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The degree distribution of network nodes exhibits scale-free features, which is a universal phenomenon in natural and social networks. It is commonly believed that growth and linear preferential attachment are the evolutionary mechanisms of scaling laws. However, the underlying cause behind these mechanisms remains unknown. In this paper, we propose the concept of the topology state of network nodes, and then define the network homomorphism ratio. Combining the total energy of the network defined in previous studies, we systematically investigate the connection between these two quantities in preferential attachment growth networks. Our results show that under the thermodynamic limit condition, the emergence of the scaling laws of the preferential attachment growth network is dominated by two principles. One principle is that the homomorphism ratio gradually tends to zero as the network grows, and the other principle is that the total energy of the system is the lowest under the condition of satisfying principle one. Interestingly, these two principles of the network are similar to the arrangement rules of electrons outside the nucleus which dominated by the Pauli exclusion principle and the principle of minimum energy.

Due to the wide applications in consumer electronics, data storage systems and communication systems, cyclic codes have been an interesting research topic in coding theory. In this paper, let p be a prime with p ≥ 7 . We determine the Hamming distances of all repeated-root cyclic codes of length 5 p s over F q , where q = p m and both s and m are positive integers. Furthermore, we find all MDS cyclic codes of length 5 p s and take quantum synchronizable codes from repeated-root cyclic codes of length 5 p s . By comparing the minimum distances of 5 p s -length repeated-root cyclic codes to BCH codes of close lengths, we illustrated that quantum synchronizable codes constructed from repeated-root cyclic codes have in general better performance in correcting Pauli errors than those from BCH codes.

Revealing the distinction between rolling and sliding at the nanoscale is crucial for understanding the nanoscale tribology. To address this issue, we studied the rolling and sliding of single-walled carbon nanotubes (CNTs) on graphene using density functional theory augmented with many-body dispersion (MBD) forces method. We find that the motion of CNTs on graphene is changed from sliding to rolling with increasing the CNT radius, in which Pauli repulsion dominates rolling and MBD interactions dictate sliding. In addition, armchair CNTs always generate larger barriers than zigzag CNTs with similar radius regardless of rolling and sliding. These phenomena originate from the decay and fluctuations of charge density with respect to the distance between CNTs and graphene. Based on the potential corrugation of CNT motion on graphene, we also extend a model to capture the viscous friction of rolling and sliding with the experimental accuracy, providing a reasonable mechanistic picture for understanding the available experimental findings.

The classical uncertainty principle plays an important role in quantum mechanics, signal processing and applied mathematics. With the development of novel signal processing methods, the research of the related uncertainty principles has gradually been one of the most hottest research topics in modern signal processing community. In this paper, the weighted Heisenberg–Pauli–Weyl uncertainty principles for the linear canonical transform (LCT) have been investigated in detail. Firstly, the Plancherel–Parseval–Rayleigh identities associated with the LCT are derived. Secondly, the weighted Heisenberg–Pauli–Weyl uncertainty principles in the LCT domain are investigated based on the derived identities. The signals that can achieve the lower bound of the uncertainty principle are also obtained. The classical Heisenberg uncertainty principles in the Fourier transform (FT) domain are shown to be special cases of our achieved results. Thirdly, examples are provided to show that our weighted Heisenberg–Pauli–Weyl uncertainty principles are sharper than those in the existing literature. Finally, applications of the derived results in time frequency resolution analysis and signal energy concentrations are also analyzed and discussed in detail.

84 pags., 45 figs., 2 tabs., In this review are summarized about 20 years of theoretical research with applications in the field of many-body physics for strongly correlated fermions with Rowe's equation of motion (R-EOM) method and extended RPA equations. One major goal is to set up, via EOM, RPA equations with a correlated ground state. Since the correlations depend on the RPA amplitudes, it follows that RPA becomes a selfconsistency problem which is called Self-Consistent RPA (SCRPA). This then also improves very much the Pauli principle violated with standard RPA. The method was successfully applied to several non trivial problems, like the nuclear pairing Hamiltonian in the particle–particle channel (pp-RPA) and the Hubbard model of condensed matter. The SCRPA has several nice properties, as for instance, it can be formulated in such a way that all very appreciated qualities of standard RPA as, e.g., appearance of zero (Goldstone) modes in the case of broken symmetries, conservation laws, Ward identities, etc. are maintained. For the Goldstone mode an explicit example of a model case is presented. The formalism has its sound theoretical basis in the fact that an extension of the usual RPA operator has been found which exactly annihilates the Coupled Cluster Doubles (CCD) ground state wave function. This has been a longstanding problem for all RPA practitioners from the beginning. There exists a rather simplified version of SCRPA which is the so-called renormalized RPA (r-RPA) where only the correlated occupation numbers are involved in the selfconsistent cycle. Because its numerical solution is rather similar to standard RPA, it has known quite a number of applications, like beta and double beta decays, which are reviewed in this article. In this review also an extended version of second RPA (ERPA)is described. This ERPA maintains all appreciable properties of standard RPA. Several realistic applications for, e.g., the damping of giant resonances are presented. Another important aspect of the extended RPA-theories is that it can be formulated symmetry conserving replacing and eventually improving symmetry (e.g., number) projected mean field approaches. A practical application is given in the review. The EOM formalism allows to treat alpha clustering and alpha particle (quartet) condensation in nuclear matter. This EOM approach succeeded where earlier attempts have failed. It is, for instance, shown how the critical temperature for alpha particle condensation in symmetric and asymmetric nuclear matter can efficiently be calculated., D.S.D. was supported by the grant PN-18090101/2019–2021 of the Romanian Ministry of Education and Research, J.D. by the Spanish Ministerio de Ciencia, Innovacion y Universidades and the European regional development fund (FEDER), Project No. PGC2018-094180-B-I00, G.R. by the German Research Foundation (DFG), Grant No. RO905/38-1, and E.L. by the US-NSF Career Grant PHY-1654379.

