Pauli Principle Research Articles

LDOS of electron pair and the role of the Pauli exclusion principle.

The local density of states (LDOS) for a pair of non-relativistic electrons, influenced by repulsive Coulomb forces, is expressed in term of one-dimensional integrals over Whittaker functions. The computation of the electron pair's LDOS relies on a two-particle Green's function (GF), a generalization of the one-particle GF applicable to a charged particle in an attractive Coulomb potential. By incorporating electron spins and considering the Pauli exclusion principle, the resulting LDOS consists of two components: one originating from an exchange-even two-particle GF and the other from an exchange-odd two-particle GF. The calculated LDOS reveals its dependence on both inter-electron distance and energy. The pseudo-LDOS, derived from the two-body contribution to the LDOS, is examined. This term ensures complete LDOS suppression at r = 0, exhibiting a limited spatial extent, and the reasons for its emergence are elucidated. It is shown that for energies exceeding the effective Hartree energy and inter-electron distances beyond the effective Bohr radius, the impact of manybody contributions to the LDOS can be disregarded. The induced LDOS for an electron pair subjected to an attractive contact potential in two dimensions is evaluated. At small distances a from the potential center, a predicted relative difference in LDOS between even and odd state pair reaches approximately 8%. The calculated LDOS is compared with available experimental findings from a two-dimensional electron gas (2DEG). Both exhibit similar oscillation periods; however, the LDOS of the electron pair decays as 1/a3, significantly faster than the 1/a decay observed for free electrons in a 2DEG.&#xD.

Spin–orbit enabled unconventional Stoner magnetism

The Stoner instability remains a cornerstone for understanding metallic ferromagnets. This instability captures the interplay of Coulomb repulsion, Pauli exclusion, and twofold fermionic spin degeneracy. In materials with spin-orbit coupling, this fermionic spin is generalized to a twofold degenerate pseudospin which is typically believed to have symmetry properties as spin. Here, we identify a distinct symmetry of this pseudospin that forbids it to couple to a Zeeman field. This "spinless" property is required to exist in five nonsymmorphic space groups and has nontrivial implications for superconductivity and magnetism. With Coulomb repulsion, Fermi surfaces composed primarily of this spinless pseudospin property give rise to Stoner instabilities into magnetic states that are qualitatively different than ferromagnets. These spinless-pseudospin ferromagnets break time-reversal symmetry, have a vanishing magnetization, are noncollinear, and exhibit momentum-dependent energy band spin-splittings. In superconductors, for all pairing symmetries and field orientations, this spinless pseudospin extinguishes paramagnetic limiting. We discuss applications to superconducting UCoGe and magnetic NiS[Formula: see text]Se[Formula: see text].

Preponderance of triaxial shapes in atomic nuclei predicted by the proxy-SU(3) symmetry

Abstract The proxy-SU(3) symmetry predicts, in a parameter-free way, based only on the Pauli principle and the short-range nature of the nucleon-nucleon interaction, non-vanishing values of the collective variable gamma almost everywhere across the nuclear chart. Substantial triaxiality with gamma between 15 and 45 degrees is proved to be expected along horizontal and vertical stripes on the nuclear chart, covering the nucleon numbers 22-26, 34-48, 74-80, 116-124, 172-182. Empirical support for these stripes is found by collecting all even-even nuclei for which the first two excited 2+ states are known, along with the B(E2)s connecting them, as well as the second 2+ state to the ground state. The stripes are related to regions in which oblate SU(3) irreducible representations appear, bearing similarity to the appearance of triaxiality within the SU(3)* dynamical symmetry of the interacting boson model-2. Detailed comparisons of the proxy-SU(3) predictions to the data and to predictions by state-of-the-art Monte Carlo shell model calculations for deformed N=94, 96, 98 isotones in the rare earth region show good overall agreement, with the exception of Z=70 and N=94, which correspond to fully symmetric proxy-SU(3) irreps, suggesting that the latter are an artifact of the method which can be amended by considering the influence of the neighboring irreps.

Search for Pauli Exclusion Principle violations with Gator at LNGS

The Pauli Exclusion Principle (PEP) appears from fundamental symmetries in quantum field theories, but its physical origin is still to be understood. High-precision experimental searches for small PEP violations permit testing key assumptions of the Standard Model with high sensitivity. We report on a dedicated measurement with Gator, a low-background, high-purity germanium detector operated at the Laboratori Nazionali del Gran Sasso, aimed at testing PEP-violating atomic transitions in lead. The experimental technique, relying on forming a new symmetry state by introducing electrons into the pre-existing electron system through a direct current, satisfies the conditions of the Messiah-Greenberg superselection rule. No PEP violation has been observed, and an upper limit on the PEP violation probability of β2/2<4.8·10-29\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta ^2/2 < 4.8 \\cdot 10^{-29}$$\\end{document} (90% CL) is set. This improves the previous constraint from a comparable measurement by more than one order of magnitude.

