arXiv subjects

Keiju Murata

Publications and source records attributed to Keiju Murata.

At least 37 records · Page 2Linked to original sources

arXiv2022

Energy extraction from AdS black holes via superradiance

Superradiance is known as a wave amplification process caused by rotating or charged black holes. We argue that the superradiance of stationary black holes in asymptotically AdS spacetimes can be characterized by the ability of energy extraction. Specifically, we demonstrate that energy can be extracted from Reissner-Nordström-AdS$_4$ and Kerr-AdS$_4$ under appropriate time-dependent boundary conditions at conformal boundaries. This indicates that energy can be extracted from thermal states dual to these black holes by applying appropriate time-dependent sources. We also show that the energy extraction can be realized as a reversible process.

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arXiv2022

Creating stars orbiting in AdS

We propose a method to create a star orbiting in an asymptotically AdS spacetime using the AdS/CFT correspondence. We demonstrate that by applying an appropriate source in the quantum field theory defined on a 2-sphere, the localized star gradually appears in the dual asymptotically AdS geometry. Once the star is created, the angular position can be observed from the response function. The relationship between the parameters of the created star and those of the source is studied. We show that information regarding the bulk geometry can be extracted from the observation of stellar motion in the bulk geometry.

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arXiv2022

A bound on energy dependence of chaos

We conjecture a chaos energy bound, an upper bound on the energy dependence of the Lyapunov exponent for any classical/quantum Hamiltonian mechanics and field theories. The conjecture states that the Lyapunov exponent $λ(E)$ grows no faster than linearly in the total energy $E$ in the high energy limit. In other words, the exponent $c$ in $λ(E) \propto E^c \,(E\to\infty)$ satisfies $c\leq 1$. This chaos energy bound stems from thermodynamic consistency of out-of-time-order correlators (OTOC's) and applies to any classical/quantum system with finite $N$ / large $N$ ($N$ is the number of degrees of freedom) under plausible physical conditions on the Hamiltonians. To the best of our knowledge the chaos energy bound is satisfied by any classically chaotic Hamiltonian system known, and is consistent with the cerebrated chaos bound by Maldacena, Shenker and Stanford which is for quantum cases at large $N$. We provide arguments supporting the conjecture for generic classically chaotic billiards and multi-particle systems. The existence of the chaos energy bound may put a fundamental constraint on physical systems and the universe.

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arXiv2021

Observing black holes through holographic superconductors

We propose a way to observe the photon ring of the asymptotically anti-de Sitter black hole dual to a superconductor on the two-dimensional sphere. We consider the electric current of the superconductor under the localized time-periodic external electromagnetic field. On the gravity side, the bulk Maxwell field is sent from the AdS boundary and then diffracted by the black hole. We construct the image of the black hole from the asymptotic data of the bulk Maxwell field that corresponds to the electric current on the field theory side. We decompose the electric current into the dissipative and non-dissipative parts and take the dissipative part for the imaging of the black hole. We investigate the effect of the charged scalar condensate on the image. We obtain the bulk images that indicate the discontinuous change of the size of the photon ring.

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arXiv2021

Multioscillating black holes

We study rotating global AdS solutions in five-dimensional Einstein gravity coupled to a multiplet complex scalar within a cohomogeneity-1 ansatz. The onset of the gravitational and scalar field superradiant instabilities of the Myers-Perry-AdS black hole mark bifurcation points to black resonators and hairy Myers-Perry-AdS black holes, respectively. These solutions are subject to the other (gravitational or scalar) instability, and result in hairy black resonators which contain both gravitational and scalar hair. The hairy black resonators have smooth zero-horizon limits that we call graviboson stars. In the hairy black resonator and graviboson solutions, multiple scalar components with different frequencies are excited, and hence these are multioscillating solutions. The phase structure of the solutions are examined in the microcanonical ensemble, i.e. at fixed energy and angular momenta. It is found that the entropy of the hairy black resonator is never the largest among them. We also find that hairy black holes with higher scalar wavenumbers are entropically dominant and occupy more of phase space than those of lower wavenumbers.