We incorporate the nuclear medium effect into α-decay calculation through a reformulation of the conventional double-folding model. The improved model enables the α cluster to simultaneously change its size at different nuclear density during the Coulomb penetration process, thus reflecting the effect from the variation of nuclear mean field and Pauli blocking at the nuclear surface. To evaluate the result of such a dynamic effect, we perform a systematic calculation of α-decay half-lives for even-even α-emitters within a deformed cluster model. We found that the medium effect optimises the shape of α-nucleus potential at the surface region, leading to a remarkable reduction in the deviations between the theoretical and experimental decay rates. The result implies the importance of the dynamic aspect of α clustering in describing a realistic α-nucleus interaction. Keywords: α decay, Half-life, Nuclear medium effect, α clustering, α-preformation factor

We study quantum processes, as one parameter families of differentiable completely positive and trace preserving (CPTP) maps. Using different representations of the generator, and the Sylvester criterion for positive semi-definite matrices, we obtain conditions for the divisibility of the process into completely positive (CP-divisibility) and positive (P-divisibility) infinitesimal maps. Both concepts are directly related to the definition of quantum non-Markovianity. For the single qubit case we show that CP- and P-divisibility only depend on the dissipation matrix in the master equation form of the generator. We then discuss three classes of processes where the criteria for the different types of divisibility result in simple geometric inequalities, among these the class of non-unital anisotropic Pauli channels., Comment: 12 pages, 4 figures

We adopt the perspective of similarity equivalence, in gate set tomography called the gauge, to analyze various properties of quantum operations belonging to a semigroup, $\Phi= e^{{\cal L}t}$,and therefore given through the Lindblad operator. We first observe that the non unital part of the channel decouples from the time evolution. Focusing on unital operations we restrict our attention to the single-qubit case, showing that the semigroup embedded inside the tetrahedron of Pauli channels is bounded by the surface composed of product probability vectors and includes the identity map together with the maximally depolarizing channel. Consequently, every member of the Pauli semigroup is unitarily equivalent to a unistochastic map, describing a coupling with one-qubit environment initially in the maximally mixed state, determined by a unitary matrix of order four., Comment: 10 pages, 2 figures

Spin-dependent transport through a spin valve consisting of two large-spin molecules, such as single molecular magnets, weakly coupled to external ferromagnetic electrodes is theoretically studied. The main focus is on the dependence of the tunneling current, its spin polarization, differential conductance and tunnel magnetoresistance on the arrangement of molecules embedded in the tunnel junction. These quantities are calculated by using the real-time diagrammatic technique in the lowest-order perturbation theory with respect to the coupling strength. When the molecules’ geometry is parallel, both an enhanced as well as inverse tunnel magnetoresistance can develop depending on the molecule’s occupation. On the other hand, if the two molecules form a serial geometry, a strong current-suppression occurs due to the Pauli spin blockade effect, resulting in negative differential conductance. In this transport regime we also find large tunnel magnetoresistance, which now exhibits strong asymmetry with respect to the bias voltage reversal. In addition, we show that an enhanced magnetoresistance and negative differential conductance can develop when a T-shaped molecular geometry is taken under consideration. These effects are explained by invoking particular occupation of molecular states and nonequilibrium spin accumulation that builds up in the case of the antiparallel magnetic configuration of the device.

The non-interacting kinetic energy is divided into the von Weizsacker term and the Pauli kinetic energy. Whereas the von Weizsacker energy is known in terms of the density, the Pauli kinetic energy is not. Consequently, its functional derivative can only be determined formally, at the solution point, from a given set of Kohn-Sham eigenfunctions. Since in a practical calculation the solution point is never reached exactly, the formal functional derivative is evaluated only in proximity of the solution point. Therefore, bifunctional expressions involving the corresponding potential are approximate. In this study the atoms from H - Xe are examined, showing that the energy deviation between the bifunctional expression and the orbital-based kinetic energy density is of a few hundred millihartrees for a quadruple basis set, while it can reach the order of a few hartrees when employing basis sets of less quality.