Quark Pauli principle and the transmutation of nuclear matter

Quark Pauli principle and the transmutation of nuclear matter

Two particles in one-dimensional confinement: the role of mass imbalance and Pauli's exclusion principle within short and long range interactions

Abstract We consider the problem of two interacting particles in one-dimensional harmonic confinement. By considering both particles are subject to the same harmonic curvature, we obtain exact numerical solutions in a straightforward way for any choice of interaction potential. The formulation is then applied in the situations of ({\it i}) non-identical particles with different masses $m_1$ and $m_2$; ({\it ii}) bosons and fermions; ({\it iii}) short and long range interactions; and ({\it iv}) combining all these ingredients within a time-dependent applied electric field. We analyze the role of the mass imbalance and Pauli's exclusion principle by investigating the formation of bound pairs, the expected value of the separation between the particles and the effects of interaction and exclusion principle on the density distributions.

Fully polarized Fermi systems at finite temperature.

We propose a simple model of an interacting, fully spin-polarized Fermi gas in dimensions d=2 and d=3, and derive the approximate expression for the energy spectrum and the corresponding formula for the Helmholtz free energy. We analyze the thermodynamics of the system and find the lines of first-order phase transitions between the low- and high-density phases terminating at critical points. The properties of the corresponding phase diagrams are qualitatively different for d=2 and 3, and sensitively depend on the interparticle attraction, which marks a departure from the standard van der Waals theory. The differences originate from the Pauli exclusion principle and are embedded in the fermionic nature of the system under study.

Investigating Entropic Dynamics of Multiqubit Cavity QED System

AbstractEntropic dynamics of a multiqubit cavity quantum electrodynamics system is simulated and various aspects of entropy are explored. In the modified version of the Tavis–Cummings–Hubbard model, atoms are held in optical cavities through optical tweezers and can jump between different cavities through the tunneling effect. The interaction of atom with the cavity results in different electronic transitions and the creation and annihilation of corresponding types of photon. Electron spin and the Pauli exclusion principle are considered. Formation and break of covalent bond and creation and annihilation of phonon are also introduced into the model. The system is bipartite. The effect of all kinds of interactions on entropy is studied. And the von Neumann entropy of different subsystems is compared. The results show that the entropic dynamics can be controlled by selectively choosing system parameters, and the entropy values of different subsystems satisfy certain inequality relationships.

Pauli Exclusion by n→π* Interactions: Implications for Paleobiology.

Proteins have evolved to function in an aqueous environment. Collagen, which provides the bodily scaffold for animals, has a special need to retain its integrity. This need was addressed early on, as intact collagen has been detected in dinosaur fossils, even though peptide bonds have a half-life of only ∼500 years in a neutral aqueous solution. We sought to discover the physicochemical basis for this remarkable resistance to hydrolysis. Using experimental and computational methods, we found that a main-chain acyl group can be protected from hydrolysis by an O···C=O n→π* interaction with a neighboring acyl group. These interactions engage virtually every peptide bond in a collagen triple helix. This protection, which arises from the Pauli exclusion principle, could underlie the preservation of ancient collagen.

Testing the Pauli Exclusion Principle across the Periodic Table with the VIP-3 Experiment.

The Pauli exclusion principle (PEP), a cornerstone of quantum mechanics and whole science, states that in a system, two fermions can not simultaneously occupy the same quantum state. Several experimental tests have been performed to place increasingly stringent bounds on the validity of PEP. Among these, the series of VIP experiments, performed at the Gran Sasso Underground National Laboratory of INFN, is searching for PEP-violating atomic X-ray transitions in copper. In this paper, the upgraded VIP-3 setup is described, designed to extend these investigations to higher-Z elements such as zirconium, silver, palladium, and tin. We detail the enhanced design of this setup, including the implementation of cutting-edge, 1 mm thick, silicon drift detectors, which significantly improve the measurement sensitivity at higher energies. Additionally, we present calculations of expected PEP-violating energy shifts in the characteristic lines of these elements, performed using the multi-configurational Dirac-Fock method from first principles. The VIP-3 realization will contribute to ongoing research into PEP violation for different elements, offering new insights and directions for future studies.

