The Smearing Out of the Thermal Initial Conditions Created in a Planck Era

In this paper the quantum heat transport in a Planck gas in the presence of the potential (other than the thermal one) is investigated. The new quantum heat transport equation which generalizes our potential-free QHT is developed. The thermal wave solution of QHT for a Planck gas is obtained and a condition for distortionless propagation of thermal wave is formulated. It is argued that the initial conditions of the Beginning (i.e., at t=0) are smeared in the time scale of the Planck time.     

Three Flavor Neutrino Mixing and Dark Energy Above GUT Scale

Neutrino mixing lead to a non zero contribution to the dark energy of the universe. We assume that the neutrino masses and mixing arise through physics at a scale intermediate between Planck Scale and the electroweak scale. The mechanism of neutrino mixing is a possible candidate to contribute the cosmological dark energy. Quantum gravitational (Planck scale) effects lead to an effective SU(2) _L ×U(1) invariant dimension-5 Lagrangian involving neutrino and Higgs fields, which gives rise to additional terms in neutrino mass matrix. There additional term can be considered to be perturbation of the GUT scale bi-maximal neutrino mass matrix. We assume that the gravitational interaction is flavor. In this paper, we discuss the three flavor neutrino mixing and cosmological dark energy contributes due to Planck scale effects.     

The time arrow in a Planck gas

In this paper the quantum heat transport equation (QHT) is applied to the study of thermal properties of Planck gas, i.e., a gas of massive particles with mass equal to the Planck massM _P = (łc/G)^1/2 and whose relaxation time equals the Planck timeτ _p = (łG/c ⁵)^1/2. The quantum of thermal energy for a Planck gas,E ^Planck = 10¹⁹GeV, and the quantum thermal diffusion coefficientD ^Planck = (ħG/c)^1/2 are calculated. Within the framework of QHT the thermal phenomena in a Planck gas can be divided into two classes: for a time period shorter thanτ _p , the time reversal symmetry holds and for a time period longer thanτ _p , time symmetry is broken, i.e., a time arrow is created.     

Kerr-Newman黑洞的熵修正

基于Majhi等人最近的工作,利用狄拉克方程,在半经典近似外讨论了Kerr-Newman黑洞的熵修正.在单位制G=c=kB=1下,由于普朗克常数与普朗克长度,普朗克质量和普朗克电荷的平方成正比,作用量的量子修正项与半经典项的比例常数被选为(Mrh-Q2/2)-1.结合视界方程的微分形式和黑洞热力学第一定律,本文得到了荷电稳态黑洞的修正熵并发现修正项同样包括Bekenstein-Hawking熵的对数项和倒数项.     

Demokrit – Planck

Demokrit – Planck A branch of physics exists closely linked to the constant h and associated with atomism. It is this h-physics that Planck originated. But atomism like existence of localized, charged particles with different masses does not follow from this physics, especially the charge quant. Hence Demokrit asserted more then quantum physics is competent to answer.     

Neutrino Mixing Matrix and Leptogenesis from Quantum Gravity

We consider non renormalization 1/M _x interaction term as a perturbation of the neutrino mass matrix. We find that for the degenerate neutrino mass spectrum. We assume that the neutrino masses and mixing arise through physics at a scale intermediate between Planck Scale and the electroweak scale. We also assume, above the electroweak breaking scale, neutrino masses are nearly degenerate and their mixing is bimaximal. The perturbation generates a non zero value of θ ₁₃, which is within reach of the high performance neutrino factory. In this paper, we find that the non zero value of θ ₁₃ due to Planck scale effects indicates the possibility of CP violation.     

Entropy correction to stationary black hole via fermions tunneling beyond semiclassical approximation

Recently, fermions tunneling beyond semiclassical approximation from an uncharged static black hole was investigated by Majhi, which was based on the work of Banerjee and Majhi, it was found that the black hole entropy correction can be produced as the quantum effect of a particle is taken into account. In this paper, we further extend this idea to the stationary Kerr black hole to discuss its entropy correction. To get the corrections correctly, the proportionality parameters of quantum corrections of action I _i to the semiclassical action I ₀ in this case are regarded as the inverse of the product of Planck Length and Planck Mass. The result shows that entropy corrections to the stationary black hole also include the logarithmic term and inverse area term in Bekenstein–Hawking entropy beyond semiclassical approximation.     

