Does boundary distinguish complexities?

Sato, Yoshiki; Watanabe, Kento

doi:10.1007/jhep11(2019)132

Cited by 48 publications

(81 citation statements)

References 59 publications

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“…Even though the theories mentioned above are not related, we find it worth remarking that a common feature seems the occurrence of the logarithmically divergent terms in the complexity in the presence of a physical boundary, with the notable exception of CA. The same divergent term has been found also in the path-integral optimization analysis [5,19] of the complexity in theories with boundaries recently performed in [20]. Thus, in these cases, the absence of the logarithmic divergence in CA seems to disfavour this proposal with respect to the other prescriptions.…”

Section: Introductionsupporting

confidence: 67%

“…It is also interesting to explore the effects of the boundaries in the connections between complexity with the laws of thermodynamics [67,68]. acknowledge Yoshiki Sato and Kento Watanabe for the kind correspondence after the appearance of their work [20]. ALC thanks the APC, ENS, and LPTHE laboratories for their kind hospitality while this paper was being completed.…”

Section: Discussionmentioning

confidence: 99%

“…The study of the effects of the boundaries on the complexity deserves further analysis. Interesting directions concern scenarios involving higher dimensions [20], non trivial time dependence [12,36,62,63], mixed states [55] and the role of spacetime singularities [64][65][66]. It is also interesting to explore the effects of the boundaries in the connections between complexity with the laws of thermodynamics [67,68].…”

Section: Discussionmentioning

confidence: 99%

“…Note added: The major results of this manuscript (including the construction of the WDW patch for CA) are contained in Paolo Braccia's master thesis, discussed in the end of July at Florence University. While we were preparing this draft, [20] appeared and had significant overlaps with the thesis, which has been sent to the authors of [20], who have agreed with the WDW patch for CA presented here in the second version of their paper.…”

Section: Introductionmentioning

confidence: 99%

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Complexity in the presence of a boundary

Paolo

Cotrone

Tonni

2020

J. High Energ. Phys.

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The effects of a boundary on the circuit complexity are studied in two dimensional theories. The analysis is performed in the holographic realization of a conformal field theory with a boundary by employing different proposals for the dual of the complexity, including the "Complexity = Volume" (CV) and "Complexity = Action" (CA) prescriptions, and in the harmonic chain with Dirichlet boundary conditions. In all the cases considered except for CA, the boundary introduces a subleading logarithmic divergence in the expansion of the complexity as the UV cutoff vanishes. Holographic subregion complexity is also explored in the CV case, finding that it can change discontinuously under continuous variations of the configuration of the subregion.

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Section: Introductionsupporting

confidence: 67%

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Complexity in the presence of a boundary

Paolo

Cotrone

Tonni

2020

J. High Energ. Phys.

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“…We first observe that (a) confinement does distinguish complexity for all stationary states, contrary to what happens in other contexts, and (b) the three complexity measures fulfill the rigorous lower bounds given by .…”

Section: Complexity Measuresmentioning

confidence: 87%

Two‐dimensional confined hydrogen: An entropy and complexity approach

Estañón

Aquino

Puertas‐Centeno

et al. 2020

Int J of Quantum Chemistry

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The position and momentum spreading of the electron distribution of the two-dimensional confined hydrogenic atom, which is a basic prototype of the general multidimensional confined quantum systems, is numerically studied in terms of the confinement radius for the 1s, 2s, 2p, and 3d quantum states by means of the main entropy and complexity information-theoretical measures. First, the Shannon entropy and the Fisher information, as well as the associated uncertainty relations, are computed and discussed. Then, the Fisher-Shannon, lopezruiz-mancini-alvet, and LMC-Rényi complexity measures are examined and mutually compared. We have found that these entropy and complexity quantities reflect the rich properties of the electron confinement extent in the two conjugated spaces. K E Y W O R D SFisher information of the two-dimensional confined hydrogen atom, Fisher-Shannon complexity measure of the two-dimensional confined hydrogen atom, LMC-Rényi complexity measure of the two-dimensional confined hydrogen atom, Shannon entropy of the two-dimensional confined hydrogen atom, two-dimensional confined hydrogen atom | INTRODUCTIONThe fundamental and practical relevance of the spherically confined quantum systems has been manifested from the early days of quantum physics [1,2] up until now. [3][4][5][6][7] They have been used as prototypes to explain numerous phenomena and systems not only in the three-dimensional world but also for nonrelativistic and relativistic D-dimensional (D ≥ 2) chemistry and physics. [8][9][10][11][12][13][14] For example, pioneered by Gerhard Ertl, the 2007 Nobel Laureate in Chemistry, and his collaborators, surface chemistry has been extensively studied and has become a key branch in chemistry. [11][12][13] In physics of materials, two-dimensional systems have been used to gain insight into the properties of semiconductors (see, eg, refs. [15, 16]), and they start to play a fundamental role in bringing strong and new forms of control to the atomic-scale limit over the dynamics of matter in the extreme confinement of electromagnetic energy by phonon polaritonics. [10] Moreover, the properties of the real fluids can be studied by means of crystalline fluids (ie, with a symmetry) with nonstandard dimensions (see, eg, ref. [17]).The idea of two-and multidimensional spherical confinement of atoms has been used not only to simulate the effect of high pressure on the static dipole polarizability in hydrogen [18] but also to model a great deal of nanotechnological objects such as quantum dots; quantum wells and quantum wires; [19,20] atoms and molecules embedded in nanocavities, for example, in fullerenes, zeolites cages, and helium droplets; [4,6,7,[21][22][23] dilute bosonic and fermionic systems in magnetic traps of extremely low temperatures; [24][25][26] and a variety of quantum-information elements. [27,28] This has provoked a fast development of a density functional theory of independent particles moving in multidimensional central potentials with various analytical forms (see, eg, refs. [5-7, 29-...

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Geometry and complexity of path integrals in inhomogeneous CFTs

Caputa

MacCormack

2021

J. High Energ. Phys.

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In this work we develop the path integral optimization in a class of inhomogeneous 2d CFTs constructed by putting an ordinary CFT on a space with a position dependent metric. After setting up and solving the general optimization problem, we study specific examples, including the Möbius, SSD and Rainbow deformed CFTs, and analyze path integral geometries and complexity for universal classes of states in these models. We find that metrics for optimal path integrals coincide with particular slices of AdS3 geometries, on which Einstein’s equations are equivalent to the condition for minimal path integral complexity. We also find that while leading divergences of path integral complexity remain unchanged, constant contributions are modified in a universal, position dependent manner. Moreover, we analyze entanglement entropies in inhomogeneous CFTs and show that they satisfy Hill’s equations, which can be used to extract the energy density consistent with the first law of entanglement. Our findings not only support comparisons between slices of bulk spacetimes and circuits of path integrations, but also demonstrate that path integral geometries and complexity serve as a powerful tool for understanding the interesting physics of inhomogeneous systems.

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Does boundary distinguish complexities?

Cited by 48 publications

References 59 publications

Complexity in the presence of a boundary

Complexity in the presence of a boundary

Two‐dimensional confined hydrogen: An entropy and complexity approach

Geometry and complexity of path integrals in inhomogeneous CFTs

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