Spin polarization effect for Cr2 molecule

Density functional theory （DFT） （B3P86） of Gaussian 03 has been used to optimize the structure of the Cr2 molecule, a transition metal element molecule. The result shows that the ground state for the Cr2 molecule is a 13- multiple state, indicating that there exists a spin polarization effect in the Cr2 molecule. Meanwhile, we have not found any spin pollution because the wave function of the ground state does not mingle with wave functions of higher-energy states. So the ground state for Cr2 molecule being a 13-multiple state is indicative of spin polarization effect of the Cr2 molecule among transition metal elements, that is, there are 12 parallel spin electrons in the Cr2 molecule. The number of non-conjugated electrons is greatest. These electrons occupy different spatial orbitals so that the energy of the Cr2 molecule is minimized. It can be concluded that the effect of parallel spin in the Cr2 molecule is larger than the effect of the conjugated molecule, which is obviously related to the effect of electron d delocalization. In addition, the Murrell Sorbie potential functions with the parameters for the ground state and other states of the Cr2 molecule are derived. The dissociation energy De for the ground state of the Cr2 molecule is 0.1034eV, equilibrium bond length Re is 0.3396 nm, and vibration frequency we is 73.81cm^-1. Its force constants f2, f3 and f4 are 0.0835, -0.2831 and 0.3535 aJ. nm^-4 respectively. The other spectroscopic data for the ground state of the Cr2 molecule ωeχe, Be and αe are 1.2105, 0.0562 and 7.2938 x 10^-4cm^-1 respectively.     

Spin polarization effect for Tc2 molecule

Density functional method (DFT) (B3p86) of Gaussian98 has been used to optimize the structure of the Tc_2 molecule. The result shows that the ground state for Tc_2 molecule is an 11-multiple state and its electronic configuration is {}^{11}Σ_g^-, which shows the spin polarization effect of Tc_2 molecule of a transition metal element for the first time. Meanwhile, we have not found any spin pollution because the wavefunction of the ground state does not mingle with wavefunctions of higher energy states. So, that the ground state for Tc_2 molecule is an 11-multiple state is indicative of the spin polarization effect of Tc_2 molecule of a transition metal element: that is, there exist 10 parallel spin electrons. The non-conjugated electron is greatest in number. These electrons occupy different spacious tracks, so that the energy of Tc_2 molecule is minimized. It can be concluded that the effect of parallel spin of the Tc_2 molecule is larger than the effect of the conjugated molecule, which is obviously related to the effect of electron d delocalization. In addition, the Murrell--Sorbie potential functions with the parameters for the ground state {}^{11}Σ_g^- and other states of Tc_2 molecule are derived. Dissociation energy D_e for the ground state of T_{c2} molecule is 2.266eV, equilibrium bond length R_e is 0.2841nm, vibration frequency ω_e is 178.52cm^{-1}. Its force constants f_2, f_3, and f_4 are 0.9200aJ·nm^{-2}, --3.5700aJ·nm^{-3}, 11.2748aJ·nm^{-4} respectively. The other spectroscopic data for the ground state of Tc_2 molecule ω_eχ_e, B_e, α_e are 0.5523cm^{-1}, 0.0426cm^{-1}, 1.6331×10^{-4}cm^{-1} respectively.     

Spin polarization effect for molecule Ta2

Density functional theory （DFT） （B3p86） has been used to optimize the structure of the molecule Ta2. The result shows that the ground state of molecule Ta2 is a 7-multiple state and its electronic configuration is ^7∑u^＋, which shows the spin polarization effect for molecule Ta2 of transition metal elements for the first time. Meanwhile, spin pollution has not been found because the wavefunction of the ground state does not mix with those of higher states. So, the fact that the ground state of molecule Ta2 is a 7-multiple state indicates a spin polarization effect of molecule Ta2 of the transition metal elements, i.e. there exist 6 parallel spin electrons and the non-conjugated electrons are greatest in number. These electrons occupy different space orbitals so that the energy of molecule Ta2 is minimized. It can be concluded that the effect of parallel spin of the molecule Ta2 is larger than the effect of the conjugated molecule, which is obviously related to the effect of d-electron delocalization. In addition, the Murrell-Sorbie potential functions with parameters for the ground state ^7∑u^＋ and other states of the molecule Ta2 are derived. The dissociation energy De, equilibrium bond length Re and vibration frequency we for the ground state of molecule Ta2 are 4.5513eV, 0.2433nm and 173.06cm^-1, respectively. Its force constants f2, f3 and f4 are 1.5965×10^2aJ.nm^-2, -6.4722×10^3aJ·nm^-3 and 29.4851×10^4aJ·nm^-4, respectively. Other spectroscopic data we xe, Be and αe for the ground state of Ta2 are 0.2078cm^-1, 0.0315 cm^-1 and 0.7858×10^-4 cm^-1, respectively.     

