Lifshitz quasinormal modes and relaxation from holography

Sybesma, Watse

doi:10.1007/jhep05(2015)021

Cited by 31 publications

(67 citation statements)

References 44 publications

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“…Note first that for the cases where z ≥ d − 1, there are no oscillations, the system is overdamped. This will be more clear when we look at the QNMs, and is in agreement with [25].…”

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confidence: 82%

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Holographic Equilibration of Nonrelativistic Plasmas

et al. 2016

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We study far-from-equilibrium physics of strongly interacting plasmas at criticality and zero charge density for a wide range of dynamical scaling exponents z in d dimensions using holographic methods. In particular, we consider homogeneous isotropization of asymptotically Lifshitz black branes with full backreaction. We find stable evolution and equilibration times that exhibit small dependence of z and are of the order of the inverse temperature. Performing a quasinormal mode analysis, we find a corresponding narrow range of relaxation times, fully characterized by the fraction z=ðd − 1Þ. For z ≥ d − 1, equilibration is overdamped, whereas for z < d − 1, we find oscillatory behavior. Finally, and most interestingly, we observe that also the nonlinear evolution, although differing significantly from a quasinormal mode fit, is to a high degree of precision characterized by the fraction z=ðd − 1Þ. Introduction.-Quantum criticality has been a focus of interest both in theoretical and experimental physics over the past few decades. It is believed to be a key ingredient in the solution to the various yet unsolved problems such as the high T c superconductivity [1]. In particular, the dynamics of a system near a continuous quantum phase transition is governed by a universal, scale invariant theory characterized by the dimensionality d, the dynamical scaling exponent z, and the various other critical exponents that are independent of the microscopic Hamiltonian of the system. In these systems, the characteristic energy scale Δ, such as the gap separating the first excited state from the ground state, vanishes as the correlation length ξ diverges as Δ ∼ ξ −z . For instance, z ¼ 1 occurs at the touching points of the band structure of monolayer graphene, z ¼ 2 can describe the case of bilayer graphene, and z ¼ 2, 3 occur in heavy fermion systems; see, e.g., Refs. [2][3][4][5][6].The existence of a quantum critical point at vanishing temperature determines the behavior of observables also at finite temperature, and even beyond the thermal equilibrium, in the so-called quantum critical region of the parameter space. In fact, a basic way to characterize this quantum critical region is to consider the response of the system to a small disturbance, determined by the equilibration time τ eq [7]. The quantum critical region corresponds to short relaxation times τ eq ∼ 1=T [8], whereas local equilibrium is reached much more slowly as τ eq ≫ 1=T outside the quantum critical region [1].In this Letter, we want to go one step further and ask the question, what happens when such a quantum critical system is taken completely out of equilibrium, when the perturbation is not small, but of the same order as the Hamiltonian? We answer this question partially in the particular situation when the collective excitations of the system are characterized by global, hydrodynamic

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“…Note first that for the cases where z ≥ d − 1, there are no oscillations, the system is overdamped. This will be more clear when we look at the QNMs, and is in agreement with [25].…”

supporting

confidence: 82%

“…The value α ¼ 1 can be found from AdS 3 , where one can show analytically that τ ¼ 1=ð4πT 0 Þ [25,29,30]. Curiously, this is not the minimal value of the relaxation time, which instead sits at α ≈ 0.847 227 and reads τ ≈ 0.989 002=ð4πT 0 Þ.…”

Section: H Y S I C a L R E V I E W L E T T E R Smentioning

confidence: 99%

Holographic Equilibration of Nonrelativistic Plasmas

et al. 2016

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“…The matter is parameterized by scalar fields minimally coupled to gravity. Then we obtain numerically the quasinormal frequencies (QNFs) for scalar fields by using the improved AIM [17], which is an improved version of the method proposed in [18,19] and which has been applied successfully in the context of quasinormal modes (QNMs) for different black hole geometries (see for instance [17,[20][21][22][23][24][25][26][27]). Then we study their stability under scalar perturbations.…”

Section: Introductionmentioning

confidence: 99%

“…Then we study their stability under scalar perturbations. We focus our study on the dependence of the dynamical exponent, the nonlinear expo-nent, the angular momentum, and the mass of the scalar field in obtaining overdamped and non-overdamped quasinormal frequencies, mainly, motivated by a recent work, where the authors showed that for d > z + 1, at zero momenta, the modes are non-overdamped, whereas for d ≤ z + 1 the system is always overdamped [24]. This is contrary to other Lifshitz black holes where the QNFs show the absence of a real part [28][29][30][31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

Quasinormal modes of four-dimensional topological nonlinear charged Lifshitz black holes

2016

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We study scalar perturbations of fourdimensional topological nonlinear charged Lifshitz black holes with spherical and plane transverse sections, and we find numerically the quasinormal modes for scalar fields. Then we study the stability of these black holes under massive and massless scalar field perturbations. We focus our study on the dependence of the dynamical exponent, the nonlinear exponent, the angular momentum, and the mass of the scalar field in the modes. It is found that the modes are overdamped, depending strongly on the dynamical exponent and the angular momentum of the scalar field for a spherical transverse section. In contrast, for plane transverse sections the modes are always overdamped.

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“…The QNFs have been calculated by means of numerical and analytical techniques; the QNMs of Lifshitz black holes under scalar field perturbations have been studied in [23,[79][80][81][82][83][84][85][86][87][88][89], and generally the scalar modes of Lifshitz black holes are stable. Non-relativistic fermion Green's functions in fourdimensional Lifshitz spacetime with z = 2 were studied in [90] by considering fermions in this background and a nonrelativistic (mixed) boundary condition, and it was shown that the Green's functions have a flat band.…”

Section: Introductionmentioning

confidence: 99%

Fermionic field perturbations of a three-dimensional Lifshitz black hole in conformal gravity

González¹,

Vásquez²,

Villalobos³

2017

Eur. Phys. J. C

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We study the propagation of massless fermionic fields in the background of a three-dimensional Lifshitz black hole, which is a solution of conformal gravity. The black-hole solution is characterized by a vanishing dynamical exponent. Then we compute analytically the quasinormal modes, the area spectrum, and the absorption cross section for fermionic fields. The analysis of the quasinormal modes shows that the fermionic perturbations are stable in this background. The area and entropy spectrum are evenly spaced. In the low frequency limit, it is observed that there is a range of values of the angular momentum of the mode that contributes to the absorption cross section, whereas it vanishes in the high frequency limit. In addition, by a suitable change of variables a gravitational soliton can also be obtained and the stability of the quasinormal modes are studied and ensured.

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Lifshitz quasinormal modes and relaxation from holography

Cited by 31 publications

References 44 publications

Holographic Equilibration of Nonrelativistic Plasmas

Holographic Equilibration of Nonrelativistic Plasmas

Quasinormal modes of four-dimensional topological nonlinear charged Lifshitz black holes

Fermionic field perturbations of a three-dimensional Lifshitz black hole in conformal gravity

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