On the Ground State Wave Function of Matrix Theory
Lin, Ying-Hsuan
2014-01-01
We propose an explicit construction of the leading terms in the asymptotic expansion of the ground state wave function of BFSS SU(N) matrix quantum mechanics. Our proposal is consistent with the expected factorization property in various limits of the Coulomb branch, and involves a different scaling behavior from previous suggestions. We comment on some possible physical implications.
On the ground state wave function of matrix theory
Lin, Ying-Hsuan; Yin, Xi
2015-11-01
We propose an explicit construction of the leading terms in the asymptotic expansion of the ground state wave function of BFSS SU( N ) matrix quantum mechanics. Our proposal is consistent with the expected factorization property in various limits of the Coulomb branch, and involves a different scaling behavior from previous suggestions. We comment on some possible physical implications.
Detecting topological order in a ground state wave function
2005-01-01
A large class of topological orders can be understood and classified using the string-net condensation picture. These topological orders can be characterized by a set of data (N, d_i, F^{ijk}_{lmn}, \\delta_{ijk}). We describe a way to detect this kind of topological order using only the ground state wave function. The method involves computing a quantity called the ``topological entropy'' which directly measures the quantum dimension D = \\sum_i d^2_i.
Universal Wave Function Overlap and Universal Topological Data from Generic Gapped Ground States
2014-01-01
We propose a way -- universal wave function overlap -- to extract universal topological data from generic ground states of gapped systems in any dimensions. Those extracted topological data should fully characterize the topological orders with gapped or gapless boundary. For non-chiral topological orders in 2+1D, this universal topological data consist of two matrices, $S$ and $T$, which generate a projective representation of $SL(2,\\mathbb Z)$ on the degenerate ground state Hilbert space on ...
Mukherjee, Sutirtha; Mandal, Sudhansu
The internal structure and topology of the ground states for fractional quantum Hall effect (FQHE) are determined by the relative angular momenta between all the possible pairs of electrons. Laughlin wave function is the only known microscopic wave function for which these relative angular momenta are homogeneous (same) for any pair of electrons and depend solely on the filling factor. Without invoking any microscopic theory, considering only the relationship between number of flux quanta and particles in spherical geometry, and allowing the possibility of inhomogeneous (different) relative angular momenta between any two electrons, we develop a general method for determining a closed-form ground state wave function for any incompressible FQHE state. Our procedure provides variationally obtained very accurate wave functions, yet having simpler structure compared to any other known complex microscopic wave functions for the FQHE states. This method, thus, has potential in predicting a very accurate ground state wave function for the puzzling states such as the state at filling fraction 5/2. We acknowledge support from Department of Science and Technology, India.
Universal Wave-Function Overlap and Universal Topological Data from Generic Gapped Ground States.
Moradi, Heidar; Wen, Xiao-Gang
2015-07-17
We propose a way-universal wave-function overlap-to extract universal topological data from generic ground states of gapped systems in any dimensions. Those extracted topological data might fully characterize the topological orders with a gapped or gapless boundary. For nonchiral topological orders in (2+1)D, these universal topological data consist of two matrices S and T, which generate a projective representation of SL(2,Z) on the degenerate ground state Hilbert space on a torus. For topological orders with a gapped boundary in higher dimensions, these data constitute a projective representation of the mapping class group MCG(M^{d}) of closed spatial manifold M^{d}. For a set of simple models and perturbations in two dimensions, we show that these quantities are protected to all orders in perturbation theory. These overlaps provide a much more powerful alternative to the topological entanglement entropy and allow for more efficient numerical implementations.
Peng, Bo; Kowalski, Karol
2016-12-01
In this paper we derive basic properties of the Green's-function matrix elements stemming from the exponential coupled-cluster (CC) parametrization of the ground-state wave function. We demonstrate that all intermediates used to express the retarded (or, equivalently, ionized) part of the Green's function in the ω representation can be expressed only through connected diagrams. Similar properties are also shared by the first-order ω derivative of the retarded part of the CC Green's function. Moreover, the first-order ω derivative of the CC Green's function can be evaluated analytically. This result can be generalized to any order of ω derivatives. Through the Dyson equation, derivatives of the corresponding CC self-energy operator can be evaluated analytically. In analogy to the CC Green's function, the corresponding CC self-energy operator can be represented by connected terms. Our analysis can easily be generalized to the advanced part of the CC Green's function.
Kolmann, Stephen J; Jordan, Meredith J T
2010-02-07
One of the largest remaining errors in thermochemical calculations is the determination of the zero-point energy (ZPE). The fully coupled, anharmonic ZPE and ground state nuclear wave function of the SSSH radical are calculated using quantum diffusion Monte Carlo on interpolated potential energy surfaces (PESs) constructed using a variety of method and basis set combinations. The ZPE of SSSH, which is approximately 29 kJ mol(-1) at the CCSD(T)/6-31G* level of theory, has a 4 kJ mol(-1) dependence on the treatment of electron correlation. The anharmonic ZPEs are consistently 0.3 kJ mol(-1) lower in energy than the harmonic ZPEs calculated at the Hartree-Fock and MP2 levels of theory, and 0.7 kJ mol(-1) lower in energy at the CCSD(T)/6-31G* level of theory. Ideally, for sub-kJ mol(-1) thermochemical accuracy, ZPEs should be calculated using correlated methods with as big a basis set as practicable. The ground state nuclear wave function of SSSH also has significant method and basis set dependence. The analysis of the nuclear wave function indicates that SSSH is localized to a single symmetry equivalent global minimum, despite having sufficient ZPE to be delocalized over both minima. As part of this work, modifications to the interpolated PES construction scheme of Collins and co-workers are presented.
Transfer ionization and its sensitivity to the ground-state wave function
Schöffler, M S; Popov, Yu V; Houamer, S; Titze, J; Jahnke, T; Schmidt, L Ph H; Jagutzki, O; Galstyan, A G; Gusev, A A
2012-01-01
We present kinematically complete theoretical calculations and experiments for transfer ionization in H$^++$He collisions at 630 keV/u. Experiment and theory are compared on the most detailed level of fully differential cross sections in the momentum space. This allows us to unambiguously identify contributions from the shake-off and two-step-2 mechanisms of the reaction. It is shown that the simultaneous electron transfer and ionization is highly sensitive to the quality of a trial initial-state wave function.
DeBeer George, S; Metz, M; Szilagyi, R K; Wang, H; Cramer, S P; Lu, Y; Tolman, W B; Hedman, B; Hodgson, K O; Solomon, E I
2001-06-20
To evaluate the importance of the electronic structure of Cu(A) to its electron-transfer (ET) function, a quantitative description of the ground-state wave function of the mixed-valence (MV) binuclear Cu(A) center engineered into Pseudomonas aeruginosa azurin has been developed, using a combination of S K-edge and Cu L-edge X-ray absorption spectroscopies (XAS). Parallel descriptions have been developed for a binuclear thiolate-bridged MV reference model complex ([(L(i)(PrdacoS)Cu)(2)](+)) and a homovalent (II,II) analogue ([L(i)(Pr2tacnS)Cu)(2)](2+), where L(i)(PrdacoS) and L(i)(Pr2tacnS) are macrocyclic ligands with attached thiolates that bridge the Cu ions. Previous studies have qualitatively defined the ground-state wave function of Cu(A) in terms of ligand field effects on the orbital orientation and the presence of a metal--metal bond. The studies presented here provide further evidence for a direct Cu--Cu interaction and, importantly, experimentally quantify the covalency of the ground-state wave function. The experimental results are further supported by DFT calculations. The nature of the ground-state wave function of Cu(A) is compared to that of the well-defined blue copper site in plastocyanin, and the importance of this wave function to the lower reorganization energy and ET function of Cu(A) is discussed. This wave function incorporates anisotropic covalency into the intra- and intermolecular ET pathways in cytochrome c oxidase. Thus, the high covalency of the Cys--Cu bond allows a path through this ligand to become competitive with a shorter His path in the intramolecular ET from Cu(A) to heme a and is particularly important for activating the intermolecular ET path from heme c to Cu(A).
Energy Technology Data Exchange (ETDEWEB)
Rosso, O.A.; Szybisz, L.
1983-12-01
The magnetic dipole and electric quadrupole moments of the ground states of /sup 148/Pm and /sup 210/Bi are evaluated with phenomenological wave functions derived from ..beta..-decay studies published in previous works. It is found that these wave functions account satisfactorily for the experimental data of both nuclear moments of the /sup 210/Bi ground state. In the case of /sup 148/Pm, while the calculated value of the electric quadrupole moment is not inconsistent with the experimental data, a strong disagreement between theory and experiment is found for the magnetic dipole moment. We attribute this failure to the use of a too small configuration space for the expansion of the nuclear wave function of /sup 148/Pm.
Rosso, O. A.; Szybisz, L.
1983-10-01
The magnetic dipole and electric quadrupole moments of the ground states of148Pm and210Bi are evaluated with phenomenological wave functions derived from β-decay studies published in previous works. It is found that these wave functions account satisfactorily for the experimental data of both nuclear moments of the210Bi ground state. In the case of148Pm, while the calculated value of the electric quadrupole moment is not inconsistent with the experimental data, a strong disagreement between theory and experiment is found for the magnetic dipole moment. We attribute this failure to the use of a too small configuration space for the expansion of the nuclear wave function of148Pm.
Energy Technology Data Exchange (ETDEWEB)
Ibral, Asmaa [Equipe d’Optique et Electronique du Solide, Département de Physique, Faculté des Sciences, Université Chouaïb Doukkali, B.P. 20 El Jadida Principale, El Jadida 24000 (Morocco); Laboratoire d’Instrumentation, Mesure et Contrôle, Département de Physique, Université Chouaïb Doukkali, B.P. 20 El Jadida Principale, El Jadida (Morocco); Zouitine, Asmae [Département de Physique, Ecole Nationale Supérieure d’Enseignement Technique, Université Mohammed V Souissi, B.P. 6207 Rabat-Instituts, Rabat (Morocco); Assaid, El Mahdi, E-mail: eassaid@yahoo.fr [Equipe d’Optique et Electronique du Solide, Département de Physique, Faculté des Sciences, Université Chouaïb Doukkali, B.P. 20 El Jadida Principale, El Jadida 24000 (Morocco); Laboratoire d’Instrumentation, Mesure et Contrôle, Département de Physique, Université Chouaïb Doukkali, B.P. 20 El Jadida Principale, El Jadida (Morocco); Feddi, El Mustapha [Département de Physique, Ecole Nationale Supérieure d’Enseignement Technique, Université Mohammed V Souissi, B.P. 6207 Rabat-Instituts, Rabat (Morocco); and others
2014-09-15
Ground state energy and wave function of a hydrogen-like off-centre donor impurity, confined anywhere in a ZnS/CdSe spherical core/shell nanostructure are determined in the framework of the envelope function approximation. Conduction band-edge alignment between core and shell of nanostructure is described by a finite height barrier. Dielectric constant mismatch at the surface where core and shell materials meet is taken into account. Electron effective mass mismatch at the inner surface between core and shell is considered. A trial wave function where coulomb attraction between electron and off-centre ionized donor is used to calculate ground state energy via the Ritz variational principle. The numerical approach developed enables access to the dependence of binding energy, coulomb correlation parameter, spatial extension and radial probability density with respect to core radius, shell radius and impurity position inside ZnS/CdSe core/shell nanostructure.
Bhatnagar, Shashank; Mengesha, Yikdem
2013-01-01
In this work we have employed Bethe-Salpeter equation (BSE) under covariant instantaneous ansatz (CIA) to study electromagnetic decays of ground state equal mass vector mesons: $\\rho$, $\\omega$, $\\phi$, $\\psi$ and $Y$ through the process $V\\rightarrow\\gamma*\\rightarrow e^+ + e^-$. We employ the generalized structure of hadron-quark vertex function $\\Gamma$ which incorporates various Dirac structures from their complete set order-by-order in powers of inverse of meson mass. The electromagnetic decay constants for the above mesons are calculated using the leading order (LO) and the next-to-leading order (NLO) Dirac structures. The relevance of various Dirac structures in this calculation is studied.
Energy Technology Data Exchange (ETDEWEB)
Peng, Bo; Kowalski, Karol
2016-12-23
In this paper we derive basic properties of the Green’s function matrix elements stemming from the exponential coupled cluster (CC) parametrization of the ground-state wave function. We demon- strate that all intermediates used to express retarded (or equivalently, ionized) part of the Green’s function in the ω-representation can be expressed through connected diagrams only. Similar proper- ties are also shared by the first order ω-derivatives of the retarded part of the CC Green’s function. This property can be extended to any order ω-derivatives of the Green’s function. Through the Dyson equation of CC Green’s function, the derivatives of corresponding CC self-energy can be evaluated analytically. In analogy to the CC Green’s function, the corresponding CC self-energy is expressed in terms of connected diagrams only. Moreover, the ionized part of the CC Green’s func- tion satisfies the non-homogeneous linear system of ordinary differential equations, whose solution may be represented in the exponential form. Our analysis can be easily generalized to the advanced part of the CC Green’s function.
Study of Ground State Wave-function of the Neutron-rich 29,30Na Isotopes through Coulomb Breakup
Directory of Open Access Journals (Sweden)
Rahaman A.
2014-03-01
Full Text Available Coulomb breakup of unstable neutron rich nuclei 29,30Na around the ‘island of inversion’ has been studied at energy around 434 MeV/nucleon and 409 MeV/nucleon respectively. Four momentum vectors of fragments, decay neutron from excited projectile and γ-rays emitted from excited fragments after Coulomb breakup are measured in coincidence. For these nuclei, the low-lying dipole strength above one neutron threshold can be explained by direct breakup model. The analysis for Coulomb breakup of 29,30Na shows that large amount of the cross section yields the 28Na, 29Na core in ground state. The predominant ground-state configuration of 29,30Na is found to be 28Na(g.s⊗νs1/2 and 29Na(g.s⊗νs1/2,respectively.
Ground state of medium-heavy doubly-closed shell nuclei in correlated basis function theory
Bisconti, C; Có, G; Fabrocini, A
2006-01-01
The correlated basis function theory is applied to the study of medium-heavy doubly closed shell nuclei with different wave functions for protons and neutrons and in the jj coupling scheme. State dependent correlations including tensor correlations are used. Realistic two-body interactions of Argonne and Urbana type, together with three-body interactions have been used to calculate ground state energies and density distributions of the 12C, 16O, 40Ca, 48Ca and 208Pb nuclei.
Kvaal, Simen; Helgaker, Trygve
2015-11-14
The relationship between the densities of ground-state wave functions (i.e., the minimizers of the Rayleigh-Ritz variation principle) and the ground-state densities in density-functional theory (i.e., the minimizers of the Hohenberg-Kohn variation principle) is studied within the framework of convex conjugation, in a generic setting covering molecular systems, solid-state systems, and more. Having introduced admissible density functionals as functionals that produce the exact ground-state energy for a given external potential by minimizing over densities in the Hohenberg-Kohn variation principle, necessary and sufficient conditions on such functionals are established to ensure that the Rayleigh-Ritz ground-state densities and the Hohenberg-Kohn ground-state densities are identical. We apply the results to molecular systems in the Born-Oppenheimer approximation. For any given potential v ∈ L(3/2)(ℝ(3)) + L(∞)(ℝ(3)), we establish a one-to-one correspondence between the mixed ground-state densities of the Rayleigh-Ritz variation principle and the mixed ground-state densities of the Hohenberg-Kohn variation principle when the Lieb density-matrix constrained-search universal density functional is taken as the admissible functional. A similar one-to-one correspondence is established between the pure ground-state densities of the Rayleigh-Ritz variation principle and the pure ground-state densities obtained using the Hohenberg-Kohn variation principle with the Levy-Lieb pure-state constrained-search functional. In other words, all physical ground-state densities (pure or mixed) are recovered with these functionals and no false densities (i.e., minimizing densities that are not physical) exist. The importance of topology (i.e., choice of Banach space of densities and potentials) is emphasized and illustrated. The relevance of these results for current-density-functional theory is examined.