Spin polarization effect for Os2 molecule

Density functional Theory （DFT） （B3p86） of Gaussian03 has been used to optimize the structure of Os2 molecule. The result shows that the ground state for Os2 molecule is 9-multiple state and its electronic configuration is ^9∑^＋g, which shows spin polarization effect of Os2 molecule of transition metal elements for the first time. Meanwhile, we have not found any spin pollution because the wavefunction of the ground state does not mingle with wavefunctions with higher energy states. So, the fact that the ground state for Os2 molecule is a 9-multiple state is indicative of spin polarization effect of Os2 molecule of transition metal elements. That is, there exist 8 parallel spin electrons. The non-conjugated electron is greatest in number. These electrons occupy different spacious tracks, so that the energy of Os2 molecule is minimized. It can be concluded that the effect of parallel spin of Os2 molecule is larger than the effect of the conjugated molecule, which is obviously related to the effect of electron d delocalization. In addition, the Murrell-Sorbie potential functions with the parameters for the ground state ^9∑^＋g and other states of Os2 molecule are derived. Dissociation energy De for the ground state of Os2 molecule is 3.3971eV, equilibrium bond length Re is 0.2403nm, vibration frequency ωe is 235.32cm^-1. Its force constants f2, f3, and f4 are 3.1032×10^2aJ·nm^-2, -14.3425×10^3aJ·nm^-3 and 50.5792×10^4aJ·nm^-4 respectively. The other spectroscopic data for the ground state of Os2 molecule ωexe, Be and ae are 0.4277cm^- 1, 0.0307cm^- 1 and 0.6491 × 10^-4cm^-1 respectively.     

The probe gain with and without inversion in a four—level atomic model：light amplification at a short wavelength

We propose a new four-level atomic model for achieving light amplification at a short wavelength, where direct incoherent pumping into the top level is avoided by the advantage of coherent pumping. In this model, the lower level of the probe transition is an excited state but not the usual ground state. By analytical as well as numerical calculations, we find that the probe gain, either with or without population inversion, which depends on the relation between spontaneous decay rates $\g_{42}$ and $\g_{21}$, can be achieved with proper parameters. We note that the Raman scattering gain always plays an important role in achieving the probe amplification.     

Change in the magnetic ground state of LaFe11.4Al1.6 compound by the substitution of Mn for Fe

The structure and magnetic properties of La(Fe_{1-x}Mn_x)_{11.4}Al_{1.6} (0≤x≤0.25)compounds have been studied. The NaZn_{13}-type structure is preserved and the lattice parameter increases linearly with increasing the Mn concentration. The magnetic ground state changes from the antiferromagnetic to the spin-glass or the cluster-glass state by the substitution of Mn for Fe. Furthermore, a field-induced transition from cluster glass to ferromagnet is found for the samples with x=0.05 and 0.10.     

Spin polarization effect for Co2 molecule

The density functional theory (DFT)(b3p86) of Gaussian 03 has been used to optimize the structure of the Co$_{2}$ molecule, a transition metal element molecule. The result shows that the ground state for the Co$_{2}$ molecule is a 7-multiple state, indicating a spin polarization effect in the Co$_{2}$ molecule. Meanwhile, we have not found any spin pollution because the wavefunction of the ground state is not mingled with wavefunctions of higher-energy states. So for the ground state of Co$_{2}$ molecule to be a 7-multiple state is the indicative of spin polarization effect of the Co$_{2}$ molecule, that is, there exist 6 parallel spin electrons in a Co$_{2}$ molecule. The number of non-conjugated electrons is the greatest. These electrons occupy different spacial orbitals so that the energy of the Co$_{2}$ molecule is minimized. It can be concluded that the effect of parallel spin in the Co$_{2}$ molecule is larger than the effect of the conjugated molecule, which is obviously related to the effect of electron d delocalization. In addition, the Murrell--Sorbie potential functions with the parameters for the ground state and the other states of the Co$_{2}$ molecule are derived. The dissociation energy $De$ for the ground state of Co$_{2}$ molecule is 4.0489eV, equilibrium bond length $R_{\rm e}$ is 0.2061~nm, and vibration frequency $\omega _\e $ is 378.13~cm$^{ - 1}$. Its diatomic molecule force constants $f_2$, $f_3$, and $f_4$ are 2.4824~aJ$\cdot$nm$^{ - 2}$, -7.3451~aJ$\cdot$nm$^{ - 3}$, and 11.2222~aJ$\cdot$nm$^{ - 4 }$respectively(1~aJ=$10^{-18}$~J). The other spectroscopic data for the ground state of Co$_{2}$ molecule $\omega_{\e}\chi _{\e}$, $B_{\e}$, and $\alpha_{\e}$ are 0.7202~cm$^{-1}$, 0.1347~cm$^{-1 }$, and 2.9120$\times $ 10$^{-1}$~cm$^{-1}$ respectively. And $\omega_{\e}\chi _{\e}$ is the non-syntonic part of frequency, $B_{\e}$ is the rotational constant, $\alpha_{\e}$ is revised constant of rotational constant for non-rigid part of Co$_2$ molecule.     