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arXiv2020

Resonating AdS soliton

The AdS soliton is a nonsingular spacetime that has a flat conformal boundary with a compact $S^1$ direction. We find a horizonless cohomogeneity-1 metric that describes nonlinear gravitational oscillations of the AdS soliton in five dimensions. We call this spacetime the resonating AdS soliton. This solution is obtained as the nonlinear extension of normal modes of the AdS soliton dual to spin-2 glueball excitations. The boundary energy momentum tensor of the resonating AdS soliton has time periodic components, and it is interpreted as a coherently excited state in the dual field theory. Physical quantities of the resonating AdS soliton are multivalued at a fixed energy, suggesting a transition between different frequency solutions. The energy of the resonating AdS soliton is higher than that of the undeformed AdS soliton, in accordance with the positive energy conjecture proposed by Horowitz and Myers.

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arXiv2020

Superradiant instability of black resonators and geons

Black resonators and geons in global AdS are rapidly rotating, low-energy solutions with a helical Killing field. We study the linear mode stability of equal angular momenta, five-dimensional black resonators and geons under scalar, electromagnetic, and gravitational perturbations. We find that black resonators are unstable to the superradiant instability, in agreement with previously known results. Perhaps surprisingly, many geons appear linearly stable, despite having an ergoregion. This apparent stability implies that geons are important long-lived, low-energy states in the dual gauge theory. However, we do find that geons are unstable within a certain range of parameter space. We comment on the nature of this instability and to its possible endpoints. We also report on new non-spinning oscillating geons, which we construct within a cohomogeneity two ansatz. Given the existing arguments that suggest our linear stability results may be extended nonlinearly, our findings indicate that most geons are generic and long-lived solutions.

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arXiv2019

Imaging black holes through AdS/CFT

Thermal states in some quantum field theories (QFTs) correspond to black holes in asymptotically AdS spacetime in the AdS/CFT correspondence. We propose a direct procedure to construct holographic images of the black hole in the bulk from a given response function of the QFT on the boundary. The response function with respect to an external source corresponds to the asymptotic data of the bulk field generated by the source on the AdS boundary. According to the wave optics, we can obtain the images from the bulk field propagating in the bulk spacetime. For a thermal state on two-dimensional sphere dual to Schwarzschild-AdS$_4$ black hole, we demonstrate that the holographic images gravitationally lensed by the black hole can be constructed from the response function. In particular, the Einstein rings on the image can be clearly observed and their radius depends on the total energy of the QFT thermal state. These results are consistent with the size of the photon sphere of the black hole calculated in geometrical optics. This implies that, if there exists a dual gravitational picture for a given quantum system, we would be able to probe existence of the dual black hole by the Einstein rings constructed from observables of the quantum system.

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arXiv2019

Photonic black resonators and photon stars in AdS$_5$

Rapidly rotating Myers-Perry-AdS$_5$ (MPAdS$_5$) black holes are shown to be unstable against rotational superradiance of a Maxwell field. From the onset of the instability, time-periodic neutral black hole solutions equipped with a nontrivial electromagnetic wave are obtained, which we call {\it photonic black resonators}. In the horizonless limit, they reduce to geon solutions which may be called {\it photon stars}. Specifically, we introduce a cohomogeneity-1 ansatz for the metric and Maxwell field and construct such solutions with an $R\times SU(2)$ isometry group. We compute thermodynamic quantities and obtain phase diagrams. It turns out that a photonic black resonator has a higher entropy than a MPAdS$_5$ black hole, while it also has a smaller entropy than a black resonator without the Maxwell field. This suggests what is expected for nonlinear dynamics following the Maxwell superradiant instability with the $SU(2)$ isometry.