We study the magnon-charged impurity interaction effects on the magnonic heat capacity (MHC) and the Pauli magnetic susceptibility (PMS) of spin-1/2 and spin-3/2 Lieb lattice within the J 1 - J 2 Heisenberg model in the presence of the Dzyaloshinskii-Moriya interaction (DMI) and the Zeeman magnetic field. In so doing, we use the Green’s function technique and the full self-consistent Born approximation. We found that in the case of J 1 Heisenberg model, the MHC and PMS increase (decrease) with impurity concentration for spin-1/2 (spin-3/2), while oscillate (decrease) when coupling constants next-nearest-neighbor (NNN), DMI, and the Zeeman field are taken into account. We have also investigated perturbed MHC and PMS by ascertained impurity for different coupling strengths, resulting in the oscillating (decreasing) behavior with NNN for spin-1/2 (spin-3/2) and a decreasing behavior with DMI and Zeeman magnetic field for both spin-1/2 and spin-3/2. Moreover, magnetic phase transitions in the case of spin-3/2 are established when tuning coupling constants on the non-zero, whilst no magnetic phase transition is observed for spin-1/2 Lieb lattice. Our findings are useful to tune the physical properties of optical lattices subjected to the electric field, magnetic field, and charged impurity.

A comparative study of pairwise quantum coherence, quantum and classical correlations is addressed for non-nearest spin pairs of the 1D Heisenberg spin-$\frac{1}{2}$ XX chain. Following the Jordan-Wigner mapping, we diagonalise the hamiltonian of the chain and we check this procedure numerically as well. Using the "Pauli basis expansion" formalism we get the pairwise quantities studied in this work at any distance. We then, show the role of quantum correlations in revealing quantum phase transitions, the robustness of quantum discord to the temperature and the dominance of quantum correlations over their classical counterpart in the magnetic and thermal interval in quantum spin chains. We conclude the paper by shedding light from a resource-driven point of view on the new born quantity "quantum coherence" where we discuss its role in detecting quantum phase transitions being a long-range quantity, and how it outclasses the usual quantum correlations measures in the robustness against the temperature, which indicates potential uses in the framework of quantum information processing., 14 pages, 9 figures

In this study, within a two-band tight-binding Harrison Hamiltonian and the Green’s function approach, the influences of both localized σ and delocalized π electrons on the Pauli paramagnetic susceptibility, heat capacity and density of states of armchair graphene nanoribbons with different widths are investigated. Temperature dependence of the paramagnetic susceptibility and electronic heat capacity are compared for s and p orbitals of every width. In the density of states, an extension in the bandwidth and the extra number of Van-Hove singularities are observed. More importantly, a paramagnetic behavior associated with the π electrons could take place. Finally, a Schottky anomaly for the heat capacity is reported. Overall, in this paper, it was observed that both the σ and the π electrons contribute significantly to the aforementioned quantities.

We propose a spin-sensitive scanning probe microscopy experiment on double quantum dots in Pauli blockade conditions. Electric spin resonance is induced by an AC voltage applied to the scanning gate which causes lifting of the Pauli blockade of the current. The stationary Hamiltonian eigenstates are used as a basis for description of the spin dynamics with the AC potential of the probe. For the two-electron system we evaluate the transition rates from triplet T+ state to singlet S or triplet T0 states, i.e. to conditions in which the Pauli blockade of the current is lifted. The rates of the spin-flip transitions are consistent with the transition matrix elements and strongly dependent on the tip position. Probing the spin densities and identification of the final transition state are discussed.

For the last years, there has been growing interest in the band gap study of 2D heterostructures due to high expectations of developing a new generation of electronic devices. In this work, using density functional theory the structural and electronic properties of several bi, tri, tetra and pentalayers of 2D graphene/hexagonal boron nitride (G/hBN) vertical heterostructures have been studied. We compared the results with the bulk (graphite, hBN) and monolayer structures (graphene, hBN). It is found that the graphene band gap can be changed from 0 to 114 meV and is sensitive to the number and configuration of graphene and hBN layers. We attribute the band gap opening in 2D heterostructures G/hBN to the decrease of the overlap for the p z orbitals in graphene, due to the Pauli repulsion.

We study configurations maximizing N-particle probability distributions of non-interacting particles obeying Fermi statistics as discussed in [1] . We consider two different types of particles' confinement: (i) trapping in a harmonic potential and (ii) constraining to the surface of a sphere. In such settings the most probable arrangements of particles correspond to characteristic geometric patterns resulting from the combined effect of confinement and the Pauli exclusion principle. We discus the geometry of these optimal configurations as well as two different methods of extracting these shapes from a number of single shot pictures of the system. The post-selection method which does not assume a priori any information on the optimal configurations is illustrated in detail.

In an influential paper, Fang (Public Choice 112: 351–371, 2002) asserts that the exclusion principle discovered by Baye et al. (1993) for all-pay auction does not apply to lottery in the case in which an organizer cares about the aggregate effort. Serena (2017) shows that the exclusion principle still applies to lottery with (sufficiently) homogeneous contestants if the organizer only cares about the effort of the winner. In this paper, we consider a Tullock lottery contest in which contestants' types are binary and stochastic and the two types are significantly different. We find that Fang's (2002) result still holds but Serena's (2017) result does not. Precisely, to increase the expected winner's effort, it is strictly beneficial to exclude all but two contestants if and only if each contestant's probability of being the weak type is small. If the probability is sufficiently high, it is optimal to include all contestants.

