scholarly journals Expectation values of minimum-length Ricci scalar

2021 ◽  
Author(s):  
Alessandro Pesci
Keyword(s):  
Minimum Distance ◽  
Direct Detection ◽  
Specific Model ◽  
Ricci Scalar ◽  
Minimum Length ◽  
Recent Past ◽  
Expectation Values ◽  
Expectation Value ◽  
Fundamental Limit ◽  
Quantum Variable

In this paper, we consider a specific model, implementing the existence of a fundamental limit distance [Formula: see text] between (space or time separated) points in spacetime, which in the recent past has exhibited the intriguing feature of having a minimum-length Ricci scalar [Formula: see text] that does not approach the ordinary Ricci scalar [Formula: see text] in the limit of vanishing [Formula: see text]. [Formula: see text] at a point has been found to depend on the direction along which the existence of minimum distance is implemented. Here, we point out that the convergence [Formula: see text] in the [Formula: see text] limit is anyway recovered in a relaxed or generalized sense, which is when we average over directions, this suggesting we might be taking the expectation value of [Formula: see text] promoted to be a quantum variable. It remains as intriguing as before the fact that we cannot identify (meaning this is much more than simply equating in the generalized sense above) [Formula: see text] with [Formula: see text] in the [Formula: see text] limit, namely, when we get ordinary spacetime. Thing is like if, even when [Formula: see text] (read here the Planck length) is far too small to have any direct detection of it feasible, the intrinsic quantum nature of spacetime might anyway be experimentally at reach, witnessed by the mentioned special feature of Ricci, not fading away with [Formula: see text] (i.e. persisting when taking the [Formula: see text] limit).

scholarly journals Gravity cells as a necessary link in string theory. The formula for the gravitational constant, the formula for the mass of the electron, the formula for the minimum distance of the gravitational interaction, the formula for the minimum distance of the Coulomb interaction. The coincidence of the results obtained by the formulas and the experimental data.

2021 ◽  
Author(s):  
Andrey Chernov
Keyword(s):  
Experimental Data ◽  
String Theory ◽  
Minimum Distance ◽  
Gravitational Constant ◽  
Casimir Effect ◽  
Gravitational Interaction ◽  
Minimum Length ◽  
Vibrational Velocity ◽  
New Formula ◽  
Schwarzschild Radius

Abstract In this study, a new concept is introduced into physics - gravitational cells. The gravitational cell hypothesis was organically integrated into string theory. As a result, using the Schwarzschild radius formula and the Coulomb formula, a gravitational formula in the region of black holes was obtained on the basis of two fundamental constants, and its exact value was determined. The value of the "usual" gravitational constant was also confirmed and the mass of the gravitational cell was obtained. The introduction of the gravitational cell hypothesis into string theory made it possible to apply Planck's constant to gravitational interaction. As a result, a formula for the energy of a gravitational quantum and a formula for the vibrational velocity of a gravitational string were obtained. On this basis, the formula for the mass of the electron was obtained and its value was calculated, which coincided with the experimental mass of the electron. According to the formula for the vibrational velocity of the gravitational string, the formula for the minimum distance of the gravitational interaction was obtained and this distance was calculated. This minimum distance of the gravitational interaction with absolute accuracy coincided with the known experimental data obtained when determining the Casimir effect (force). Another great scientific result is the determination by a new formula of the minimum distance of the onset of the action of Coulomb forces between electric 3 charges and obtaining the minimum length of a standing electric wave between charges.

scholarly journals Evaluation of the one electron expectation values for different wave function of Be atom

2007 ◽  
Vol 4 (3) ◽  
pp. 393-396
Author(s):  
Baghdad Science Journal
Keyword(s):  
Wave Function ◽  
Slater Determinant ◽  
Open Shell ◽  
Expectation Values ◽  
Electronic Density ◽  
Expectation Value ◽  
Hartree Fock ◽  
Shell System ◽  
Electronic Wave Function ◽  
The One

The aim of this work is to evaluate the one- electron expectation value from the radial electronic density function D(r1) for different wave function for the 2S state of Be atom . The wave function used were published in 1960,1974and 1993, respectavily. Using Hartree-Fock wave function as a Slater determinant has used the partitioning technique for the analysis open shell system of Be (1s22s2) state, the analyze Be atom for six-pairs electronic wave function , tow of these are for intra-shells (K,L) and the rest for inter-shells(KL) . The results are obtained numerically by using computer programs (Mathcad).