Roemelt, Michael; Neese, Frank
2013-04-11
A spin-adapted configuration interaction with singles method that is based on a restricted open-shell reference function (ROCIS) with general total spin S is presented. All excited configuration state functions (CSFs) are generated with the aid of a spin-free second quantization formalism that only leads to CSFs within the first order interacting space. By virtue of the CSF construction, the formalism involves higher than singly excited determinants but not higher than singly excited configurations. Matrix elements between CSFs are evaluated on the basis of commutator relationships using a symbolic algebra program. The final equations were, however, hand-coded in order to maximize performance. The method can be applied to fairly large systems with more than 100 atoms in reasonable wall-clock times and also parallelizes well. Test calculations demonstrate that the approach is far superior to UHF-based configuration interaction with single excitations but necessarily falls somewhat short of quantitative accuracy due to the lack of dynamic correlation contributions. In order to implicitly account for dynamic correlation in a crude way, the program optionally allows for the use of Kohn-Sham orbitals in combination with a modest downscaling of two-electron integrals (DFT/ROCIS). All two-electron integrals of Kohn-Sham orbitals that appear in the Hamiltonian matrix are reduced by a total of three scaling parameters that are suitable for a wide range of molecules. Test calculations on open-shell organic radicals as well as transition metal complexes demonstrate the wide applicability of the method and its ability to calculate the electronic spectra of large molecular systems.
Chong, D. P.; Langhoff, S. R.
1986-01-01
A modified coupled pair functional (CPF) method is presented for the configuration interaction problem that dramatically improves properties for cases where the Hartree-Fock reference configuration is not a good zeroth-order wave function description. It is shown that the tendency for CPF to overestimate the effect of higher excitations arises from the choice of the geometric mean for the partial normalization denominator. The modified method is demonstrated for ground state dipole moment calculations of the NiH, CuH, and ZnH transition metal hydrides, and compared to singles-plus-doubles configuration interaction and the Ahlrichs et al. (1984) CPF method.
Lower ground state due to counter-rotating wave interaction in trapped ion system
Liu, T; Feng, M
2007-01-01
We consider a single ion confined in a trap under radiation of two traveling waves of lasers. In the strong-excitation regime and without the restriction of Lamb-Dicke limit, the Hamiltonian of the system is similar to a driving Jaynes-Cummings model without rotating wave approximation (RWA). The approach we developed enables us to present a complete eigensolutions, which makes it available to compare with the solutions under the RWA. We find that, the ground state in our non-RWA solution is energically lower than the counterpart under the RWA. If we have the ion in the ground state, it is equivalent to a spin dependent force on the trapped ion. Discussion is made for the difference between the solutions with and without the RWA, and for the relevant experimental test, as well as for the possible application in quantum information processing.
Convergence of the partial wave expansion of the He ground state
Bromley, M W J
2006-01-01
The Configuration Interaction (CI) method using a very large Laguerre orbital basis is applied to the calculation of the He ground state. A minimum of 35 radial orbitals for each partial wave ranging from 0 to 12 are included resulting in a basis with a total of 465 orbitals. The convergence of the energy and electron-electron $\\delta$-function with respect to J (the maximum angular momenta of the orbitals included in the CI expansion) are investigated in detail. It is seen that the convergence properties of some previous very large calculations show irregularities. The J to infinity limit of the energy was obtained by fitting to expansions of the type Delta E_J = A_E/(J+1/2)^4 + B_E/(J+1/2)^5 + ..., giving an energy about 10^-7 hartree from the exact energy. Convergence issues caused problems when trying to determine the J to infinity limit of using a similar asymptotic expansion and the biggest calculations achieved accuracies between 0.2 and 0.5%.
On the ground state energy of the delta-function Fermi gas
Tracy, Craig A.; Widom, Harold
2016-10-01
The weak coupling asymptotics to order γ of the ground state energy of the delta-function Fermi gas, derived heuristically in the literature, is here made rigorous. Further asymptotics are in principle computable. The analysis applies to the Gaudin integral equation, a method previously used by one of the authors for the asymptotics of large Toeplitz matrices.
Structure and analytical potential energy function for the ground state of the BCx (x=0, -1)
Institute of Scientific and Technical Information of China (English)
Geng Zhen-Duo; Zhang Yan-Song; Fan Xiao-Wei; Lu Zhan-Sheng; Luo Gai-Xia
2006-01-01
In this paper, the electronic states of the ground states and dissociation limits of BC and BC- are correctly determined based on group theory and atomic and molecular reaction statics. The equilibrium geometries, harmonic frequencies and dissociation energies of the ground state of BC and BC- are calculated by using density function theory and quadratic CI method including single and double substitutions. The analytical potential energy functions of these states have been fitted with Murrell-Sorbie potential energy function from our ab initio calculation results. The spectroscopic data (αe, ωe and ωeXe) of each state is calculated via the relation between analytical potential energy function and spectroscopic data. All the calculations are in good agreement with the experimental data.
Analytical Potential Energy Function for the Ground State X1∑+ of Lanthanum Monofluoride
Institute of Scientific and Technical Information of China (English)
CHEN Lin-Hong; SHANG Ren-Cheng
2003-01-01
The equilibrium geometry, harmonic frequency and bond dissociation energy of lanthanum monofluoride have been calculated using Density-Functional Theory (DFT), post-HF methods MP2 and CCSD(T) with the energyconsistent relativistic effective core potentials. The possible electronic state and reasonable dissociation limit of the ground state of LaF are determined based on atomic and molecular reaction statics. Potential energy curve scans for the ground state X 1∑+ have been performed at B3LYP and CCSD(T) levels, due to their better results of harmonic frequency and bond dissociation energy. We find that the potential energy calculated with CCSD(T) is about 0.6 eV larger than the bond dissociation energy, when the internuclear distance is as large as 0.8 nm. The problem that single-reference ab initio methods do not meet dissociation limit during calculations of lanthanide heavy-metal elements is analyzed. We propose the calculation scheme to derive the analytical Murrell-Sorbie potential energy function. Vibrotational spectroscopic constants Be, ωe, ωeχe, αe, βe, De and He obtained by the standard Dunham treatment coincide well with the results of rotational analyses on spectroscopic experiments.
Pieper, Steven C.; Wiringa, R. B.; Pandharipande, V. R.
1990-01-01
A variational method is used to study the ground state of 16O. Expectation values are computed with a cluster expansion for the noncentral correlations in the wave function; the central correlations and exchanges are treated to all orders by Monte Carlo integration. The expansion has good convergence. Results are reported for the Argonne v14 two-nucleon and Urbana VII three-nucleon potentials.
Whitfield, J D; Biamonte, J D
2012-01-01
Designing and optimizing cost functions and energy landscapes is a problem encountered in many fields of science and engineering. These landscapes and cost functions can be embedded and annealed in experimentally controllable spin Hamiltonians. Using an approach based on group theory and symmetries, we examine the embedding of Boolean logic gates into the ground state subspace of such spin systems. We describe parameterized families of diagonal Hamiltonians and symmetry operations which preserve the ground state subspace encoding the truth tables of Boolean formulas. The ground state embeddings of adder circuits are used to illustrate how gates are combined and simplified using symmetry. Our work is relevant for experimental demonstrations of ground state embeddings found in both classical optimization as well as adiabatic quantum optimization.
Covariant energy density functionals: nuclear matter constraints and global ground state properties
Afanasjev, A V
2016-01-01
The correlations between global description of the ground state properties (binding energies, charge radii) and nuclear matter properties of the state-of-the-art covariant energy density functionals have been studied. It was concluded that the strict enforcement of the constraints on the nuclear matter properties (NMP) defined in Ref.\\ \\cite{RMF-nm} will not necessary lead to the functionals with good description of the binding energies and other ground and excited state properties. In addition, it will not substantially reduce the uncertainties in the predictions of the binding energies in neutron-rich systems. It turns out that the functionals, which come close to satisfying these NMP constraints, have some problems in the description of existing data. On the other hand, these problems are either absent or much smaller in the functionals which are carefully fitted to finite nuclei but which violate some NMP constraints. This is a consequence of the fact that the properties of finite nuclei are defined not o...
Many-body Expanded Analytical Potential Energy Function for Ground State PuOH Molecule
Institute of Scientific and Technical Information of China (English)
LI Yue-Xun; GAO Tao; ZHU Zheng-He
2006-01-01
Using the density functional method B3LYP with relativistic effective core potential (RECP) for Pu atom, the low-lying excited states (4∑+, 6∑+, 8∑+) for three structures of PuOH molecule were optimized. The results show that the ground state is X6∑+of the linear Pu-O-H (C∞v), its corresponding equilibrium geometry and dissociation energy are RPu-O=0.20595 nm, RO-H=0.09581 nm and -8.68 eV, respectively. At the same time, two other metastable structures [PuOH (Cs) and H-Pu-O (C∞v)] were found. The analytical potential energy function has also been derived for whole range using the many-body expansion method. This potential energy function represents the considerable topographical features of PuOH molecule in detail, which is adequately accurate in the whole potential surface and can be used for the molecular reaction dynamics research.
Analytical expressions for partial wave two-body Coulomb transition matrices at ground-state energy
Kharchenko, V. F.
2016-11-01
Leaning upon the Fock method of the stereographic projection of the three-dimensional momentum space onto the four-dimensional unit sphere the possibility of the analytical solving of the Lippmann-Schwinger integral equation for the partial wave two-body Coulomb transition matrix at the ground bound state energy has been studied. In this case new expressions for the partial p-, d- and f-wave two-body Coulomb transition matrices have been obtained in the simple analytical form. The developed approach can also be extended to determine analytically the partial wave Coulomb transition matrices at the energies of excited bound states.
Kohn, W.
1983-01-01
It is shown that if n(r) is the discrete density on a lattice (enclosed in a finite box) associated with a nondegenerate ground state in an external potential v(r) (i.e., is 'v-representable'), then the density n(r) + mu(r), with m(r) arbitrary (apart from trivial constraints) and mu small enough, is also associated with a nondegenerate ground state in an external potential v'(r) near v(r); i.e., n(r) + m(r) is also v-representable. Implications for the Hohenberg-Kohn variational principle and the Kohn-Sham equations are discussed.
DEFF Research Database (Denmark)
Johnsen, Kristinn; Yngvason, Jakob
1996-01-01
and the electron number N tend to infinity with N/Z fixed, and the magnetic field B tends to infinity in such a way that B/Z4/3→∞. We have calculated electronic density profiles and ground-state energies for values of the parameters that prevail on neutron star surfaces and compared them with results obtained...
Ghosh, Soumen; Sonnenberger, Andrew L; Hoyer, Chad E; Truhlar, Donald G; Gagliardi, Laura
2015-08-11
The correct description of charge transfer in ground and excited states is very important for molecular interactions, photochemistry, electrochemistry, and charge transport, but it is very challenging for Kohn-Sham (KS) density functional theory (DFT). KS-DFT exchange-correlation functionals without nonlocal exchange fail to describe both ground- and excited-state charge transfer properly. We have recently proposed a theory called multiconfiguration pair-density functional theory (MC-PDFT), which is based on a combination of multiconfiguration wave function theory with a new type of density functional called an on-top density functional. Here we have used MC-PDFT to study challenging ground- and excited-state charge-transfer processes by using on-top density functionals obtained by translating KS exchange-correlation functionals. For ground-state charge transfer, MC-PDFT performs better than either the PBE exchange-correlation functional or CASPT2 wave function theory. For excited-state charge transfer, MC-PDFT (unlike KS-DFT) shows qualitatively correct behavior at long-range with great improvement in predicted excitation energies.
Dugave, Maxime; Kozlowski, Karol K; Suzuki, Junji
2016-01-01
We use the form factors of the quantum transfer matrix in the zero-temperature limit in order to study the two-point ground-state correlation functions of the XXZ chain in the antiferromagnetic massive regime. We obtain novel form factor series representations of the correlation functions which differ from those derived either from the q-vertex-operator approach or from the algebraic Bethe Ansatz approach to the usual transfer matrix. We advocate that our novel representations are numerically more efficient and allow for a straightforward calculation of the large-distance asymptotic behaviour of the two-point functions. Keeping control over the temperature corrections to the two-point functions we see that these are of order $T^\\infty$ in the whole antiferromagnetic massive regime. The isotropic limit of our result yields a novel form factor series representation for the two-point correlation functions of the XXX chain at zero magnetic field.
Ground state correlations and mean field in 16O
Heisenberg, Jochen H.; Mihaila, Bogdan
1999-03-01
We use the coupled cluster expansion [exp(S) method] to generate the complete ground state correlations due to the NN interaction. Part of this procedure is the calculation of the two-body G matrix inside the nucleus in which it is being used. This formalism is being applied to 16O in a configuration space of 50ħω. The resulting ground state wave function is used to calculate the binding energy and one- and two-body densities for the ground state of 16O.
Ground state correlations and mean-field in $^{16}$O
Heisenberg, J H; Heisenberg, Jochen H.; Mihaila, Bogdan.
1999-01-01
We use the coupled cluster expansion ($\\exp(S)$ method) to generate the complete ground state correlations due to the $NN$ interaction. Part of this procedure is the calculation of the two-body ${\\mathbf G}$ matrix inside the nucleus in which it is being used. This formalism is being applied to $^{16}$O in a configuration space of 35 $\\hbar\\omega$. The resulting ground state wave function is used to calculate the binding energy and one- and two-body densities for the ground state of~$^{16}$O.
Institute of Scientific and Technical Information of China (English)
Zeng Hui; Zhao Jun
2012-01-01
In this paper,the energy,equilibrium geometry,and harmonic frequency of the ground electronic state of PO2 are computed using the B3LYP,B3P86,CCSD(T),and QCISD(T) methods in conjunction with the 6-311++G(3df,3pd) and cc-pVTZ basis sets.A comparison between the computational results and the experimental values indicates that the B3P86/6-311++G(3df,3pd) method can give better energy calculation results for the PO2 molecule.It is shown that the ground state of the PO2 molecule has C2v symmetry and its ground electronic state is X2A1.The equilibrium parameters of the structure are Rp-O =0.1465 nm,∠OPO =134.96°,and the dissociation energy is Ed =19.218 eV.The bent vibrational frequency v1 =386 cm-1,symmetric stretching frequency v2 =1095 cm-1,and asymmetric stretching frequency v3 =1333 cm-1 are obtained.On the basis of atomic and molecular reaction statics,a reasonable dissociation limit for the ground state of the PO2 molecule is determined.Then the analytic potential energy function of the PO2 molecule is derived using many-body expansion theory.The potential curves correctly reproduce the configurations and the dissociation energy for the PO2 molecule.
Choi, Jinwoo; Chang, Eonho; Anstine, Dylan M.; Chakraborty, Himadri
2016-05-01
We study the ground state properties of C60 and C240 molecules in a spherical frame of local density approximation (LDA). Within this mean-field theory, two different approximations to the exchange-correlation (xc) functional are used: (i) The Gunnerson-Lundqvist parametrization augmented by a treatment to correct for the electron self-interaction and (ii) the van Leeuwen and Baerends (LB94) model potential that inclusively restores electron's asymptotic properties. Results show differences in the ground-state potential, level energies and electron densities between the two xc choices. We then use the ground structure to find the excited and ionized states of the systems and calculate dipole single-photoionization cross sections in a time-dependent LDA method that incorporates linear-response dynamical correlations. Comparative effects of the choices of xc on collective plasmon and single-excitation Auger resonances as well as on geometry driven cavity oscillations are found significant. The work is supported by the NSF, USA.
Energy Technology Data Exchange (ETDEWEB)
Hopper, D.G.
1980-05-01
The ground state potential energy surface for the nitrogen dioxide positive ion, NO/sup +//sub 2/X /sup 1/..sigma../sup +//sub g/(..sigma../sup +/,A/sub 1/,A'), has been scanned with a correlated wave function to obtain directly, for the first time, the gas phase equilibrium geometry, force constants, vibrational frequencies, and dipole moment function. The wave function for this scan was constructed from a double-zeta plus polarization one-electron basis with a 12 configuration MCSCF determination of the orbital basis for a full valence /sup 1/..sigma../sup +//sub g/ configuration interaction expansion. The calculated equilibrium bond length is 1.12 A. The vibrational frequencies are computed to be ..nu../sub 1/=1514, ..nu../sub 2/=679, and ..nu../sub 3/=2614 cm/sup -1/ The present ab initio results differ significantly from crystalline spectroscopic studies and are, thus, the best values available for the gas phase vibrational frequencies. The dipole moment function is nonzero at the ..sigma../sup +/, A/sub 1/, and A' geometries included in the potential surface scan, and is obtained here to provide for the future a priori calculation of the infrared band intensities.
Nawa, Kenji; Kitaoka, Yukie; Nakamura, Kohji; Imamura, Hiroshi; Akiyama, Toru; Ito, Tomonori; Weinert, M.
