Maximum Momentum,Minimal Length and Quantum Gravity Effects of Compact Star Cores

Based on the generalized uncertainty principle with maximum momentum and minimal length,we discuss the equation of state of ideal ultra-relativistic Fermi gases at zero temperature.Maximum momentum avoids the problem that the Fermi degenerate pressure blows up since the increase of the Fermi energy is not limited.Applying this equation of state to the Tolman-Oppenheimer-Volkoff(TOV) equation,the quantum gravitational effects on the cores of compact stars are discussed.In the center of compact stars,we obtain the singularity-free solution of the metric component,g_(tt) ~-(1 + 0.2185 x r~2).By numerically solving the TOV equation,we find that quantum gravity plays an important role in the region r ~10~4a_0(△x)_(min).Current observed masses of neutron stars indicate that the dimensionless parameter z_0 cannot exceed 10~(19).     

Modified Anti Snyder Model with Minimal Length,Momentum Cutoff and Convergent Partition Function

International Journal of Theoretical Physics - In this paper we consider the possible modification of the anti Snyder model so that it have the non-zero minimal length, momentum cutoff and the...     

Black Holes and Photons with Entropic Force

We study the entropic force effects on black holes and photons. It is found that application of an entropic analysis restricts the radial change △R of a black hole of radius RH, due to a test particle of a Schwarzschild radius Rn moving towards the black hole by △x near a black body surface, to be given by a relation RH△R = Rh△x/2, or △ R/λM = △x /2λm. We suggest a new rule regarding entropy changes in different dimensions, △S = 2πkD △l/λ, which unifies Verlinde＇s conjecture and the black hole entropy formula. We also propose the extension of the entropic force idea to massless particles such as photons. It is realized that there is an entropic force on a photon of energy Eγ with F = GM（Eγ/c^2）/R^2, and therefore the photon has an effective gravitational mass mγ= Eγ/c^2.     

Debye Entropic Force and Modified Newtonian Dynamics

Verlinde has suggested that the gravity has an entropic origin, and agravitational system could be regarded as a thermodynamical system. It is well-known that the equipartition law of energy is invalid at very low temperature. Therefore, entropic force should be modified while the temperature of the holographic screen is very low. It is shown that the modified entropic force is proportional to the square of the acceleration, while the temperature of the holographic screen is much lower than the Debye temperature T_D. The modified entropic force returns to the Newton's law of gravitation while the temperature of the holographic screen is much higher than the Debye temperature. The modified entropic force is connected with modified Newtonian dynamics (MOND). The constant a₀ involved in MOND is linear in the Debye frequency ω_D, which can be regarded as the largest frequency of the bits in screen.We find that there do have a strong connection between MOND and cosmology in the framework of Verlinde's entropic force, if the holographic screen is takento be bound of the Universe. The Debye frequency is linear in the Hubble constant H₀.     

Modified Friedmann Equations on the Brane from Entropic Force

The well-known area relation of the black hole entropy can be modified from the inclusion of quantum effects, motivated from the loop quantum gravity. Applying this modified entropy-area relation to brane cosmology, we derive the modified cosmological equations governing the evolution of the universe on the brane. We adopt the viewpoint that interprets gravity as an entropic force caused by the changes in the information when a material body moves away from the holographic screen.     

The Minimal Length Uncertainty and the Nonextensive Thermodynamics

In this paper, we study the thermodynamics of quantum harmonic oscillator in the Tsallis framework and in the presence of a minimal length uncertainty. The existence of the minimal length is motivated by various theories such as string theory, loop quantum gravity, and black-hole physics. We analytically obtain the partition function, probability function, internal energy, and the specific heat capacity of the vibrational quantum system for \(1<q<\frac {3}{2}\) and compare the results with those of Tsallis and Boltzmann-Gibbs statistics without the minimal length scale.     

动量守恒定律的建立

在宏观领域中,动量守恒定律的建立主要从科学家们对碰撞现象的研究人手,建立了该定律,同时也具体的描述了在此过程中对运动量度的大争论．     

Classical Dynamics Based on the Minimal Length Uncertainty Principle

In this paper we consider the quadratic modification of the Heisenberg algebra and its classical limit version which we call the β-deformed Poisson bracket for corresponding classical variables. We use the β-deformed Poisson bracket to discuss some physical problems in the β-deformed classical dynamics. Finally, we consider the (α,β)- deformed classical dynamics in which minimal length uncertainty principle is given by \( [ \hat {x} , \hat {p}] = i \hbar (1 + \alpha \hat {x}^{2} + \beta \hat {p}^{2} ) \). For two small parameters α,β, we discuss the free fall of particle and a composite system in a uniform gravitational field.     

