptotic Virasoro algebra. We compute the central charge for the theory and compares Cardy's formula with the Bekenstein-Hawking entropy. It turns out that the functional form does agree, but the overall numerical coefficient does not. This is because this approach gives the "maximum possible entropy" for the numerical coefficient.

hep-th↗

arXiv1997

On scattering off the extreme Reissner-Nordström black hole in N=2 supergravity

The scattering amplitudes for the perturbed fields of the N=2 supergravity about the extreme Reissner-Nordström black hole is examined. Owing to the fact that the extreme hole is a BPS state of the theory and preserves an unbroken global supersymmetry(N=1), the scattering amplitudes of the component fields should be related to each other. In this paper, we derive the formula of the transformation of the scattering amplitudes.

gr-qc↗

arXiv1997

General Theorem about Gravitational Lensing

We study the general theorem about gravitational lensing which states the relationship between the numbers of images with different parities. Our formulation allows an extension to the nontransparent and singular model.

astro-ph↗

arXiv1996

Perturbing Supersymmetric Black Hole

An investigation of the perturbations of the Reissner-Nordström black hole in the $N=2$ supergravity is presented. We prove in the extremal limit that the black hole responds to the perturbation of each field in the same manner. We conjecture that we can match the modes of the graviton, gravitino and photon because of supersymmetry transformations.

gr-qc↗

arXiv1996

Quasinormal modes of maximally charged black holes

A new algorithm for computing the accurate values of quasinormal frequencies of extremal Reissner-Nordström black holes is presented. The numerically computed values are consistent with the values earlier obtained by Leaver and those obtained through the WKB method. Our results are more precise than other results known to date. We also find a curious fact that the resonant frequencies of gravitational waves with multi-pole index $l$ coincide with those of electromagnetic waves with multi-pole index $l-1$ in the extremal limit.

gr-qc↗

arXiv1996

On Divergence of Decoherence Factor in Quantum Cosmology

To discuss the quantum to classical transition in quantum cosmology, we study the decoherence factor and the peak of the Wigner function, which respectively represent the degree of decoherence and the degree to which the classical motion of the Universe is defined, in a Robertson-Walker universe model coupled with a scalar field. It is known that the decoherence factor is divergent in some cases. This implies that perfect decoherence occurs, and classical correlation criterion fails. In this paper we discuss the divergence of the decoherence factor in some detail and obtain the constraints for decoherence factor to be convergent, making use of the arbitrariness defining the reduced density matrix. The result is discussed in connection with the arbitrariness of {\it system/environment} splitting.

gr-qc↗