2016-07-01
The ground-state electronic configurations of the correlated organometallic metallocenes, M Cp2,M =V , Cr, Mn, Fe, Co, and Ni, are investigated using constraint density functional theory combined with nonempirical Ueff parameters determined from linear-response theory. The relative stability of the various d -orbital electronic configurations of these organometallic molecules is found to be sensitive to the amount of correlation. Using nonempirical values of Ueff, the calculated electronic configurations are in agreement with the experiments: 4A2 g ,3E2 g ,6A1 g ,1A1 g ,2E1 g , and 3A2 g for the VCp2,CrCp2,MnCp2,FeCp2,CoCp2 , and NiCp2, respectively.
Global Dipole Moment Function for the X1 Sigma+ Ground State of CO
Langhoff, Stephen R.; Bauschlicher, Charles W., Jr.
1994-01-01
We have studied the dipole moment function (DMF) for the X(sup 1)Sigma(sup +) state of CO as a function of the completeness of the one- and n-particle treatments. Our best DMF is obtained using an augmented correlation-consistent quadruple-zeta basis set with external correlation included using the averaged-coupled-pair functional (ACPF) approach from a complete-active-space self-consistent-field zeroth-order reference. The DMF evaluated using the finite-field approach is in far better agreement with the experimentally deduced DMF than all previous theoretical determinations, but systematic differences still remain in the DMF at larger internuclear distances that give rise to significant discrepancies between the theoretical and experimental Einstein coefficients for transitions involving vibrational quantum numbers above about Upsilon=15.
Systematic of Nuclear Ground State Properties in Sr Isotope by Covariant Density Functional Theory
Institute of Scientific and Technical Information of China (English)
TIAN; Yuan
2012-01-01
<正>The hyperfine structure and isotope shifts of Sr-isotopes, both even-even and odd-even nuclei, are studied in the covariant density functional theory (DFT) with the new parameter set DD-PC1. Pairing correlation is treated by using the Bogoliubov with a separable form of the pairing interaction. Spin-parity,
Dugave, Maxime; Göhmann, Frank; Kozlowski, Karol K.; Suzuki, Junji
2016-09-01
We use the form factors of the quantum transfer matrix in the zero-temperature limit in order to study the two-point ground-state correlation functions of the XXZ chain in the antiferromagnetic massive regime. We obtain novel form factor series representations of the correlation functions which differ from those derived either from the q-vertex-operator approach or from the algebraic Bethe Ansatz approach to the usual transfer matrix. We advocate that our novel representations are numerically more efficient and allow for a straightforward calculation of the large-distance asymptotic behaviour of the two-point functions. Keeping control over the temperature corrections to the two-point functions we see that these are of order {T}∞ in the whole antiferromagnetic massive regime. The isotropic limit of our result yields a novel form factor series representation for the two-point correlation functions of the XXX chain at zero magnetic field. Dedicated to the memory of Petr Petrovich Kulish.
Ground-state properties of rare-earth metals: an evaluation of density-functional theory.
Söderlind, Per; Turchi, P E A; Landa, A; Lordi, V
2014-10-15
The rare-earth metals have important technological applications due to their magnetic properties, but are scarce and expensive. Development of high-performance magnetic materials with less rare-earth content is desired, but theoretical modeling is hampered by complexities of the rare earths electronic structure. The existence of correlated (atomic-like) 4f electrons in the vicinity of the valence band makes any first-principles theory challenging. Here, we apply and evaluate the efficacy of density-functional theory for the series of lanthanides (rare earths), investigating the influence of the electron exchange and correlation functional, spin-orbit interaction, and orbital polarization. As a reference, the results are compared with those of the so-called 'standard model' of the lanthanides in which electrons are constrained to occupy 4f core states with no hybridization with the valence electrons. Some comparisons are also made with models designed for strong electron correlations. Our results suggest that spin-orbit coupling and orbital polarization are important, particularly for the magnitude of the magnetic moments, and that calculated equilibrium volumes, bulk moduli, and magnetic moments show correct trends overall. However, the precision of the calculated properties is not at the level of that found for simpler metals in the Periodic Table of Elements, and the electronic structures do not accurately reproduce x-ray photoemission spectra.
Accurate Ground-State Energies of Solids and Molecules from Time-Dependent Density-Functional Theory
DEFF Research Database (Denmark)
Olsen, Thomas; Thygesen, Kristian Sommer
2014-01-01
We demonstrate that ground-state energies approaching chemical accuracy can be obtained by combining the adiabatic-connection fluctuation-dissipation theorem with time-dependent densityfunctional theory. The key ingredient is a renormalization scheme, which eliminates the divergence...
Estimation of beryllium ground state energy by Monte Carlo simulation
Energy Technology Data Exchange (ETDEWEB)
Kabir, K. M. Ariful [Department of Physical Sciences, School of Engineering and Computer Science, Independent University, Bangladesh (IUB) Dhaka (Bangladesh); Halder, Amal [Department of Mathematics, University of Dhaka Dhaka (Bangladesh)
2015-05-15
Quantum Monte Carlo method represent a powerful and broadly applicable computational tool for finding very accurate solution of the stationary Schrödinger equation for atoms, molecules, solids and a variety of model systems. Using variational Monte Carlo method we have calculated the ground state energy of the Beryllium atom. Our calculation are based on using a modified four parameters trial wave function which leads to good result comparing with the few parameters trial wave functions presented before. Based on random Numbers we can generate a large sample of electron locations to estimate the ground state energy of Beryllium. Our calculation gives good estimation for the ground state energy of the Beryllium atom comparing with the corresponding exact data.
Institute of Scientific and Technical Information of China (English)
CAO, Xiao-Yan(曹晓燕); HONG, Gong-Yi(洪功义); WANG, Dian-Xun(王殿勋); LI, Le-Min(黎乐民); XU, Guang-Xian(徐光宪)
2000-01-01
Density Functional Theory (DFT) studies on the ground states (2A＇2) of NO3 radical and on the ground state (1A＇1) and the first triplet state (3E") of NO3+ cation provide an unambiguous prediction about their geometrical structure: the ground states of both NO3 radical and NO3+ cation have D3h symmetry and the geometrical configuration of the first triplet state 3E" of NO3+ cation has C2v symmetry. It is shown that s far as the ionization energy calculations on NO3 radical are concerned, the results are only slightly different, no mater that gradient corrections of the exchange-correlation energy are included during self-consistent iterations of they are included as perturbations after the self-consistent iterations.
Hara, Akito; Awano, Teruyoshi
2017-06-01
Ultrashallow thermal donors (USTDs), which consist of light element impurities such as carbon, hydrogen, and oxygen, have been found in Czochralski silicon (CZ Si) crystals. To the best of our knowledge, these are the shallowest hydrogen-like donors with negative central-cell corrections in Si. We observed the ground-state splitting of USTDs by far-infrared optical absorption at different temperatures. The upper ground-state levels are approximately 4 meV higher than the ground-state levels. This energy level splitting is also consistent with that obtained by thermal excitation from the ground state to the upper ground state. This is direct evidence that the wave function of the USTD ground state is made up of a linear combination of conduction band minimums.
Qin, Mingpu; Shi, Hao; Zhang, Shiwei
2017-08-01
Optical lattice experiments with ultracold fermion atoms and quantum gas microscopy have recently realized direct measurements of magnetic correlations at the site-resolved level. We calculate the short-range spin-correlation functions in the ground state of the two-dimensional repulsive Hubbard model with the auxiliary-field quantum Monte Carlo (AFQMC) method. The results are numerically exact at half filling where the fermion sign problem is absent. Away from half filling, we employ the constrained path AFQMC approach to eliminate the exponential computational scaling from the sign problem. The constraint employs unrestricted Hartree-Fock trial wave functions with an effective interaction strength U , which is optimized self-consistently within AFQMC. Large supercells are studied, with twist averaged boundary conditions as needed, to reach the thermodynamic limit. We find that the nearest-neighbor spin correlation always increases with the interaction strength U , contrary to the finite-temperature behavior where a maximum is reached at a finite U value. We also observe a change of sign in the next-nearest-neighbor spin correlation with increasing density, which is a consequence of the buildup of the long-range antiferromagnetic correlation. We expect the results presented in this paper to serve as a benchmark as lower temperatures are reached in ultracold atom experiments.
Argument for charge density wave sub-phases in the ground state of α-(BEDT-TTF) 2KHg(SCN) 4
Biskup, N.; Perenboom, J. A. A. J.; Brooks, J. S.; Qualls, J. S.
1998-07-01
A resistive anomaly at temperature Tp in the title compound is associated with a Fermi surface reconstruction from a metallic to a (spin or charge) density wave state. At high magnetic fields a corresponding feature in the magnetoresistance above a field BK indicates the breaking of this state. We argue that TP indicates a second order phase line identical to that measured by specific heat methods and show that it decreases monotonically up to 30T. We find that Pauli (rather than orbital) effects, dominate the reduction in Tp. We further argue that BK is a first-order transition between two subphases below Tp. We compare the phase diagram with recent theoretical models for CDW and SDW ground states in high magnetic fields.
Dóra, B.; Maki, K.; Virosztek, A.; Ványolos, A.
2004-04-01
We have investigated theoretically the thermoelectric power and the Nernst effect in unconventional density waves (UDW). Due to the presence of magnetic field, Landau levels are formed, and the low energy excitations change from gapless to gapped. The present results account consistently for the recent data of magnetothermopower in α-(BEDT-TTF)2KHg(SCN)4 obtained by Choi et al. (Phys. Rev. B, 65, 205119 (2002)). This confirms further our identification of low temperature phase (LTP) in this salt as UCDW. Key words. density waves, α-(BEDT-TTF)2KHg(SCN)4, thermoelectric power.
Haykal, I.; Margules, L.; Huet, T. R.; Motiyenko, R. A.; Carvajal, M.; Kleiner, I.; Guillemin, J. C.; Tercero, B.; Cernicharo, J.
2013-06-01
The detection of nineteen new rotational transitions of the parent molecule of methylformate (HCOOCH_{3}) in the second lowest excited torsional mode (ν_{t} =2) was recently reported in Orion-KL, as well as the detection of eighty new lines corresponding to the two ^{18}O isotopologs of methylformate in their ground states. The laboratory work on HCOO^{13}CH_{3} was continued. A wide spectral range from 50 to 940 GHz was recorded in Lille with the submillimeter-wave spectrometer based on harmonic generation of a microwave synthesizer source, using a multiplication chain of solid state sources (50-100 and 150-940 GHz) and a backward wave oscillator (100-150 GHz), and coupled to a 2.2 m cell. The absolute accuracy of the line positions is better than 30 kHz up to 630 GHz and 50 kHz above. The two states (ν_{t} = 0 and 1) were fitted together using the RAM Hamiltonian of the BELGI program and a new set of 45 parameters was accurately determined. The fit contains 7050 lines corresponding to the ground state up to J = 78 and K_{a} = 34 and 1907 lines related to ν_{t} =1 up to J = 59 and K_{a} = 24. The detection of new ν_{t} =1 lines in Orion KL will be reported and discussed. This work is supported by the French Programme National de Physico-Chimie du Milieu Interstellaire (CNRS), by CNES, and by the Spanish Government through the grants FIS2011-28738-C02-02 and CONSOLIDER 2009-00038. S. Takano, Y. Sakai, S. Kakimoto, M. Sasaki, and K. Kobayashi PASJ. {64}, 89, 2012. B. Tercero, et al. A& A. {538}, A199, 2012. M. Carvajal, et al. A& A. {500}, 1109, 2009.
Schmidt, Matthew; Constable, Steve; Ing, Christopher; Roy, Pierre-Nicholas
2014-06-21
We developed and studied the implementation of trial wavefunctions in the newly proposed Langevin equation Path Integral Ground State (LePIGS) method [S. Constable, M. Schmidt, C. Ing, T. Zeng, and P.-N. Roy, J. Phys. Chem. A 117, 7461 (2013)]. The LePIGS method is based on the Path Integral Ground State (PIGS) formalism combined with Path Integral Molecular Dynamics sampling using a Langevin equation based sampling of the canonical distribution. This LePIGS method originally incorporated a trivial trial wavefunction, ψT, equal to unity. The present paper assesses the effectiveness of three different trial wavefunctions on three isotopes of hydrogen for cluster sizes N = 4, 8, and 13. The trial wavefunctions of interest are the unity trial wavefunction used in the original LePIGS work, a Jastrow trial wavefunction that includes correlations due to hard-core repulsions, and a normal mode trial wavefunction that includes information on the equilibrium geometry. Based on this analysis, we opt for the Jastrow wavefunction to calculate energetic and structural properties for parahydrogen, orthodeuterium, and paratritium clusters of size N = 4 - 19, 33. Energetic and structural properties are obtained and compared to earlier work based on Monte Carlo PIGS simulations to study the accuracy of the proposed approach. The new results for paratritium clusters will serve as benchmark for future studies. This paper provides a detailed, yet general method for optimizing the necessary parameters required for the study of the ground state of a large variety of systems.
Energy Technology Data Exchange (ETDEWEB)
Schmidt, Matthew; Constable, Steve; Ing, Christopher; Roy, Pierre-Nicholas, E-mail: pnroy@uwaterloo.ca [Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1 (Canada)
2014-06-21
We developed and studied the implementation of trial wavefunctions in the newly proposed Langevin equation Path Integral Ground State (LePIGS) method [S. Constable, M. Schmidt, C. Ing, T. Zeng, and P.-N. Roy, J. Phys. Chem. A 117, 7461 (2013)]. The LePIGS method is based on the Path Integral Ground State (PIGS) formalism combined with Path Integral Molecular Dynamics sampling using a Langevin equation based sampling of the canonical distribution. This LePIGS method originally incorporated a trivial trial wavefunction, ψ{sub T}, equal to unity. The present paper assesses the effectiveness of three different trial wavefunctions on three isotopes of hydrogen for cluster sizes N = 4, 8, and 13. The trial wavefunctions of interest are the unity trial wavefunction used in the original LePIGS work, a Jastrow trial wavefunction that includes correlations due to hard-core repulsions, and a normal mode trial wavefunction that includes information on the equilibrium geometry. Based on this analysis, we opt for the Jastrow wavefunction to calculate energetic and structural properties for parahydrogen, orthodeuterium, and paratritium clusters of size N = 4 − 19, 33. Energetic and structural properties are obtained and compared to earlier work based on Monte Carlo PIGS simulations to study the accuracy of the proposed approach. The new results for paratritium clusters will serve as benchmark for future studies. This paper provides a detailed, yet general method for optimizing the necessary parameters required for the study of the ground state of a large variety of systems.
Lofrumento, C; Arci, F; Carlesi, S; Ricci, M; Castellucci, E; Becucci, M
2015-02-25
The analysis of ground state structural and vibrational properties of Safranin-O is presented. The experimental results, obtained by FTIR, Raman and SERS spectroscopy, are discussed in comparison to the results of DFT calculations carried out at the B3LYP/6-311+G(d,p) level of theory. The calculated spectra reproduce quite satisfactorily the experimental data. The calculated Safranin-O equilibrium structure and the assignment of the vibrational spectra are reported as well. From the changes between Raman and SERS spectra a model is presented for the interaction of Safranin-O with silver nanoparticles.
Mihaila, Bogdan; Heisenberg, Jochen
2000-04-01
We continue the investigations of ground state properties of closed-shell nuclei using the Argonne v18 realistic NN potential, together with the Urbana IX three-nucleon interaction. The ground state wave function is used to calculate the charge form factor and charge density. Starting with the ground state wave function of the closed-shell nucleus, we use the equation of motion technique to calculate the ground state and excited states of a neighboring nucleus. We then generate the corresponding magnetic form factor. We correct for distortions due to the interaction between the electron probe and the nuclear Coulomb field using the DWBA picture. We compare our results with the available experimental data. Even though our presentation will focus mainly on the ^16O and ^15N nuclei, results for other nuclei in the p and s-d shell will also be presented.
Density functional calculations of spin-wave dispersion curves.
Kleinman, Leonard; Niu, Qian
1998-03-01
Extending the density functional method of Kubler et al( J. Kubler et al, J. Phys. F 18, 469 (1983) and J. Phys. Condens. Matter 1, 8155 (1989). ) for calcuating spin density wave ground states (but not making their atomic sphere approximation which requires a constant spin polarization direction in each WS sphere) we dicuss the calculation of frozen spin-wave eigenfunctions and their total energies. From these and the results of Niu's talk, we describe the calculation of spin-wave frequencies.