High-resolution calorimetric study of pb(mg_{1/3}nb_{2/3})o_{3} single crystal

Motivated by the long-standing unresolved enigma of the relaxor ferroelectric ground state, we performed a high-resolution heat capacity and polarization study of the field-induced phase transition in the relaxor ferroelectric single crystal Pb(Mg_{1/3}Nb_{2/3})O_{3} (PMN) oriented along the [110] direction. We show that the discontinuous evolution of polarization as a function of the electric field or temperature is a consequence of a true first order transition from a glassy to ferroelectric state, which is accompanied by an excess heat capacity anomaly and released latent heat. We also find that in a zero field there is no ferroelectric phase transition in bulk PMN at any temperature, indicating that the nonergodic dipolar glass phase persists down to the lowest temperatures.     

Spin waves and quantum criticality in the frustrated XY pyrochlore antiferromagnet Er2Ti2O7

We report detailed measurements of the low temperature magnetic phase diagram of Er2Ti2O7. Heat capacity and time-of-flight neutron scattering studies of single crystals reveal unconventional low-energy states. Er3+ magnetic ions reside on a pyrochlore lattice in Er2Ti2O7, where local XY anisotropy and antiferromagnetic interactions give rise to a unique frustrated system. In zero field, the ground state exhibits coexisting short and long-range order, accompanied by soft collective spin excitations previously believed to be absent. The application of finite magnetic fields tunes the ground state continuously through a landscape of noncollinear phases, divided by a zero temperature phase transition at micro{0}H{c} approximately 1.5 T. The characteristic energy scale for spin fluctuations is seen to vanish at the critical point, as expected for a second order quantum phase transition driven by quantum fluctuations.     

$\mathcal{PT}$ Symmetry in Statistical Mechanics and the Sign Problem

Generalized PT\mathcal{PT} symmetry provides crucial insight into the sign problem for two classes of models. In the case of quantum statistical models at non-zero chemical potential, the free energy density is directly related to the ground state energy of a non-Hermitian, but generalized PT\mathcal{PT}-symmetric Hamiltonian. There is a corresponding class of PT\mathcal{PT}-symmetric classical statistical mechanics models with non-Hermitian transfer matrices. We discuss a class of Z(N) spin models with explicit PT\mathcal{PT} symmetry and also the ANNNI model, which has a hidden PT\mathcal{PT} symmetry. For both quantum and classical models, the class of models with generalized PT\mathcal{PT} symmetry is precisely the class where the complex weight problem can be reduced to real weights, i.e., a sign problem. The spatial two-point functions of such models can exhibit three different behaviors: exponential decay, oscillatory decay, and periodic behavior. The latter two regions are associated with PT\mathcal{PT} symmetry breaking, where a Hamiltonian or transfer matrix has complex conjugate pairs of eigenvalues. The transition to a spatially modulated phase is associated with PT\mathcal{PT} symmetry breaking of the ground state, and is generically a first-order transition. In the region where PT\mathcal{PT} symmetry is unbroken, the sign problem can always be solved in principle using the equivalence to a Hermitian theory in this region. The ANNNI model provides an example of a model with PT\mathcal{PT} symmetry which can be simulated for all parameter values, including cases where PT\mathcal{PT} symmetry is broken.     