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arXiv2019

Einstein Rings in Holography

Clarifying conditions for the existence of a gravitational picture for a given quantum field theory (QFT) is one of the fundamental problems in the AdS/CFT correspondence. We propose a direct way to demonstrate the existence of the dual black holes: imaging an Einstein ring. We consider a response function of the thermal QFT on a two-dimensional sphere under a time-periodic localized source. The dual gravity picture, if it exists, is a black hole in an asymptotic global AdS$_4$ and a bulk probe field with a localized source on the AdS boundary. The response function corresponds to the asymptotic data of the bulk field propagating in the black hole spacetime. We find a formula that converts the response function to the image of the dual black hole: The view of the sky of the AdS bulk from a point on the boundary. Using the formula, we demonstrate that, for a thermal state dual to the Schwarzschild-AdS$_4$ spacetime, the Einstein ring is constructed from the response function. The evaluated Einstein radius is found to be determined by the total energy of the dual QFT. Our theoretical proposal opens a door to gravitational phenomena on strongly correlated materials.

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arXiv2019

Chaos of QCD string from holography

It is challenging to quantify chaos of QCD, because non-perturbative QCD accompanies non-local observables. By using holography, we find that QCD strings at large $N_c$ and strong coupling limit exhibit chaos, and measure their Lyapunov exponent at zero temperature. A pair of a quark and an antiquark separated by $L_q$ in the large $N_c$ QCD is dual to a Nambu-Goto string hanging from the spatial boundary of the D4-soliton geometry. We numerically solve the motion of the string after putting a pulse force on its boundaries. The chaos is observed for the amplitude of the force larger than a certain lower bound. The bound increases as $L_q$ grows, and its dependence is well approximated by a hypothesis that the chaos originates in the endpoints of the QCD string.

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arXiv2018

Floquet superconductor in holography

We study nonequilibrium steady states in a holographic superconductor under time periodic driving by an external rotating electric field. We obtain the dynamical phase diagram. Superconducting phase transition is of first or second order depending on the amplitude and frequency of the external source. The rotating electric field decreases the superconducting transition temperature. The system can also exhibit a first order transition inside the superconducting phase. It is suggested this transition exists all the way down to zero temperature. The existence of nonequilibrium thermodynamic potential for such steady solutions is also discussed from the holographic point of view. The current induced by the electric field is decomposed into normal and superconducting components, and this makes it clear that the superconducting one dominates in low temperatures.

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arXiv2018

Black resonators and geons in AdS$_5$

We construct dynamical black hole solutions with a helical symmetry in AdS$_5$, called black resonators, as well as their horizonless limits, called geons. We introduce a cohomogeneity-1 metric describing a class of black resonators and geons whose isometry group is $R\times SU(2)$. This allows us to study them in a wide range of parameters. We obtain the phase diagram for the black resonators, geons, and Myers-Perry-AdS$_5$, where the black resonators emerge from the onset of a superradiant instability of the Myers-Perry-AdS$_5$ with equal angular momenta and are connected to the geons in the small horizon limit. The angular velocities of the black resonators always satisfy $Ω>1$ in units of the AdS radius. A black resonator is shown to have higher entropy than a Myers-Perry-AdS$_5$ black hole with the same asymptotic charges. This implies that the Myers-Perry-AdS$_5$ can dynamically evolve into the black resonator under the exact $SU(2)$-symmetry although its endpoint will be further unstable to $SU(2)$-violating perturbations.

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arXiv2018

Stability of Squashed Kaluza-Klein Black Holes

The stability of squashed Kaluza-Klein black holes is studied. The squashed Kaluza-Klein black hole looks like five dimensional black hole in the vicinity of horizon and four dimensional Minkowski spacetime with a circle at infinity. In this sense, squashed Kaluza-Klein black holes can be regarded as black holes in the Kaluza-Klein spacetimes. Using the symmetry of squashed Kaluza-Klein black holes, $SU(2)\times U(1)\simeq U(2)$, we obtain master equations for a part of the metric perturbations relevant to the stability. The analysis based on the master equations gives a strong evidence for the stability of squashed Kaluza-Klein black holes. Hence, the squashed Kaluza-Klein black holes deserve to be taken seriously as realistic black holes in the Kaluza-Klein spacetime.