Singlet Ground State Magnetism:
DEFF Research Database (Denmark)
Loidl, A.; Knorr, K.; Kjems, Jørgen;
1979-01-01
The magneticGamma 1 –Gamma 4 exciton of the singlet ground state system TbP has been studied by inelastic neutron scattering above the antiferromagnetic ordering temperature. Considerable dispersion and a pronounced splitting was found in the [100] and [110] directions. Both the band width...... and the splitting increased rapidly as the transition temperature was approached in accordance with the predictions of the RPA-theory. The dispersion is analysed in terms of a phenomenological model using interactions up to the fourth nearest neighbour....
Energy Technology Data Exchange (ETDEWEB)
Säkkinen, Niko; Leeuwen, Robert van [Department of Physics, Nanoscience Center, University of Jyväskylä, Survontie 9, 40014 Jyväskylä (Finland); Peng, Yang [Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, 14195 Berlin (Germany); Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin-Dahlem (Germany); Appel, Heiko [Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin-Dahlem (Germany)
2015-12-21
We study ground-state properties of a two-site, two-electron Holstein model describing two molecules coupled indirectly via electron-phonon interaction by using both exact diagonalization and self-consistent diagrammatic many-body perturbation theory. The Hartree and self-consistent Born approximations used in the present work are studied at different levels of self-consistency. The governing equations are shown to exhibit multiple solutions when the electron-phonon interaction is sufficiently strong, whereas at smaller interactions, only a single solution is found. The additional solutions at larger electron-phonon couplings correspond to symmetry-broken states with inhomogeneous electron densities. A comparison to exact results indicates that this symmetry breaking is strongly correlated with the formation of a bipolaron state in which the two electrons prefer to reside on the same molecule. The results further show that the Hartree and partially self-consistent Born solutions obtained by enforcing symmetry do not compare well with exact energetics, while the fully self-consistent Born approximation improves the qualitative and quantitative agreement with exact results in the same symmetric case. This together with a presented natural occupation number analysis supports the conclusion that the fully self-consistent approximation describes partially the bipolaron crossover. These results contribute to better understanding how these approximations cope with the strong localizing effect of the electron-phonon interaction.
Calculation of electron wave functions and refractive index of Ne
Institute of Scientific and Technical Information of China (English)
2008-01-01
The radial wave functions of inner electron shell and outer electron shell of a Ne atom were obtained by the approximate analytical method and tested by calculating the ground state energy of the Ne atom. The equivalent volume of electron cloud and the refractive index of Ne were calculated. The calculated refractive index agrees well with the experimental result. Relationship between the refractive index and the wave function of Ne was discovered.
Ground State Correlations and the Multiconfiguration Mixing Method
Pillet, N; Van Giai, N; Berger, J F; Giai, Nguyen Van
2004-01-01
We study the convergence properties of a truncation scheme in describing the ground state properties of a many-particle system of fermions. The model wave function is built within a multiconfiguration mixing approach where the many-body wave function is described as a superposition of multiparticle-multihole configurations constructed upon a Slater determinant. The convergence properties of physical quantities such as correlation energies and single-particle occupation probabilities in terms of the increasing number of particle-hole configurations are investigated for the case of an exactly solvable pairing hamiltonian.
Ground states of linearly coupled Schrodinger systems
Directory of Open Access Journals (Sweden)
Haidong Liu
2017-01-01
Full Text Available This article concerns the standing waves of a linearly coupled Schrodinger system which arises from nonlinear optics and condensed matter physics. The coefficients of the system are spatially dependent and have a mixed behavior: they are periodic in some directions and tend to positive constants in other directions. Under suitable assumptions, we prove that the system has a positive ground state. In addition, when the L-infinity-norm of the coupling coefficient tends to zero, the asymptotic behavior of the ground states is also obtained.
Flammer, Carson
2005-01-01
Intended to facilitate the use and calculation of spheroidal wave functions, this applications-oriented text features a detailed and unified account of the properties of these functions. Addressed to applied mathematicians, mathematical physicists, and mathematical engineers, it presents tables that provide a convenient means for handling wave problems in spheroidal coordinates.Topics include separation of the scalar wave equation in spheroidal coordinates, angle and radial functions, integral representations and relations, and expansions in spherical Bessel function products. Additional subje
Reduced M(atrix) theory models: ground state solutions
López, J L
2015-01-01
We propose a method to find exact ground state solutions to reduced models of the SU($N$) invariant matrix model arising from the quantization of the 11-dimensional supermembrane action in the light-cone gauge. We illustrate the method by applying it to lower dimensional toy models and for the SU(2) group. This approach could, in principle, be used to find ground state solutions to the complete 9-dimensional model and for any SU($N$) group. The Hamiltonian, the supercharges and the constraints related to the SU($2$) symmetry are built from operators that generate a multicomponent spinorial wave function. The procedure is based on representing the fermionic degrees of freedom by means of Dirac-like gamma matrices, as was already done in the first proposal of supersymmetric (SUSY) quantum cosmology. We exhibit a relation between these finite $N$ matrix theory ground state solutions and SUSY quantum cosmology wave functions giving a possible physical significance of the theory even for finite $N$.
Lanczos steps to improve variational wave functions
Becca, Federico; Hu, Wen-Jun; Iqbal, Yasir; Parola, Alberto; Poilblanc, Didier; Sorella, Sandro
2015-09-01
Gutzwiller-projected fermionic states can be efficiently implemented within quantum Monte Carlo calculations to define extremely accurate variational wave functions for Heisenberg models on frustrated two-dimensional lattices, not only for the ground state but also for low-energy excitations. The application of few Lanczos steps on top of these states further improves their accuracy, allowing calculations on large clusters. In addition, by computing both the energy and its variance, it is possible to obtain reliable estimations of exact results. Here, we report the cases of the frustrated Heisenberg models on square and Kagome lattices.
Klaiman, Shachar; Cederbaum, Lorenz S
2014-11-21
Many-body processes inevitably lead to the transition from one many-body wavefunction to another. Due to the complexity of the initial and final states many-body wavefunctions, one often wishes to try and describe such transitions using only a single-particle function. While there are numerous types of orbitals and densities which are commonly used, the question remains which one is optimal and in which sense. Here we present the optimal one and two body functions whose anti-symmetrized product with the initial state yields the maximal overlap with the final state. A definition of the above optimal condition and its rigorous proof are given. The resulting optimal functions shed additional light on the well-known Dyson orbital and reduced transition matrix, demonstrating further their physical meaning as independent functions.
Trajectory approach to the Schrödinger–Langevin equation with linear dissipation for ground states
Energy Technology Data Exchange (ETDEWEB)
Chou, Chia-Chun, E-mail: ccchou@mx.nthu.edu.tw
2015-11-15
The Schrödinger–Langevin equation with linear dissipation is integrated by propagating an ensemble of Bohmian trajectories for the ground state of quantum systems. Substituting the wave function expressed in terms of the complex action into the Schrödinger–Langevin equation yields the complex quantum Hamilton–Jacobi equation with linear dissipation. We transform this equation into the arbitrary Lagrangian–Eulerian version with the grid velocity matching the flow velocity of the probability fluid. The resulting equation is simultaneously integrated with the trajectory guidance equation. Then, the computational method is applied to the harmonic oscillator, the double well potential, and the ground vibrational state of methyl iodide. The excellent agreement between the computational and the exact results for the ground state energies and wave functions shows that this study provides a synthetic trajectory approach to the ground state of quantum systems.
Wigner’s phase-space function and atomic structure: II. Ground states for closed-shell atoms
DEFF Research Database (Denmark)
Springborg, Michael; Dahl, Jens Peder
1987-01-01
display and analyze the function for the closed-shell atoms helium, beryllium, neon, argon, and zinc in the Hartree-Fock approximation. The quantum-mechanical exact results are compared with those obtained with the approximate Thomas-Fermi description of electron densities in phase space....
Sini, Gjergji
2011-03-08
We have evaluated the performance of several density functional theory (DFT) functionals for the description of the ground-state electronic structure and charge transfer in donor/acceptor complexes. The tetrathiafulvalene- tetracyanoquinodimethane (TTF-TCNQ) complex has been considered as a model test case. Hybrid functionals have been chosen together with recently proposed long-range corrected functionals (ωB97X, ωB97X-D, LRC-ωPBEh, and LC-ωPBE) in order to assess the sensitivity of the results to the treatment and magnitude of exact exchange. The results show an approximately linear dependence of the ground-state charge transfer with the HOMO TTF-LUMOTCNQ energy gap, which in turn depends linearly on the percentage of exact exchange in the functional. The reliability of ground-state charge transfer values calculated in the framework of a monodeterminantal DFT approach was also examined. © 2011 American Chemical Society.
Alternative ground states enable pathway switching in biological electron transfer
Abriata, Luciano A.; Álvarez-Paggi, Damián; Ledesma, Gabriela N.; Blackburn, Ninian J.; Vila, Alejandro J.; Murgida, Daniel H.
2012-01-01
Electron transfer is the simplest chemical reaction and constitutes the basis of a large variety of biological processes, such as photosynthesis and cellular respiration. Nature has evolved specific proteins and cofactors for these functions. The mechanisms optimizing biological electron transfer have been matter of intense debate, such as the role of the protein milieu between donor and acceptor sites. Here we propose a mechanism regulating long-range electron transfer in proteins. Specifically, we report a spectroscopic, electrochemical, and theoretical study on WT and single-mutant CuA redox centers from Thermus thermophilus, which shows that thermal fluctuations may populate two alternative ground-state electronic wave functions optimized for electron entry and exit, respectively, through two different and nearly perpendicular pathways. These findings suggest a unique role for alternative or “invisible” electronic ground states in directional electron transfer. Moreover, it is shown that this energy gap and, therefore, the equilibrium between ground states can be fine-tuned by minor perturbations, suggesting alternative ways through which protein–protein interactions and membrane potential may optimize and regulate electron–proton energy transduction. PMID:23054836
Agbemava, S E; Ring, P
2016-01-01
A systematic investigation of octupole deformed nuclei is presented for even-even systems with $Z\\leq 106$ located between the two-proton and two-neutron drip lines. For this study we use five most up-to-date covariant energy density functionals of different types, with a non-linear meson coupling, with density dependent meson couplings, and with density-dependent zero-range interactions. Pairing correlations are treated within relativistic Hartree-Bogoliubov (RHB) theory based on an effective separable particle-particle interaction of finite range. This allows us to assess theoretical uncertainties within the present covariant models for the prediction of physical observables relevant for octupole deformed nuclei. In addition, a detailed comparison with the predictions of non-relativistic models is performed. A new region of octupole deformation, centered around $Z\\sim 98, N\\sim 196$ is predicted for the first time. In terms of its size in the $(Z,N)$ plane and the impact of octupole deformation on binding e...
Szmytkowski, Radosław
2016-01-01
The ground state of the Dirac one-electron atom, placed in a weak, static electric field of definite $2^{L}$-polarity, is studied within the framework of the first-order perturbation theory. The Sturmian expansion of the generalized Dirac-Coulomb Green function [R. Szmytkowski, J. Phys. B 30 (1997) 825, erratum: 30 (1997) 2747] is used to derive closed-form analytical expressions for various far-field and near-nucleus static electric multipole susceptibilities of the atom. The far-field multipole susceptibilities --- the polarizabilities $\\alpha_{L}$, electric-to-magnetic cross-susceptibilities $\\alpha_{\\mathrm{E}L\\to\\mathrm{M}(L\\mp1)}$ and electric-to-toroidal-magnetic cross-susceptibilities $\\alpha_{\\mathrm{E}L\\to\\mathrm{T}L}$ --- are found to be expressible in terms of one or two non-terminating generalized hypergeometric functions ${}_{3}F_{2}$ with the unit argument. Counterpart formulas for the near-nucleus multipole susceptibilities --- the electric nuclear shielding constants $\\sigma_{\\mathrm{E}L\\to\\m...
Lima, A. F.; Lalic, M. V.
2016-10-01
With objective to determine ground state magnetic structure of multiferroic hexagonal YMnO3 we performed systematic non-collinear spin density-functional-theory (DFT) study of six possible magnetic configurations of Mn ions, treating exchange and correlation effects by standard local-spin-density approximation (LSDA), by LSDA including Hubbard correction (LSDA+U), and taking into account the spin-orbit interaction. We found that P63 and P6´3 configurations are the most stable ones, with very small energy difference between them. This result substantiates conclusions of latest neutron-diffraction studies. Both configurations are characterized by canting of Mn spins that produces weak ferro- (P63) or anti-ferromagnetism (P6‧3) along the hexagonal c-axis. The calculated Mn magnetic moments are found to be in good agreement with experiment, and electronic structure generally agrees with previous non-collinear spin DFT studies that used different basis sets and exchange and correlation functionals.
New ground state for quantum gravity
Magueijo, Joao
2012-01-01
In this paper we conjecture the existence of a new "ground" state in quantum gravity, supplying a wave function for the inflationary Universe. We present its explicit perturbative expression in the connection representation, exhibiting the associated inner product. The state is chiral, dependent on the Immirzi parameter, and is the vacuum of a second quantized theory of graviton particles. We identify the physical and unphysical Hilbert sub-spaces. We then contrast this state with the perturbed Kodama state and explain why the latter can never describe gravitons in a de Sitter background. Instead, it describes self-dual excitations, which are composites of the positive frequencies of the right-handed graviton and the negative frequencies of the left-handed graviton. These excitations are shown to be unphysical under the inner product we have identified. Our rejection of the Kodama state has a moral tale to it: the semi-classical limit of quantum gravity can be the wrong path for making contact with reality (w...
Traces of Lorentz symmetry breaking in a hydrogen atom at ground state
Borges, L. H. C.; Barone, F. A.
2016-02-01
Some traces of a specific Lorentz symmetry breaking scenario in the ground state of the hydrogen atom are investigated. We use standard Rayleigh-Schrödinger perturbation theory in order to obtain the corrections to the ground state energy and the wave function. It is shown that an induced four-pole moment arises, due to the Lorentz symmetry breaking. The model considered is the one studied in Borges et al. (Eur Phys J C 74:2937, 2014), where the Lorentz symmetry is broken in the electromagnetic sector.
Traces of Lorentz symmetry breaking in a Hydrogen atom at ground state
Borges, Luiz Henrique de Campos
2016-01-01
Some traces of a specific Lorentz symmetry breaking scenario in the ground state of the Hydrogen atom are investigated. It is used standard Rayleigh-Schr\\"odinger perturbation theory in order to obtain the corrections to the the ground state energy and wave function. It is shown that an induced four-pole moment arises, due to the Lorentz symmetry breaking. The model considered is the one studied in reference Eur. Phys. J. C {\\bf 74}, 2937 (2014), where the Lorentz symmetry is broken in the electromagnetic sector.
Traces of Lorentz symmetry breaking in a hydrogen atom at ground state
Energy Technology Data Exchange (ETDEWEB)
Borges, L.H.C. [Universidade Federal do ABC, Centro de Ciencias Naturais e Humanas, Santo Andre, SP (Brazil); Barone, F.A. [IFQ-Universidade Federal de Itajuba, Itajuba, MG (Brazil)
2016-02-15
Some traces of a specific Lorentz symmetry breaking scenario in the ground state of the hydrogen atom are investigated. We use standard Rayleigh-Schroedinger perturbation theory in order to obtain the corrections to the ground state energy and the wave function. It is shown that an induced four-pole moment arises, due to the Lorentz symmetry breaking. The model considered is the one studied in Borges et al. (Eur Phys J C 74:2937, 2014), where the Lorentz symmetry is broken in the electromagnetic sector. (orig.)
First observation of $^{13}$Li ground state
Kohley, Z; DeYoung, P A; Volya, A; Baumann, T; Bazin, D; Christian, G; Cooper, N L; Frank, N; Gade, A; Hall, C; Hinnefeld, J; Luther, B; Mosby, S; Peters, W A; Smith, J K; Snyder, J; Spyrou, A; Thoennessen, M
2013-01-01
The ground state of neutron-rich unbound $^{13}$Li was observed for the first time in a one-proton removal reaction from $^{14}$Be at a beam energy of 53.6 MeV/u. The $^{13}$Li ground state was reconstructed from $^{11}$Li and two neutrons giving a resonance energy of 120$^{+60}_{-80}$ keV. All events involving single and double neutron interactions in the Modular Neutron Array (MoNA) were analyzed, simulated, and fitted self-consistently. The three-body ($^{11}$Li+$n+n$) correlations within Jacobi coordinates showed strong dineutron characteristics. The decay energy spectrum of the intermediate $^{12}$Li system ($^{11}$Li+$n$) was described with an s-wave scattering length of greater than -4 fm, which is a smaller absolute value than reported in a previous measurement.
