On Estimating the Total Number of Intermediate Mass Black Holes

Caputo, Daniel P.; Vries, Nathan de; Patruno, A.; Zwart, Simon Portegies

doi:10.1093/mnras/stw3336

Cited by 21 publications

(19 citation statements)

References 22 publications

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“…is potential energy,h β and D α,β are two scale coefficients, which we introduce into the framework of time fractional quantum mechanics, ∆ is the 1D Laplace operator, ∆ = ∂ 2 /∂x 2 , and, finally, ∂ β t is the left Caputo fractional derivative [7] of order β defined by…”

Section: Space-time Fractional Schrödinger Equationmentioning

confidence: 99%

“…To get the time fractional Schrödinger equation, Naber implemented the Wick rotation in complex t-plane by rising the imaginary unit i to the same fractional power as the fractional order of the time derivative in the time fractional diffusion equation. The time fractional derivative in the time fractional Schrödinger equation is the Caputo fractional derivative [7]. Naber has found the exact solutions to the time fractional Schrödinger equation for a free particle and a particle in a potential well [5].…”

Section: Introductionmentioning

confidence: 99%

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Fractional Quantum Mechanics

Laskin

2017

225

256

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A path integral approach to quantum physics has been developed. Fractional path integrals over the paths of the Lévy flights are defined. It is shown that if the fractality of the Brownian trajectories leads to standard quantum and statistical mechanics, then the fractality of the Lévy paths leads to fractional quantum mechanics and fractional statistical mechanics. The fractional quantum and statistical mechanics have been developed via our fractional path integral approach. A fractional generalization of the Schrödinger equation has been found. A relationship between the energy and the momentum of the nonrelativistic quantum-mechanical particle has been established. The equation for the fractional plane wave function has been obtained. We have derived a free particle quantum-mechanical kernel using Fox's H function. A fractional generalization of the Heisenberg uncertainty relation has been established. Fractional statistical mechanics has been developed via the path integral approach. A fractional generalization of the motion equation for the density matrix has been found. The density matrix of a free particle has been expressed in terms of the Fox's H function. We also discuss the relationships between fractional and the well-known Feynman path integral approaches to quantum and statistical mechanics.

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Section: Space-time Fractional Schrödinger Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fractional Quantum Mechanics

Laskin

2017

225

256

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“…We assume the total number of IBHs born in the past in the Galaxy to be 10 8 , roughly consistent with past estimates (e.g. Shapiro & Teukolsky 1983;van den Heuvel 1992;Samland 1998;Fender et al 2013;Caputo et al 2017). The distribution of black holes at birth is assumed to have disc and bulge components, whose birth locations and histories are modelled to follow the observed stellar profiles in the Galaxy.…”

Section: Distribution Of Ibhs and Ismmentioning

confidence: 82%

Radio emission from accreting isolated black holes in our galaxy

Tsuna

Kawanaka

2019

Monthly Notices of the Royal Astronomical Society

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Apart from the few tens of stellar-mass black holes discovered in binary systems, an order of 10 8 isolated black holes (IBHs) are believed to be lurking in our Galaxy. Although some IBHs are able to accrete matter from the interstellar medium, the accretion flow is usually weak and thus radiatively inefficient, which results in significant material outflow. We study electron acceleration generated by the shock formed between this outflow and the surrounding material, and the subsequent radio synchrotron emission from accelerated electrons. By numerically calculating orbits of IBHs to obtain their spatial and velocity distributions, we estimate the number of IBHs detectable by surveys using SKA1-mid (SKA2) as ∼ 30 (∼ 700) for the most optimistic case. The SKA's parallax measurements may accurately give their distances, possibly shedding light on the properties of the black holes in our Galaxy.

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“…where 0 D 1Àβ t is the Rieman-Liouville fractional derivative [43][44][45][46][47][48] which is denoted by…”

Section: Non-exponential Relaxationmentioning

confidence: 99%

A Simple Model for Stretched Exponential Relaxation in Three‐Level Jumping Process

Aydıner¹

2019

Physica Status Solidi (b)

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In this study, operator formalism is briefly introduced which is used to model Debye‐type relaxation with three‐level jumping based on Markovian framework. The author generalizes this formalism to the non‐Markovian process to model the non‐exponential relaxation and internal friction of real bcc metals or systems like Snoek‐type. By using this formalism, stretched exponential relaxation and the frequency and temperature dependence of internal friction depending upon β parameter are obtained. For β = 1, it is shown that the relaxation is exponential which obeys Debye law, and the frequency and temperature dependence of internal peak are represented by a single Debye peak. However, for 0 < β < 1 the author shows that relaxation is given by stretched exponential form, and the internal friction deviates from single Debye peak. It is concluded that β represents the memory, aging, and coupling effects of stochastic dynamics in complex materials.

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On Estimating the Total Number of Intermediate Mass Black Holes

Cited by 21 publications

References 22 publications

Fractional Quantum Mechanics

Fractional Quantum Mechanics

Radio emission from accreting isolated black holes in our galaxy

A Simple Model for Stretched Exponential Relaxation in Three‐Level Jumping Process

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