arXiv subjects

Yu-Sen An

Publications and source records attributed to Yu-Sen An.

24 records · Page 2Linked to original sources

arXiv2019

Holographic complexity growth in a FLRW universe

We investigate the holographic complexity growth rate of a conformal field theory in a FLRW universe. We consider two ways to realize a FLRW spacetime from an Anti-de Sitter Schwarzschild geometry. The first one is obtained by introducing a new foliation of the Schwarzschild geometry such that the conformal boundary takes the FLRW form. The other one is to consider a brane universe moving in the Schwarzschild background. For each case, we compute the complexity growth rate in a closed universe and a flat universe by using both the complexity-volume and complexity-action dualities. We find that there are two kinds of contributions to the growth rate: one is from the interaction among the degrees of freedom, while the other one from the change of the spatial volume of the universe. The behaviors of the growth rate depend on the details to realize the FLRW universe as well as the holographic conjecture for the complexity. For the realization of the FLRW universe on the asymptotic boundary, the leading divergent term for the complexity growth rate obeys a volume law which is natural from the field theory viewpoint. For the brane universe scenario, the complexity-volume and complexity-action conjectures give different results for the closed universe case. A possible explanation of the inconsistency when the brane crosses the black hole horizon is given based on the Lloyd bound.

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arXiv2019

To be unitary-invariant or not?: a simple but non-trivial proposal for the complexity between states in quantum mechanics/field theory

We make comments on some shortcomings of the non-unitary-invariant and non-bi-invariant complexity in quantum mechanics/field theory and argue that the unitary-invariant and bi-invariant complexity is still a competitive candidate in quantum mechanics/field theory, contrary to quantum circuits in quantum computation. Based on the unitary-invariance of the complexity and intuitions from the holographic complexity, we propose a novel complexity formula between two states. Our proposal shows that i) the complexity between certain states in two dimensional CFTs is given by the Liouville action, which is compatible with the path-integral complexity; ii) it also gives natural interpretation for both the CV and CA holographic conjectures and identify what the reference states are in both cases. Our proposal explicitly produces the conjectured time dependence of the complexity: linear growth in chaotic systems. Last but not least, we present interesting relations between the complexity and the Lyapunov exponent: the Lyapunov exponent is proportional to the complexity growth rate in linear growth region.

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arXiv2019

More on complexity of operators in quantum field theory

Recently it has been shown that the complexity of SU($n$) operator is determined by the geodesic length in a bi-invariant Finsler geometry, which is constrained by some symmetries of quantum field theory. It is based on three axioms and one assumption regarding the complexity in continuous systems. By relaxing one axiom and an assumption, we find that the complexity formula is naturally generalized to the Schatten $p$-norm type. We also clarify the relation between our complexity and other works. First, we show that our results in a bi-invariant geometry are consistent with the ones in a right-invariant geometry such as $k$-local geometry. Here, a careful analysis of the sectional curvature is crucial. Second, we show that our complexity can concretely realize the conjectured pattern of the time-evolution of the complexity: the linear growth up to saturation time. The saturation time can be estimated by the relation between the topology and curvature of SU($n$) groups.

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arXiv2019

Principles and symmetries of complexity in quantum field theory

Based on general and minimal properties of the {\it discrete} circuit complexity, we define the complexity in {\it continuous} systems in a geometrical way. We first show that the Finsler metric naturally emerges in the geometry of the complexity in continuous systems. Due to fundamental symmetries of quantum field theories, the Finsler metric is more constrained and consequently, the complexity of SU($n$) operators is uniquely determined as a length of a geodesic in the Finsler geometry. Our Finsler metric is bi-invariant contrary to the right-invariance of discrete qubit systems. We clarify why the bi-invariance is relevant in quantum field theoretic systems. After comparing our results with discrete qubit systems we show most results in $k$-local right-invariant metric can also appear in our framework. Based on the bi-invariance of our formalism, we propose a new interpretation for the Schrödinger's equation in isolated systems - the quantum state evolves by the process of minimizing "computational cost."

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arXiv2018

Time Dependence of Holographic Complexity in Gauss-Bonnet Gravity

We study the effect of the Gauss-Bonnet term on the complexity growth rate of dual field theory using the "Complexity--Volume" (CV) and CV2.0 conjectures. We investigate the late time value and full time evolution of the complexity growth rate of the Gauss-Bonnet black holes with horizons with zero curvature ($k=0$), positive curvature ($k=1$) and negative curvature ($k=-1$) respectively. For the $k=0$ and $k=1$ cases we find that the Gauss-Bonnet term suppresses the growth rate as expected, while in the $k=-1$ case the effect of the Gauss-Bonnet term may be opposite to what is expected. The reason for it is briefly discussed, and the comparison of our results to the result obtained by using the "Complexity--Action" (CA) conjecture is also presented. We also briefly investigate two proposals applying some generalized volume functionals dual to the complexity in higher curvature gravity theories, and find their behaviors are different for $k=0$ at late times.

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arXiv2018

The effect of Dilaton on the holographic complexity growth

In this paper, we investigate the action growth in various backgrounds in Einstein-Maxwell-Dilaton theory. We calculate the full time evolution of action growth in AdS dilaton black hole and find it approaches the late time bound from above. We investigate the black hole which is asymptotically Lifshitz and obtain its late-time and full time behavior. We find the violation of Lloyd bound in late time limit and show the full time behavior exhibiting some new features for z sufficiently large.

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