Perspectives about Quantum Mechanics in a Model of a Three-Dimensional Quantum Vacuum Where Time is a Mathematical Dimension

2014 ◽  
Vol 2014 (3) ◽  
pp. 11-38 ◽  
Author(s):  
Davide Fiscaletti ◽  
◽  
Amrit Sorli ◽  
Keyword(s):  
Quantum Mechanics ◽  
Three Dimensional ◽  
Quantum Vacuum

scholarly journals Topological correlators and surface defects from equivariant cohomology

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Rodolfo Panerai ◽  
Antonio Pittelli ◽  
Konstantina Polydorou
Keyword(s):  
Quantum Mechanics ◽  
Equivariant Cohomology ◽  
Surface Defects ◽  
Star Product ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Dimensional System ◽  
The Novel ◽  
One Dimensional ◽  
Dual Quantum

Abstract We find a one-dimensional protected subsector of $$ \mathcal{N} $$ N = 4 matter theories on a general class of three-dimensional manifolds. By means of equivariant localization we identify a dual quantum mechanics computing BPS correlators of the original model in three dimensions. Specifically, applying the Atiyah-Bott-Berline-Vergne formula to the original action demonstrates that this localizes on a one-dimensional action with support on the fixed-point submanifold of suitable isometries. We first show that our approach reproduces previous results obtained on S3. Then, we apply it to the novel case of S2× S1 and show that the theory localizes on two noninteracting quantum mechanics with disjoint support. We prove that the BPS operators of such models are naturally associated with a noncom- mutative star product, while their correlation functions are essentially topological. Finally, we couple the three-dimensional theory to general $$ \mathcal{N} $$ N = (2, 2) surface defects and extend the localization computation to capture the full partition function and BPS correlators of the mixed-dimensional system.

Energy and Momentum Eigenspectrum of the Hulthén-screened Cosine Kratzer Potential Using Proper Quantization Rule and SUSYQM Method

2021 ◽  
Author(s):  
Kaushal R Purohit ◽  
Rajendrasinh H PARMAR ◽  
Ajay Kumar Rai
Keyword(s):  
Quantum Mechanics ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Numerical Data ◽  
Time Dependent ◽  
Quantization Rule ◽  
Approximation Approach ◽  
Momentum Spectra ◽  
Energy And Momentum ◽  
Three Dimensional Space

Abstract Using the Qiang-Dong proper quantization rule (PQR) and the supersymmetric quantum mechanics approach, we obtained the eigenspectrum of the energy and momentum for time independent and time dependent Hulthen-screened cosine Kratzer potentials. For the suggested time independent Hulthen-screened cosine Kratzer potential, we solved the Schrodinger equation in D dimensions (HSCKP). The Feinberg-Horodecki equation for time-dependent Hulthen-screened cosine Kratzer potential was also solved (tHSCKP). To address the inverse square term in the time independent and time dependent equations, we employed the Greene-Aldrich approximation approach. We were able to extract time independent and time dependent potentials, as well as their accompanying energy and momentum spectra. In three-dimensional space, we estimated the rotational vibrational (RV) energy spectrum for many homodimers ($H_2, I_2, O_2$) and heterodimers ($MnH, ScN, LiH, HCl$). We also used the recently introduced formula approach to obtain the relevant eigen function. We also calculated momentum spectra for the dimers $MnH$ and $ScN$. The method is compared to prior methodologies for accuracy and validity using numerical data for heterodimer $LiH, HCl$ and homodimer $I_2, O_2,H_2$. The calculated energy and momentum spectra are tabulated and analysed.

scholarly journals Brownian motion and polarized three-dimensional quantum vacuum

2021 ◽  
Vol 67 (4 Jul-Aug) ◽  
Author(s):  
Davide Fiscaletti
Keyword(s):  
Dark Matter ◽  
Brownian Motion ◽  
Energy Density ◽  
Nonlinear Model ◽  
Vacuum Energy ◽  
Three Dimensional ◽  
Vacuum Energy Density ◽  
Quantum Vacuum ◽  
Virtual Particles ◽  
Fundamental Entity

A nonlinear model of Brownian motion is developed in a three-dimensional quantum vacuum defined by a variable quantum vacuum energy density corresponding to processes of creation/annihilation of virtual particles. In this model, the polarization of the quantum vacuum determined by a perturbative fluctuation of the quantum vacuum energy density associated with a fluctuating viscosity, which mimics the action of dark matter, emerges as the fundamental entity which generates the Brownian motion.