A recent paper Ohkubo (2017) [1] found that the measured S 0 1 phase shifts can be reproduced using a deeply attractive nucleon–nucleon potential. We find that the deuteron would decay strongly via pion emission to the deeply bound state arising in this potential. Therefore the success of a deeply attractive potential in describing phase shifts must be regarded only as an interesting curiosity.

In the framework of the energy density method with the use of the wave function of the two-center shell model, the influence of the simultaneous account for the Pauli exclusion principle and the monopole and quadrupole polarizations of nuclei on the nuclear part of the potential of their interaction by the example of the Ca 40 + Ca 40 system is considered. The calculations performed in the framework of the adiabatic approximation show that the consideration of the Pauli exclusion principle and the polarization of nuclei, especially the quadrupole one, essentially affects the nucleus–nucleus interaction potential.

How well can we manipulate the state of a particle via a discrete-time quantum walk? We show that the discrete-time quantum walk on a one-dimensional infinite chain with coin operators that are independent of the position can only realize product operators of the form e i ξ A ⊗ 1 p , which cannot change the position state of the walker. We present a scheme to construct all possible realizations of all the product operators of the form e i ξ A ⊗ 1 p . When the coin operators are dependent on the position, we show that the translation operators on the position can not be realized via a DTQW with coin operators that are either the identity operator 1 or the Pauli operator σ x .

Sulphur is one of the most abundant chemical elements in the universe and a large number of lines have been observed in the spectra of astrophysical object. The S IV and SV ions considered in this work have received much interest in the last decade. The main objective of the present work is to report on photoionization cross-sections of S IV using the Breit-Pauli R-matrix (BPRM) method. We have carried out extensive non-relativistic and relativistic calculations of the photoionization cross sections to focus on relativistic effects. The reliability of the atomic data presented here has been carefully tested. We have exploited the BPRM code to describe the atomic wavefunctions and generate the energy levels for the SV 81 fine-structure bound target states and the corresponding A-values for transitions between these levels. The partial and total cross sections for the photoionization of the Al-like S3+ ground and excited states are determined for photon energy ranging from the S4+ 3s2 threshold up to the S4+ 4s threshold. We present statistically weighted, level resolved ground photoionization cross sections for the S IV ion. Both resonance positions and the oscillator strengths are presented. Extensive comparison of the present calculated values with those obtained from direct theoretical scattering calculation is also presented. To the best of our knowledge, the work reported herein describes for the first time a detailed relativistic photoionization calculation for this system, and the results are relevant to the laboratory and astrophysical plasmas.

The discovery of two-dimensional (2D) material graphene has opened a door towards a class of layered novel nanomaterials with unique photonic and optoelectronic properties. Recently many new 2D materials have been reported, including topological insulators (TIs), transition metal dichalcogenides (TMDs) and black phosphorus (BP). These materials have been demonstrated high optical nonlinearity and Pauli blocking used as saturable absorbers (SAs) in pulsed lasers. In this paper, we summarize the current specifications from these 2D materials based mode-locked and Q-switched lasers. The laser performance in operating wavelength, optical bandwidth, repetition rate and pulse energy is reviewed. Finally future perspective is suggested.

There have been extended studies on the appearance of ferromagnetism in transition-metal–metalloid (MD) glasses. In particular, the paramagnetic (PM) to ferromagnetic (FM) transition has been investigated on numerous (Ni100-xFex)-MD alloys upon the introduction of Fe where MD can represent a combination of various metalloid elements, while keeping the metal/metalloid ratio constant. It has been reported that adding a sufficient amount of Fe to a Pauli PM Ni-MD alloy matrix first induces a spin-glass (SG) state at low temperatures which goes over to a PM state at higher temperatures. Beyond a certain Fe content, xc, the SG state transforms to a FM state upon increasing the temperature. By plotting the characteristic transition temperatures as a function of the Fe content, a magnetic phase diagram can be constructed for each Ni-Fe-MD system which has a multicritical point (MCP) at xc. By using the reported magnetic phase diagrams of various Ni-Fe-MD alloy systems, it is shown that the critical Fe content, xc scales inversely with the density of states at the Fermi level, N(EF), of the parent Ni-MD matrix. This means that the higher the N(EF), the lower the critical Fe content to induce ferromagnetism in the Ni-MD matrix. This is then discussed in terms of the Stoner enhancement factor, S, which characterizes the tendency of the matrix to become ferromagnetic.

Discrete quantum Boltzmann model together with the introduction of an external-field-tuned orientation parameter as well as the acoustic analog are adopted to study the possible localization of electron (fermion) flux in cosmic rays considering the precision measurement with the Alpha Magnetic Spectrometer (AMS) on the International Space Station (ISS). Our approximate results match qualitatively with those data measured with the AMS on the ISS.

We give a simple proof of quantitative stability for the Heisenberg–Pauli–Weyl inequality in L 2 distance, with explicit constants.

