An analytic study on the excited states of holographic superconductors

Qiao, Xiongying; Wang, Dong; Ouyang, Liang; Wang, Mengjie; Pan, Qiyuan; Jing, Jiliang

doi:10.1016/j.physletb.2020.135864

Cited by 18 publications

(10 citation statements)

References 17 publications

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“…Working in the probe limit with the holographic duality, Wang et al studied the optical conductivity and the condensate in the excited states via the numerical method in the background of Schwarzschild-AdS black hole and found that the higher excited state has a lower critical temperature than the corresponding ground state in this relativistic case [13], which was analytically confirmed in Ref. [14]. Meanwhile, the conductivity σ of each excited state has a delta function in Re[σ] and an additional pole in Im[σ] arising at the low temperature inside the gap [13].…”

Section: Introductionmentioning

confidence: 88%

“…3. On the other hand, recent efforts showed that the difference of the dimensionless critical chemical potential between the consecutive states is around 5 [13,14]. It is of great interest to consider the effect of the hyperscaling violation on this difference.…”

Section: Numerical Analysismentioning

confidence: 99%

“…In order to analytically investigate the excited states of the holographic superconductors with the hyperscaling violation, we choose the ninth order of u in the trial function F (u), i.e., F (u) = 1 − k=9 k=2 a k u k for the operator O, where a k is a constant [14,16]. As an example, we set the hyperscaling violation θ = 1.5 and obtain the critical chemical potential µ c from ground state to the fifth excited state which can been seen in Table III by using Eq.…”

Section: Analytical Investigationmentioning

confidence: 99%

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Excited states of holographic superconductors with hyperscaling violation

Zhang,

Zhao,

Pan

et al. 2021

Preprint

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We employ the numerical and analytical methods to study the effects of the hyperscaling violation on the ground and excited states of holographic superconductors. For both the holographic s-wave and p-wave models with the hyperscaling violation, we observe that the excited state has a lower critical temperature than the corresponding ground state, which is similar to the relativistic case, and the difference of the dimensionless critical chemical potential between the consecutive states decreases as the hyperscaling violation increases. Interestingly, as we amplify the hyperscaling violation in the s-wave model, the critical temperature of the ground state first decreases and then increases, but that of the excited states always decreases. In the p-wave model, regardless of the the ground state or the excited states, the critical temperature always decreases with increasing the hyperscaling violation. In addition, we find that the hyperscaling violation affects the conductivity σ which has 2n + 1 poles in Im[σ] and 2n poles in Re[σ] for the n-th excited state, and changes the relation in the gap frequency for the excited states in both s-wave and p-wave models.

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Section: Introductionmentioning

confidence: 88%

Section: Numerical Analysismentioning

confidence: 99%

Section: Analytical Investigationmentioning

confidence: 99%

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Excited states of holographic superconductors with hyperscaling violation

Zhang,

Zhao,

Pan

et al. 2021

Preprint

Self Cite

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“…For ∆ = 2, we have M 3 = 117.4 which roughly agrees with the results M 3 = 119 of ref. [12] and M 3 = 144 of ref. [4].…”

Section: O ∆ Near Critical Temperaturementioning

confidence: 99%

Heun's equation and analytic structure of the Gap in Holographic superconductivity

Choun,

Cai,

Sin

2021

Preprint

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We analytically calculate physical observables of holographic superconductor including the critical temperature and the condensation as functions of ρ, T, ∆, which are density, temperature and the scaling dimension of the Cooper pair operator respectively. In two spatial dimension, e.g, the critical temperature has the power law dependence on the coupling, T c ∼ (gρ) 1/2 , which can be much higher than the exponential suppression in the BCS theory, T c ∼ exp(−C/g) for small g.

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“…As alluded to above, the studies of ref. [11] and [12] focused exclusively on the linear response in the holographic model of the excited state superconductors (see also [13] where JHEP11(2020)059 an analytical study is performed). In condensed matter physics, especially for the mesoscopic nanomaterials, under the thermal fluctuation, the system may transit to metastable states and remain in these states for a long time due to the complicated free energy surface [14].…”

Section: Introductionmentioning

confidence: 99%

Nonequilibrium dynamical transition process between excited states of holographic superconductors

Wang

et al. 2020

J. High Energ. Phys.

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We study the dynamics of the holographic s-wave superconductors described by the Einstein-Maxwell-complex scalar field theory with a negative cosmological constant. If the eigenfunction of the linearized equation of motion of the scalar field in the planar RNAdS black hole background is chosen as the initial data, the bulk system will evolve to the intermediate state that corresponds to the excited state superconductor on the boundary. The process can be regarded as the non-equilibrium condensation process of the excited state of holographic superconductor. When the linear superposition of the eigenfunctions is chosen as the initial data, the system will go through a series of the intermediate states corresponding to different overtone numbers, which can be regarded as the dynamical transition process between the excited states of holographic superconductor. Because the intermediate states are metastable, the bulk system eventually evolves to the stationary state that corresponds the ground state of the holographic superconductor. We also provide a global and physical picture of the evolution dynamics of the black hole and the corresponding superconducting phase transition from the funneled landscape view, quantifying the weights of the states and characterizing the transitions and cascades towards the ground state.

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An analytic study on the excited states of holographic superconductors

Cited by 18 publications

References 17 publications

Excited states of holographic superconductors with hyperscaling violation

Excited states of holographic superconductors with hyperscaling violation

Heun's equation and analytic structure of the Gap in Holographic superconductivity

Nonequilibrium dynamical transition process between excited states of holographic superconductors

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