scholarly journals Characterization of density oscillations in confined and degenerate Fermi gases

2018 ◽  
Vol 32 (32) ◽  
pp. 1850393
Author(s):  
Coskun Firat ◽  
Altug Sisman ◽  
Alhun Aydin
Keyword(s):  
Symmetry Breaking ◽  
Pauli Exclusion Principle ◽  
Upper And Lower Bounds ◽  
Exclusion Principle ◽  
Fermi Gases ◽  
True Nature ◽  
Spatial Coordinates ◽  
Analytical Formulas ◽  
Degenerate Fermi Gases ◽  
Analytical Expressions

Friedel oscillations appear in density of Fermi gases due to Pauli exclusion principle and translational symmetry breaking nearby a defect or impurity. In confined Fermi gases, this symmetry breaking occurs also near to boundaries. Here, density oscillations of a degenerate and confined Fermi gas are considered and characterized. True nature of density oscillations are represented by analytical formulas for degenerate conditions. Analytical characterization is first done for completely degenerate case, then temperature effects are also incorporated with a finer approximation. Envelope functions defining the upper and lower bounds of these oscillations are determined. It is shown that the errors of obtained expressions are negligible as long as the system is degenerate. Numbers, amplitudes, averages and spatial coordinates of oscillations are also given by analytical expressions. The results may be helpful to efficiently predict and easily calculate the oscillations in density and density-dependent properties of confined electrons at nanoscale.

Hardness and HOMO-LUMO Gap Probed by the Helium Atom Pushing the Molecular Surface of the First-Row Hydride Molecules

2003 ◽  
Vol 68 (12) ◽  
pp. 2344-2354 ◽  
Author(s):  
Edyta Małolepsza ◽  
Lucjan Piela
Keyword(s):  
Helium Atom ◽  
Pauli Exclusion Principle ◽  
Structure Change ◽  
Molecular Surface ◽  
Exclusion Principle ◽  
Probe Position ◽  
Repulsion Energy ◽  
Ionic Dissociation ◽  
Probe Site ◽  
Homo Lumo

A molecular surface defined as an isosurface of the valence repulsion energy may be hard or soft with respect to probe penetration. As a probe, the helium atom has been chosen. In addition, the Pauli exclusion principle makes the electronic structure change when the probe pushes the molecule (at a fixed positions of its nuclei). This results in a HOMO-LUMO gap dependence on the probe site on the isosurface. A smaller gap at a given probe position reflects a larger reactivity of the site with respect to the ionic dissociation.

Identical Particles and Second Quantization: Occupation Number Representation

2018 ◽  
Author(s):  
Norman J. Morgenstern Horing
Keyword(s):  
Occupation Number ◽  
Annihilation Operator ◽  
Pauli Exclusion Principle ◽  
Exclusion Principle ◽  
Number Representation ◽  
Second Quantization ◽  
Identical Particles ◽  
Fundamental Properties ◽  
Minimum Uncertainty ◽  
Creation Operators

Focusing on systems of many identical particles, Chapter 2 introduces appropriate operators to describe their properties in terms of Schwinger’s “measurement symbols.” The latter are then factorized into “creation” and “annihilation” operators, whose fundamental properties and commutation/anticommutation relations are derived in conjunction with the Pauli exclusion principle. This leads to “second quantization” with the Hamiltonian, number, linear and angular momentum operators expressed in terms of the annihilation and creation operators, as well as the occupation number representation. Finally, the concept of coherent states, as eigenstates of the annihilation operator, having minimum uncertainty, is introduced and discussed in detail.

scholarly journals Testing the Pauli Exclusion Principle for Electrons at LNGS

2015 ◽  
Vol 61 ◽  
pp. 552-559 ◽  
Author(s):  
H. Shi ◽  
S. Bartalucci ◽  
S. Bertolucci ◽  
C. Berucci ◽  
A.M. Bragadireanu ◽  
...  
Keyword(s):  
Pauli Exclusion Principle ◽  
Exclusion Principle

Production of Degenerate Fermi Gases of 6Li Atoms in an Optical Dipole Trap

2021 ◽  
Vol 38 (5) ◽  
pp. 056701
Author(s):  
Xiang-Chuan Yan ◽  
Da-Li Sun ◽  
Lu Wang ◽  
Jing Min ◽  
Shi-Guo Peng ◽  
...  
Keyword(s):  
Fermi Gases ◽  
Dipole Trap ◽  
Optical Dipole Trap ◽  
Degenerate Fermi Gases

Thermonuclear plasma conditions in stellar interiors

1981 ◽  
Vol 300 (1456) ◽  
pp. 641-648
Keyword(s):  
Nuclear Reactions ◽  
Pauli Exclusion Principle ◽  
Significant Rise ◽  
Exclusion Principle ◽  
Reaction Products ◽  
Thermonuclear Reactions ◽  
Radiated Energy ◽  
Large Numbers ◽  
Stellar Interiors ◽  
Late Stages