The emission of electron pairs from surfaces has the power to reveal details about the electron–electron interaction in condensed matter. This process, stimulated by a primary electron or photon beam, has been studied both in experiment and theory over the last two decades. An additional pathway, namely positron–electron pair emission, holds the promise to provide additional information. It is based on the notion that the Pauli exclusion principle does not need to be considered for this process. We have commissioned a laboratory based positron source and performed a systematic study on a variety of solid surfaces. In a symmetric emission geometry we can explore the fact that positron and electron are distinguishable particles. Following fundamental symmetry arguments we have to expect that the available energy is shared unequally among positron and electron. Experimentally we observe such a behavior for all materials studied. We find an universal feature for all materials in the sense that on average the positron carries a larger fraction of the available energy. This is qualitatively accounted for by a simplified scattering model. Numerical results, which we obtained by a microscopic theory of positron–electron emission from surfaces, reveal however that there are also cases in which the electron carries more energy. Whether the positron or the electron is more energetic depends on details of the bound electron state and of the emission geometry. The coincidence intensity is strongly material dependent and there exists an almost monotonic relation between the singles and coincidence intensity. These results resemble the findings obtained in electron and photon stimulated electron pair emission. An additional reaction channel is the emission of an electron pair upon positron impact. We will discuss the energy distributions and the material dependence of the coincidence signal which shows similar features as those for positron–electron pairs.

There have been suggestions that the Pauli exclusion principle alone can lead a non-interacting (free) system of identical fermions to form crystalline structures dubbed Pauli crystals. Single-shot imaging experiments for the case of ultra-cold systems of free spin-polarized fermionic atoms in a two-dimensional harmonic trap appear to show geometric arrangements that cannot be characterized as Wigner crystals. This work explores this idea and considers a well-known approach that enables one to treat a quantum system of free fermions as a system of classical particles interacting with a statistical interaction potential. The model under consideration, though classical in nature, incorporates the quantum statistics by endowing the classical particles with an effective interaction potential. The reasonable expectation is that possible Pauli crystal features seen in experiments may manifest in this model that captures the correct quantum statistics as a first order correction. We use the Monte Carlo simulated annealing method to obtain the most stable configurations of finite two-dimensional systems of confined particles that interact with an appropriate statistical repulsion potential. We consider both an isotropic harmonic and a hard-wall confinement potential. Despite minor differences, the most stable configurations observed in our model correspond to the reported Pauli crystals in single-shot imaging experiments of free spin-polarized fermions in a harmonic trap. The crystalline configurations observed appear to be different from the expected classical Wigner crystal structures that would emerge should the confined classical particles had interacted with a pair-wise Coulomb repulsion.

We evaluate the electromagnetic Ξ c γ → Ξ c ′ transition on 2+1 flavor lattices corresponding to a pion mass of ∼ 156 MeV . We extract the magnetic Sachs and Pauli form factors which give the Ξ c – Ξ c ′ transition magnetic moment and the decay widths of Ξ c ′ baryons. We did not find a signal for the magnetic form factor of the neutral transition Ξ c 0 γ → Ξ c ′ 0 , which is suppressed by the U-spin flavor symmetry. As a byproduct, we extract the magnetic form factors and the magnetic moments of Ξ c and Ξ c ′ baryons, which give an insight to the dynamics of u / d , s and c quarks having masses at different scales.

Electron correlations in a two-electron two-dimensional ‘artificial atom’ or quantum dot (with harmonic confining potential) in the presence of a uniform magnetic field in an excited singlet state are studied via quantal density functional theory (QDFT). QDFT allows for the separation of the electron correlations due to the Pauli exclusion principle and Coulomb repulsion, as well as the determination of the contribution of these correlations to the kinetic energy. The QDFT mapping is from the excited state of the quantum dot to one of noninteracting fermions in their ground state possessing the same basic variables of the density and physical current density, and the same orbital and spin angular momentum. A detailed analysis of these correlations in terms of their quantal sources, the corresponding ‘classical’ fields, and resulting potentials and energies is presented. The key conclusions are that as in natural atoms, the contributions of the Pauli and Coulomb correlations relative to the total energy for the excited state, are less than but of the same order of magnitude as those for the ground state of a quantum dot. However, in contrast, the correlation-kinetic contributions are an order of magnitude greater than those for a quantum dot in its ground state. These correlations constitute nearly 75 % of the kinetic and 25 % of the total energy. This result is consistent with prior work on low electron density Wigner systems in three-dimensions in which correlation-kinetic effects too play a significant role. The significance of these correlations to traditional excited state density functional theory is noted.

Standard computational methods used to take account of the Pauli Exclusion Principle into Monte Carlo (MC) simulations of electron transport in semiconductors may give unphysical results in low field regime, where obtained electron distribution function takes values exceeding unity. Modified algorithms were already proposed and allow to correctly account for electron scattering on phonons or impurities. Present paper extends this approach and proposes improved simulation scheme allowing including Pauli exclusion principle for electronelectron (ee) scattering into MC simulations. Simulations with significantly reduced computational cost recreate correct values of the electron distribution function. Proposed algorithm is applied to study transport properties of degenerate electrons in graphene with ee interactions. This required adapting the treatment of ee scattering in the case of linear band dispersion relation. Hence, this part of the simulation algorithm is described in details.