scholarly journals GEOMETRIC MOMENTUM IN THE MONGE PARAMETRIZATION OF TWO-DIMENSIONAL SPHERE

2013 ◽  
Vol 10 (03) ◽  
pp. 1220031 ◽  
Author(s):  
D. M. XUN ◽  
Q. H. LIU
Keyword(s):  
Quantum Mechanics ◽  
Laplace Operator ◽  
Three Dimensional ◽  
Dimensional Sphere ◽  
Two Dimensional ◽  
Constrained Motion ◽  
Geometric Invariant ◽  
Gradient Operator ◽  
The Laplace Operator

A two-dimensional (2D) surface can be considered as three-dimensional (3D) shell whose thickness is negligible in comparison with the dimension of the whole system. The quantum mechanics on surface can be first formulated in the bulk and the limit of vanishing thickness is then taken. The gradient operator and the Laplace operator originally defined in bulk converges to the geometric ones on the surface, and the so-called geometric momentum and geometric potential are obtained. On the surface of 2D sphere the geometric momentum in the Monge parametrization is explicitly explored. Dirac's theory on second-class constrained motion is resorted to for accounting for the commutator [xi, pj] = iℏ(δij - xixj/r2) rather than [xi, pj] = iℏδij that does not hold true anymore. This geometric momentum is geometric invariant under parameters transformation, and self-adjoint.

3D Structural Bioinformatics of Proteins and Antibodies: State of the Art Perspectives and Challenges

2013 ◽  
Vol 2 (3) ◽  
pp. 67-74
Author(s):  
Arianna Filntisi ◽  
Dimitrios Vlachakis ◽  
George Matsopoulos ◽  
Sophia Kossida
Keyword(s):  
Quantum Mechanics ◽  
Quantum Chemical ◽  
State Of The Art ◽  
Three Dimensional ◽  
Research Field ◽  
Important Class ◽  
Structural Components ◽  
Molecular Systems ◽  
Mechanical Methods ◽  
Harmful Substances

Proteins are an important class of biochemical molecules, as the structural components of animal and human tissue are based on them. Antibodies are proteins that play a crucial role in the preservation of life since they are produced by the body's immune system as a response to harmful substances. The modelling of proteins and antibodies in particular is a vibrant research field which facilitates the design of drugs, a process otherwise demanding in terms of time and resources. A variety of computational methods and tools are being developed towards that goal, among which are hybrid quantum chemical/molecular mechanical methods and three-dimensional antibody modelling. In this review the authors discuss the knowledge concerning proteins and antibodies, as well as the use of quantum mechanics in the simulation of molecular systems and the three-dimensional antibody modelling.

scholarly journals Entropy Balance in the Expanding Universe: A Novel Perspective

Entropy ◽  
2019 ◽  
Vol 21 (4) ◽  
pp. 406
Author(s):  
Arturo Tozzi ◽  
James F. Peters
Keyword(s):  
Quantum Mechanics ◽  
Second Law Of Thermodynamics ◽  
Quantum Systems ◽  
Second Law ◽  
Quantum Vacuum ◽  
Expanding Universe ◽  
Cosmic Expansion ◽  
Thermodynamic Entropy ◽  
Local Observer ◽  
Relational Mechanism

We describe cosmic expansion as correlated with the standpoints of local observers’ co-moving horizons. In keeping with relational quantum mechanics, which claims that quantum systems are only meaningful in the context of measurements, we suggest that information gets ergodically “diluted” in our isotropic and homogeneous expanding Universe, so that an observer detects just a limited amount of the total cosmic bits. The reduced bit perception is due the decreased density of information inside the expanding cosmic volume in which the observer resides. Further, we show that the second law of thermodynamics can be correlated with cosmic expansion through a relational mechanism, because the decrease in information detected by a local observer in an expanding Universe is concomitant with an increase in perceived cosmic thermodynamic entropy, via the Bekenstein bound and the Laudauer principle. Reversing the classical scheme from thermodynamic entropy to information, we suggest that the cosmological constant of the quantum vacuum, which is believed to provoke the current cosmic expansion, could be one of the sources of the perceived increases in thermodynamic entropy. We conclude that entropies, including the entangled entropy of the recently developed framework of quantum computational spacetime, might not describe independent properties, but rather relations among systems and observers.

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