Ground state for CH2 and symmetry for methane decomposition

Using the different level of methods B3P86, BLYP, B3PW91, HF, QCISD、 CASSCF （4,4） and MP2 with the various basis functions 6-311G^＊＊, D95, cc-pVTZ and DGDZVP, the calculations of this paper confirm that the ground state is X^-3B1 with C2v group for CH2. Furthermore, the three kinds of theoretical methods, i.e. B3P86、 CCSD（T, MP4） and G2 with the same basis set cc-pVTZ only are used to recalculate the zero-point energy revision which are modified by scaling factor 0.989 for the high level based on the virial theorem, and also with the correction for basis set superposition error. These results are also contrary to X^-3∑^-g for the ground state of CH2 in reference. Based on the atomic and molecular reaction statics, this paper proves that the decomposition type （1） i.e. CH4 →CH2＋H2, is forbidden and the decomposition type （2） i.e. CH4→CHa＋H is allowed for CH4. This is similar to the decomposition of SiH4.     

Molecular matter-wave amplifier

We describe a matter-wave amplifier for vibrational ground-state molecules which uses a Feshbach resonance to first form quasibound molecules starting from an atomic Bose-Einstein condensate. The quasibound molecules are then driven into their stable vibrational ground state via a two-photon Raman transition inside an optical cavity. The transition from the quasibound state to the electronically excited state is driven by a classical field. Amplification of ground state molecules is then achieved by using a strongly damped cavity mode for the transition from the electronically excited molecules to the molecular ground state.     

Magnetic field and pressure dependence of small angle neutron scattering in MnSi

We report small angle neutron scattering of spontaneous and magnetic field aligned components of the helical spin polarization in MnSi for temperatures T down to 0.35 K, at pressures p up to 21 kbar, and magnetic field B up to 0.7 T. The parameter range of our study spans the first order transition between helical order and partial magnetic order at p{c}=14.6 kbar, which coincides with the onset of an extended regime of non-Fermi liquid resistivity. Our study suggests that MnSi above p{c} is not dominated by the remnants of the first order transition at p{c}, but that an unidentified mechanism favors stabilization of a new ground state other than helical order.     

A Refined Threshold Theorem for (1 + 2)-Dimensional Wave Maps into Surfaces

The recently established threshold theorem for energy critical wave maps states that wave maps with energy less than that of the ground state (i.e., a minimal energy nontrivial harmonic map) are globally regular and scatter on \({\mathbb{R}^{1+2}}\). In this note we give a refinement of this theorem when the target is a closed orientable surface, by taking into account an additional invariant of the problem, namely the topological degree. We show that the sharp energy threshold for global regularity and scattering is in fact twice the energy of the ground state for wave maps with degree zero, whereas wave maps with nonzero degree necessarily have at least the energy of the ground state. We also give a discussion on the formulation of a refined threshold conjecture for the energy critical SU(2) Yang–Mills equation on \({\mathbb{R}^{1+4}}\).     

Multireference configuration interaction potential curve and analytical potential energy function of the ground and low-lying excited states of CdSe

The potential energy curves (PECs) of the ground state ($^{3}\Pi )$ and three low-lying excited states ($^{1}\Sigma $, $^{3}\Sigma $,$^{ 1}\Pi )$ of CdSe dimer have been studied by employing quasirelativistic effective core potentials on the basis of the complete active space self-consistent field method followed by multireference configuration interaction calculation. The four PECs are fitted to analytical potential energy functions using the Murrel--Sorbie potential function. Based on the PECs, the vibrational levels of the four states are determined by solving the Schr\"{o}dinger equation of nuclear motion, and corresponding spectroscopic constants are accurately calculated. The equilibrium positions as well as the spectroscopic constants and the vibrational levels are reported. By our analysis, the $^{3}\Pi $ state, of which the dissociation asymptote is Cd($^{1}$S) + Se($^{3}$P), is identified as a ground state of CdSe dimer, and the corresponding dissociation energy is estimated to be 0.39\,eV. However, the first excited state is only 1132.49\,cm$^{ - 1}$ above the ground state and the $^{3}\Sigma $ state is the highest in the four calculated states.     

