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Recent experiments on sound waves in a unitary Fermi gas reveal many transport properties about strongly interacting fermions. Sound propagates through the coupling of momentum and heat transport, and attenuates strongly with the presence of a phase transition. In this work, focusing on the temperature regimes near and below the superfluid critical temperature $$T_c$$ T c in the BCS-BEC crossover, we present a Kubo-based microscopic calculation of thermal conductivity $$\kappa$$ κ , which has not attracted much attention compared to the shear viscosity. Our approach primarily addresses the contributions of the fermionic quasiparticles to thermal transport and our results return to the kinetic descriptions at high temperatures. $$\kappa$$ κ drops upon crossing the pseudogap temperature $$T^*$$ T ∗ , and its temperature dependence changes below $$T_c$$ T c . The drops become more pronounced on the weakly coupled BCS side, where the Pauli blocking causes the upturn of $$\kappa$$ κ above $$T^*$$ T ∗ . Our calculations fit well with the sound measurement on the damping rate.

An assumption that all the six flavour quarks are attributed to be the components of a same, a common isospin multiplets space named STS is proposed. Base on Pauli Exclusion Principle, every quark is assigned to different flavour marks in STS. Every flavour quark possesses its own colour spectral line array specially appointed. The collection of colour spectral line arrays of the six flavour quarks constructs together the CSDF, Colour Spectrum Diagram of Flavour, further baryons and mesons could be constructed from CSDF. STS, Spin Topological Space is a math frame with infinite dimensional matrix representation for spin angular momentum. Flavours is an isospin angular momentum coupling phenomena of the three-colour-quarks.

The mechanism and origin of stereoselectivity of silver-catalyzed hydroalkylation of alkynes were computationally investigated at the B3LYP-D3BJ/6-311+G(d,p)-SDD//B3LYP/6-31G(d)-LANL2DZ level. The complex of alkynyl trialkylboronate with cationic silver is a key intermediate, which triggers the rate- and stereoselectivity-determining 1,2-migration step. Energy decomposition analysis indicates that the difference of Pauli repulsion dominates the stereoselectivity.

In this paper we study the quantum graphs of mixed-unitary channels generated by tensor products of Pauli operators, which we call Pauli channels. We show that most quantum graphs arising from Pauli channels have non-trivial quantum cliques or quantum anticliques which are stabilizer codes. However, a reformulation of Nik Weaver's quantum Ramsey theorem in terms of stabilizer codes and Pauli channels fails. Specifically, for every positive integer $n$, there exists an $n$-qubit Pauli channel for which any non-trivial quantum clique or quantum anticlique fails to be a stabilizer code., 11 pages, final version. To appear in IEEE Transactions on Information Theory

Cage-like metal nanoclusters are rarely found due to the densely packed property of metals. Recently, single crystallography has unraveled for the first time that multi-shell golden cages are formed in large-size thiolate (SR) and alkynl (CCR) protected neutral Au144 nanoclusters, denoted as Au144(SR)60 and Au144(CCR)60. In this study, the origin of the structural stability of golden cage Au144 clusters is studied based on the density functional theory (DFT) energy calculation and energy decomposition analysis (EDA). The formation of hollow cages rather than centre-filled icosahedrons in the Au144 clusters is attributed to the significant Pauli repulsion between the central gold atom and the surrounding metal shell, which leads to the decrease of the averaged formation energy of the clusters. The present study also shows that the Au144 cluster is unique in size. The smaller size clusters Au133 and Au130 and the larger size cluster Au279 both preferred the centre-filled golden icosahedrons, decahedrons or octahedrons.

This paper presents a new bidirectional quantum teleportation (BQT) protocol in which users can simultaneously transmit an arbitrary number of particles to each other via a four-qubit cluster state as quantum channel. With the use of auxiliary qubits and controlled-not gates, transformation circuits are introduced which transform n-qubit states into single superposition state and then teleport them over the channel by using Bell-state measurement and applying a proper Pauli operator. At last, with the aid of another transformation circuit, the initial states can be reconstructed. With this method, the BQT purpose is realized more advantageous compared to recent presented protocols.

In this work, the 2s+2s (face-to-face) prototypical example of a photochemical reaction has been re-examined to characterize the evolution of chemical bonding. The analysis of the electron localization function (as an indirect measure of the Pauli principle) along the minimum energy path provides strong evidence in support that CC bond formation occurs not in the excited state but at the ground electronic state after crossing the rhombohedral S1/S0 conical intersection.