Thermonuclear reactions provide the main source of radiated energy for stars and they are also believed to be responsible for the production of most of the heavy elements in the Universe. The thermonuclear plasma is confined by the force of gravitation and for most of a star’s history the reactions occur slowly and steadily. In some circumstances, the properties of a star change very rapidly and explosive nuclear reactions occur. In very dense stellar interiors the energy states available to electrons may be limited by the Pauli exclusion principle. When thermonuclear reactions start in such a degenerate gas, a rise in temperature is not accompanied by a significant rise in pressure and as a result there may be a runaway increase in reaction rate. In contrast, when reactions start in a non-degenerate gas, there is normally an effective thermostat. A star is usually opaque to reaction products, so that there is no problem in maintaining the reaction temperature, but at late stages of stellar evolution nuclear or elementary particle reactions may produce large numbers of neutrinos and antineutrinos that do escape.

scholarly journals Two-Cooper-pair problem and the Pauli exclusion principle

2010 ◽  
Vol 81 (17) ◽  
Author(s):  
Walter V. Pogosov ◽  
Monique Combescot ◽  
Michel Crouzeix
Keyword(s):  
Cooper Pair ◽  
Pauli Exclusion Principle ◽  
Exclusion Principle

scholarly journals X rays on quantum mechanics: Pauli Exclusion Principle and collapse models at test

2015 ◽  
Vol 631 ◽  
pp. 012068 ◽  
Author(s):  
C Curceanu ◽  
S Bartalucci ◽  
A Bassi ◽  
S Bertolucci ◽  
C Berucci ◽  
...  
Keyword(s):  
Quantum Mechanics ◽  
Pauli Exclusion Principle ◽  
Exclusion Principle ◽  
X Rays ◽  
Collapse Models

scholarly journals MUTUAL COUPLING COEFFICIENTS OF ROTATING RECTANGULAR DIELECTRIC RESONATORS IN CUT-OFF RECTANGULAR WAVEGUIDE

2021 ◽  
pp. 48-54
Author(s):  
Alexander Trubin
Keyword(s):  
Transmission Lines ◽  
Rectangular Waveguide ◽  
Information Transfer ◽  
Dielectric Resonators ◽  
Coupling Coefficients ◽  
Metal Waveguide ◽  
Communication Devices ◽  
Dielectric Filter ◽  
Analytical Formulas ◽  
Analytical Expressions

Background. A further increase in the speed of information transfer is determined by more stringent requirements for the elements of communication devices. One of the most important components of such devices is various filters, which are often made on the basis of dielectric resonators. Calculation of the parameters of multi-section filters is impossible without further development of the theory of their design. The development of filter theory is based on electrodynamic modelling, which involves calculating the coupling coefficients of dielectric resonators in various transmission lines. Objective. The aim of the research is to calculate and study the coupling coefficients of rectangular dielectric resonators with a rectangular metal waveguide when their axes rotate. Investigation of new effects to improve the performance of filters and other devices based on them. Methods. Methods of technical electrodynamics are used to calculate and analyse the coupling coefficients. The end result is to obtain new analytical formulas for new structures with rectangular dielectric resonators, which make it possible to analyse and calculate their coupling coefficients. Results. New analytical expressions are found for the coupling coefficients of dielectric resonators with the rotation of their axes in a rectangular waveguide. Conclusions. The theory of designing filters based on new structures of dielectric resonators with rotation of their axes in metal waveguides has been expanded. New analytical relationships and new patterns of change in the coupling coefficients are found. Keywords: dielectric filter; rectangular dielectric resonator; rotation; coupling coefficients.

scholarly journals VIP: AN EXPERIMENT TO SEARCH FOR A VIOLATION OF THE PAULI EXCLUSION PRINCIPLE

2007 ◽  
Vol 22 (02n03) ◽  
pp. 242-248 ◽  
Author(s):  
E. Milotti ◽  
S. Bartalucci ◽  
S. Bertolucci ◽  
M. Bragadireanu ◽  
M. Cargnelli ◽  
...  
Keyword(s):  
Quantum Mechanics ◽  
Basic Principle ◽  
Pauli Exclusion Principle ◽  
Experimental Results ◽  
Underground Laboratory ◽  
Exclusion Principle

The Pauli Exclusion Principle is a basic principle of Quantum Mechanics, and its validity has never been seriously challenged. However, given its fundamental standing, it is very important to check it as thoroughly as possible. Here we describe the VIP (VIolation of the Pauli exclusion principle) experiment, an improved version of the Ramberg and Snow experiment (E. Ramberg and G. Snow, Phys. Lett. B238, 438 (1990)); VIP has just completed the installation at the Gran Sasso underground laboratory, and aims to test the Pauli Exclusion Principle for electrons with unprecedented accuracy, down to β2/2 ≈ 10-30 - 10-31. We report preliminary experimental results and briefly discuss some of the implications of a possible violation.

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