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We consider the case that four spin-3 atoms are confined in an optical trap. The temperature is so low that the spatial degrees of freedom have been frozen. Exact numerical and analytical solutions for the spin-states have been both obtained. Two kinds of phase-diagrams for the ground states (g.s.) have been plotted. In general, the eigen-states with the total-spin S (a good quantum number) can be expanded in terms of a few basis-states $$f_{S,i}$$ f S , i . Let $$P_{f_{S,i}}^{\lambda }$$ P f S , i λ be the probability of a pair of spins coupled to $$\lambda =0, 2, 4$$ λ = 0 , 2 , 4 , and 6 in the $$f_{S,i}$$ f S , i state. Obviously, when the strength $$g_{\lambda }$$ g λ of the $$\lambda $$ λ -channel is more negative, the basis-state with the largest $$P_{f_{S,i}}^{\lambda }$$ P f S , i λ would be more preferred by the g.s.. When two strengths are more negative, the two basis-states with the two largest probabilities would be more important components. Thus, based on the probabilities, the spin-structures (described via the basis-states) can be understood. Furthermore, all the details in the phase-diagrams, say, the critical points of transition, can also be explained. Note that, for $$f_{S,i}$$ f S , i , $$P_{f_{S,i}}^{\lambda }$$ P f S , i λ is completely determined by symmetry. Thus, symmetry plays a very important role in determining the spin-structure of the g.s..

The degeneracy of Landau levels in perforated two-dimensional electronic structures is lifted in a perpendicular magnetic field. The cylindrical symmetry of the problem with a circular antidot holds and the magnetic quantum number m = 0, ±1, ±2, … is a good quantum number. The splitting of Landau levels for the antidot smaller than the magnetic length, as well as the frequencies and intensities of interband transition lines for normal semiconductors and transition metal dichalcogenide monolayers, has been analytically found.

Valley pseudospin has emerged as a good quantum number to encode information, analogous to spin in spintronics. Two-dimensional transition metal dichalcogenides (2D TMDCs) recently attracted enormous attention for their easy access to the valley pseudospin through valley-dependent optical transitions. Different ways have been reported to read out the valley pseudospin state. For practical applications, on-chip access to and manipulation of valley pseudospins is paramount, not only to read out but especially to initiate the valley pseudospin state. Here, we experimentally demonstrate the selective on-chip, optical near-field initiation of valley pseudospins at room temperature. We exploit a nanowire optical waveguide, such that the local transverse optical spin of its guided modes selectively excites a specific valley pseudospin. Furthermore, spin-momentum locking of the transverse optical spin enables us to flip valley pseudospins with the opposite propagation direction. Thus, we open up ways to realize integrated hybrid opto-valleytronic devices.

Nonstatistical dynamics is important for many chemical reactions. The Rice-Ramsperger-Kassel-Marcus (RRKM) theory of unimolecular kinetics assumes a reactant molecule maintains a statistical microcanonical ensemble of vibrational states during its dissociation so that its unimolecular dynamics are time independent. Such dynamics results when the reactant's atomic motion is chaotic or irregular. Intrinsic non-RRKM dynamics occurs when part of the reactant's phase space consists of quasiperiodic/regular motion and a bottleneck exists, so that the unimolecular rate constant is time dependent. Nonrandom excitation of a molecule may result in short-time apparent non-RRKM dynamics. For rotational activation, the 2J + 1 K levels for a particular J may be highly mixed, making K an active degree of freedom, or K may be a good quantum number and an adiabatic degree of freedom. Nonstatistical dynamics is often important for bimolecular reactions and their intermediates and for product-energy partitioning of bimolecular and unimolecular reactions. Post–transition state dynamics is often highly complex and nonstatistical.

