Periodicity in One-Dimensional Finite Linear Cellular Automata

Tadaki, Shin–ichi; Matsufuji, Shinya

doi:10.1143/ptp.89.325

Cited by 8 publications

(15 citation statements)

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“…Although we have not set up an explicit quantum field theory and completed the calculation of the stress tensor in 4-d, there is support for our conjecture. The existence of quantum states for S-dS whose stress tensor is static has been shown explicitly for the 2-d case of S-dS for which the angular dependence is neglected [14]. Our results therefore also offers an understanding of this from the Euclidean approach.…”

Section: Remarkssupporting

confidence: 58%

Quantum field theory with and without conical singularities: black holes with a cosmological constant and the multi-horizon scenario

Lin

Soo

1999

Class. Quantum Grav.

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Boundary conditions and the corresponding states of a quantum field theory depend on how the horizons are taken into account. There is ambiguity as to which method is appropriate because different ways of incorporating the horizons lead to different results. We propose that a natural way of including the horizons is to first consider the Kruskal extension and then define the quantum field theory on the Euclidean section. Boundary conditions emerge naturally as consistency conditions of the Kruskal extension. We carry out the proposal for the explicit case of the Schwarzschild-de Sitter manifold with two horizons. The required period β is the interesting condition that it is the lowest common multiple of 2π divided by the surface gravity of both horizons. Restricting the ratio of the surface gravity of the horizons to rational numbers yields finite β. The example also highlights some of the difficulties of the off-shell approach with conical singularities in the multihorizon scenario; and serves to illustrate the much richer interplay that can occur among horizons, quantum field theory and topology when the cosmological constant is not neglected in black hole processes.

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Section: Remarkssupporting

confidence: 58%

Quantum field theory with and without conical singularities: black holes with a cosmological constant and the multi-horizon scenario

Lin

Soo

1999

Class. Quantum Grav.

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“…Thermal behaviour of T µν for massless scalar fields near plane walls in four spacetime dimensions has been investigated in Refs. [6] and [9]. The present work extends the investigation by examining the thermal dependence of T µν on ξ near a reflecting plane wall of an infinite cavity in flat spacetime with arbitrary number of dimensions.…”

Section: Introductionmentioning

confidence: 57%

Hot scalar radiation setting bounds on the curvature coupling parameter

Lorenci

Gomes

Moreira

2015

Class. Quantum Grav.

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This paper addresses the interplay between vacuum and thermal local averages for massless scalar radiation near a plane wall of a large cavity where the Dirichlet boundary condition is assumed to hold. The main result is that stable thermodynamic equilibrium is possible only if the curvature coupling parameter is restricted to a certain range. In more than three spacetime dimensions such a range contains the conformal coupling, but it does not contain the minimal coupling. Since this same range for possible values of the curvature coupling parameter also applies to massive scalar radiation, it may be relevant in settings where arbitrarily coupled scalar fields are present.

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“…This is called a cylindrical cellular automata [77] because evolution of the rule can be represented as taking place on a cylinder. If the lattice is isomorphic to f0; : : : ; n 1g, null, or Dirchlet boundary conditions are set [78,79,80]. That is, the symbol assigned to all sites in L outside of this set is the null symbol.…”

Section: Boundary Conditions and Additivitymentioning

confidence: 99%

Additive Cellular Automata

Voorhees¹

2012

Computational Complexity

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Periodicity in One-Dimensional Finite Linear Cellular Automata

Cited by 8 publications

References 0 publications

Quantum field theory with and without conical singularities: black holes with a cosmological constant and the multi-horizon scenario

Quantum field theory with and without conical singularities: black holes with a cosmological constant and the multi-horizon scenario

Hot scalar radiation setting bounds on the curvature coupling parameter

Additive Cellular Automata

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