Ground states of bilayered and extended t-J-U models
Energy Technology Data Exchange (ETDEWEB)
Voo, Khee-Kyun, E-mail: kkvoo@mail.oit.edu.tw
2015-09-04
The ground states of bilayered and extended t-J-U models are investigated with renormalized mean field theory. The trial wave functions are Gutzwiller projected Hartree–Fock states, and the site double occupancies are variational parameters. It is found that a spontaneous interlayer phase separation (PS) may arise in bilayers. In electron–hole doping asymmetric systems, the propensity for PS is stronger in electron doped bands. Via a PS, superconductivity can survive to lower doping densities, and antiferromagnetism in electron doped systems may survive to higher doping densities. The result is related to the superconducting cuprates. - Highlights: • Ground states in doped bilayered t-J-U models are studied. • Variational wave functions are Gutzwiller projected wave functions. • Site double occupancies are variational parameters. • Spontaneous interlayer phase separation may occur in bilayers. • Stronger tendency toward phase separation in electron doped bilayers.
Energy Technology Data Exchange (ETDEWEB)
March, N.H
2002-12-30
The first-order density matrix {gamma}(r{sub 1},r{sub 2}) for the ground-state of a model two-electron atom is explicitly constructed from the electron density {rho}(r). The model has harmonic confinement plus interparticle harmonic interactions. {gamma}(r{sub 1},r{sub 2}) and {rho}(r) are related non-locally, even though no density gradients and no quadratures appear.
Ground state correlations and mean-field in $^{16}O$, 2
Mihaila, B; Mihaila, Bogdan; Heisenberg, Jochen H.
2000-01-01
We continue the investigations of the $^{16}$O ground state using the coupled-cluster expansion [$\\exp({\\bf S})$] method with realistic nuclear interaction. In this stage of the project, we take into account the three nucleon interaction, and examine in some detail the definition of the internal Hamiltonian, thus trying to correct for the center-of-mass motion. We show that this may result in a better separation of the internal and center-of-mass degrees of freedom in the many-body nuclear wave function. The resulting ground state wave function is used to calculate the "theoretical" charge form factor and charge density. Using the "theoretical" charge density, we generate the charge form factor in the DWBA picture, which is then compared with the available experimental data. The longitudinal response function in inclusive electron scattering for $^{16}$O is also computed.
Electronic Ground State of Higher Acenes
Jiang, De-en
2007-01-01
We examine the electronic ground state of acenes with different number of fused benzene rings (up to 40) by using first principles density functional theory. Their properties are compared with those of infinite polyacene. We find that the ground state of acenes that consist of more than seven fused benzene rings is an antiferromagnetic (in other words, open-shell singlet) state, and we show that this singlet is not necessarily a diradical, because the spatially separated magnetizations for the spin-up and spin-down electrons increase with the size of the acene. For example, our results indicate that there are about four spin-up electrons localized at one zigzag edge of 20-acene. The reason that both acenes and polyacene have the antiferromagnetic ground state is due to the zigzag-shaped boundaries, which cause pi-electrons to localize and form spin orders at the edges. Both wider graphene ribbons and large rectangular-shaped polycyclic aromatic hydrocarbons have been shown to share this antiferromagnetic grou...
Wave function calculations in finite nuclei
Energy Technology Data Exchange (ETDEWEB)
Pieper, S.C.
1993-07-01
One of the central problems in nuclear physics is the description of nuclei as systems of nucleons interacting via realistic potentials. There are two main aspects of this problem: (1) specification of the Hamiltonian, and (2) calculation of the ground (or excited) states of nuclei with the given interaction. Realistic interactions must contain both two- and three-nucleon potentials and these potentials have a complicated non-central operator structure consisting, for example, of spin, isospin and tensor dependencies. This structure results in formidable many-body problems in the computation of the ground states of nuclei. At Argonne and Urbana, the authors have been following a program of developing realistic NN and NNN interactions and the methods necessary to compute nuclear properties from variational wave functions suitable for these interactions. The wave functions are used to compute energies, density distributions, charge form factors, structure functions, momentum distributions, etc. Most recently they have set up a collaboration with S. Boffi and M. Raduci (University of Pavia) to compute (e,e{prime}p) reactions.
Wave function calculations in finite nuclei
Energy Technology Data Exchange (ETDEWEB)
Pieper, S.C.
1993-01-01
One of the central problems in nuclear physics is the description of nuclei as systems of nucleons interacting via realistic potentials. There are two main aspects of this problem: (1) specification of the Hamiltonian, and (2) calculation of the ground (or excited) states of nuclei with the given interaction. Realistic interactions must contain both two- and three-nucleon potentials and these potentials have a complicated non-central operator structure consisting, for example, of spin, isospin and tensor dependencies. This structure results in formidable many-body problems in the computation of the ground states of nuclei. At Argonne and Urbana, the authors have been following a program of developing realistic NN and NNN interactions and the methods necessary to compute nuclear properties from variational wave functions suitable for these interactions. The wave functions are used to compute energies, density distributions, charge form factors, structure functions, momentum distributions, etc. Most recently they have set up a collaboration with S. Boffi and M. Raduci (University of Pavia) to compute (e,e[prime]p) reactions.
Ground state energy of the modified Nambu-Goto string
Hadasz, L
1998-01-01
We calculate, using zeta function regularization method, semiclassical energy of the Nambu-Goto string supplemented with the boundary, Gauss-Bonnet term in the action and discuss the tachyonic ground state problem.
Ground states of fermionic lattice Hamiltonians with permutation symmetry
Kraus, Christina V.; Lewenstein, Maciej; Cirac, J. Ignacio
2013-08-01
We study the ground states of lattice Hamiltonians that are invariant under permutations, in the limit where the number of lattice sites N→∞. For spin systems, these are product states, a fact that follows directly from the quantum de Finetti theorem. For fermionic systems, however, the problem is very different, since mode operators acting on different sites do not commute, but anticommute. We construct a family of fermionic states, F, from which such ground states can be easily computed. They are characterized by few parameters whose number only depends on M, the number of modes per lattice site. We also give an explicit construction for M=1,2. In the first case, F is contained in the set of Gaussian states, whereas in the second it is not. Inspired by that construction, we build a set of fermionic variational wave functions, and apply it to the Fermi-Hubbard model in two spatial dimensions, obtaining results that go beyond the generalized Hartree-Fock theory.
Study of some electronics properties of new superconductor Sr2VO3FeAs in ground state
Directory of Open Access Journals (Sweden)
M Majidiyan
2010-09-01
Full Text Available In this paper, some electronics properties of new superconductor Sr2VO3FeAs, such as density of states, band structure, density of electron cloud and bound lengths in the ground state have been calculated. According to N(Ef in ground state CV/T value has been estimated. The calculations were performed in the framework of density functional theory (DFT, using the full potential linearized augmented plane wave (FP-LAPW method with the general gradient approximation (GGA.
Relativistic Covariance and Quark-Diquark Wave Functions
Dillig, M
2006-01-01
We derive covariant wave functions for hadrons composed of two constituents for arbitrary Lorentz boosts. Focussing explicitly on baryons as quark-diquark systems, we reduce their manifestly covariant Bethe-Salpeter equation to covariant 3-dimensional forms by projecting on the relative quark-diquark energy. Guided by a phenomenological multi gluon exchange representation of covariant confining kernels, we derive explicit solutions for harmonic confinement and for the MIT Bag Model. We briefly sketch implications of breaking the spherical symmetry of the ground state and the transition from the instant form to the light cone via the infinite momentum frame.
DEFF Research Database (Denmark)
Dahl, Jens Peder; Varro, S.; Wolf, A.
2007-01-01
We derive explicit expressions for the Wigner function of wave functions in D dimensions which depend on the hyperradius-that is, of s waves. They are based either on the position or the momentum representation of the s wave. The corresponding Wigner function depends on three variables......: the absolute value of the D-dimensional position and momentum vectors and the angle between them. We illustrate these expressions by calculating and discussing the Wigner functions of an elementary s wave and the energy eigenfunction of a free particle....
Ground-state structures of Hafnium clusters
Energy Technology Data Exchange (ETDEWEB)
Ng, Wei Chun; Yoon, Tiem Leong [School of Physics, Universiti Sains Malaysia, 11800 USM, Penang (Malaysia); Lim, Thong Leng [Faculty of Engineering and Technoloty, Multimedia University, Melaca Campus, 75450 Melaka (Malaysia)
2015-04-24
Hafnium (Hf) is a very large tetra-valence d-block element which is able to form relatively long covalent bond. Researchers are interested to search for substitution to silicon in the semi-conductor industry. We attempt to obtain the ground-state structures of small Hf clusters at both empirical and density-functional theory (DFT) levels. For calculations at the empirical level, charge-optimized many-body functional potential (COMB) is used. The lowest-energy structures are obtained via a novel global-minimum search algorithm known as parallel tempering Monte-Carlo Basin-Hopping and Genetic Algorithm (PTMBHGA). The virtue of using COMB potential for Hf cluster calculation lies in the fact that by including the charge optimization at the valence shells, we can encourage the formation of proper bond hybridization, and thus getting the correct bond order. The obtained structures are further optimized using DFT to ensure a close proximity to the ground-state.
Properties of the approximate Yang-Mills ground-state wave functional in 2+1 dimensions
Greensite, J.; Olejnik, S.
2010-01-01
Comment: 3 pages, 3 EPS figures, uses aipproc.cls; talk presented by S. Olejnik at the conference "Quark Confinement and the Hadron Spectrum IX", Madrid, Spain, Aug. 30-Sep. 3, 2010; submitted to AIP Conference Proceedings; after publication, it will be found at http://link.aip.org/link/?apc
Anatomy of quantum critical wave functions in dissipative impurity problems
Blunden-Codd, Zach; Bera, Soumya; Bruognolo, Benedikt; Linden, Nils-Oliver; Chin, Alex W.; von Delft, Jan; Nazir, Ahsan; Florens, Serge
2017-02-01
Quantum phase transitions reflect singular changes taking place in a many-body ground state; however, computing and analyzing large-scale critical wave functions constitutes a formidable challenge. Physical insights into the sub-Ohmic spin-boson model are provided by the coherent-state expansion (CSE), which represents the wave function by a linear combination of classically displaced configurations. We find that the distribution of low-energy displacements displays an emergent symmetry in the absence of spontaneous symmetry breaking while experiencing strong fluctuations of the order parameter near the quantum critical point. Quantum criticality provides two strong fingerprints in critical low-energy modes: an algebraic decay of the average displacement and a constant universal average squeezing amplitude. These observations, confirmed by extensive variational matrix-product-state (VMPS) simulations and field theory arguments, offer precious clues into the microscopics of critical many-body states in quantum impurity models.
High-precision quadrupole moment reveals significant intruder component in 20 13 33Al ground state
Heylen, H.; De Rydt, M.; Neyens, G.; Bissell, M. L.; Caceres, L.; Chevrier, R.; Daugas, J. M.; Ichikawa, Y.; Ishibashi, Y.; Kamalou, O.; Mertzimekis, T. J.; Morel, P.; Papuga, J.; Poves, A.; Rajabali, M. M.; Stödel, C.; Thomas, J. C.; Ueno, H.; Utsuno, Y.; Yoshida, N.; Yoshimi, A.
2016-09-01
The electric quadrupole moment of the 20 13 33Al ground state, located at the border of the island of inversion, was obtained using continuous-beam β -detected nuclear quadrupole resonance (β -NQR). From the measured quadrupole coupling constant νQ=2.31 (4 ) MHz in an α -Al2O3 crystal, a precise value for the electric quadrupole moment is extracted: 33Al>Qs 141 (3 ) mb. A comparison with large-scale shell model calculations shows that 33Al has at least 50% intruder configurations in the ground state wave function, favoring the excitation of two neutrons across the N =20 shell gap. 33Al therefore clearly marks the gradual transition north of the deformed Na and Mg nuclei towards the normal Z ≥14 isotopes.
High-precision quadrupole moment reveals significant intruder component in 33Al20 ground state
Heylen, H; Neyens, G; Bissell, M L; Caceres, L; Chevrier, R; Daugas, J M; Ichikawa, Y; Ishibashi, Y; Kamalou, O; Mertzimekis, T J; Morel, P; Papuga, J; Poves, A; Rajabali, M M; Stodel, C; Thomas, J C; Ueno, H; Utsuno, Y; Yoshida, N; Yoshimi, A
2016-01-01
The electric quadrupole moment of the 33Al20 ground state, located at the border of the island of inversion, was obtained using continuous-beam beta-detected nuclear quadrupole resonance (beta-NQR). From the measured quadrupole coupling constant Q = 2.31(4) MHz in an alpha-Al2O3 crystal, a precise value for the electric quadrupole moment is extracted: Qs= 141(3) mb. A comparison with large-scale shell model calculations shows that 33Al has at least 50% intruder configurations in the ground state wave function, favoring the excitation of two neutrons across the N = 20 shell gap. 33Al therefore clearly marks the gradual transition north of the deformed Na and Mg nuclei towards the normal Z>14 isotopes.
Lattice effects on Laughlin wave functions and parent Hamiltonians
Glasser, Ivan; Cirac, J. Ignacio; Sierra, Germán; Nielsen, Anne E. B.
2016-12-01
We investigate lattice effects on wave functions that are lattice analogs of bosonic and fermionic Laughlin wave functions with number of particles per flux ν =1 /q in the Landau levels. These wave functions are defined analytically on lattices with μ particles per lattice site, where μ may be different than ν . We give numerical evidence that these states have the same topological properties as the corresponding continuum Laughlin states for different values of q and for different fillings μ . These states define, in particular, particle-hole symmetric lattice fractional quantum Hall states when the lattice is half filled. On the square lattice it is observed that for q ≤4 this particle-hole symmetric state displays the topological properties of the continuum Laughlin state at filling fraction ν =1 /q , while for larger q there is a transition towards long-range ordered antiferromagnets. This effect does not persist if the lattice is deformed from a square to a triangular lattice, or on the kagome lattice, in which case the topological properties of the state are recovered. We then show that changing the number of particles while keeping the expression of these wave functions identical gives rise to edge states that have the same correlations in the bulk as the reference lattice Laughlin states but a different density at the edge. We derive an exact parent Hamiltonian for which all these edge states are ground states with different number of particles. In addition this Hamiltonian admits the reference lattice Laughlin state as its unique ground state of filling factor 1 /q . Parent Hamiltonians are also derived for the lattice Laughlin states at other fillings of the lattice, when μ ≤1 /q or μ ≥1 -1 /q and when q =4 also at half filling.
Modular matrices from universal wave-function overlaps in Gutzwiller-projected parton wave functions
Mei, Jia-Wei; Wen, Xiao-Gang
2015-03-01
We implement the universal wave-function overlap (UWFO) method to extract modular S and T matrices for topological orders in Gutzwiller-projected parton wave functions (GPWFs). The modular S and T matrices generate a projective representation of S L (2 ,Z ) on the degenerate-ground-state Hilbert space on a torus and may fully characterize the 2+1D topological orders, i.e., the quasiparticle statistics and chiral central charge (up to E8 bosonic quantum Hall states). We use the variational Monte Carlo method to computed the S and T matrices of the chiral spin liquid (CSL) constructed by the GPWF on the square lattice, and we confirm that the CSL carries the same topological order as the ν =1/2 bosonic Laughlin state. We find that the nonuniversal exponents in the UWFO can be small, and direct numerical computation can be applied on relatively large systems. The UWFO may be a powerful method to calculate the topological order in GPWFs.
Ground state correlations and mean field in 16O. II. Effects of a three-nucleon interaction
Mihaila, Bogdan; Heisenberg, Jochen H.
2000-05-01
We continue the investigations of the 16O ground state using the coupled-cluster expansion [exp(S)] method with realistic nuclear interaction. In this stage of the project, we take into account the three nucleon interaction, and examine in some detail the definition of the internal Hamiltonian, thus trying to correct for the center-of-mass motion. We show that this may result in a better separation of the internal and center-of-mass degrees of freedom in the many-body nuclear wave function. The resulting ground state wave function is used to calculate the ``theoretical'' charge form factor and charge density. Using the ``theoretical'' charge density, we generate the charge form factor in the DWBA picture, which is then compared with the available experimental data. The longitudinal response function in inclusive electron scattering for 16O is also computed.
Isegawa, Miho; Truhlar, Donald G.