Paramagnetism and diamagnetism of a material characterized by its magnetic susceptibility. When a material is exposed to an external magnetic field, magnetic susceptibility is defined as the ratio of the induced magnetization and the magnetic field. A paramagnetic material has magnetic susceptibility with positive sign. On the other hand, a diamagnetic material has magnetic susceptibility with negative sign. Atomically, paramagnetic materials consist of atoms that has orbital with unpaired electrons. Theoretical study of paramagnetic susceptibility and diamagnetic susceptibility are well described by Pauli paramagnetism and Landau diamagnetism, respectively. Although paramagnetism and diamagnetism are among the simplest magnetic properties of material that are studied in basic physics, theoretical derivations of Pauli paramagnetic and Landau diamagnetic susceptibility require second quantization formalism of quantum mechanics. We aim to discuss the paramagnetic and diamagnetic susceptibilities for simple three-dimensional quantum well using first quantization formalism.

Binding energies of the CH3O radical on hexagonal water ice (Ih) and amorphous solid water (ASW) were calculated using the ONIOM(QM:MM) method. A range of binding energies is found (0.10-0.50 eV), and the average binding energy is 0.32 eV. The CH3O radical binding on the ASW surfaces is stronger than on the Ih surfaces. The computed binding energies from the ONIOM(wB97X-D/def2-TZVP:AMBER) and wB97X-D/def2-TZVP methods agree quite well. Therefore, the ONIOM(QM:MM) method is expected to give accurate binding energies at a low computational cost. Binding energies from the ONIOM(wB97X-D/def2-TZVP:AMBER) and ONIOM(wB97X-D/def2-TZVP:AMOEBA09) methods differ noticeably, indicating that the choice of force field matters. According to the energy decomposition analysis, the electrostatic interactions and Pauli repulsions between the CH3O radical and ice play a crucial role in the binding energy. This study gives quantitative insights into the CH3O radical binding on interstellar ices.

Indefinite causal order has introduced disruptive procedures to improve the fidelity of quantum communication by introducing the superposition of { orders} on a set of quantum channels. It has been applied to several well characterized quantum channels as depolarizing, dephasing and teleportation. This work analyses the behavior of a parametric quantum channel for single qubits expressed in the form of Pauli channels. Combinatorics lets to obtain affordable formulas for the analysis of the output state of the channel when it goes through a certain imperfect quantum communication channel when it is deployed as a redundant application of it under indefinite causal order. In addition, the process exploits post-measurement on the associated control to select certain components of transmission. Then, the fidelity of such outputs is analysed to characterize the generic channel in terms of its parameters. As a result, we get notable enhancement in the transmission of information for well characterized channels due to the combined process: indefinite causal order plus post-measurement.

The modern state of the Pauli Exclusion Principle (PEP) is discussed. PEP can be considered from two viewpoints. On the one hand, it asserts that particles with half-integer spin (fermions) are described by antisymmetric wave functions, and particles with integer spin (bosons) are described by symmetric wave functions. This is the so-called spin-statistics connection (SSC). As we will discuss, the physical reasons why SSC exists are still unknown. On the other hand, according to PEP, the permutation symmetry of the total wave functions can be only of two types: symmetric or antisymmetric, both belong to one-dimensional representations of the permutation group, all other types of permutation symmetry are forbidden; whereas the solution of the Schrodinger equation may have any permutation symmetry. It is demonstrated that the proof in some textbooks on quantum mechanics that only symmetric and antisymmetric states can exist is wrong. However, the scenarios, in which arbitrary permutation symmetry (degenerate permutation states) is permitted, lead to contradictions with the concepts of particle identity and their independence. Thus, the existence in our Nature of particles only in nondegenerate permutation states (symmetric and antisymmetric) is not accidental and so-called symmetrization postulate should not be considered as a postulate, since all other symmetry options for the total wave function may not be realized. From this an important conclusion follows: we may not expect that in the future some unknown elementary particles can be discovered that are not fermions or bosons.

We investigate the propagation characteristics of nonlinear kinetic Alfven waves in quantum plasma with effects of Pauli paramagnetism and degeneracy temperature. In an arbitrary amplitude regime, we derive the energy integral equation by employing the quantum magnetohydrodynamic model. From the graphical analysis, it is found that the width of soliton structure decreases by enhancing the value of factor $$\chi \left[ =T_\mathrm{e}/T_\mathrm{F}\right] $$ for nearly degenerate plasma state and increases by increasing the value of factor $$z\left[ =\exp (\mu /k_\mathrm{B}T_\mathrm{e})\right] $$ for nearly non-degenerate plasma state, while there is no change in its amplitude. Moreover, it is also revealed that by changing the value of magnetic field strength H the width of the nonlinear structure is modified more in case of nearly degenerate plasma state as compared to a nearly non-degenerate plasma state with no change in its amplitude. The importance of the present work to astrophysical plasmas such as white dwarfs and neutron stars is also highlighted.