Influence of a static electric field on a one-dimensional Bose-Fermi mixture confined in a double-well potential

In this study, we conducted a detailed investigation into the time evolution of the probability density within a 1D double-well potential hosting a Bose-Fermi mixture. This system comprised spinless bosons and spin one-half fermions with weak repulsive contact interactions. Notably, even at very low effective coupling constants, periodic probabilities were observed, indicating correlated tunneling of both bosons and fermions, leading to complete miscibility, which disappears when an external electric field is turned on. The electric field accentuated fermion-fermion interactions due to the Pauli exclusion principle, altering both boson density and interactions and leading to spatial redistribution of particles. These findings underscore the complex interplay between interactions, external fields, and spatial distributions within confined quantum systems. Our exploration of higher interaction strengths revealed conditions under which probability density functions are decoupled. Furthermore, we observed that increased fermion interaction, driven by the electric field, led to higher tunneling frequencies for both species because of the repulsive nature of the boson-fermion interaction. Conversely, increased boson-boson interaction resulted in complete tunneling of both species, especially when boson density was high, leading to effective fermion repulsion. Expanding our analysis to scenarios involving four bosons demonstrated that higher interaction values corresponded to increased oscillation frequencies in tunneling probabilities. Finally, by manipulating interaction parameters and activating the electric field, we achieved complete tunneling of both species, further increasing oscillation frequencies and resulting in intervals characterized by overlapping probability functions.

Comparison of pauling and Ulianov electron distribution models

This study presents a comprehensive comparison between the traditional Pauling electron distribution model and the innovative Ulianov model proposed by Dr. Policarpo Yoshin Ulianov. The Pauling model, which relies on the Aufbau principle, Hund’s rule, and the Pauli Exclusion Principle, has been a cornerstone in understanding electron configurations within atoms, organizing electrons into s, p, d, and f orbitals. In contrast, the Ulianov model introduces a novel linear progression for electron occupancy, proposing additional orbitals (g and h) to account for electron distribution in a manner that deviates from conventional methodologies. Through an analytical comparison, this paper evaluates both models in terms of functionality, energy levels, and methodology, highlighting the advantages and disadvantages inherent to each. The Pauling model is recognized for its empirical support and wide acceptance, offering a well-established framework for electron configuration. Meanwhile, the Ulianov model provides a fresh perspective that could potentially explain anomalies unaddressed by the Pauling model and predict new chemical properties, despite its current lack of empirical validation. Concluding, while the Pauling model remains the standard for electron configuration, the Ulianov model’s innovative approach challenges existing paradigms and invites further investigation into its validity and potential applications in the scientific community.

Beyond isotropic repulsion: Classical anisotropic repulsion by inclusion of p orbitals.

Accurate modeling of intermolecular repulsion is an integral component in force field development. Although repulsion can be explicitly calculated by applying the Pauli exclusion principle, this approach is computationally viable only for systems of limited sizes. Instead, it has previously been shown that repulsion can be reformulated in a "classical" picture: the Pauli exclusion principle prohibits electrons from occupying the same state, leading to a depletion of electronic charge between atoms, giving rise to an enhanced nuclear-nuclear electrostatic repulsion. This classical picture is called the isotropic S2/R approximation, where S is the overlap and R is the interatomic distance. This approximation accurately captures the repulsion of isotropic atoms such as noble gas dimers; however, a key deficiency is that it fails to capture the angular dependence of the repulsion of anisotropic molecules. To include directionality, the wave function must at least be a linear combination of s and p orbitals. We derive a new anisotropic S2/R repulsion model through the inclusion of the anisotropic p orbital term in the total wave function. Because repulsion is pairwise and decays rapidly, it can be truncated at a short range, making it amenable for efficient calculation of energy and forces in complex biomolecular systems. We present a parameterization of the S101 dimer database against the abinitio benchmark symmetry-adapted perturbation theory, which yields an rms error of only 0.9 kcal/mol. The importance of the anisotropic term is demonstrated through angular scans of water-water dimers and dimers involving halobenzene. Simulation of liquid water shows that the model can be computed efficiently for realistic system sizes.

Reimagining and reinterpreting Cooper pairs, the Fermi sea, Pauli blocking and superfluidity: The Pauli principle in collective motion

Identifying possible microscopic mechanisms underlying superfluidity has been the goal of various studies since the introduction of the original BCS theory. Recently a series of papers have proposed microscopic dynamics based on normal modes to describe superfluidity without the use of real-space Cooper pairs. Multiple properties were determined with excellent agreement with experimental data. The group theoretic basis of this general N-body approach has allowed the microscopic behavior underlying these results to be analyzed in detail. This reimagination is now used to reinterpret several interrelated phenomena including Cooper pairs, the Fermi sea, and Pauli blocking. This approach adheres closely to the early tenets of superconductivity/superfluidity which assumed pairing only in momentum space, not in real space. The Pauli principle is used, in its recently revealed role in collective motion, to select the allowed normal modes. The expected properties of superfluidity including the rigidity of the wave function, interactions between the fermions in different pairs, convergence of the momentum and the gap in the excitation spectrum are discussed.