We complete and improve the results of a recent paper by Ekholm, Kovařik and Portmann in connection with a question of C. Guillarmou about the semiclassical expansion of the lowest eigenvalue of the Pauli operator with Dirichlet conditions. We exhibit connections with the properties of the torsion function in mechanics, the exit time of a Brownian motion and the analysis of the low eigenvalues of some Witten Laplacian.

U 3 Si 2 reversibly absorbs hydrogen at very low H 2 pressures (kPa range), yielding U 3 Si 2 H 1.8 . One characteristic desorption temperature implies that there is only one type of H sites. U 3 Si 2 is a weak Pauli paramagnet ( χ −8 m 3 /mol U) with the shortest inter-uranium distances between the U atoms in different sheets ( d U-U = 332 pm). The volume-expanded (10%) hydride is a spin fluctuator with temperature dependent magnetic susceptibility and a weak ferromagnetic component gradually arising below T = 100 K. The location of U 3 Si 2 H 1.8 at the verge of magnetic ordering is evidenced by the low temperature specific heat with an upturn in C / T and a dramatic enhancement of the Sommerfeld coefficient of electronic specific heat γ , which reaches 500 mJ/mol f.u. K 2 .

For a quantum system, its density matrix usually has a size growing exponentially with the number of particles in the system, and quantum state tomography techniques often encounter an exponential complexity problem for recovering the density matrix based on experimental data. Recent statistical methods for estimating a large density matrix have been developed for the cases that (i) the entries of the density matrix with respect to the Pauli basis are sparse, or (ii) the density matrix has a low rank, and its eigenvectors are sparse. Their performances depend on the assumed structures, and it is important to test for the structures and choose appropriate estimation methods accordingly. This paper investigates hypothesis tests for sparsity. Specifically, we propose hypothesis test procedures and establish asymptotic theories for the proposed tests. Numerical studies are conducted to check the finite sample performances of the proposed hypothesis tests.

The dissipation phenomenon in the heavy-ion reaction at incident energy near Fermi energy is studied by simulating the reactions 129Xe + 129Sn and 58Ni + 58Ni with isospin-dependent quantum molecular dynamics model (IQMD). The isotropy ratio in terms of transverse and longitudinal energies of the free protons emitted in the final states of these reactions is quantitatively analyzed to explore the in-medium correlation of the binary collisions. Comparison of the calculations with the experimental data recently released by INDRA collaboration exhibits that the ratio is very sensitive to the Pauli blocking effect in two-body collisions and Pauli exclusion principle is indispensable in the theoretical simulations for the heavy-ion reactions near the Fermi energy.

We construct new equations of state for baryons at sub-nuclear densities for the use in core-collapse supernova simulations. The abundance of various nuclei is obtained together with thermodynamic quantities. The formulation is an extension of the previous model, in which we adopted the relativistic mean field theory with the TM1 parameter set for nucleons, the quantum approach for $d$, $t$, $h$ and $\alpha$ as well as the liquid drop model for the other nuclei under the nuclear statistical equilibrium. We reformulate the model of the light nuclei other than $d$, $t$, $h$ and $\alpha$ based on the quasi-particle description. Furthermore, we modify the model so that the temperature dependences of surface and shell energies of heavy nuclei could be taken into account. The pasta phases for heavy nuclei and the Pauli- and self-energy shifts for $d$, $t$, $h$ and $\alpha$ are taken into account in the same way as in the previous model. We find that nuclear composition is considerably affected by the modifications in this work, whereas thermodynamical quantities are not changed much. In particular, the washout of shell effect has a great impact on the mass distribution above $T \sim 1$ MeV. This improvement may have an important effect on the rates of electron captures and coherent neutrino scatterings on nuclei in supernova cores., Comment: 39 pages, 6 figures, 2 tables, Accepted for publication in Nucl.Phys. A. This article draws heavily from arXiv:1305.1508. The EOS table available at http://sites.google.com/site/furusawashun/eosdata

We compute the optical conductivity of gapped graphene taking into account the effects of interaction between electrons and Einstein phonons beyond the usual Dirac-cone approximation. Our study is based on the Kubo formula that is established upon the retarded self-energy. Specially we report the frequency dependence of optical absorption of the structure. We find numerical results for frequency dependence of optical absorption for different values of gap parameter in the presence of Holstein phonons. We have also studied the effects of electron-phonon coupling strength and electronic concentration on the behavior of optical absorption of the gapped graphene structure. Our results show the increase of electronic chemical potential in doped case leads to appear optical band gap in the structure. This optical gap arises from Pauli blocking of vertical transitions when conduction band is doped. Electron-phonon coupling broadens the peak in the optical spectral and decreases the intensity of optical absorption. However the frequency position of the peak is not considerably affected by electron-phonon coupling.

The formation of the chemical bond is considered from the general theoretical standpoint as the interaction of different fermions. It is shown that using the modern classical concepts of chemical bond, it is impossible to obtain (strictly theoretically) a physical justification of the cause of the formation of a chemical bond. The shows the inapplicability of the Pauli principle to chemical bond and a new theoretical model of the chemical bond is proposed based on the Heisenberg uncertainty principle.