Electronic structure and energy relaxation in strained InAs/GaAs quantum pyramids

We perform experimental and theoretical studies of the electronic structure and relaxation processes in pyramid shaped InAs/GaAs quantum dots (QDs), grown by molecular beam epitaxy in the Stranski-Krastanow growth mode. Structural properties are characterized with plan view and cross section transmission electron microscopy.Finite difference calculations of the strain and the 3D Schrödinger equation, taking into account piezoelectric and excitonic effects, agree with experimental results on transition energies of ground and excited states, revealed in luminescence and absorption spectra. We find as relative standard deviation of the size fluctuation ξ=0.04; the pyramid shape fluctuates between {101} and {203} side facets.Carrier capture into the QD ground state after carrier excitation above barrier is a very efficient process. No luminescence from excited states is observed at low excitation density. Energy relaxation processes in the zero-dimensional energy states are found to be dominated by phonon energy selection rules. However, multi-phonon emission (involving GaAs barrier, InAs wetting layer, InAs QD and interface modes) allows for a large variety of relaxation channels and thus a phonon bottleneck effect does not exist here.     

Quantum numbers of the pentaquark states ${{\rm{P}}}_{{\rm{c}}}^{+}$ via symmetry analysis

We investigate the quantum numbers of the pentaquark states ${{\rm{P}}}_{{\rm{c}}}^{+}$, which are composed of 4 (three flavors) quarks and an antiquark, by analyzing their inherent nodal structure in this paper. Assuming that the four quarks form a tetrahedron or a square, and the antiquark is at the ground state, we determine the nodeless structure of the states with orbital angular moment L≤3, and in turn, the accessible low-lying states. Since the inherent nodal structure depends only on the inherent geometric symmetry, we propose the quantum numbers J^P of the low-lying pentaquark states ${{\rm{P}}}_{c}^{+}$ may be ${\tfrac{3}{2}}^{-}$, ${\tfrac{5}{2}}^{-}$, ${\tfrac{3}{2}}^{+}$and ${\tfrac{5}{2}}^{+}$, independent of dynamical models.     

Solvent effects on the S0→S2 absorption spectra of β-carotene

Absorption spectra of β -carotene in 31 solvents are measured in ambient conditions. Solvent effects on the 0--0 band energy, the bandwidth, and the transition moment of the S₀ → S₂ transition are analysed. The discrepancies between published results of the solvent effects on the 0--0 band energy are explained by taking into account microscopic solute-solvent interactions. The contributions of polarity and polarizability of solvents to 0--0 band energy and bandwidth are quantitatively distinguished. The 0--0 transition energy of the S₂ state at the gas phase is predicted to locate between 23000 and 23600~cm^-1.     

Quantum simulation of lattice gauge theories on superconducting circuits: Quantum phase transition and quench dynamics

Recently,quantum simulation of low-dimensional lattice gauge theories(LGTs)has attracted many interests,which may improve our understanding of strongly correlated quantum many-body systems.Here,we propose an implementation to approximate Z;LGT on superconducting quantum circuits,where the effective theory is a mixture of a LGT and a gauge-broken term.By using matrix product state based methods,both the ground state properties and quench dynamics are systematically investigated.With an increase of the transverse(electric)field,the system displays a quantum phase transition from a disordered phase to a translational symmetry breaking phase.In the ordered phase,an approximate Gauss law of the Z;LGT emerges in the ground state.Moreover,to shed light on the experiments,we also study the quench dynamics,where there is a dynamical signature of the spontaneous translational symmetry breaking.The spreading of the single particle of matter degree is diffusive under the weak transverse field,while it is ballistic with small velocity for the strong field.Furthermore,due to the emergent Gauss law under the strong transverse field,the matter degree can also exhibit confinement dynamics which leads to a strong suppression of the nearest-neighbor hopping.Our results pave the way for simulating the LGT on superconducting circuits,including the quantum phase transition and quench dynamics.     

Coherent phase control in ionization of magnesium by a bichromatic laser field of frequencies \(\mathsf\omega \) and 2 \(\mathsf\omega \)

We have investigated the coherent phase control on the 3p² autoionizing state (AIS) resonantly coupled with the ground state for Mg through a two- and a four-photon transition simultaneously, using a bichromatic linearly polarized laser field. The frequency is chosen such that the lasers are tunable around resonance with the transition , which implies eV and eV. We are interested in the modification of autoionizing (AI) line shape through the relative phase and laser intensities. A strong phase dependence on the total ionization yield and ionization rate is found. We also performed a time-dependent calculation which takes into consideration all the resonant states of the process.Received: 5 November 2003, Published online: 9 March 2004PACS: 32.80.Qk Coherent control of atomic interactions with photons - 32.80.Rm Multiphoton ionization and excitation to highly excited states (e.g., Rydberg states) - 32.80.Dz AutoionizationG. Buic-Zloh: Permanent address: Institute for Space Sciences, P.O. Box MG-23, 77125 Bucharest-Mgurele, Romania.