2013-04-01
Time-dependent density functional theory (TDDFT) holds great promise for studying photochemistry because of its affordable cost for large systems and for repeated calculations as required for direct dynamics. The chief obstacle is uncertain accuracy. There have been many validation studies, but there are also many formulations, and there have been few studies where several formulations were applied systematically to the same problems. Another issue, when TDDFT is applied with only a single exchange-correlation functional, is that errors in the functional may mask successes or failures of the formulation. Here, to try to sort out some of the issues, we apply eight formulations of adiabatic TDDFT to the first valence excitations of ten molecules with 18 density functionals of diverse types. The formulations examined are linear response from the ground state (LR-TDDFT), linear response from the ground state with the Tamm-Dancoff approximation (TDDFT-TDA), the original collinear spin-flip approximation with the Tamm-Dancoff (TD) approximation (SF1-TDDFT-TDA), the original noncollinear spin-flip approximation with the TDA approximation (SF1-NC-TDDFT-TDA), combined self-consistent-field (SCF) and collinear spin-flip calculations in the original spin-projected form (SF2-TDDFT-TDA) or non-spin-projected (NSF2-TDDFT-TDA), and combined SCF and noncollinear spin-flip calculations (SF2-NC-TDDFT-TDA and NSF2-NC-TDDFT-TDA). Comparing LR-TDDFT to TDDFT-TDA, we observed that the excitation energy is raised by the TDA; this brings the excitation energies underestimated by full linear response closer to experiment, but sometimes it makes the results worse. For ethylene and butadiene, the excitation energies are underestimated by LR-TDDFT, and the error becomes smaller making the TDA. Neither SF1-TDDFT-TDA nor SF2-TDDFT-TDA provides a lower mean unsigned error than LR-TDDFT or TDDFT-TDA. The comparison between collinear and noncollinear kernels shows that the noncollinear kernel
Thermodynamic ground states of platinum metal nitrides
Energy Technology Data Exchange (ETDEWEB)
Aberg, D; Sadigh, B; Crowhurst, J; Goncharov, A
2007-10-09
We have systematically studied the thermodynamic stabilities of various phases of the nitrides of the platinum metal elements using density functional theory. We show that for the nitrides of Rh, Pd, Ir and Pt two new crystal structures, in which the metal ions occupy simple tetragonal lattice sites, have lower formation enthalpies at ambient conditions than any previously proposed structures. The region of stability can extend up to 17 GPa for PtN{sub 2}. Furthermore, we show that according to calculations using the local density approximation, these new compounds are also thermodynamically stable at ambient pressure and thus may be the ground state phases for these materials. We further discuss the fact that the local density and generalized gradient approximations predict different values of the absolute formation enthalpies as well different relative stabilities between simple tetragonal and the pyrite or marcasite structures.
Kinetic energy partition method applied to ground state helium-like atoms.
Chen, Yu-Hsin; Chao, Sheng D
2017-03-28
We have used the recently developed kinetic energy partition (KEP) method to solve the quantum eigenvalue problems for helium-like atoms and obtain precise ground state energies and wave-functions. The key to treating properly the electron-electron (repulsive) Coulomb potential energies for the KEP method to be applied is to introduce a "negative mass" term into the partitioned kinetic energy. A Hartree-like product wave-function from the subsystem wave-functions is used to form the initial trial function, and the variational search for the optimized adiabatic parameters leads to a precise ground state energy. This new approach sheds new light on the all-important problem of solving many-electron Schrödinger equations and hopefully opens a new way to predictive quantum chemistry. The results presented here give very promising evidence that an effective one-electron model can be used to represent a many-electron system, in the spirit of density functional theory.
Ferromagnetic Ground States in Face-Centered Cubic Hubbard Clusters
Souza, T. X. R.; Macedo, C. A.
2016-01-01
In this study, the ground state energies of face-centered cubic Hubbard clusters are analyzed using the Lanczos method. Examination of the ground state energy as a function of the number of particle per site n showed an energy minimum for face-centered cubic structures. This energy minimum decreased in n with increasing coulombic interaction parameter U. We found that the ground state energy had a minimum at n = 0.6, when U = 3W, where W denotes the non-interacting energy bandwidth and the face-centered cubic structure was ferromagnetic. These results, when compared with the properties of nickel, shows strong similarity with other finite temperature analyses in the literature and supports the Hirsh’s conjecture that the interatomic direct exchange interaction dominates in driving the system into a ferromagnetic phase. PMID:27583653
Langevin equation path integral ground state.
Constable, Steve; Schmidt, Matthew; Ing, Christopher; Zeng, Tao; Roy, Pierre-Nicholas
2013-08-15
We propose a Langevin equation path integral ground state (LePIGS) approach for the calculation of ground state (zero temperature) properties of molecular systems. The approach is based on a modification of the finite temperature path integral Langevin equation (PILE) method (J. Chem. Phys. 2010, 133, 124104) to the case of open Feynman paths. Such open paths are necessary for a ground state formulation. We illustrate the applicability of the method using model systems and the weakly bound water-parahydrogen dimer. We show that the method can lead to converged zero point energies and structural properties.
Ground State Correlations Using exp(S) Method for the ^16O Nucleus.
Mihaila, Bogdan; Heisenberg, Jochen
1998-04-01
We use the Argonne-v18 potential together with a phenomenological three-nucleon interaction to do the calculation of the mean-field single particle wave functions and the correlation operator describing the ground state of the ^16O nucleus. Our correlation operator includes the contributions from up to 4p4h terms. We present a breakdown of the contributions to the binding from the two- and the three-body interactions. The one- and the two-body densities for ^16O are presented. Effects of the center-of-mass correction on the charge density and form factor are also discussed.
Ground states of bilayered and extended t-J-U models
Voo, Khee-Kyun
2015-09-01
The ground states of bilayered and extended t-J-U models are investigated with renormalized mean field theory. The trial wave functions are Gutzwiller projected Hartree-Fock states, and the site double occupancies are variational parameters. It is found that a spontaneous interlayer phase separation (PS) may arise in bilayers. In electron-hole doping asymmetric systems, the propensity for PS is stronger in electron doped bands. Via a PS, superconductivity can survive to lower doping densities, and antiferromagnetism in electron doped systems may survive to higher doping densities. The result is related to the superconducting cuprates.
Ensemble Theory for Stealthy Hyperuniform Disordered Ground States
Directory of Open Access Journals (Sweden)
S. Torquato
2015-05-01
Full Text Available It has been shown numerically that systems of particles interacting with isotropic “stealthy” bounded long-ranged pair potentials (similar to Friedel oscillations have classical ground states that are (counterintuitively disordered, hyperuniform, and highly degenerate. Disordered hyperuniform systems have received attention recently because they are distinguishable exotic states of matter poised between a crystal and liquid that are endowed with novel thermodynamic and physical properties. The task of formulating an ensemble theory that yields analytical predictions for the structural characteristics and other properties of stealthy degenerate ground states in d-dimensional Euclidean space R^{d} is highly nontrivial because the dimensionality of the configuration space depends on the number density ρ and there is a multitude of ways of sampling the ground-state manifold, each with its own probability measure for finding a particular ground-state configuration. The purpose of this paper is to take some initial steps in this direction. Specifically, we derive general exact relations for thermodynamic properties (energy, pressure, and isothermal compressibility that apply to any ground-state ensemble as a function of ρ in any d, and we show how disordered degenerate ground states arise as part of the ground-state manifold. We also derive exact integral conditions that both the pair correlation function g_{2}(r and structure factor S(k must obey for any d. We then specialize our results to the canonical ensemble (in the zero-temperature limit by exploiting an ansatz that stealthy states behave remarkably like “pseudo”-equilibrium hard-sphere systems in Fourier space. Our theoretical predictions for g_{2}(r and S(k are in excellent agreement with computer simulations across the first three space dimensions. These results are used to obtain order metrics, local number variance, and nearest-neighbor functions across dimensions. We also derive
Ensemble Theory for Stealthy Hyperuniform Disordered Ground States
Torquato, S.; Zhang, G.; Stillinger, F. H.
2015-04-01
It has been shown numerically that systems of particles interacting with isotropic "stealthy" bounded long-ranged pair potentials (similar to Friedel oscillations) have classical ground states that are (counterintuitively) disordered, hyperuniform, and highly degenerate. Disordered hyperuniform systems have received attention recently because they are distinguishable exotic states of matter poised between a crystal and liquid that are endowed with novel thermodynamic and physical properties. The task of formulating an ensemble theory that yields analytical predictions for the structural characteristics and other properties of stealthy degenerate ground states in d -dimensional Euclidean space Rd is highly nontrivial because the dimensionality of the configuration space depends on the number density ρ and there is a multitude of ways of sampling the ground-state manifold, each with its own probability measure for finding a particular ground-state configuration. The purpose of this paper is to take some initial steps in this direction. Specifically, we derive general exact relations for thermodynamic properties (energy, pressure, and isothermal compressibility) that apply to any ground-state ensemble as a function of ρ in any d , and we show how disordered degenerate ground states arise as part of the ground-state manifold. We also derive exact integral conditions that both the pair correlation function g2(r ) and structure factor S (k ) must obey for any d . We then specialize our results to the canonical ensemble (in the zero-temperature limit) by exploiting an ansatz that stealthy states behave remarkably like "pseudo"-equilibrium hard-sphere systems in Fourier space. Our theoretical predictions for g2(r ) and S (k ) are in excellent agreement with computer simulations across the first three space dimensions. These results are used to obtain order metrics, local number variance, and nearest-neighbor functions across dimensions. We also derive accurate analytical
Three-body correlations in the ground-state decay of 26O
Kohley, Z; Christian, G; DeYoung, P A; Finck, J E; Frank, N; Luther, B; Lunderberg, E; Jones, M; Mosby, S; Smith, J K; Spyrou, A; Thoennessen, M
2015-01-01
Background: Theoretical calculations have shown that the energy and angular correlations in the three-body decay of the two-neutron unbound O26 can provide information on the ground-state wave function, which has been predicted to have a dineutron configuration and 2n halo structure. Purpose: To use the experimentally measured three-body correlations to gain insight into the properties of O26, including the decay mechanism and ground-state resonance energy. Method: O26 was produced in a one-proton knockout reaction from F27 and the O24+n+n decay products were measured using the MoNA-Sweeper setup. The three-body correlations from the O26 ground-state resonance decay were extracted. The experimental results were compared to Monte Carlo simulations in which the resonance energy and decay mechanism were varied. Results: The measured three-body correlations were well reproduced by the Monte Carlo simulations but were not sensitive to the decay mechanism due to the experimental resolutions. However, the three-body...
Magnetic excitons in singlet-ground-state ferromagnets
DEFF Research Database (Denmark)
Birgeneau, R.J.; Als-Nielsen, Jens Aage; Bucher, E.
1971-01-01
The authors report measurements of the dispersion of singlet-triplet magnetic excitons as a function of temperature in the singlet-ground-state ferromagnets fcc Pr and Pr3Tl. Well-defined excitons are observed in both the ferromagnetic and paramagnetic regions, but with energies which are nearly...
Analytical potential energy function for the ground state (～X1A1) of hydrogen isotopic D2O molecule
Institute of Scientific and Technical Information of China (English)
RUAN Wen; LUO WenLang; ZHANG Li; ZHU ZhengHe
2009-01-01
The present work is to construct the potential energy function of Isotopic molecules. The so-called molecular potential energy function is the electronic energy function under Born-Oppenheimer ap-proximation, in which the nuclear motions (translational, rotational and vibration motions) are not in-cluded, therefore, its nuclear vibration motion and isotopic effect need to be considered. Based on group theory and atomic and molecular reactive statics (AMRS), the reasonable dissociation limits of D2O(～X1A1) are determined, its equilibrium geometry and dissociation energy are calculated by den-sity-functional theory (DFT) B3lyp, and then, using the many-body expansion method the potential en-ergy function of D2O (～X1A1) Is obtained for the first time. The potential contours are drawn, in which It is found that the reactive channel D + OD→D2O has no threshold energy, so it is a free radical reaction. But the reactive channel O + DD→D2P has a saddle point. The study of collision for D2O (～X1A1) is under way.
On the ground state of metallic hydrogen
Chakravarty, S.; Ashcroft, N. W.
1978-01-01
A proposed liquid ground state of metallic hydrogen at zero temperature is explored and a variational upper bound to the ground state energy is calculated. The possibility that the metallic hydrogen is a liquid around the metastable point (rs = 1.64) cannot be ruled out. This conclusion crucially hinges on the contribution to the energy arising from the third order in the electron-proton interaction which is shown here to be more significant in the liquid phase than in crystals.
A global approach to ground state solutions
Directory of Open Access Journals (Sweden)
Philip Korman
2008-08-01
Full Text Available We study radial solutions of semilinear Laplace equations. We try to understand all solutions of the problem, regardless of the boundary behavior. It turns out that one can study uniqueness or multiplicity properties of ground state solutions by considering curves of solutions of the corresponding Dirichlet and Neumann problems. We show that uniqueness of ground state solutions can sometimes be approached by a numerical computation.
A global approach to ground state solutions
2008-01-01
We study radial solutions of semilinear Laplace equations. We try to understand all solutions of the problem, regardless of the boundary behavior. It turns out that one can study uniqueness or multiplicity properties of ground state solutions by considering curves of solutions of the corresponding Dirichlet and Neumann problems. We show that uniqueness of ground state solutions can sometimes be approached by a numerical computation.
Wave function and CKM renormalization
Espriu, Doménec
2002-01-01
In this presentation we clarify some aspects of the LSZ formalism and wave function renormalization for unstable particles in the presence of electroweak interactions when mixing and CP violation are considered. We also analyze the renormalization of the CKM mixing matrix which is closely related to wave function renormalization. The effects due to the electroweak radiative corrections that are described in this work are small, but they will need to be considered when the precision in the measurement of the charged current sector couplings reaches the 1% level. The work presented here is done in collaboration with Julian Manzano and Pere Talavera.
The thermodynamic and ground state properties of the TIP4P water octamer.
Asare, E; Musah, A-R; Curotto, E; Freeman, David L; Doll, J D
2009-11-14
Several stochastic simulations of the TIP4P [W. L. Jorgensen, J. Chandrasekhar, J. D. Madura, R. W. Impey, and M. L. Klein, J. Chem. Phys. 79, 926 (1983)] water octamer are performed. Use is made of the stereographic projection path integral and the Green's function stereographic projection diffusion Monte Carlo techniques, recently developed in one of our groups. The importance sampling for the diffusion Monte Carlo algorithm is obtained by optimizing a simple wave function using variational Monte Carlo enhanced with parallel tempering to overcome quasiergodicity problems. The quantum heat capacity of the TIP4P octamer contains a pronounced melting peak at 160 K, about 50 K lower than the classical melting peak. The zero point energy of the TIP4P water octamer is 0.0348+/-0.0002 hartree. By characterizing several large samples of configurations visited by both guided and unguided diffusion walks, we determine that both the TIP4P and the SPC [H. J. C. Berendsen, J. P. Postma, W. F. von Gunsteren, and J. Hermans, (Intermolecular Forces, Reidel, 1981). p. 331] octamer have a ground state wave functions predominantly contained within the D(2d) basin of attraction. This result contrasts with the structure of the global minimum for the TIP4P potential, which is an S(4) cube. Comparisons of the thermodynamic and ground-state properties are made with the SPC octamer as well.
Second-Order Perturbation Theory for Generalized Active Space Self-Consistent-Field Wave Functions.
Ma, Dongxia; Li Manni, Giovanni; Olsen, Jeppe; Gagliardi, Laura
2016-07-12
A multireference second-order perturbation theory approach based on the generalized active space self-consistent-field (GASSCF) wave function is presented. Compared with the complete active space (CAS) and restricted active space (RAS) wave functions, GAS wave functions are more flexible and can employ larger active spaces and/or different truncations of the configuration interaction expansion. With GASSCF, one can explore chemical systems that are not affordable with either CASSCF or RASSCF. Perturbation theory to second order on top of GAS wave functions (GASPT2) has been implemented to recover the remaining electron correlation. The method has been benchmarked by computing the chromium dimer ground-state potential energy curve. These calculations show that GASPT2 gives results similar to CASPT2 even with a configuration interaction expansion much smaller than the corresponding CAS expansion.
Energy Technology Data Exchange (ETDEWEB)
Christiansen, P.A.; Pitzer, K.S.
1980-07-01
The dissociation curve for the ground state of TlH was computed using a relativistic {omega}-{omega} coupling formalism. The relativistic effects represented by the Dirac equation were introduced using effective potentials generated from atomic Dirac-Fock wave functions using a generalization of the improved effective potential formulation of Christiansen, Lee, and Pitzer. The multiconfiguration SCF treatment used is a generalization of the two-component molecular spinor formalism of Lee, Ermler, and Pitzer. Using a five configuration wave function we were able to obtain approximately 85% of the experimental dissociation energy. Our computations indicate that the bond is principally sigma in form, despite the large spin-orbit splitting in atomic thallium. Furthermore the bond appears to be slightly ionic (Tl{sup +}H{sup -}) with about 0.3 extra electron charge on the hydrogen.