The modeling of non-local-thermodynamic-equilibrium plasmas is crucial for many aspects of high-energy-density physics. It often requires collisional-radiative models coupled with radiative-hydrodynamics simulations. Therefore, there is a strong need for fast and as accurate as possible calculations of the cross-sections and rates of the different collisional and radiative processes. We present an analytical approach for the computation of the electron-impact excitation (EIE) cross-sections in the Plane Wave Born (PWB) approximation. The formalism relies on the screened hydrogenic model. The EIE cross-section is expressed in terms of integrals, involving spherical Bessel functions, which can be calculated analytically. In order to remedy the fact that the PWB approximation is not correct at low energy (near threshold), we consider different correcting factors (Elwert-Sommerfeld, Cowan-Robb, Kilcrease-Brookes). We also investigate the role of plasma density effects such as Coulomb screening and quantum degeneracy on the EIE rate. This requires to integrate the collision strength multiplied by the Fermi-Dirac distribution and the Pauli blocking factor. We show that, using an analytical fit often used in collisional-radiative models, the EIE rate can be calculated accurately without any numerical integration, and compare our expression with a correction factor presented in a recent work., Comment: submitted to High Energy Density Phys

Within the framework of Breit Pauli R-matrix approach, a close-coupling calculation has been carried out for the process of photoionization of ground and excited states of Ne-like Mo XXXIII ion. The calculation includes 60 fine-structure levels and 15 parities for the target states. Level specific photoionization cross sections are computed for all levels at a fine energy mesh of 10−5 scaled Ryd, with 19500 energies for each Jπ = 0± - 6± symmetry, up to 2s22p43s (2S1/2) threshold at 212.33 Ryd above the first ionization threshold, 1s22s22p5 2Po3/2. In this article are presented cross sections for the photoionization of ground 1s22s22p6 1S0 and 1s22s22p5(2Po)3p 3P0, 1s22s22p5(2Po)3p 1S0, 1s22s2p63s 1S0, 1s22s22p53s(3Po2,1,0), 1s22s22p53s (1Po1) excited states. To explore the role of particle-hole, channels coupling and electron-electron correlation effects on the photoionization cross sections we have compared two calculation models, namely 8-target basic configurations and 5-target basic configurations, with and without 2s2p53l target states included into the model. Effects are highlighted in the photoionization cross section behavior of the excited of 2s2p63s of Mo XXXIII. We believe that this is the first such calculation for this ion to obtain the photoionization cross section and results are important for the modeling and diagnostics of laboratory and astrophysical plasmas.

We prove a quantitative stability result for the Heisenberg–Pauli–Weyl inequality. This leads to a next, and next-to-next order correction terms in the inequality.

We present a formal extension of the Pauli exclusion principle to the arbitrary-order jumping up and down excited Schrodinger’s cats. We show that the excited symmetric Schrodinger’s cat of the n-order will occupy the same n-order excited eigenstate of the harmonic oscillator when the “alive” and “dead” cat’s constituents closely approach in space and time each other. The antisymmetric n-order cat states, vice versa, will never occupy the same excited n-order eigenstate. For example, the respective probabilities for antisymmetric cat states of n = 1, 2, and 3 orders to jump up onto the corresponding energy levels with n = 2, 3, and 4, and, at the same time, jump down onto the levels with n = 0, 1, and 2, are found to be in the ratios: 2/3:1/3, 3/5:2/5, and 4/7:3/7, with the asymptotic saturated ratio of 1/2:1/2 for the cat states distributed over the higher-energy levels. Moreover, we demonstrate the remarkable analogies between linear and nonlinear dynamics of the higher-order Schrodinger’s cats revealed in the framework of the nonlinear Schrodinger equation model with harmonic oscillator potential.

We consider the dynamics of the simplest Schrodinger's cat composed by a superposition of two canonical coherent states of the Schrodinger quantum harmonic oscillator. We demonstrate that the interchange of the “alive” and “dead” constituents in the whole Schrodinger's cat wave function opens the possibility to reveal one interesting, but obviously, only formal analogy with the Pauli exclusion principle. We show analytically and computationally that the symmetric cat states will occupy the ground state of the harmonic oscillator, whereas the antisymmetric cat states, vice versa, will never occupy the ground state when these states closely approach in space each other. The antisymmetric overlapping in space and time “alive” and “dead” Schrodinger cat states simply jump onto the first excited energy level of the quantum harmonic oscillator. This effect could be considered as the formal analogy of the Pauli exclusion principle applied to the antisymmetric “jumping off” Schrodinger cats. As the name suggests, the main feature of the “jumping off” Schrodinger cat consists in the transformation of the probability distribution (both in ordinary coordinate space and in the momentum space as well) in such a way that antisymmetric “alive” and “dead” cats are found to be in the first excited energy state of the quantum harmonic oscillator. We conclude that the wave and particle-like analogies in the dynamics of the symmetric and antisymmetric Schrodinger's cat states confirm at least formally the famous Pauli statements that “a symmetric solution can never develop into an antisymmetric one, and vice versa”, and that “for particles with antisymmetric states it can, therefore, never happen that two particles find themselves in the same state”

In this paper we analyze the spatial distribution of elements around points of interest. Based on a spatial exclusion principle we model the system by means of a Fermi–Dirac distribution defined by two easily interpretable parameters. By means of image analysis, two real cases are studied and compared to the theory: people in an open-air concert and cars in a mall parking-lot. We show that they closely obey the proposed fermion-like statistics.