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arXiv2018

Chaos of Wilson Loop from String Motion near Black Hole Horizon

To find the origin of chaos near black hole horizon in string-theoretic AdS/CFT correspondence, we perform a chaos analysis of a suspended string in AdS black hole backgrounds. It has a definite CFT interpretation: chaos of Wilson loops, or in other words, sensitive time-evolution of a quark antiquark force in thermal gauge theories. Our nonlinear numerical simulation of the suspended Nambu-Goto string shows chaos, which would be absent in pure AdS background. The calculated Lyapunov exponent $λ$ satisfies the universal bound $λ\leq 2πT_{\rm H}$ for the Hawking temperature $T_{\rm H}$. We also analyze a toy model of a rectangular string probing the horizon and show that it contains a universal saddle characterized by the surface gravity $2πT_{\rm H}$. Our work demonstrates that the black hole horizon is the origin of the chaos, and suggests a close interplay between chaos and quark deconfinement.

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arXiv2017

Holographic Floquet states II: Floquet condensation of vector mesons in nonequilibrium phase diagram

With the aim to reveal universal features of hadronic matter and correlated Dirac insulators in strong AC-electric fields, we study the $\mathcal{N}=2$ supersymmetric QCD with a finite quark mass driven by a rotating electric field $\mathcal{E}_x+i\mathcal{E}_y= E e^{iΩt}$. The analysis is done in the holographically dual D3/D7 system in the co-rotating frame, effectively. The nonequilibrium phase diagram is determined from the threshold electric field at which the insulator phase breaks down to a conductive phase due to the AC version of the Schwinger mechanism. The external field induces a rotating current $\mathcal{J}_x + i \mathcal{J}_y = J e^{iΩt}$ originating from vacuum polarization and dissipative current in the insulating and conductive phases respectively. Intriguing features are observed as the frequency $Ω$ approaches resonance with the meson excitation energy $Ω_{\rm meson}$. There, the threshold minimizes and a condensate of vector mesons with oscillating current exists even in the zero driving field limit. This state, which we call Floquet condensate of vector mesons, is expected to be dynamically stable realizing a non-thermal fixed point that breaks time translational and reversal symmetries. Our finding has many similarities with exciton BEC discussed in solid state systems, where the semiconductor is to be replaced by materials hosting gapped Dirac electrons, e.g. 3D topological insulators or bismuth. Vector meson Floquet condensate may also have implications in the pre-thermalized dynamics in heavy ion collision experiments.

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arXiv2017

Fast scrambling in holographic Einstein-Podolsky-Rosen pair

We demonstrate that a holographic model of the Einstein-Podolsky-Rosen pair exhibits fast scrambling. Strongly entangled quark and antiquark in $\mathcal{N}=4$ super Yang-Mills theory are considered. Their gravity dual is a fundamental string whose endpoints are uniformly accelerated in opposite direction. We slightly increase the acceleration of the endpoint and show that it quickly destroys the correlation between the quark and antiquark. The proper time scale of the destruction is $τ_\ast\sim β\ln S$ where $β$ is the inverse Unruh temperature and $S$ is the entropy of the accelerating quark. We also evaluate the Lyapunov exponent from correlation function as $λ_L=2π/β$, which saturates the Lyapunov bound. Our results suggest that the fast scrambling or saturation of the Lyapunov bound do not directly imply the existence of an Einstein dual. When we slightly decrease the acceleration, the quark and antiquark are causally connected and an "one-way traversable wormhole" is created on the worldsheet. It causes the divergence of the correlation function between the quark and antiquark.

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arXiv2017

Out-of-time-order correlators in quantum mechanics

The out-of-time-order correlator (OTOC) is considered as a measure of quantum chaos. We formulate how to calculate the OTOC for quantum mechanics with a general Hamiltonian. We demonstrate explicit calculations of OTOCs for a harmonic oscillator, a particle in a one-dimensional box, a circle billiard and stadium billiards. For the first two cases, OTOCs are periodic in time because of their commensurable energy spectra. For the circle and stadium billiards, they are not recursive but saturate to constant values which are linear in temperature. Although the stadium billiard is a typical example of the classical chaos, an expected exponential growth of the OTOC is not found. We also discuss the classical limit of the OTOC. Analysis of a time evolution of a wavepacket in a box shows that the OTOC can deviate from its classical value at a time much earlier than the Ehrenfest time.

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