On the chaos bound in rotating black holes Jahnke, Viktor; Kim, Keun-Young; Yoon, Junggi
The journal of high energy physics,
05/2019, Volume:
2019, Issue:
5
Journal Article
Peer reviewed
Open access
A
bstract
We study out-of-time-order correlators (OTOCs) of rotating BTZ black holes using two different approaches: the elastic eikonal gravity approximation, and the Chern-Simons formulations of ...3-dimensional gravity. Within both methods the OTOC is given as a sum of two contributions, corresponding to left and right moving modes. The contributions have different Lyapunov exponents,
λ
L
±
=
2
π
β
1
1
∓
ℓ
Ω
, where Ω is the angular velocity and
ℓ
is the AdS radius. Since
λ
L
−
≤
2
π
β
≤
λ
L
+
, there is an apparent contradiction with the chaos bound. We discuss how the result can be made consistent with the chaos bound if one views the parameters
β
±
=
β
(1 ∓
ℓ
Ω) as the effective inverse temperatures of the left and right moving modes.
A
bstract
We provide a detailed examination of a thermal out-of-time-order correlator (OTOC) growing exponentially in time in systems without chaos. The system is a one-dimensional quantum mechanics ...with a potential whose part is an inverted harmonic oscillator. We numerically observe the exponential growth of the OTOC when the temperature is higher than a certain threshold. The Lyapunov exponent is found to be of the order of the classical Lyapunov exponent generated at the hilltop, and it remains non-vanishing even at high temperature. We adopt various shape of the potential and find these features universal. The study confirms that the exponential growth of the thermal OTOC does not necessarily mean chaos when the potential includes a local maximum. We also provide a bound for the Lyapunov exponent of the thermal OTOC in generic quantum mechanics in one dimension, which is of the same form as the chaos bound obtained by Maldacena, Shenker and Stanford.
This paper proposes a noise-robust and accurate bearing fault diagnosis model based on time-frequency multi-domain 1D convolutional neural networks (CNNs) with attention modules. The proposed model, ...referred to as the TF-MDA model, is designed for an accurate bearing fault classification model based on vibration sensor signals that can be implemented at industry sites under a high-noise environment. Previous 1D CNN-based bearing diagnosis models are mostly based on either time domain vibration signals or frequency domain spectral signals. In contrast, our model has parallel 1D CNN modules that simultaneously extract features from both the time and frequency domains. These multi-domain features are then fused to capture comprehensive information on bearing fault signals. Additionally, physics-informed preprocessings are incorporated into the frequency-spectral signals to further improve the classification accuracy. Furthermore, a channel and spatial attention module is added to effectively enhance the noise-robustness by focusing more on the fault characteristic features. Experiments were conducted using public bearing datasets, and the results indicated that the proposed model outperformed similar diagnosis models on a range of noise levels ranging from -6 to 6 dB signal-to-noise ratio (SNR).
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A
bstract
We compute the time-dependent complexity of the thermofield double states by four different proposals: two holographic proposals based on the “complexity-action” (CA) conjecture and ...“complexity-volume” (CV) conjecture, and two quantum field theoretic proposals based on the Fubini-Study metric (FS) and Finsler geometry (FG). We find that four different proposals yield both similarities and differences, which will be useful to deepen our understanding on the complexity and sharpen its definition. In particular, at early time the complexity linearly increase in the CV and FG proposals, linearly decreases in the FS proposal, and does not change in the CA proposal. In the late time limit, the CA, CV and FG proposals all show that the growth rate is 2
E/
(πℏ) saturating the Lloyd’s bound, while the FS proposal shows the growth rate is zero. It seems that the holographic CV conjecture and the field theoretic FG method are more correlated.
A
bstract
We study the holographic duality between the reflected entropy and the entanglement wedge cross section with the first order correction. In the field theory side, we consider the reflected ...entropy for
ρ
AB
m
, where
ρ
AB
is the reduced density matrix for two intervals in the ground state. The reflected entropy in the 2d holographic conformal field theories is computed perturbatively up to the first order in
m −
1 by using the semiclassical conformal block. In the gravity side, we compute the entanglement wedge cross section in the backreacted geometry by cosmic branes with tension
T
m
which are anchored at the AdS boundary. Comparing both results we find a perfect agreement, showing the duality works with the first order correction in
m −
1.
Classification of electroencephalography (EEG)-based motor imagery (MI) is a crucial non-invasive application in brain-computer interface (BCI) research. This paper proposes a novel convolutional ...neural network (CNN) architecture for accurate and robust EEG-based MI classification that outperforms the state-of-the-art methods.