Expectation Value Calculation of Grid QoS Parameters Based on Algorithm Prim

2010 ◽  
Vol 34-35 ◽  
pp. 2016-2020
Author(s):  
Kai Jian Liang ◽  
Lin Feng Bai ◽  
Xi Long Qu
Keyword(s):  
Service Providers ◽  
Computation Method ◽  
Expectation Values ◽  
Expectation Value ◽  
Qos Parameters ◽  
System Resources ◽  
Selection Of

From the perspective of selecting service by QoS attributes, a computation method of QoS expectation value, which is based on Algorithm Prim, was presented to provide support for selection of service. On the basis of the ability of service providers, by Algorithm Prim, this method succeded in calculating a set of balanced expectation values of QoS. Selection of service based on these QoS values would be beneficial to optimization of system resources and protection of the users of those services. An example with analysis has been provided to demonstrate the feasibility and effectiveness of the method.

scholarly journals Symmetry Constrained Decoherence of Conditional Expectation Values

Universe ◽  
2019 ◽  
Vol 5 (2) ◽  
pp. 46 ◽  
Author(s):  
M. Mohammady ◽  
Alessandro Romito
Keyword(s):  
Conditional Expectation ◽  
Sufficient Conditions ◽  
Specific Model ◽  
Quantum Mechanical ◽  
Conserved Quantities ◽  
System State ◽  
Quantum Thermodynamics ◽  
Expectation Values ◽  
Thermal Measurements

Conditional expectation values of quantum mechanical observables reflect unique non-classical correlations, and are generally sensitive to decoherence. We consider the circumstances under which such sensitivity to decoherence is removed, namely, when the measurement process is subjected to conservation laws. Specifically, we address systems with additive conserved quantities and identify sufficient conditions for the system state such that its coherence plays no role in the conditional expectation values of observables that commute with the conserved quantity. We discuss our findings for a specific model where the system-detector coupling is given by the Jaynes-Cummings interaction, which is relevant to experiments tracking trajectories of qubits in cavities. Our results clarify, among others, the role of coherence in thermal measurements in current architectures for quantum thermodynamics experiments.

Comment on “Linear and bent triatomic molecules are not qualitatively different!”

2021 ◽  
pp. 1-2
Author(s):  
T. Amano
Keyword(s):  
Quantum Mechanics ◽  
Basic Principle ◽  
Stationary States ◽  
Expectation Values ◽  
Theoretical Justification ◽  
Bending Angle ◽  
Expectation Value ◽  
Triatomic Molecules

Jensen (Can. J. Phys. 98, 506 (2020). doi: 10.1139/cjp-2019-0395 ) presents theoretical justification for the claim that linear triatomic molecules are necessarily observed to be bent. The basis of the assertion is that the expectation value of the supplement of the bending angle, [Formula: see text] used in Jensen’s paper, is calculated to be positive. In this comment, we examine the interpretation of the expectation values of [Formula: see text] in stationary states, and indicate that Jensen’s claim contradicts a basic principle of quantum mechanics that the energy and geometrical variables cannot have definite values at the same time.

"VECTAL" REPRESENTATION OF THE WAVE FUNCTION AND ITS PHYSICAL MEANING

1967 ◽  
Vol 45 (11) ◽  
pp. 3667-3676
Author(s):  
C. S. Lin
Keyword(s):  
Wave Function ◽  
Wave Functions ◽  
Electron Wave Function ◽  
Electron Wave ◽  
Expectation Values ◽  
Expectation Value ◽  
Hartree Fock ◽  
The One ◽  
The Relationship ◽  
Determinantal Form

A new form of one-electron wave function, "vectal," is introduced. It is shown that an arbitrary CI geminal and a certain class of many-electron wave functions can be represented in a single-determinantal form in terms of the vectal. Eigenvalue equations for the vectal, similar to that of the Hartree–Fock theory, are derived and the vectal representation is shown to enable a formal interpretation of the CI theory in the Hartree–Fock manner. The eigenvalue, vectal energy, is interpreted as the negative of an ionization potential, in Koop-man's sense, of the system described by the CI wave function. It is also shown that the expectation value of any one-electron operator, [Formula: see text], where Ψ is the CI wave function, is expressible in terms of the expectation values of the same operator with respect to the vectals. The vectals are interpreted as the one-electron wave function in the CI space.A possible application of the vectal representation is briefly described, and the relationship between the vectal representation and the "scalar representation" is discussed.