Proceedings of the National Academy of Sciences of the United States of America 117(48), 30220 - 30227 (2020). doi:10.1073/pnas.2005701117, Using inelastic X-ray scattering beyond the dipole limit and hard X-ray photoelectron spectroscopy we establish the dual nature of the U 5f electrons in UM$_2$Si$_2$ (M = Pd, Ni, Ru, Fe), regardless of their degree of delocalization. We have observed that the compounds have in common a local atomic-like state that is well described by the U 5f$^2$ configuration with the $Γ^{(1)}_1$ and $Γ_2$ quasi-doublet symmetry. The amount of the U 5f$^3$ configuration, however, varies considerably across the UM$_2$Si$_2$ series, indicating an increase of U 5f itineracy in going from M = Pd to Ni to Ru and to the Fe compound. The identified electronic states explain the formation of the very large ordered magnetic moments in UPd$_2$Si$_2$ and UNi$_2$Si$_2$, the availability of orbital degrees of freedom needed for the hidden order in URu2Si2 to occur, as well as the appearance of Pauli paramagnetism in UFe$_2$Si$_2$. A unified and systematic picture of the UM$_2$Si$_2$ compounds may now be drawn, thereby providing suggestions for additional experiments to induce hidden order and/or superconductivity in U compounds with the tetragonal body-centered ThCr$_2$Si$_2$ structure., Published by National Acad. of Sciences, Washington, DC

Electric quadrupole $$\gamma$$ -ray transition energies $$E_{\gamma}$$ , rotational frequencies $$\hbar\omega$$ and dynamic $$J^{(2)}$$ and kinematic $$J^{(1)}$$ moments of inertia have been calculated for yrast and excited superdeformed (SD) bands in Hg, Tl, Pb isotonic ( $$N=113$$ ) nuclei by using two-parameter power-law formula. The model parameters and the bandhead spins were determined using a $$\chi^{2}$$ fit by random minimization via Monte Carlo simulation technique with a uniform distribution of random numbers. The calculated results of $$E_{\gamma}$$ agreed with the experimental data published in National Nuclear Data Center (nndc) very well, and present assigned spins of the studied superdeformed rotational bands (SDRB’s) are consistent with the spins suggested by other previous formulae. The majority of the studied SD bands displayed the same large, smooth increase in $$J^{(2)}$$ by increasing $$\hbar\omega$$ . A saturation of $$J^{(2)}$$ at higher values of $$\hbar\omega$$ was observed for the two bands (1, 2) in $${}^{195}$$ Pb due to the Pauli blocking of the quasineutron alignment in the presence of quasiproton alignment. The studied SD bands exhibited staggering in their transition energies. Five pairs of signature partner SDRBs exhibited an $$\Delta I=1$$ staggering effect in their transition energies, namely $${}^{193}$$ Hg (SD1, SD2), $${}^{193}$$ Hg (SD3, SD4), $${}^{194}$$ Tl (SD1, SD2), $${}^{195}$$ Pb (SD1, SD2), and $${}^{195}$$ Pb (SD3, SD4). To investigate this $$\Delta I=1$$ staggering, we extracted the difference between the average transition $$I+2\to I$$ and $$I\to I-2$$ energies in one band and the transition $$I+1\to I-1$$ energies in the signature partner. Also, a $$\Delta I=2$$ staggering exists in three SD bands of odd–odd $${}^{194}$$ Tl. This $$\Delta I=2$$ staggering effect was determined by calculating the energy difference between two consecutive $$\gamma$$ -ray transitions as a function of rotational frequency after subtracting a smooth reference expressed in the notation of Cederwall.

The Clar Goblet, the first radical bowtie nanographene proposed by Erich Clar nearly 50 years ago, was recently synthesized. Bowtie nanographenes present quasi-degenerate magnetic ground states which make them so elusive as unique. We present a thorough analysis of the spin states energetics of Clar Goblet and bowtie nanographenes by a battery of existing and novel ab initio procedures ranging from density functional theory to complete active space Hamiltonians. With this, we prove that π radicals of bowtie nanographenes sit on BP (Benzo[cd]Pyrene) moieties driven by their local aromaticity, a purely chemical concept, which confers global stability to the whole structure. Besides, we present a novel Pauli energy densities analysis providing a visual intuitive explanation for this preference. These findings allow envisioning that analogous bowtie nanographenes with arbitrary polyradical character are not only feasible at the molecular scale but that will share Clar Goblet's peculiar properties.