Ground states for nonuniform periodic Ising chains
Martínez-Garcilazo, J. P.; Ramírez, C.
2015-04-01
We generalize Morita's works [J. Phys. A 7, 289 (1974), 10.1088/0305-4470/7/2/014; J. Phys. A 7, 1613 (1974), 10.1088/0305-4470/7/13/015] on ground states of Ising chains, for chains with a periodic structure and different spins, to any interaction order. The main assumption is translational invariance. The length of the irreducible blocks is a multiple of the period of the chain. If there is parity invariance, it restricts the length in general only in the diatomic case. There are degenerated states and under certain circumstances there could be nonregular ground states. We illustrate the results and give the ground state diagrams in several cases.
Trapped Antihydrogen in Its Ground State
Gabrielse, G; Kolthammer, W S; McConnell, R; Richerme, P; Grzonka, D; Oelert, W; Sefzick, T; Zielinski, M; Fitzakerley, D W; George, M C; Hessels, E A; Storry, C H; Weel, M; Mullers, A; Walz, J
2012-01-01
Antihydrogen atoms are confined in an Ioffe trap for 15 to 1000 seconds -- long enough to ensure that they reach their ground state. Though reproducibility challenges remain in making large numbers of cold antiprotons and positrons interact, 5 +/- 1 simultaneously-confined ground state atoms are produced and observed on average, substantially more than previously reported. Increases in the number of simultaneously trapped antithydrogen atoms H are critical if laser-cooling of trapped antihydrogen is to be demonstrated, and spectroscopic studies at interesting levels of precision are to be carried out.
Modification of AMD wave functions and application to the breaking of the N=20 magic number
Energy Technology Data Exchange (ETDEWEB)
Kimura, Masaaki; Horiuchi, Hisashi [Kyoto Univ. (Japan). Dept. of Physics
2001-09-01
By using the deformed Gaussian instead of the spherical one, we have modified the AMD (Antisymmetrized Molecular Dynamics) wave functions. The calculation results with this modified AMD shows the drastic improvement of the deformation properties of Mg isotopes. This improvement means that this new version of AMD can treat the deformation of mean field properly than before and the deformation of mean field is important in Mg isotopes. With this new version of AMD, we have also calculated 32Mg in which the breaking of magic number N=20 is experimentally known. In this nucleus, {beta}-energy surface is also drastically changed by the modification AMD wave function. Our results show that this nucleus is indeed deformed and neutron's 2p2h state is dominant in its ground state. This ground state reproduces the experimental data and shows the breaking of the magic number N=20 clearly. Additionally, near the ground state, there is also very interesting state which has neutron's 4p4h structure and shows parity violating density distribution and cluster-like nature. (author)
Revised Iterative Solution of Ground State of Double-Well Potential
Institute of Scientific and Technical Information of China (English)
ZHAO Wei-Qin
2005-01-01
The revised new iterative method for solving the ground state of Schrodinger equation is deduced. Based on Green functions defined by quadratures along a single trajectory this iterative method is applied to solve the ground state of the double-well potential. The result is compared to the one based on the original iterative method. The limitation of the asymptotic expansion is also discussed.
Stefańska, Patrycja
2011-01-01
The Sturmian expansion of the generalized Dirac-Coulomb Green function [R. Szmytkowski, J. Phys. B 30 (1997) 825; erratum 30 (1997) 2747] is exploited to derive closed-form expressions for electric ($\\sigma_{\\mathrm{E}}$) and magnetic ($\\sigma_{\\mathrm{M}}$) dipole shielding constants for the ground state of the relativistic hydrogen-like atom with a point-like and spinless nucleus of charge $Ze$. It is found that $\\sigma_{\\mathrm{E}}=Z^{-1}$ (as it should be) and $$\\sigma_{\\mathrm{M}}=-(2Z\\alpha^{2}/27)(4\\gamma_{1}^{3}+6\\gamma_{1}^{2}-7\\gamma_{1}-12) /[\\gamma_{1}(\\gamma_{1}+1)(2\\gamma_{1}-1)],$$ where $\\gamma_{1}=\\sqrt{1-(Z\\alpha)^{2}}$ ($\\alpha$ is the fine-structure constant). This expression for $\\sigma_{\\mathrm{M}}$ agrees with earlier findings of several other authors, obtained with the use of other analytical techniques, and is elementary compared to an alternative one presented recently by Cheng \\emph{et al.} [J. Chem. Phys. 130 (2009) 144102], which involves an infinite series of ratios of the Euler'...
Ground state of a confined Yukawa plasma
Henning, C; Block, D; Bonitz, M; Golubnichiy, V; Ludwig, P; Piel, A
2006-01-01
The ground state of an externally confined one-component Yukawa plasma is derived analytically. In particular, the radial density profile is computed. The results agree very well with computer simulations on three-dimensional spherical Coulomb crystals. We conclude in presenting an exact equation for the density distribution for a confinement potential of arbitrary geometry.
Garrido, Nephtali
2012-01-01
We put to the test an effective three-dimensional electrostatic potential, obtained effectively by considering an electrostatic source inside a (5+$p$)-dimensional braneworld scenario with $p$ compact and one infinite spacial extra dimensions in the RS II-$p$ model, for $p=1$ and $p=2$. This potential is regular at the source and matches the standard Coulomb potential outside a neighborhood. We use variational and perturbative approximation methods to calculate corrections to the ground energy of the Helium atom modified by this potential, by making use of a 6 and 39-parameter trial wave function of Hylleraas type for the ground state. These corrections to the ground-state energy are compared with experimental data for Helium atom in order to set bounds for the extra dimensions length scale. We find that these bounds are less restrictive than the ones obtained by Morales et. al. through a calculation using the Lamb shift in Hydrogen.
Cluster expansion for ground states of local Hamiltonians
Bastianello, Alvise; Sotiriadis, Spyros
2016-08-01
A central problem in many-body quantum physics is the determination of the ground state of a thermodynamically large physical system. We construct a cluster expansion for ground states of local Hamiltonians, which naturally incorporates physical requirements inherited by locality as conditions on its cluster amplitudes. Applying a diagrammatic technique we derive the relation of these amplitudes to thermodynamic quantities and local observables. Moreover we derive a set of functional equations that determine the cluster amplitudes for a general Hamiltonian, verify the consistency with perturbation theory and discuss non-perturbative approaches. Lastly we verify the persistence of locality features of the cluster expansion under unitary evolution with a local Hamiltonian and provide applications to out-of-equilibrium problems: a simplified proof of equilibration to the GGE and a cumulant expansion for the statistics of work, for an interacting-to-free quantum quench.
Ground-state structures of atomic metallic hydrogen.
McMahon, Jeffrey M; Ceperley, David M
2011-04-22
Ab initio random structure searching using density functional theory is used to determine the ground-state structures of atomic metallic hydrogen from 500 GPa to 5 TPa. Including proton zero-point motion within the harmonic approximation, we estimate that molecular hydrogen dissociates into a monatomic body-centered tetragonal structure near 500 GPa (r(s)=1.23) that remains stable to 1 TPa (r(s)=1.11). At higher pressures, hydrogen stabilizes in an …ABCABC… planar structure that is similar to the ground state of lithium, but with a different stacking sequence. With increasing pressure, this structure compresses to the face-centered cubic lattice near 3.5 TPa (r(s)=0.92).
Cluster expansion for ground states of local Hamiltonians
Directory of Open Access Journals (Sweden)
Alvise Bastianello
2016-08-01
Full Text Available A central problem in many-body quantum physics is the determination of the ground state of a thermodynamically large physical system. We construct a cluster expansion for ground states of local Hamiltonians, which naturally incorporates physical requirements inherited by locality as conditions on its cluster amplitudes. Applying a diagrammatic technique we derive the relation of these amplitudes to thermodynamic quantities and local observables. Moreover we derive a set of functional equations that determine the cluster amplitudes for a general Hamiltonian, verify the consistency with perturbation theory and discuss non-perturbative approaches. Lastly we verify the persistence of locality features of the cluster expansion under unitary evolution with a local Hamiltonian and provide applications to out-of-equilibrium problems: a simplified proof of equilibration to the GGE and a cumulant expansion for the statistics of work, for an interacting-to-free quantum quench.
Asymptotics of Ground State Degeneracies in Quiver Quantum Mechanics
Cordova, Clay
2015-01-01
We study the growth of the ground state degeneracy in the Kronecker model of quiver quantum mechanics. This is the simplest quiver with two gauge groups and bifundamental matter fields, and appears universally in the context of BPS state counting in four-dimensional N=2 systems. For large ranks, the ground state degeneracy is exponential with slope a modular function that we are able to compute at integral values of its argument. We also observe that the exponential of the slope is an algebraic number and determine its associated algebraic equation explicitly in several examples. The speed of growth of the degeneracies, together with various physical features of the bound states, suggests a dual string interpretation.
Cluster expansion for ground states of local Hamiltonians
Energy Technology Data Exchange (ETDEWEB)
Bastianello, Alvise, E-mail: abastia@sissa.it [SISSA, via Bonomea 265, 34136 Trieste (Italy); INFN, Sezione di Trieste (Italy); Sotiriadis, Spyros [SISSA, via Bonomea 265, 34136 Trieste (Italy); INFN, Sezione di Trieste (Italy); Institut de Mathématiques de Marseille (I2M), Aix Marseille Université, CNRS, Centrale Marseille, UMR 7373, 39, rue F. Joliot Curie, 13453, Marseille (France); University of Roma Tre, Department of Mathematics and Physics, L.go S.L. Murialdo 1, 00146 Roma (Italy)
2016-08-15
A central problem in many-body quantum physics is the determination of the ground state of a thermodynamically large physical system. We construct a cluster expansion for ground states of local Hamiltonians, which naturally incorporates physical requirements inherited by locality as conditions on its cluster amplitudes. Applying a diagrammatic technique we derive the relation of these amplitudes to thermodynamic quantities and local observables. Moreover we derive a set of functional equations that determine the cluster amplitudes for a general Hamiltonian, verify the consistency with perturbation theory and discuss non-perturbative approaches. Lastly we verify the persistence of locality features of the cluster expansion under unitary evolution with a local Hamiltonian and provide applications to out-of-equilibrium problems: a simplified proof of equilibration to the GGE and a cumulant expansion for the statistics of work, for an interacting-to-free quantum quench.
Ground State of a Two-Electron Quantum Dot with a Gaussian Confining Potential
Institute of Scientific and Technical Information of China (English)
XIE Wen-Fang
2006-01-01
We investigate the ground-state properties of a two-dimensional two-electron quantum dot with a Gaussian confining potential under the influence of perpendicular homogeneous magnetic field. Calculations are carried out by using the method of numerical diagonalization of Hamiltonian matrix within the effective-mass approximation. A ground-state behaviour (singlet→triplet state transitions) as a function of the strength of a magnetic field has been found. It is found that the dot radius R of the Gaussian potential is important for the ground-state transition and the feature of ground-state for the Gaussian potential quantum dot (QD), and the parabolic potential QDs are similar when R is larger. The larger the quantum dot radius, the smaller the magnetic field for the singlet-triplet transition of the ground-state of two interacting electrons in the Gaussian quantum dot.
Zhang, Tianyuan; Evangelista, Francesco A
2016-09-13
In this work we propose a novel approach to solve the Schrödinger equation which combines projection onto the ground state with a path-filtering truncation scheme. The resulting projector configuration interaction (PCI) approach realizes a deterministic version of the full configuration interaction quantum Monte Carlo (FCIQMC) method [Booth, G. H.; Thom, A. J. W.; Alavi, A. J. Chem. Phys. 2009, 131, 054106]. To improve upon the linearized imaginary-time propagator, we develop an optimal projector scheme based on an exponential Chebyshev expansion in the limit of an infinite imaginary time step. After writing the exact projector as a path integral in determinant space, we introduce a path filtering procedure that truncates the size of the determinantal basis and approximates the Hamiltonian. The path filtering procedure is controlled by one real threshold that determines the accuracy of the PCI energy and is not biased toward any determinant. Therefore, the PCI approach can equally well describe static and dynamic electron correlation effects. This point is illustrated in benchmark computations on N2 at both equilibrium and stretched geometries. In both cases, the PCI achieves chemical accuracy with wave functions that contain less than 0.5% determinants of full CI space. We also report computations on the ground state of C2 with up to quaduple-ζ basis sets and wave functions as large as 200 million determinants, which allow a direct comparison of the PCI, FCIQMC, and density matrix renormalization group (DMRG) methods. The size of the PCI wave function grows modestly with the number of unoccupied orbitals, and its accuracy may be tuned to match that of FCIQMC and DMRG.
Magnetic properties of ground-state mesons
Energy Technology Data Exchange (ETDEWEB)
Simonis, V. [Vilnius University Institute of Theoretical Physics and Astronomy, Vilnius (Lithuania)
2016-04-15
Starting with the bag model a method for the study of the magnetic properties (magnetic moments, magnetic dipole transition widths) of ground-state mesons is developed. We calculate the M1 transition moments and use them subsequently to estimate the corresponding decay widths. These are compared with experimental data, where available, and with the results obtained in other approaches. Finally, we give the predictions for the static magnetic moments of all ground-state vector mesons including those containing heavy quarks. We have a good agreement with experimental data for the M1 decay rates of light as well as heavy mesons. Therefore, we expect our predictions for the static magnetic properties (i.e., usual magnetic moments) to be of sufficiently high quality, too. (orig.)
Magnetic properties of ground-state mesons
Simonis, Vytautas
2016-01-01
Starting with the bag model a method for the study of the magnetic properties (magnetic moments, magnetic dipole transition widths) of ground-state mesons is developed. We calculate the M1 transition moments and use them subsequently to estimate the corresponding decay widths. These are compared with experimental data, where available, and with the results obtained in other approaches. Finally, we give the predictions for the static magnetic moments of all ground-state vector mesons including those containing heavy quarks. We have a good agreement with experimental data for the M1 decay rates of light as well as heavy mesons. Therefore, we expect our predictions for the static magnetic properties (usual magnetic moments) to be of sufficiently high quality, too.
Thermal ground state and nonthermal probes
Grandou, Thierry
2015-01-01
The Euclidean formulation of SU(2) Yang-Mills thermodynamics admits periodic, (anti)selfdual solutions to the fundamental, classical equation of motion which possess one unit of topological charge: (anti)calorons. A spatial coarse graining over the central region in a pair of such localised field configurations with trivial holonomy generates an inert adjoint scalar field $\\phi$, effectively describing the pure quantum part of the thermal ground state in the induced quantum field theory. The latter's local vertices are mediated by just-not-resolved (anti)caloron centers of action $\\hbar$. This is the basic reason for a rapid convergence of the loop expansion of thermodynamical quantities, polarization tensors, etc., their effective loop momenta being severely constrained in entirely fixed and physical unitary-Coulomb gauge. Here we show for the limit of zero holonomy how (anti)calorons associate a temperature independent electric permittivity and magnetic permeability to the thermal ground state of SU(2)$_{\\t...
Electronic ground state of Ni$_2^+$
Zamudio-Bayer, V; Bülow, C; Leistner, G; Terasaki, A; Issendorff, B v; Lau, J T
2016-01-01
The $^{4}\\Phi_{9/2}$ ground state of the Ni$_2^+$ diatomic molecular cation is determined experimentally from temperature and magnetic-field-dependent x-ray magnetic circular dichroism spectroscopy in a cryogenic ion trap, where an electronic and rotational temperature of $7.4 \\pm 0.2$ K was achieved by buffer gas cooling of the molecular ion. The contribution of the magnetic dipole term to the x-ray magnetic circular dichroism spin sum rule amounts to $7\\, T_z = 0.17 \\pm 0.06$ $\\mu_B$ per atom, approximately 11 \\% of the spin magnetic moment. We find that, in general, homonuclear diatomic molecular cations of $3d$ transition metals seem to adopt maximum spin magnetic moments in their electronic ground states.
Trapping cold ground state argon atoms.
Edmunds, P D; Barker, P F
2014-10-31
We trap cold, ground state argon atoms in a deep optical dipole trap produced by a buildup cavity. The atoms, which are a general source for the sympathetic cooling of molecules, are loaded in the trap by quenching them from a cloud of laser-cooled metastable argon atoms. Although the ground state atoms cannot be directly probed, we detect them by observing the collisional loss of cotrapped metastable argon atoms and determine an elastic cross section. Using a type of parametric loss spectroscopy we also determine the polarizability of the metastable 4s[3/2](2) state to be (7.3±1.1)×10(-39) C m(2)/V. Finally, Penning and associative losses of metastable atoms in the absence of light assisted collisions, are determined to be (3.3±0.8)×10(-10) cm(3) s(-1).