Search for charge non-conservation and Pauli exclusion principle violation with the Majorana Demonstrator

Search for charge non-conservation and Pauli exclusion principle violation with the Majorana Demonstrator

N -body antibunching in a degenerate Fermi gas of He*3 atoms

A key set of observables for investigating quantum systems are the n-body correlation functions, which provide a powerful tool for experimentally determining coherence and directly probing the many-body wave function. While the (bosonic) correlations of photonic systems are well explored, the correlations present in matter-wave systems, particularly for fermionic atoms, are still an emerging field. In this work, we use the unique single-atom detection properties of He*3 atoms to perform simultaneous measurements of the n-body quantum correlations, up to the fifth order, of a degenerate Fermi gas. In a direct demonstration of the Pauli exclusion principle, we observe clear antibunching at all orders and find good agreement with predicted correlation volumes. Our results pave the way for using correlation functions to probe some of the rich physics associated with fermionic systems. Published by the American Physical Society 2024

Presenting the Ulianov Electron Distribution Model: A New Way to Define Electronic Orbitals

This study presents a comprehensive comparison between the traditional Pauling electron distribution model and the innovative Ulianov model proposed by Dr. Policarpo Yoshin Ulianov. The Pauling model, which relies on the Aufbau principle, Hund’s rule, and the Pauli exclusion principle, has been a cornerstone in understanding electron configurations within atoms, organizing electrons into s, p, d, and f orbitals. In contrast, the Ulianov model introduces a novel linear progression for electron occupancy, proposing additional orbitals (g and h) to account for electron distribution in a manner that deviates from conventional methodologies. Through an analytical comparison, this paper evaluates both models in terms of functionality, energy levels, and methodology, highlighting the advantages and disadvantages inherent to each. The Pauling model is recognized for its empirical support and wide acceptance, offering a wellestablished framework for electron configuration. Meanwhile, the Ulianov model provides a fresh perspective that could potentially explain anomalies unaddressed by the Pauling model and predict new chemical properties, despite its current lack of empirical validation. Concluding, while the Pauling model remains the standard for electron configuration, the Ulianov model’s innovative approach challenges existing paradigms and invites further investigation into its validity and potential applications in the scientific community.

Bands renormalization and superconductivity in the strongly correlated Hubbard model using composite operators method

We use the composite operator method (COM) to analyze the strongly correlated repulsive Hubbard model, investigating the effect of nearest-neighbor hoppings up to fourth order on a square lattice. We consider two sets of self-consistent equations, one enforcing the Pauli principle and the other imposing charge-charge, spin-spin, and pair–pair correlations using a decoupling scheme developed by Roth (1969 Phys. Rev. 184 451–9). We extract three distinct solutions from these equations: COM1 and COM2 by imposing the Pauli principle and one from Roth decoupling. An overview of the method studying the validity of particle-hole symmetry and the Luttinger theorem for each solution is presented. Additionally, we extend the initial basis to study superconductivity, concluding that it is induced by the Van Hove singularity. Finally, we include higher-order hoppings using realistic estimates for tight binding parameters and compare our results with ARPES measurements on cuprates.

Quantum parameter estimation with many-body fermionic systems and application to the Hall effect

We calculate the quantum Fisher information for a generic many-body fermionic system in a pure state depending on a parameter. We discuss the situations where the parameter is imprinted in the basis states, in the state coefficients, or both. In the case where the parameter dependence of coefficients results from a Hamiltonian evolution, we derive a particularly simple expression for the quantum Fisher information. We apply our findings to the quantum Hall effect, and evaluate the quantum Fisher information associated with the optimal measurement of the magnetic field for a system in the ground state of the effective Hamiltonian. The occupation of electron states with high momentum enforced by the Pauli principle leads to a ``super-Heisenberg’’ scaling of the sensitivity with a power law that depends on the geometry of the sensor.

Collective non-Hermitian skin effect: point-gap topology and the doublon-holon excitations in non-reciprocal many-body systems

Open quantum systems provide a plethora of exotic topological phases of matter that have no Hermitian counterpart. Non-Hermitian skin effect, macroscopic collapse of bulk states to the boundary, has been extensively studied in various experimental platforms. However, it remains an open question whether such topological phases persist in the presence of many-body interactions. Previous studies have shown that the Pauli exclusion principle suppresses the skin effect. In this study, we present a counterexample by demonstrating the presence of the skin effect in doublon-holon excitations. While the ground state of the spin-half Hatano-Nelson model shows no skin effect, the doublon-holon pairs, as its collective excitations, display the many-body skin effect even in strong coupling limit. We establish the robustness of this effect by revealing a bulk-boundary correspondence mediated by the point gap topology within the many-body energy spectrum. Our findings underscore the existence of non-Hermitian topological phases in collective excitations of many-body interacting systems.