Seniority has proved to be a unique and simple probe to address some of the complex issues underlying nuclear structure of nuclei close to magic numbers. An extension from the concept of seniority in single-j shell to generalized seniority in multi-j shell has recently been provided by us. We have, consequently, established new selection rules for gamma decays and discovered the new seniority isomers decaying via odd electric multipole operators. We have successfully explained the B(EL; L=1,2,3) behavior of various high spin isomers and other excited states. More specifically, we have been able to explain the long-standing puzzle of double hump in the B(E2) values for the first excited 2+ states of even-even Z=50 (Sn) isotopes. In the present paper, we review these generalized seniority calculations with emphasis on even-even Sn isotopes. We first discuss the generalized seniority results for the E1 decaying 13- isomers and E2 decaying 10+, 15- isomers, and then present the cases of first-excited 2+ and 3- states. The generalized seniority proves out to be a reasonably good quantum number. The significance of configuration mixing is found to be true. The calculated results has been validated till high seniority v=4 states and expected to be valid for higher seniority v=6,… states also.

The question of the number and origin of isomeric states in $^{256}\mathrm{Rf}$ arose from two independent experiments but remained unanswered for a decade. To shed light on this puzzle, we studied isomeric decay in $^{256}\mathrm{Rf}$ by measuring conversion electrons with fast fully digital electronics. $^{256}\mathrm{Rf}$ was produced in the fusion-evaporation reactions of $^{50}\mathrm{Ti}+^{207}\mathrm{Pb}$ and $^{50}\mathrm{Ti}+^{208}\mathrm{Pb}$ at the gas-filled recoil separator TransActinide Separator and Chemistry Apparatus. Among a total of 120 decays of $^{256}\mathrm{Rf}$, we detected 22 and 12 decays proceeding through one and two isomeric states. Half-lives of the low- and higher-lying states were assigned to be ${T}_{1/2}={14}_{\ensuremath{-}4}^{+6}$ and ${10}_{\ensuremath{-}3}^{+5}\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{s}$, respectively. Population rates of these isomeric states were estimated to be $\ensuremath{\approx}18%$ and $g10%$, which are similar to those for two-quasiparticle $K$ isomeric states in this region of nuclei. The results, thus, confirm an earlier claim on the existence of multiple $K$ isomeric states in $^{256}\mathrm{Rf}$ and show their population rates are as high as in No isotopes. Suggestively, $K$ remains a good quantum number in isotopes of heavier elements like Sg and Hs, where yet unknown high-$K$ isomeric states still could exist. The present experimental results demonstrate that the ``triggerless'' measurement guarantees an efficient detection of delayed conversion electron signals. Thus, it is a very efficient method for the identification of isomeric states in experiments with one nucleus-at-a-time production rates.

We study the ground state of a system with an interface between $\nu=4$ and $\nu=3$ in the quantum Hall regime. Far from the interface, for a range of interaction strengths, the $\nu=3$ region is fully polarized but $\nu=4$ region is locally a singlet. Upon varying the strength of the interactions and the width of the interface, the system chooses one of two distinct edge/interface phases. In phase A, stabilized for wide interfaces, spin is a good quantum number, and there are no gapless long-wavelength spin fluctuations. In phase B, stabilized for narrow interfaces, spin symmetry is spontaneously broken at the Hartree-Fock level. Going beyond Hartree-Fock, we argue that phase B is distinguished by the emergence of gapless long-wavelength spin excitations bound to the interface, which can, in principle, be detected by a measurement of the relaxation time $T_2$ in nuclear magnetic resonance., Comment: 9 pages 10 figures including supplemental material

Molecular line lists, particularly those computed for high temperature applications, often have very few states assigned local quantum numbers, i.e rotational and vibrational quantum labels. These are often important components for accurately determining line shape parameters required for radiative transfer simulations. Through variational calculations, the projection of the total angular momentum onto the molecule fixed axis ( k ) is investigated in the Radau internal coordinate system to determine when it can be considered a good quantum number. In the Radau coordinate system, when the square of the th component of the wavefunction is greater than one half, then we can classify k as a good quantum number in accordance with the theorem of Hose and Taylor, a quantum analogue of the Kolmogorov–Arnold–Moser theorem. When the theorem is satisfied, it is shown that k can reliably be used to determine oblate and prolate quantum labels K a and K c . This approach is tested on the states of the water and ozone molecules.