熵测不准关系与光场的熵压缩

用熵作为光场量子涨落的量度,根据熵测不准关系,建立了熵压缩的概念,具体研究了光场与原子相互作用时的熵压缩,结果显示,熵压缩实现了对光场压缩效应的高灵敏量度。     

Temperature and Energy of 4-Dimensional Axisymmetric Black Holes from Entropic Force

We investigate the temperature and energy on holographic screens for 4-dimensional axisymmetric black holes with the entropic force idea proposed by Verlinde. According to the principle of thermal equilibrium, the location of holographic screen outside the axisymmetric black hole horizon is not a equivalent radius surface. The location of isothermal holographic screen outside the axisymmetric black hole horizon is obtained. Using the equipartition rule, we derive the correction expression of energy of isothermal holographic screen. When holographic screens are far away the black hole horizon, the entropic force of charged rotating particles can be expressed as Newton’s law of gravity. When the screen crosses the event horizon, the temperature of the screen agrees with the Hawking temperature and the entropic force gives rise to the surface gravity for both of the black holes.     

Quantization of Space in the Presence of a Minimal Length

In this article,we apply the Generalized Uncertainty Principle(GUP),which is consistent with quantum gravity theories to an elementary particle in a finite potential well,and study the quantum behavior in this system.The generalized Hamiltonian contains two additional terms,which are proportional to αp~3(the result of the maximum momentum assumption) and α~2p~4(the result of the minimum length assumption),where α ~ 1/M_(PIC) is the GUP parameter.On the basis of the work by Ali et al.,we solve the generalized Schrodinger equation which is extended to include the α~2 correction term,and find that the length L of the finite potential well must be quantized.Then a generalization to the double-square-well potential is discussed.The result shows that all the measurable lengths especially the distance between the two potential wells are quantized in units of α_0l_(PI) in GUP scenario.     

From the Komar Mass and Entropic Force Scenarios to the Einstein Field Equations on the Ads Brane

By bearing the Komar’s definition for the mass, together with the entropic origin of gravity in mind, we find the Einstein field equations in (n + 1)-dimensional spacetime. Then, by reflecting the (4 + 1)-dimensional Einstein equations on the (3 + 1)-hypersurface, we get the Einstein equations onto the 3-brane. The corresponding energy conditions are also addressed. Since the higher dimensional considerations modify the Einstein field equations in the (3 + 1)-dimensions and thus the energy-momentum tensor, we get a relation for the Komar mass on the brane. In addition, the strongness of this relation compared with existing definition for the Komar mass on the brane is addressed.     

Solution of the Dipoles in Noncommutative Space with Minimal Length *

The single neutral spin-half particle with electric dipole moment and magnetic dipole moment moving in an external electromagnetic field is studied. The Aharonov-Casher effect and He-McKellar-Wilkens effect are emphatically discussed in noncommutative (NC) space with minimal length. The energy eigenvalues of the systems are obtained exactly in terms of the Jacobi polynomials. Additionally, a special case is discussed and the related energy spectra are plotted.     

Relativistic Approach to the Hydrogen Atom in a Minimal Length Scenario

We show that relativistic contributions to the ground-state energy of the hydrogen atom from a minimal length introduced by a Lorentz-covariant algebra are more important than non-relativistic contributions; the non-relativistic approach is therefore unsuitable. We compare our result with experimental data to estimate an upper bound of the order 10^?20m for the minimal length.     

机械能守恒定律及动量守恒定律演示仪器的制作

制作一种可以同时验证机械能守恒和动量守恒的实验装置,并通过这两个实验现象的对比更显著地体现了两个实验的物理现象与原理,有利于学生对机械能守恒与动量守恒原理的理解与认知。     

Effect of the Minimal Length on the Thermodynamics of Ultra-Relativistic Ideal Fermi Gas

Based on the generalized uncertainty principle, the thermodynamics ot Petrol gas m mgl~ u~ll~l~y, H,8,, ~ and high temperature are calculated. As the temperature and density increases, the energy and entropy becomes saturated and the pressure blows up without any bound. Using the conservation equation of the Robertson- Walker cosmology, we find that, when the energy exceeds the EH = β0-1/2c2Mp, the expansion cannot be driven by the photon gas and the fermion gas. This requires some new physical mechanism related to quantum gravitym such as tachyons and dilatons.