The relativistic wave equation is well-known for a spin 3/2 particle proposed by W. E. Pauli and M. E. Fierz and based on the 16-component wave function with the transformation properties of the vector-bispinor. In this paper, we investigated the nonrelativistic approximation in this theory. Starting with the first-order equation formalism and representation of Pauli – Fierz equation in the Petras basis, also applying the method of generalized Kronecker symbols and elements of the complete matrix algebras, and decomposing the wave function into large and small nonrelativistic constituents with the help of projective operators, we have derived a Pauli-like equation for the 4-component wave function describing the non-relativistic particle with a 3/2 spin.

In the frame of the general Gel’fand – Yaglom formalism, the Fradkin theory for a spin 3/2 particle in presence of external fields is investigated. Applying the standard requirements of relativistic invariance, P-symmetry, existence of a Lagrangian for the model, we derive a set of spinor equations, first in absence of external fields. The wave function consists of a bispinor and a vector-bispinor. It is shown that in absence of external fields the Fradkin model is reduced to the Pauli – Fierz theory. Taking into account the presence of external electromagnetic fields, the Fradkin theory can be turned to the minimal form of the equation for the main bispinor. This equation contains an additional interaction term governed by the electromagnetic tensor F αβ . Meanwhile, there appears a parameter in the Fradkin equation related to any characteristic of the particle additional to its charge. The theory is generalized for taking into account the pseudo-Riemannian space-time geometry. In this case, the Fradkin equation contains an additional interaction term, governed by the Ricci tensor R αβ . If the electric charge of the particle is zero, the Fradkin model remains correct and describes a neutral spin 3/2 particle of the Majorana type interacting nonminimally with the geometrical background through the Ricci tensor. To clarify the meaning of the additional physical characteristics underlying the Fradkin model in contrast to the Pauli – Fierz one we have considered nonrelativistic approximation for both theories in presence of an external uniform magnetic field, and found respective energy spectra. The structure of the ninrelativistic Fradkin equation permits to consider such an additional parameter as polarizability.

We start with a brief classical description of the hydrogen atom including a supplementary section that reveals the hidden symmetry responsible in part for the incredibly simple structure of the energy spectrum of the hydrogen atom. Niel’s Bohr’s simple but incorrect derivation of the energy spectrum of the Hydrogen atom is then described. Although his derivation was flawed it led to the correct energy spectrum which in turn reproduces the observed emission and absorption spectrum of the hydrogen atom. We provide the correct derivation of the stationary states and corresponding energy spectrum of the Hydrogen atom by solving the full three dimensional time independent Schrodinger equation. This would be a very difficult task without invoking symmetry to simplify the equations. Using the Pauli exclusion principle for the electron states and applying key properties of these solutions to Hydrogen-like atoms that have many protons and electrons, we can account qualitatively for the chemical structure of the elements in the periodic table. It is quite remarkable that many important features of chemistry can be explained using just fundamental physics and symmetry!

Polymer self-consistent field theory techniques are used to find radial electron densities and total binding energies for isolated atoms. Quantum particles are modelled as Gaussian threads with ring-polymer architecture in a four dimensional thermal-space, and a Pauli potential is postulated based on classical excluded volume implemented in the thermal-space using Edwards/Flory-Huggins interactions in a mean-field approximation. Other approximations include a Fermi-Amaldi correction for electron-electron self-interactions, a spherical averaging approximation to reduce the dimensionality of the problem, and the neglect of correlations. Polymer scaling theory is used to show that the excluded volume form of Pauli potential reduces to the known Thomas-Fermi energy density in the uniform limit. Self-consistent equations are solved using a bilinear Fourier expansion, with radial basis functions, for the first eighteen elements of the periodic table. Radial electron densities show correct shell structure, and the errors on the total binding energies compared to known binding energies are less than 9% for the lightest elements and drop to 3% or less for atoms heavier than nitrogen. More generally, it is suggested that only two postulates are needed within classical statistical mechanics to achieve equivalency of predictions with static, non-relativistic quantum mechanics: First, quantum particles are modelled as Gaussian threads in four dimensional thermal-space and, second, pairs of threads (allowing for spin) are subject to classical excluded volume in the thermal-space. It is shown that these two postulates in thermal-space become the same as the Heisenberg uncertainty principle and the Pauli exclusion principle in three dimensional space., Comment: 23 pages, 3 figures, 1 table