Background: Resonance scattering has been extensively used to study the structure of exotic, neutron-deficient nuclei. Extension of the resonance scattering technique to neutron-rich nuclei was suggested more than 20 years ago. This development is based on the isospin conservation law. In spite of broad field of the application, it has never gained a wide-spread acceptance.Purpose: To benchmark the experimental approach to study the structure of exotic neutron-rich nuclei through resonance scattering on a proton target.Method: The excitation function for $p+^{8}\mathrm{Li}$ resonance scattering is measured using a thick target by recording coincidence between light and heavy recoils, populating $T=3/2$ isobaric analog states (IAS) in $^{9}\mathrm{Be}$.Results: A good fit of the $^{8}\mathrm{Li}(p,p)^{8}\mathrm{Li}$ resonance elastic scattering excitation function was obtained using previously tentatively known $5/{2}^{\ensuremath{-}}\phantom{\rule{4pt}{0ex}}T=3/2$ state at 18.65 MeV in $^{9}\mathrm{Be}$ and a new broad $T=3/2\phantom{\rule{4pt}{0ex}}s$-wave state---the $5/{2}^{+}$ at 18.5 MeV. These results fit the expected isomirror properties for the $T=3/2\phantom{\rule{4pt}{0ex}}A=9$ isoquartet.Conclusions: Our analysis confirmed isospin as a good quantum number for the investigated highly excited $T=3/2$ states and demonstrated that studying the structure of neutron-rich exotic nuclei through IAS is a promising approach.

In this work, a new protocol for the calculation of valence-to-core resonant X-ray emission (VtC RXES) spectra is introduced. The approach is based on the previously developed restricted open configuration interaction with singles (ROCIS) method and its parametrized version, based on a ground-state Kohn–Sham determinant (DFT/ROCIS) method. The ROCIS approach has the following features: (1) In the first step approximation, many-particle eigenstates are calculated in which the total spin is retained as a good quantum number. (2) The ground state with total spin S and excited states with spin S′ = S, S ± 1, are obtained. (3) These states have a qualitatively correct multiplet structure. (4) Quasi-degenerate perturbation theory is used to treat the spin–orbit coupling operator variationally at the many-particle level. (5) Transition moments are obtained between the relativistic many-particle states. The method has shown great potential in the field of X-ray spectroscopy, in particular in the field of transition-metal L-edge, which cannot be described correctly with particle–hole theories. In this work, the method is extended to the calculation of resonant VtC RXES [alternatively referred to as 1s-VtC resonant inelastic X-ray scattering (RIXS)] spectra. The complete Kramers–Dirac–Heisenerg equation is taken into account. Thus, state interference effects are treated naturally within this protocol. As a first application of this protocol, a computational study on the previously reported VtC RXES plane on a molecular managanese(V) complex is performed. Starting from conventional X-ray absorption spectra (XAS), we present a systematic study that involves calculations and electronic structure analysis of both the XAS and non-resonant and resonant VtC XES spectra. The very good agreement between theory and experiment, observed in all cases, allows us to unravel the complicated intensity mechanism of these spectroscopic techniques as a synergic function of state polarization and interference effects. In general, intense features in the RIXS spectra originate from absorption and emission processes that involve nonorthogonal transition moments. We also present a graphical method to determine the sign of the interference contributions., A DFT/ROCIS protocol for the calculation of valence-to-core resonant X-ray emission spectra.

We extend to open surfaces with simple singularities the theorem proposed by Xavier Jarque and Zbigniew Nitecki for Hamiltonian flows in the plane that are structurally stable among Hamiltonian flo...

We have recently shown that the general trends of partition-wise fission fragment mass distribution in heavy-ion-induced compound nuclear (CN) fission of heavy nuclei can be reproduced reasonably well by using the concept of isospin conservation, hence providing a direct evidence of isospin conservation in neutron-rich systems [Jain et al, Nucl Data Sheets 120, 123 (2014); Garg and Jain, Phys. Scr. 92, 094001 (2017); Jain and Garg, EPJ Web of Conference 178, 05007 (2018); Garg et al, Phys. Scr. 93, 124008 (2018)]. In this paper, we test the concept of isospin conservation to reproduce the fission fragment mass distribution emerging from thermal neutron-induced CN fission reaction, $$^{245}\mathrm{Cm}(n_{\mathrm{th}}, \hbox {f})$$ . As earlier, we use Kelson’s conjectures [I Kelson, Proceedings of the Conference on Nuclear Isospin (Academic Press, New York, 1969)] to assign isospin to neutron-rich fragments emitted in fission, which suggest the formation of fission fragments in isobaric analogue states. We calculate the relative yields of neutron-rich fragments using the concept of isospin conservation and basic isospin algebra. The calculated results reproduce the experimentally known partition-wise mass distributions quite well. This highlights the usefulness of isospin as an approximately good quantum number in neutron-rich nuclei. This also allows us to predict the fragment distribution of the most symmetric Cd–Cd partition and the heavier mass fragment distributions, both not measured so far.