Extended Scale Relativity, p-Loop Harmonic Oscillator, and Logarithmic Corrections to the Black Hole Entropy

An extended scale relativity theory, actively developed by one of the authors, incorporates Nottale's scale relativity principle where the Planck scale is the minimum impassible invariant scale in Nature, and the use of polyvector-valued coordinates in C-spaces (Clifford manifolds) where all lengths, areas, volumes are treated on equal footing. We study the generalization of the ordinary point-particle quantum mechanical oscillator to the p-loop (a closed p-brane) case in C-spaces. Its solution exhibits some novel features: an emergence of two explicit scales delineating the asymptotic regimes (Planck scale region and a smooth region of a quantum point oscillator). In the most interesting Planck scale regime, the solution recovers in an elementary fashion some basic relations of string theory (including string tension quantization and string uncertainty relation). It is shown that the degeneracy of the first collective excited state of the p-loop oscillator yields not only the well-known Bekenstein–Hawking area-entropy linear relation but also the logarithmic corrections therein. In addition we obtain for any number of dimensions the Hawking temperature, the Schwarschild radius, and the inequalities governing the area of a black hole formed in a fusion of two black holes. One of the interesting results is a demonstration that the evaporation of a black hole is limited by the upper bound on its temperature, the Planck temperature.     

Numerical algorithm for the time fractional Fokker–Planck equation

Anomalous diffusion is one of the most ubiquitous phenomena in nature, and it is present in a wide variety of physical situations, for instance, transport of fluid in porous media, diffusion of plasma, diffusion at liquid surfaces, etc. The fractional approach proved to be highly effective in a rich variety of scenarios such as continuous time random walk models, generalized Langevin equations, or the generalized master equation. To investigate the subdiffusion of anomalous diffusion, it would be useful to study a time fractional Fokker–Planck equation. In this paper, firstly the time fractional, the sense of Riemann–Liouville derivative, Fokker–Planck equation is transformed into a time fractional ordinary differential equation (FODE) in the sense of Caputo derivative by discretizing the spatial derivatives and using the properties of Riemann–Liouville derivative and Caputo derivative. Then combining the predictor–corrector approach with the method of lines, the algorithm is designed for numerically solving FODE with the numerical error O(k^min{1+2α,2})+O(h²), and the corresponding stability condition is got. The effectiveness of this numerical algorithm is evaluated by comparing its numerical results for α=1.0 with the ones of directly discretizing classical Fokker–Planck equation, some numerical results for time fractional Fokker–Planck equation with several different fractional orders are demonstrated and compared with each other, moreover for α=0.8 the convergent order in space is confirmed and the numerical results with different time step sizes are shown.     

The Planck Constant for the Definition and Realization of the Kilogram

On May 20, 2019 the values of the Planck, h, and Avogadro, N_A, constants will be fixed, revising our measurement system, the International System of Units (SI), and providing a new way to get mass traceability. While the famous energy relations mc² and hf may remind many that the Planck constant is indeed related to mass, it is less recognized how this is also true for the Avogadro constant. These concepts are reviewed in the context of the upcoming revision of the SI. How the fixed values were chosen and how mass traceability will be maintained with the smallest uncertainty are also discussed.     

Radiative breaking scenario for the GUT gauge symmetry

The origin of the grand unified theory (GUT) scale from the top-down perspective is explored. The GUT gauge symmetry is broken by the renormalization group effects, which is an extension of the radiative electroweak symmetry breaking scenario to the GUT models. That is, in the same way as the origin of the electroweak scale, the GUT scale is generated from the Planck scale through the radiative corrections to the soft supersymmetry breaking mass parameters. This mechanism is applied to a perturbative SO(10) GUT model, recently proposed by us. In the SO(10) model, the relation between the GUT scale and the Planck scale can naturally be realized by using order-one coupling constants. PACS 12.10.-g, 12.10.Dm, 12.10.Kt     

Natural suppression of proton decay in supersymmetric type III seesaw models

Supersymmetric Standard Model (MSSM) has two sources of rapid proton decay: (i) R-parity breaking terms and (ii) higher dimensional Planck induced B-violating terms; its extensions to include neutrino masses via the type I seesaw mechanism need not have the first of these problems due to the existence of B−L as a gauge symmetry but for sure always have the second one. If instead, neutrino masses are explained in a type III seesaw extension of standard model, an anomaly free gauge symmetry different from B−L is known to exist. In this note, it is shown that a realistic supersymmetric versions of this model can be constructed (MSSM as well as SUSY left–right with type III seesaw) which eliminate R-parity violating couplings and suppress Planck scale contributions to proton decay. The degree of suppression of the latter depends on the weak gauge group. For the left–right case, the suppression to the desired level is easily achieved.     

