Quantum Behavior Arises Because Our Universe is a Fractal

Tao, Yong

doi:10.1142/s2424942417500062

Cited by 3 publications

(5 citation statements)

References 29 publications

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“…where Ã denotes the ultraviolet cut-o®, [18][19][20] z denotes the quantum dynamical exponent and T Ã denotes a characteristic temperature below which quantum e®ect dominates the°uctuation. By the dimensional analysis, Tao has shown that z ¼ 1.…”

Section: Superconducting Quantum Critical Equation (Sqce)mentioning

confidence: 99%

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Superconducting Quantum Critical Phenomena

Tao

2018

Rep. Adv. Phys. Sci.

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When the superconducting transition temperature [Formula: see text] sufficiently approaches zero, quantum fluctuations are expected to be overwhelmingly amplified around zero temperature so that the mean-field approximation may break down. This implies that quantum critical phenomena may emerge in highly underdoped and overdoped regions, where the transition temperature [Formula: see text] is sufficiently low. By using Gor’kov’s Green function method, we propose a superconducting quantum critical equation (SQCE) for describing such critical phenomena. For two-dimensional (2D) overdoped materials, SQCE shows that the transition temperature [Formula: see text] and the zero-temperature superfluid phase stiffness [Formula: see text] will obey a two-class scaling combined by linear and parabolic parts, which agrees with the existing experimental investigation [I. Božović et al., Dependence of the critical temperature in overdoped copper oxides on superfluid density, Nature 536 (2016) 309–311]. For three-dimensional (3D) overdoped materials, SQCE predicts that the two-class scaling will be replaced by the linear scaling. Furthermore, we show that SQCE can be applied into highly underdoped region by using Anderson’s non-Fermi liquid model.

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Section: Superconducting Quantum Critical Equation (Sqce)mentioning

confidence: 99%

“…where we have used Eqs. (17), (18) and (20). Equation (35) indicates that Anderson's non-Fermi liquid model predicts T c / s ð0Þ 0:5 in the highly underdoped region (for 2D¯lms).…”

Section: Application In Anderson's Non-fermi Liquid Modelmentioning

confidence: 99%

Superconducting Quantum Critical Phenomena

Tao

2018

Rep. Adv. Phys. Sci.

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“…where denotes the ultraviolet cut-off. The cut-off may be associated with some fundamental graininess of space-time (please see page 402 in reference [23] or see reference [24]). However, here we only regard as a physical parameter describing the quantum effect: The quantum fluctuations with length scales less than 1 can be omitted.…”

Section: Renormalization Group Equationmentioning

confidence: 99%

“…Adopting the procedure of renormalization group we first write down the quantum partition function (11) at 𝑇 = 0: 𝑍(𝑇 = 0) = ∫ ,𝒟𝜙 * (𝑥, 𝜏)-Λ ∫ ,𝒟𝜙(𝑥, 𝜏)-Λ 𝑒 −𝑆(0) , ( 12) where 𝛬 denotes the ultraviolet cut-off. The cut-off 𝛬 may be associated with some fundamental graininess of space-time (please see page 402 in reference [23] or see reference [24]). However, here we only regard 𝛬 as a physical parameter describing the quantum effect: The quantum fluctuations with length scales less than…”

Section: Renormalization Group Equationmentioning

confidence: 99%

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BCS quantum critical phenomena

Tao

2017

EPL

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Theoretically, we recently showed that the scaling relation between the transition temperature and the superfluid density at zero temperature (0) might exhibit a parabolic pattern:It is significantly different from the linear scaling described by Homes' law, which is well known as a mean-field result. More recently, Božović et al. have observed such a parabolic scaling in the overdoped copper oxides with a sufficiently low transition temperature [Nature 536 (2016) 309-311]. They further point out that this experimental finding is incompatible with the standard Bardeen-Cooper-Schrieffer (BCS) description. Here we report that if is sufficiently low, applying the renormalization group approach into the BCS action at zero temperature will naturally lead to the parabolic scaling. Our result indicates that when sufficiently approaches zero, quantum fluctuations will be overwhelmingly amplified so that the mean-field approximation may break down at zero temperature.

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A Model of Spacetime Dynamics with Embedded Quantum Objects

Diel

2017

Rep. Adv. Phys. Sci.

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General relativity theory (GRT) tells us that (a) space and time should be viewed as an entity (called spacetime), (b) the spacetime of a world that contains gravitational objects should be viewed as curved, and (c) spacetime is a dynamical object with a dynamically changing extent and curvature. Attempts to achieve compatibility of GRT with quantum theory (QT) have typically resulted in proposing elementary units of spacetime as building blocks for the emergence of larger spacetime objects. In the present paper, a model of curved discrete spacetime is presented in which the basic space elements are derived from Causal Dynamical Triangulation. Spacetime can be viewed as the container for physical objects, and in GRT, the energy distribution of the contained physical objects determines the dynamics of spacetime. In the proposed model of curved discrete spacetime, the primary objects contained in spacetime are \quantum objects". Other larger objects are collections of quantum objects. This approach results in an accordance of GRT and quantum (¯eld) theory, while coincidently the areas in which their laws are in force are separated. In the second part of the paper, a rough mapping of quantum¯eld theory to the proposed model of spacetime dynamics is described.

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Quantum Behavior Arises Because Our Universe is a Fractal

Cited by 3 publications

References 29 publications

Superconducting Quantum Critical Phenomena

Superconducting Quantum Critical Phenomena

BCS quantum critical phenomena

A Model of Spacetime Dynamics with Embedded Quantum Objects

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