The Schr\"odinger Hamiltonian of a spin zero particle as well as the Pauli Hamiltonian with spin-orbit coupling included of a spin one-half particle in electromagnetic fields that are confined to a curved surface embedded in a three-dimensional space spanned by a general Orthogonal Curvilinear Coordinate (OCC) are constructed. A new approach, based on the physical argument that upon squeezing the particle to the surface by a potential, then it is the physical gauge-covariant kinematical momentum operator (velocity operator) transverse to the surface that should be dropped from the Hamiltonian(s). In both cases,the resulting Hermitian gauge-invariant Hamiltonian on the surface is free from any reference to the component of the vector potential transverse to the surface, and the approach is completely gauge-independent. In particular, for the Pauli Hamiltonian these results are obtained exactly without any further assumptions or approximations. Explicit covariant plug-and-play formulae for the Schr\"odinger Hamiltonians on the surfaces of a cylinder, a sphere and a torus are derived., Comment: 7 pages, 1 figure, references added

In this work detailed transition assignments and wavenumbers for interstate transitions from the lowest lying trans-state to higher lying gauche-states ( o 1 and e 1 ) for doubly deuterated asymmetric methanol (CHD 2 OH) in the high resolution Fourier transform far infrared (FIR) spectrum are presented. The assignment methods and the structure of the spectra are described. The observations are in agreement with previous predictions of the term values and the transition matrix elements. The matrix elements of the transition dipole moment suggest that the pure symmetry properties of the internal rotational states are broken. In other words, the asymmetry induced in the threefold internal rotational potential barrier mixes the symmetry species heavily so that the transitions between levels within a symmetry species could be as strong as interspecies transitions. Therefore the symmetry is not a good quantum number. The identified transitions are analyzed in terms of the Q -branch origins and state dependent parameters. The use of “Loomis Wood” type spectral arrangements made the assignment easier with the help of a priori knowledge of the term values. In all, a catalogue of some 700 new such transitions have been prepared. A refinement of the rotational parameters were possible but confident improvement of the torsional parameters need assignments connecting excited torsional vibrational states, which is in progress. The present work should be useful for interstellar detection in the star forming regions in “Radio Astronomy” and discovery of new spontaneously amplified light sources in the far infrared and sub-millimeter wave (SMMW) regions. Lastly the accurately measured transition lines in the atlas could be used as a secondary standard in the far infrared regions.

In quantum calculations a transformed Hamiltonian is often used to avoid singularities in a certain basis set or to reduce computation time. We demonstrate for the Fourier basis set that the Hamiltonian can not be arbitrarily transformed. Otherwise, the Hamiltonian matrix becomes non-hermitian, which may lead to numerical problems. Methods for correctly constructing the Hamiltonian operators are discussed. Specific examples involving the Fourier basis functions for a triatomic molecular Hamiltonian (J=0) in bond-bond angle and Radau coordinates are presented. For illustration, absorption spectra are calculated for the OClO molecule using the time-dependent wavepacket method. Numerical results indicate that the non-hermiticity of the Hamiltonian matrix may also result from integration errors. The conclusion drawn here is generally useful for quantum calculation using basis expansion method using quadrature scheme.