New hierarchy for the Liouville equation,irreversibility and Fokker‐Planck‐like structures

The issue of irreversibility is revisited for a closed system formed by N classical non‐relativistic particles inside a volume Ω, interacting through two‐body potentials, for large N and Ω. The classical phase‐space distribution function f, multiplied by suitable Hermite polynomials and integrated over all momenta, yields new moments. The Liouville equation and the initial distribution f_in imply a new non‐equilibrium linear infinite hierarchy for the moments. That hierarchy differs from the BBGKY one for distribution functions and displays some suggestive Fokker‐Planck‐like structures. A physically motivated ansatz for f_in (which introduces statistical assumptions), used by previous authors, is chosen. All moments of order n ≥ n₀ are expressed in terms of those of order n₀ — 1 and of f_in. The properties of the Fokker‐Planck‐like structures (hermiticity, non‐negative eigenvalues) allow for implementing a natural long‐time approximation in the hierarchy, so as to introduce relaxation to equilibrium and irreversibility, consistently with the hydrodynamical balance equations. Further (more restrictive) assumptions and approximations lead to new irreversible models, generalizing non‐trivially the Fokker‐Planck equation. They are described through a truncated hierarchy of linear equations for moments of order n ≤ n₀ — 1 (n₀ being finite). The connections with Brownian particle dynamics and Fluid Dynamics are analyzed, for consistency.     

Review: Gas of Wormholes: A Possible Ground State of Quantum Gravity

In order to gain insight into the possible Ground State of Quantized Einstein's Gravity, we have derived a variational calculation of the energy of the quantum gravitational field in an open space, as measured by an asymptotic observer living in an asymptotically flat space-time. We find that for Quantum Gravity (QG) it is energetically favourable to perform its quantum fluctuations not upon flat space-time but around a "gas" of wormholes of mass m _p, the Planck mass (m _p 10¹⁹ GeV) and average distance l _p, the Planck length a _p(a _p 10^–33 cm). As a result, assuming such configuration to be a good approximation to the true Ground State of Quantum Gravity, space-time, the arena of physical reality, turns out to be well described by Wheeler's quantum foam and adequately modeled by a space-time lattice with lattice constant l _p, the Planck lattice.     

Commentary on the analysis of statistical distributions

We present an analysis of general statistical distributions, from which we obtain the Maxwell and Planck distributions. Using the derived relationships among the moments of the distributions, when they are confined to the interval (0, ∞) or the finite interval (0,d) of index values, it is possible to determine more reliably the degree of correlation between the theoretical distribution and the experimental one. It is shown that the Planck distribution for the spectral power of radiation does not describe the solar spectrum in the visible wavelength range. State University, Zaporog. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 39–44, November, 1998.     

Deviation from Tetra-Maximal Neutrino Mixing Above the GUT scale

We consider non-renormalizable interaction term as perturbation of the conventional neutrino mass matrix. We assume that the neutrino masses and mixing arise through physics at a scale intermediate between Planck scale and the electroweak breaking scale. We also assume that, just above the electroweak breaking scale, neutrino masses are nearly degenerate and their mixing is tetra-maximal. Quantum gravity (Planck scale effects) lead to an effective SU(2) _L ×U(1) invariant dimension-5 Lagrangian involving neutrino and Higgs fields. On electroweak symmetry breaking, this operator gives rise to correction to the above masses and mixing. These additional term can be consider as a perturbation to the Tetra-maximal mass matrix. The nature of gravitational interaction demands that the element of this perturbation matrix should be independent of flavor indices. We compute the deviation of three neutrino mixing angles due to Planck scale effects. We find that there is no change in θ ₁₃ and θ ₂₃ but change in solar mixing angle θ ₁₂ is suppress by 3.0°.     

Quantum de Sitter algebra and some possible applications in cosmology

I summarize results recently obtained in collaboration with Amelino-Camelia, Bruno and Mandanici (preprint University of Rome “La Sapienza”, August, 2005) that concern an analysis of the path of a massless particle in a q-de Sitter space-time and an approximation scheme suitable for the corresponding analysis in a quantum FRW Universe. On the basis of some arguments in the quantum-gravity literature, the q deformation parameter is assumed to depend on both the Planck scale and the curvature, leading to results that are significantly different from those of other studies of Planck-scale effects in cosmology, where the possibility of an interplay between curvature and Planck scale was ignored. Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.     

谈普朗克质量

简要介绍了普朗克于1912年提出的三个基本物理量：普朗克质量、普朗克长度和普朗克时间，它们巳被列入1986和1998年基本物理常数表，该文只讨论普朗克质量，假定原子核内存在量子化的核力场，命名其场量子为“引斥子”，其质量推算出恰好等于普朗克质量，由此可用4个耦合常数定量地描述四种相互作用的强度比，从而还可找到一种测定G的新方法。     

The Operator Formulation of Classical Mechanics and Semiclassical Limit

The algebra of polynomials in operators that represent generalized coordinate and momentum and depend on the Planck constant is defined. The Planck constant is treated as the parameter taking values between zero and some nonvanishing h ₀. For the later of these two extreme values, introduced operator algebra becomes equivalent to the algebra of observables of quantum mechanical system defined in the standard manner by operators in the Hilbert space. For the vanishing Planck constant, the generalized algebra gives the operator formulation of classical mechanics since it is equivalent to the algebra of variables of classical mechanical system defined, as usually, by functions over the phase space. In this way, the semiclassical limit of kinematical part of quantum mechanics is established through the generalized operator framework.