COMBINATIONAL APPROACH, Au+Au COLLISIONS AT $\sqrt{s_{NN}}=200~{\rm GeV}$ AND AT TWO RAPIDITIES, AND THE NATURE OF CENTRALITY-DEPENDENCE OF SOME SECONDARIES

2006 ◽  
Vol 21 (07) ◽  
pp. 603-619 ◽  
Author(s):  
BHASKAR DE ◽  
S. K. BISWAS ◽  
S. BHATTACHARYYA
Keyword(s):  
Specific Model ◽  
Recent Past ◽  
Independent Manner ◽  
Centrality Dependence ◽  
Collision Centrality ◽  
Gold Collisions ◽  
Charged Hadrons ◽  
Model Independent

BRAHMS collaboration1 had studied in the recent past some properties of the detected identified charged hadrons in gold–gold collisions at [Formula: see text] as a function of pT and collision-centrality at two rapidity values. The reported characteristics, which are not offshoots of any specific model whatsoever, and are measured in a model-independent manner, would be dealt with in the light of a phenomenological framework named combinational approach.

scholarly journals Gravity cells as a necessary link in string theory. The formula for the gravitational constant, the formula for the mass of the electron, the formula for the minimum distance of the gravitational interaction, the formula for the minimum distance of the Coulomb interaction. The coincidence of the results obtained by the formulas and the experimental data.

2021 ◽  
Author(s):  
Andrey Chernov
Keyword(s):  
Experimental Data ◽  
String Theory ◽  
Minimum Distance ◽  
Gravitational Constant ◽  
Casimir Effect ◽  
Gravitational Interaction ◽  
Minimum Length ◽  
Vibrational Velocity ◽  
New Formula ◽  
Schwarzschild Radius

Abstract In this study, a new concept is introduced into physics - gravitational cells. The gravitational cell hypothesis was organically integrated into string theory. As a result, using the Schwarzschild radius formula and the Coulomb formula, a gravitational formula in the region of black holes was obtained on the basis of two fundamental constants, and its exact value was determined. The value of the "usual" gravitational constant was also confirmed and the mass of the gravitational cell was obtained. The introduction of the gravitational cell hypothesis into string theory made it possible to apply Planck's constant to gravitational interaction. As a result, a formula for the energy of a gravitational quantum and a formula for the vibrational velocity of a gravitational string were obtained. On this basis, the formula for the mass of the electron was obtained and its value was calculated, which coincided with the experimental mass of the electron. According to the formula for the vibrational velocity of the gravitational string, the formula for the minimum distance of the gravitational interaction was obtained and this distance was calculated. This minimum distance of the gravitational interaction with absolute accuracy coincided with the known experimental data obtained when determining the Casimir effect (force). Another great scientific result is the determination by a new formula of the minimum distance of the onset of the action of Coulomb forces between electric 3 charges and obtaining the minimum length of a standing electric wave between charges.

The effect of backreaction on inflationary Brans–Dicke cosmology

2016 ◽  
Vol 25 (10) ◽  
pp. 1650097 ◽  
Author(s):  
M. Sahraee ◽  
M. R. Setare
Keyword(s):  
Energy Momentum Tensor ◽  
Equations Of Motion ◽  
Dimensional Regularization ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Momentum Tensor ◽  
Expectation Values ◽  
Quantum Energy ◽  
Expectation Value ◽  
Dimensional Spacetime

In this paper, we study the effect of the quantum backreaction on Brans–Dicke cosmology in inflation era. We consider an inflaton field in the [Formula: see text]-dimensional spacetime in the framework of Brans–Dicke model. We use a new notation for the Brans–Dicke field in terms of the dilaton field. Then we obtain the vacuum expectation value of the full energy–momentum tensor using WKB approximation of the mode functions which satisfy the equations of motion. The obtained vacuum expectation values of energy–momentum tensor are divergent. In order to renormalize it, we introduce a constant cut-off [Formula: see text]. The vacuum expectation value of energy–momentum tensor is separated to the UV and IR parts by using [Formula: see text] cut-off. Then, we use the dimensional regularization method to eliminate divergences by introducing a counterterm action. Also, we calculate the IR contribution of the vacuum expectation value of energy–momentum tensor. Thus, we obtain a physically finite result for the quantum energy–momentum tensor. Finally, we find the effect of backreaction on scale factor.

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