The spectrum of charmonium resonances contains a number of unanticipated states along with several conventional quark-model excitations. The hadrons of different quantum numbers $J^P$ appear in a fairly narrow energy band, where $J^P$ refers to the spin-parity of a hadron at rest. This poses a challenge for Lattice QCD studies of (coupled-channel) meson-meson scattering aimed at the determination of scattering amplitudes and resonance pole positions. A wealth of information for this purpose can be obtained from the lattice spectra in frames with nonzero total momentum. These are particularly dense since hadrons with different $J^P$ contribute to any given lattice irreducible representation. This is because $J^P$ is not a good quantum number in flight, and also because the continuum symmetry is reduced on the lattice. In this paper we address the assignment of the underlying continuum $J^P$ quantum numbers to charmonia in flight using a $N_f = 2 + 1$ CLS ensemble. As a first step, we apply the single-hadron approach, where only interpolating fields of quark-antiquark type are used. The approach follows techniques previously applied to the light meson spectrum by the Hadron Spectrum Collaboration. The resulting spectra of charmonia with assigned $J^P$ will provide valuable information for the parameterization of (resonant) amplitudes in future determinations of resonance properties with lattice QCD., Comment: 19 pages, 17 figures, Version published in Physical Review D

A non-self-adjoint bosonic Hamiltonian H possessing real eigenvalues is investigated. It is shown that the operator can be diagonalized by making use of pseudo-bosonic operators. The biorthogonal sets of eigenvectors for the Hamiltonian and its adjoint are explicitly constructed. The positive definite operator which connects both sets of eigenvectors is also given. The dynamics of the model is briefly analyzed.

A successful and commonly used ab initio method for the calculation of crystal field levels and magnetic anisotropy of lanthanide complexes consists of spin-adapted state-averaged CASSCF calculations followed by state interaction with spin-orbit coupling (SI-SO). Based on two observations valid for Ln(III) complexes, namely: (i) CASSCF 4f orbitals are expected to change very little when optimized for different states belonging to the 4f electronic configuration, (ii) due to strong spin-orbit coupling the total spin is not a good quantum number, we show here via a straightforward analysis and direct calculation that the CASSCF/SI-SO method can be simplified to a single configuration-averaged HF calculation and one complete active space CI diagonalization, including spin-orbit coupling, on determinant basis. Besides its conceptual simplicity, this approach has the advantage that all spin states of the 4f$^n$ configuration are automatically included in the SO coupling, thereby overcoming one of the computational limitations of the existing CASSCF/SI-SO approach. As an example, we consider three isostructural complexes [Ln(acac)$_3$(H$_2$O)$_2$], Ln = Dy$^{3+}$, Ho$^{3+}$, Er$^{3+}$, and find that the proposed simplified method yields crystal field levels and magnetic g-tensors that are in very good agreement with those obtained with CASSCF/SI-SO., Comment: 8 pages

We present the derivation of the frequency-dependent scalar, vector, and tensor dynamical polarizabilities for the two hyperfine levels of the $^{87}\mathrm{Rb}$ atom $5s$ ground state. Based on the characterization of the dynamical polarizabilities, we analyze and measure the differential vector and tensor light shift between the $5s$ ground-state sublevels with near-resonant, stimulated Raman transitions. These results clarify that the tensor polarizabilities for the ground states of alkali atoms are absent when the light field is far detuned from the atomic resonance and the total electronic angular momentum $J$ is a good quantum number. In the near-resonant case, the light shifts are nontrivial and the determination of the frequency-dependent vector and tensor dynamic polarizabilities will help to achieve higher fidelities for applications of neutral atoms in quantum information and precision measurements.

The following paper tries to derive a Black-Scholes equation by using tools of quantum physics pertaining in that sense to Hamiltonian operator, path integrals, completeness equation, introducing ket and bra vectors. Schrodinger Hamiltonian is presented and compared to Black-Scholes-Schrodinger Hamiltonian. Similarity was demonstrated and it was proved that Schrodinger Hamiltonian was Hermitian while Black-Scholes Hamiltonian was anti-Hermitian. By using Schrodinger equation, price of option was implemented in the Schrodinger equation and by using Black-Scholes Hamiltonian. Black-Scholes equation was derived and a new and really powerful approach was demonstrated that could have immense application in the quantitative analysis and asset pricing.

The classical development is followed in the case where the configuration manifold is the vector space \(\mathbb{R}^{n}\). A Lagrangian function \(L: \mathbb{R}^{n} \rightarrow \mathbb{R}^{1}\) is introduced and variational methods are used to derive Euler–Lagrange equations and Hamilton’s equations. Several mechanical systems are studied to illustrate the developments.