Dark matter can capture in neutron stars and heat them to observable luminosities. We study relativistic scattering of dark matter on highly degenerate electrons. We develop a Lorentz invariant formalism to calculate the capture probability of dark matter that accounts for the relativistic motion of the target particles and Pauli exclusion principle. We find that the actual capture probability can be five orders of magnitude larger than the one estimated using a nonrelativistic approach. For dark matter masses $10~{\rm eV}\textup{--}10~{\rm PeV}$, neutron star heating complements and can be more sensitive than terrestrial direct detection searches. The projected sensitivity regions exhibit characteristic features that demonstrate a rich interplay between kinematics and Pauli blocking of the DM--electron system. Our results show that old neutron stars could be the most promising target for discovering leptophilic dark matter., 7 pages, 1 figure. v2 matches published version

We investigate the weak interactions taking place in the tetraphenylporphyrin dimers by using Wannier orbitals and DFT. The Van der Waals interaction energies for various geometric configurations of the dimers are then compared to the differences between the total DFT energies of dimers and those of sums over the energies of monomers. The comparison allows us to estimate the weight of the Van der Waals contribution to the total interaction energy since the DFT values include all contributions such as weak chemical interaction or Pauli repulsion to the binding energy. We show that the interaction energy computed with vdW-DF-cx exchange-correlation functional is almost identical with the one computed using Wannier orbitals. By analyzing the properties of Wannier orbitals in monomer and dimer structures, we check the fact the Van der Waals energy can be accurately calculated by using only the orbitals corresponding to the single molecule, which is useful from a practical perspective.

We study the interplay between dispersion due to the electron degeneracy parameter and dissipation caused by plasma resistivity, in degenerate Fermi–Dirac Pauli quantum plasma. Considering relativistic degeneracy pressure for electrons, we investigate both arbitrary and small amplitude nonlinear structures. The corresponding trajectories are also plotted in the phase plane. The linear analysis for the dispersion relation yields interesting features. The present work is anticipated to be of physical relevance in the study of compact magnetized astrophysical objects like white dwarfs.

In this study, the role of many-body interactions, Pauli blocking, and impurity-carrier interactions on the band gap variation were used to analyze the observed blue shift of the Al doped ZnO thin films. The optical constants and the band gap variations of our samples were obtained using spectroscopic ellipsometry method. Tauc-Lorentz model and effective medium approximation were used to model the dielectric function. We demonstrated for the first time that the combination of the Tauc formalism for absorption and the proposed model by Jain et al. for the band gap variation, can be used to determine both electron and hole effective masses. Reasonable results were obtained for carriers effective mass and their dependence on carrier concentration.

The present work is concerned with a report on the effects of Pauli, Rashba and Dresselhaus spin–orbit interactions (SOI) on the energy levels of a 2D circular hydrogenic quantum anti-dot(QAD). To pursue this aim, we first present a brief review on the analytical solutions to the Schrodinger equation of electronic states in a quantum anti-dot when a hydrogenic donor is placed at the center, revealing the degeneracies involved in the ground, first and second excited states. We then proceed by adding the aforementioned spin–orbit interactions to the Hamiltonian and treat them as perturbation, thereby, calculating the energy shifts to the first three states. As we show, the Rashba spin–orbit interaction gives rise to a shift in the energies of the ground and second excited states, while it partially lifts the degeneracy of the first excited state. Our calculations also indicate that the Dresselhaus effect, while keeping the degeneracy of the ground and second excited states intact, removes the degeneracy of the first excited state in the opposite sense. The Pauli spin–orbit interaction, on the other hand, is diagonal in the appropriate bases, and thus its effect is readily calculated. The results show that degeneracy of l = 0 (prevailing in the ground and second excited state) remains but the degeneracy of l = 1 (prevailing in the first excited state) is again partially lifted. Moreover, we present the energy corrections due to the three spin–orbit interactions as functions of anti-dot's radius, Rashba and Dresselhaus strengths discussing how they affect the corresponding states. The material presented in the article conceives the possibility of generating spin currents in the hydrogenic circular anti-dots.

A simple procedure to estimate the quadrupole Potential-Energy-Surface (PES) is presented, using mainly structural information, namely the content of the shell model space and the Pauli exclusion principle. Further microscopic properties are implicitly contained through the use of results from the Moller and Nix tables or experimental information. A mapping to the geometric potential is performed yielding the PES. The General Collective Model is used in order to obtain an estimate on the spectrum and quadrupole transitions, adjusting only the mass parameter. First, we test the conjecture on known nuclei, deriving the PES and compare them to known data. We will see that the PES approximates very well the structure expected. Having acquired a certain confidence, we predict the PES of several chain of isotopes of heavy and super-heavy nuclei and at the end we investigate the structure of nuclei in the supposed island of stability. One of the main points to show is that simple assumptions can provide already important information on the structure of nuclei outside known regions and that spectra and electromagnetic transitions can be estimated without using involved calculations and assumptions. The procedure does not allow to calculate binding energies. The method presented can be viewed as a starting point for further improvements.