The proposed CNN model, namely EEG-inception, is built on the backbone of the inception-time network, which has showed to be highly efficient and accurate for time-series classification. Also, the proposed network is an end-to-end classification, as it takes the raw EEG signals as the input and does not require complex EEG signal-preprocessing. Furthermore, this paper proposes a novel data augmentation method for EEG signals to enhance the accuracy, at least by 3%, and reduce overfitting with limited BCI datasets.
The proposed model outperforms all state-of-the-art methods by achieving the average accuracy of 88.4% and 88.6% on the 2008 BCI Competition IV 2a (four-classes) and 2b datasets (binary-classes), respectively. Furthermore, it takes less than 0.025 s to test a sample suitable for real-time processing. Moreover, the classification standard deviation for nine different subjects achieves the lowest value of 5.5 for the 2b dataset and 7.1 for the 2a dataset, which validates that the proposed method is highly robust.
From the experiment results, it can be inferred that the EEG-inception network exhibits a strong potential as a subject-independent classifier for EEG-based MI tasks.
A
bstract
We investigate the time evolution of the complexity of the operator by the Sachdev-Ye-Kitaev (SYK) model with
N
Majorana fermions. We follow Nielsen’s idea of complexity geometry and ...geodesics thereof. We show that it is possible that the bi- invariant complexity geometry can exhibit the conjectured time evolution of the complexity in chaotic systems: i) linear growth until
t ∼ e
N
, ii) saturation and small fluctuations after then. We also show that the Lloyd’s bound is realized in this model. Interestingly, these characteristic features appear only if the complexity geometry is the most natural “non-Riemannian” Finsler geometry. This serves as a concrete example showing that the bi-invariant complexity may be a competitive candidate for the complexity in quantum mechanics/field theory (QM/QFT). We provide another argument showing a naturalness of bi-invariant complexity in QM/QFT. That is that the bi-invariance naturally implies the equivalence of the right-invariant complexity and left-invariant complexity, either of which may correspond to the complexity of a given operator. Without bi-invariance, one needs to answer why only right (left) invariant complexity corresponds to the “complexity”, instead of only left (right) invariant complexity.
A
bstract
We investigate the properties of pole-skipping of the sound channel in which the translational symmetry is broken explicitly or spontaneously. For this purpose, we analyze, in detail, not ...only the holographic axion model, but also the magnetically charged black holes with two methods: the near-horizon analysis and quasi-normal mode computations. We find that the pole-skipping points are related with the chaotic properties, Lyapunov exponent (
λ
L
) and butterfly velocity (
v
B
), independently of the symmetry breaking patterns. We show that the diffusion constant (
D
) is bounded by
D
≥
v
B
2
/
λ
L
, where
D
is the energy diffusion (crystal diffusion) bound for explicit (spontaneous) symmetry breaking. We confirm that the lower bound is obtained by the pole-skipping analysis in the low temperature limit.
A
bstract
We study diffusion and butterfly velocity (
v
B
) in two holographic models, linear axion and axion-dilaton model, with a momentum relaxation parameter (
β
) at finite density or chemical ...potential (
μ
). Axion-dilaton model is particularly interesting since it shows linear-
T
-resistivity, which may have something to do with the universal bound of diffusion. At finite density, there are two diffusion constants
D
±
describing the coupled diffusion of charge and energy. By computing
D
±
exactly, we find that in the incoherent regime (
β/T
≫ 1
, β/μ
≫ 1)
D
+
is identified with the charge diffusion constant (
D
c
) and
D
−
is identified with the energy diffusion constant (
D
e
). In the coherent regime, at very small density,
D
±
are ‘maximally’ mixed in the sense that
D
+
(
D
−
) is identified with
D
e
(
D
c
), which is opposite to the case in the incoherent regime. In the incoherent regime
D
e
∼
C
−
ℏv
B
2
/
k
B
T
where
C
−
= 1
/
2 or 1 so it is universal independently of
β
and
μ
. However,
D
c
∼
C
+
ℏ
v
B
2
/
k
B
T
where
C
+
= 1 or
β
2
/
16
π
2
T
2
so, in general,
C
+
may not saturate to the lower bound in the incoherent regime, which suggests that the characteristic velocity for charge diffusion may not be the butterfly velocity. We find that the finite density does not affect the diffusion property at zero density in the incoherent regime.
A
bstract
We study a notion of operator growth known as Krylov complexity in free and interacting massive scalar quantum field theories in
d
-dimensions at finite temperature. We consider the effects ...of mass, one-loop self-energy due to perturbative interactions, and finite ultraviolet cutoffs in continuous momentum space. These deformations change the behavior of Lanczos coefficients and Krylov complexity and induce effects such as the “staggering” of the former into two families, a decrease in the exponential growth rate of the latter, and transitions in their asymptotic behavior. We also discuss the relation between the existence of a mass gap and the property of staggering, and the relation between our ultraviolet cutoffs in continuous theories and lattice theories.
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