A well-studied scenario in quantum parameter estimation theory arises when the parameter to be estimated is imprinted on the initial state by a Hamiltonian of the form $\theta G$. For such "phase shift Hamiltonians" it has been shown that one cannot improve the channel quantum Fisher information by adding ancillas and letting the system interact with them. Here we investigate the general case, where the Hamiltonian is not necessarily a phase shift, and show that in this case in general it \emph{is} possible to increase the quantum channel information and to reach an upper bound. This can be done by adding a term proportional to the derivative of the Hamiltonian, or by subtracting a term to the original Hamiltonian. Both methods do not make use of any ancillas and show therefore that for quantum channel estimation with arbitrary parameter-dependent Hamiltonian, entanglement with an ancillary system is not necessary to reach the best possible sensitivity. By adding an operator to the Hamiltonian we can also modify the time scaling of the channel quantum Fisher information. We illustrate our techniques with NV-center magnetometry and the estimation of the direction of a magnetic field in a given plane using a single spin-1 as probe., Comment: New references included

Background: The interplay between collective and single-particle degrees of freedom is an important structure aspect to study. The nuclei in theA ≈ 180 mass region are often denoted as good examples to study such problems because these nuclei are known to exhibit many rotational bands based on multi-quasiparticle K isomers. Purpose: A large set of high-quality experimental data on high-K isomeric states in the A ≈ 180 mass region has accumulated. A systematic description of them is a theoretical challenge as it requires a method going beyond the usual mean field with multi-quasiparticle configurations built in the shell-model basis. The K-isomer data provide an ideal testing ground for theoretical models. Method: The recently extended projected shell model (PSM) by the Pfaffian method is employed with a sufficiently large configuration space including up to 10 quasiparticles. The restoration of rotational symmetry which is broken in the deformed mean field is obtained by means of angular-momentum projection. With axial symmetry in the basis deformation, each multi-quasiparticle state, classified by a K quantum number, represents the major component of a rotational K band. Shell-model diagonalization in such a projected basis defines the K mixing, which is the key ingredient of the present method. Results: Quasiparticle structure and rotational properties of high-K isomers in even-even neutron-rich 174−186W isotopes are described. The rotational evolution of the yrast and near-yrast bands is discussed with successive band crossings. Multi-quasiparticle K isomers and associated rotational bands in each W isotope are studied with detailed quasiparticle configurations given. Electromagnetic transition properties are also studied and the calculated B(E2), B(M1), and g-factors are compared with experiment if data exist. Conclusions: Many nuclei of the A ≈ 180 mass region exhibit properties of an axially symmetric shape and K is approximately a good quantum number. For such nuclei, the extended PSM assuming an axially symmetric basis but including K mixing through diagonalization of the two-body Hamiltonian is an appropriate method to study multi-quasiparticle K isomers and K violations in these states. For special examples where one finds highly K-forbidden transitions the present model needs to be further improved.

Recent investigations of excitonic absorption spectra in cuprous oxide (${\mathrm{Cu}}_{2}\mathrm{O}$) have shown that it is indispensable to account for the complex valence-band structure in the theory of excitons. In ${\mathrm{Cu}}_{2}\mathrm{O}$, parity is a good quantum number and thus the exciton spectrum falls into two parts: the dipole-active exciton states of negative parity and odd angular momentum, which can be observed in one-photon absorption (${\mathrm{\ensuremath{\Gamma}}}_{4}^{\ensuremath{-}}$ symmetry), and the exciton states of positive parity and even angular momentum, which can be observed in two-photon absorption (${\mathrm{\ensuremath{\Gamma}}}_{5}^{+}$ symmetry). The unexpected observation of $D$ excitons in two-photon absorption has given first evidence that the dispersion properties of the ${\mathrm{\ensuremath{\Gamma}}}_{5}^{+}$ orbital valence band are giving rise to a coupling of the yellow and green exciton series. However, a first theoretical treatment by Uihlein et al. [Phys. Rev. B 23, 2731 (1981)] was based on a simplified spherical model. The observation of $F$ excitons in one-photon absorption is a further proof of a coupling between yellow and green exciton states. Detailed investigations on the fine structure splitting of the $F$ exciton by F. Schweiner et al. [Phys. Rev. B 93, 195203 (2016)] have proved the importance of a more realistic theoretical treatment including terms with cubic symmetry. In this paper we show that the even and odd parity exciton system can be consistently described within the same theoretical approach. However, the Hamiltonian of the even parity system needs, in comparison to the odd exciton case, modifications to account for the very small radius of the yellow and green $1S$ exciton. In the presented treatment, we take special care of the central-cell corrections, which comprise a reduced screening of the Coulomb potential at distances comparable to the polaron radius, the exchange interaction being responsible for the exciton splitting into ortho and para states, and the inclusion of terms in the fourth power of $p$ in the kinetic energy being consistent with ${O}_{\mathrm{h}}$ symmetry. Since the yellow $1S$ exciton state is coupled to all other states of positive parity, we show how the central-cell corrections affect the whole even exciton series. The close resonance of the $1S$ green exciton with states of the yellow exciton series has a strong impact on the energies and oscillator strengths of all implied states. The consistency between theory and experiment with respect to energies and oscillator strengths for the even and odd exciton system in ${\mathrm{Cu}}_{2}\mathrm{O}$ is a convincing proof for the validity of the applied theory.

Study of the combined effects of strong electronic correlations with spin-orbit coupling (SOC) represents a central issue in quantum materials research. Predicting emergent properties represents a huge theoretical problem since the presence of SOC implies that the spin is not a good quantum number. Existing theories propose the emergence of a multitude of exotic quantum phases, distinguishable by either local point symmetry breaking or local spin expectation values, even in materials with simple cubic crystal structure such as Ba$_2$NaOsO$_6$. Experimental tests of such theories by local probes are highly sought for. Here, we report on local measurements designed to concurrently probe spin and orbital/lattice degrees of freedom of Ba$_2$NaOsO$_6$. We find that a novel canted ferromagnetic phase which is preceded by local point symmetry breaking is stabilized at low temperatures, as predicted by quantum theories involving multipolar spin interactions., to appear in Nature Communications

For a self-adjoint spectral boundary value problem for a linear Hamiltonian system of ordinary differential equations, an indexing of the eigenvalues is found that is invariant under smooth variations in the parameters of the problem.

Hamiltonian mechanics can be used to constrain temperature simultaneously with energy. We illustrate the interesting situations that develop when two different temperatures are imposed within a composite Hamiltonian system. The model systems we treat are "phi-4" chains, with quartic tethers and quadratic nearest-neighbor Hooke's-law interactions. This model is known to satisfy Fourier's law. Our prototypical problem sandwiches a Newtonian subsystem between hot and cold Hamiltonian reservoir regions. We have characterized four different Hamiltonian reservoir types. There is no tendency for any of these two-temperature Hamiltonian simulations to transfer heat from the hot to the cold degrees of freedom. Evidently steady heat flow simulations require energy sources and sinks, and are therefore incompatible with Hamiltonian mechanics., 17 pages with four figures ; see also the many arXiv contributions mentioned in the references. Published in Communications in Nonlinear Science and Numerical Simulation 18, 3365-3372(2013); (received and accepted 10 May 2013, available online 17 May 2013)

This paper deals with discrete Hamiltonian systems with one singular endpoint. Using Hermitian linear relation generalized by linear Hamiltonian system, the invariance of the minimal and maximal deficiency indices under bounded perturbation for discrete Hamiltonian systems is built. This parallels the well-known results for linear Hamiltonian differential systems obtained by F.V. Atkinson.

Motivated by novel 5d-electron systems such as Sr2IrO4 and Ba2IrO4, we study the ground state of a three-orbital Hubbard model with a spin-orbit coupling by using a variational Monte Carlo method. The obtained ground-state phase diagram reveals that an antiferromagnetic state, stable at around the electron density n = 5, is destabilized by carrier doping and that the ground state becomes superconducting. Similar to high-Tc cuprates, a large asymmetry of the phase diagram between electron doping (n > 5) and hole doping (n < 5) is also found, which can be understood as the band structure effect. Due to the large spin-orbit coupling which entangles spin and orbital degrees of freedom, the pseudospin becomes a good quantum number, and the superconductivity found here is characterized by the \(d_{x^2 - y^2 }\)-wave “pseudospin singlet” pairing.