Strangeness in the baryon ground states
Semke, A
2012-01-01
We compute the strangeness content of the baryon ground states based on an analysis of recent lattice simulations of the BMW, PACS, LHPC and HSC groups for the pion-mass dependence of the baryon masses. Our results rely on the relativistic chiral Lagrangian and large-$N_c$ sum rule estimates of the counter terms relevant for the baryon masses at N$^3$LO. A partial summation is implied by the use of physical baryon and meson masses in the one-loop contributions to the baryon self energies. A simultaneous description of the lattice results of the BMW, LHPC, PACS and HSC groups is achieved. We predict the pion- and strangeness sigma terms and the pion-mass dependence of the octet and decuplet ground states at different strange quark masses.
Assessment of large basis shell model wave functions for the Li isotopes
Energy Technology Data Exchange (ETDEWEB)
Karataglidis, S.; Brown, B.A. [Michigan State Univ., East Lansing, MI (United States); Dortmans, P.J.; Amos, K. [Melbourne Univ., Parkville, VIC (Australia). School of Physics
1997-06-01
The Li isotopes are good examples with which the shell model can be tested for cluster-like behaviour, as large space (no core) shell model wave functions may be constructed. The cross sections and analysing power for the inelastic scattering of electron and proton scattering data for {sup 6,7}Li ground states were analysed using the same shell model wave functions. It was found that the results obtained by using 0{Dirac_h}{omega} structure model wave functions is unable to reproduce the magnitude of the data. Meanwhile, those obtained by using the larger space models are able to reproduce the low-angle part of the cross section, but all model results severely underestimate the cross section above 20 deg. Meanwhile, in the case of analysing power, all model calculations give reasonable representation of the data. 13 refs., 3 figs.
U (1 )×U (1 ) symmetry-protected topological order in Gutzwiller wave functions
Liu, Zheng-Xin; Mei, Jia-Wei; Ye, Peng; Wen, Xiao-Gang
2014-12-01
Gutzwiller projection is a way to construct many-body wave functions that could carry topological order or symmetry-protected topological (SPT) order. However, an important issue is to determine whether or not a given Gutzwiller-projected wave function (GWF) carries a nontrivial SPT order, and which SPT order is carried by the wave function. In this paper, we numerically study the SPT order in a spin S =1 GWF on the kagome lattice. Using the standard Monte Carlo method, we directly confirm that the GWF has (1) gapped bulk with short-range correlations, (2) a trivial topological order via a nondegenerate ground state, and zero topological entanglement entropy, (3) a nontrivial U (1 )×U (1 ) SPT order via the Hall conductances of the protecting U (1 )×U (1 ) symmetry, and (4) a symmetry-protected gapless boundary. This represents numerical evidence of continuous symmetry-protected topological order in two-dimensional bosonic lattice systems.
Ground states for the fractional Schrodinger equation
Directory of Open Access Journals (Sweden)
Binhua Feng
2013-05-01
Full Text Available In this article, we show the existence of ground state solutions for the nonlinear Schrodinger equation with fractional Laplacian $$ (-Delta ^alpha u+ V(xu =lambda |u|^{p}uquadhbox{in $mathbb{R}^N$ for $alpha in (0,1$}. $$ We use the concentration compactness principle in fractional Sobolev spaces $H^alpha$ for $alpha in (0,1$. Our results generalize the corresponding results in the case $alpha =1$.
The Wave Function of Quantum de Sitter
Castro, Alejandra; Maloney, Alexander
2012-01-01
We consider quantum general relativity in three dimensions with a positive cosmological constant. The Hartle-Hawking wave function is computed as a function of metric data at asymptotic future infinity. The analytic continuation from Euclidean Anti-de Sitter space provides a natural integration contour in the space of metrics, allowing us -- with certain assumptions -- to compute the wave function exactly, including both perturbative and non-perturbative effects. The resulting wave function i...
Doma, S B; Farag, A M; El-Gammal, F N
2016-01-01
The variational Monte Carlo method is applied to investigate the ground state energy of the lithium atom and its ions up to Z=10 in the presence of an external magnetic field regime. Our calculations are based on using three forms of compact and accurate trial wave functions, which were put forward in calculating energies in the absence of magnetic field. The obtained results are in good agreement with the most recent accurate values and also with the exact values.
Ground State Geometries of Polyacetylene Chains from Many-Particle Quantum Mechanics.
Barborini, Matteo; Guidoni, Leonardo
2015-09-08
Due to the crucial role played by electron correlation, the accurate determination of ground state geometries of π-conjugated molecules is still a challenge for many quantum chemistry methods. Because of the high parallelism of the algorithms and their explicit treatment of electron correlation effects, Quantum Monte Carlo calculations can offer an accurate and reliable description of the electronic states and of the geometries of such systems, competing with traditional quantum chemistry approaches. Here, we report the structural properties of polyacetylene chains H-(C₂H₂)(N)-H up to N = 12 acetylene units, by means of Variational Monte Carlo (VMC) calculations based on the multi-determinant Jastrow Antisymmetrized Geminal Power (JAGP) wave function. This compact ansatz can provide for such systems an accurate description of the dynamical electronic correlation as recently detailed for the 1,3-butadiene molecule [J. Chem. Theory Comput. 2015 11 (2), 508-517]. The calculated Bond Length Alternation (BLA), namely the difference between the single and double carbon bonds, extrapolates, for N → ∞, to a value of 0.0910(7) Å, compatible with the experimental data. An accurate analysis was able to distinguish between the influence of the multi-determinantal AGP expansion and of the Jastrow factor on the geometrical properties of the fragments. Our size-extensive and self-interaction-free results provide new and accurate ab initio references for the structures of the ground state of polyenes.
On the excited state wave functions of Dirac fermions in the random gauge potential
Indian Academy of Sciences (India)
H Milani Moghaddam
2010-04-01
In the last decade, it was shown that the Liouville field theory is an effective theory of Dirac fermions in the random gauge potential (FRGP). We show that the Dirac wave functions in FRGP can be written in terms of descendents of the Liouville vertex operator. In the quasiclassical approximation of the Liouville theory, our model predicts 22.2 that the localization length scales with the energy as $ ∼ E^{−b^{2}(1+b^{2})^{2}}$, where is the strength of the disorder. The self-duality of the theory under the transformation → 1/ is discussed. We also calculate the distribution functions of 0 = |0 ()|2, (i.e. (0); 0 () is the ground state wave function), which behaves as the log-normal distribution function. It is also shown that in small 0, (0) behaves as a chi-square distribution.
Thermodynamic Ground States of Complex Oxide Heterointerfaces
DEFF Research Database (Denmark)
Gunkel, F.; Hoffmann-Eifert, S.; Heinen, R. A.
2017-01-01
The formation mechanism of 2-dimensional electron gases (2DEGs) at heterointerfaces between nominally insulating oxides is addressed with a thermodynamical approach. We provide a comprehensive analysis of the thermodynamic ground states of various 2DEG systems directly probed in high temperature...... equilibrium conductivity measurements. We unambiguously identify two distinct classes of oxide heterostructures: For epitaxial perovskite/perovskite heterointerfaces (LaAlO3/SrTiO3, NdGaO3/SrTiO3, and (La,Sr)(Al,Ta)O3/SrTiO3), we find the 2DEG formation being based on charge transfer into the interface...
Superimposed particles in 1D ground states
Energy Technology Data Exchange (ETDEWEB)
Sueto, Andras, E-mail: suto@szfki.hu [Research Institute for Solid State Physics and Optics, Hungarian Academy of Sciences, PO Box 49, H-1525 Budapest (Hungary)
2011-01-21
For a class of nonnegative, range-1 pair potentials in one-dimensional continuous space we prove that any classical ground state of lower density {>=}1 is a tower-lattice, i.e. a lattice formed by towers of particles the heights of which can differ only by 1, and the lattice constant is 1. The potential may be flat or may have a cusp at the origin; it can be continuous, but its derivative has a jump at 1. The result is valid on finite intervals or rings of integer length and on the whole line.
Parniak, Michał; Wasilewski, Wojciech
2015-01-01
We demonstrate an interface between light coupled to transition between excited states of rubidium and long-lived ground-state atomic coherence. In our proof-of-principle experiment a non-linear process of four-wave mixing in an open-loop configuration is used to achieve light emission proportional to independently prepared ground-state atomic coherence. We demonstrate strong correlations between Raman light heralding generation of ground-state coherence and the new four-wave mixing signal. Dependance of the efficiency of the process on laser detunings is studied.
Unitary Networks from the Exact Renormalization of Wave Functionals
Fliss, Jackson R; Parrikar, Onkar
2016-01-01
The exact renormalization group (ERG) for $O(N)$ vector models (at large $N$) on flat Euclidean space can be interpreted as the bulk dynamics corresponding to a holographically dual higher spin gauge theory on $AdS_{d+1}$. This was established in the sense that at large $N$ the generating functional of correlation functions of single trace operators is reproduced by the on-shell action of the bulk higher spin theory, which is most simply presented in a first-order (phase space) formalism. In this paper, we extend the ERG formalism to the wave functionals of arbitrary states of the $O(N)$ vector model at the free fixed point. We find that the ERG flow of the ground state and a specific class of excited states is implemented by the action of unitary operators which can be chosen to be local. Consequently, the ERG equations provide a continuum notion of a tensor network. We compare this tensor network with the entanglement renormalization networks, MERA, and its continuum version, cMERA, which have appeared rece...
The significant role of covalency in determining the ground state of cobalt phthalocyanines molecule
Directory of Open Access Journals (Sweden)
Jing Zhou
2016-03-01
Full Text Available To shed some light on the metal 3d ground state configuration of cobalt phthalocyanines system, so far in debate, we present an investigation by X-ray absorption spectroscopy (XAS at Co L2,3 edge and theoretical calculation. The density functional theory calculations reveal highly anisotropic covalent bond between central cobalt ion and nitrogen ligands, with the dominant σ donor accompanied by weak π-back acceptor interaction. Our combined experimental and theoretical study on the Co-L2,3 XAS spectra demonstrate a robust ground state of 2A1g symmetry that is built from 73% 3d7 character and 27% 3 d 8 L ¯ ( L ¯ denotes a ligand hole components, as the first excited-state with 2Eg symmetry lies about 158 meV higher in energy. The effect of anisotropic and isotropic covalency on the ground state was also calculated and the results indicate that the ground state with 2A1g symmetry is robust in a large range of anisotropic covalent strength while a transition of ground state from 2A1g to 2Eg configuration when isotropic covalent strength increases to a certain extent. Here, we address a significant anisotropic covalent effect of short Co(II-N bond on the ground state and suggest that it should be taken into account in determining the ground state of analogous cobalt complexes.
Natural generalization of the ground-state Slater determinant to more than one dimension
Sunko, D. K.
2016-06-01
The basic question is addressed of how the space dimension d is encoded in the Hilbert space of N identical fermions. There appears a finite number N !d-1 of many-body wave functions, called shapes, which cannot be generated by trivial combinatorial extension of the one-dimensional ones. A general algorithm is given to list them all in terms of standard Slater determinants. Conversely, excitations which can be induced from the one-dimensional case are bosonized into a system of distinguishable bosons, called Euler bosons, much like the electromagnetic field is quantized in terms of photons distinguishable by their wave numbers. Their wave functions are given explicitly in terms of elementary symmetric functions, reflecting the fact that the fermion sign problem is trivial in one dimension. The shapes act as vacua for the Euler bosons. They are the natural generalization of the single-Slater-determinant form for the ground state to more than one dimension. In terms of algebraic invariant theory, the shapes are antisymmetric invariants which finitely generate the N -fermion Hilbert space as a graded algebra over the ring of symmetric polynomials. Analogous results hold for identical bosons.
Yanagisawa, Takashi
2016-11-01
The ground state of the two-dimensional (2D) Hubbard model is investigated by adopting improved wave functions that take into account intersite electron correlation beyond the Gutzwiller ansatz. The ground-state energy is lowered considerably, giving the best estimate of the ground-state energy for the 2D Hubbard model. There is a crossover from weakly to strongly correlated regions as the on-site Coulomb interaction U increases. The antiferromagnetic correlation induced by U is reduced for hole doping when U is large, being greater than the bandwidth, thus increasing the kinetic energy gain. The spin and charge fluctuations are induced in the strongly correlated region. These antiferromagnetic and kinetic charge fluctuations induce electron pairings, which results in high-temperature superconductivity.
Spheroidal Wave Functions in Electromagnetic Theory
Li, Le-Wei; Kang, Xiao-Kang; Leong, Mook-Seng
2001-11-01
The flagship monograph addressing the spheroidal wave function and its pertinence to computational electromagnetics Spheroidal Wave Functions in Electromagnetic Theory presents in detail the theory of spheroidal wave functions, its applications to the analysis of electromagnetic fields in various spheroidal structures, and provides comprehensive programming codes for those computations. The topics covered in this monograph include: Spheroidal coordinates and wave functions Dyadic Green's functions in spheroidal systems EM scattering by a conducting spheroid EM scattering by a coated dielectric spheroid Spheroid antennas SAR distributions in a spheroidal head model The programming codes and their applications are provided online and are written in Mathematica 3.0 or 4.0. Readers can also develop their own codes according to the theory or routine described in the book to find subsequent solutions of complicated structures. Spheroidal Wave Functions in Electromagnetic Theory is a fundamental reference for scientists, engineers, and graduate students practicing modern computational electromagnetics or applied physics.
Mandrà, Salvatore; Zhu, Zheng; Katzgraber, Helmut G.
2017-02-01
We study the performance of the D-Wave 2X quantum annealing machine on systems with well-controlled ground-state degeneracy. While obtaining the ground state of a spin-glass benchmark instance represents a difficult task, the gold standard for any optimization algorithm or machine is to sample all solutions that minimize the Hamiltonian with more or less equal probability. Our results show that while naive transverse-field quantum annealing on the D-Wave 2X device can find the ground-state energy of the problems, it is not well suited in identifying all degenerate ground-state configurations associated with a particular instance. Even worse, some states are exponentially suppressed, in agreement with previous studies on toy model problems [New J. Phys. 11, 073021 (2009), 10.1088/1367-2630/11/7/073021]. These results suggest that more complex driving Hamiltonians are needed in future quantum annealing machines to ensure a fair sampling of the ground-state manifold.
Wind wave source functions in opposing seas
Langodan, Sabique
2015-08-26
The Red Sea is a challenge for wave modeling because of its unique two opposed wave systems, forced by opposite winds and converging at its center. We investigate the different physical aspects of wave evolution and propagation in the convergence zone. The two opposing wave systems have similar amplitude and frequency, each driven by the action of its own wind. Wave patterns at the centre of the Red Sea, as derived from extensive tests and intercomparison between model and measured data, suggest that the currently available wave model source functions may not properly represent the evolution of the local fields that appear to be characterized by a less effective wind input and an enhanced white-capping. We propose and test a possible simple solution to improve the wave-model simulation under opposing winds and waves condition. This article is protected by copyright. All rights reserved.
Ground state of high-density matter
Copeland, ED; Kolb, Edward W.; Lee, Kimyeong
1988-01-01
It is shown that if an upper bound to the false vacuum energy of the electroweak Higgs potential is satisfied, the true ground state of high-density matter is not nuclear matter, or even strange-quark matter, but rather a non-topological soliton where the electroweak symmetry is exact and the fermions are massless. This possibility is examined in the standard SU(3) sub C tensor product SU(2) sub L tensor product U(1) sub Y model. The bound to the false vacuum energy is satisfied only for a narrow range of the Higgs boson masses in the minimal electroweak model (within about 10 eV of its minimum allowed value of 6.6 GeV) and a somewhat wider range for electroweak models with a non-minimal Higgs sector.
Ground State Properties of Neutron Magic Nuclei
Saxena, G
2016-01-01
A systematic study of the ground state properties of the entire chains of even even neutron magic nuclei represented by isotones of traditional neutron magic numbers N = 8, 20, 40, 50, 82 and 126 has been carried out using relativistic mean field (rmf) plus Bardeen Cooper Schrieffer (BCS) approach. Our present investigation includes deformation, binding energy, two proton separation energy, single particle energy, rms radii along with proton and neutron density profiles, etc. Several of these results are compared with the results calculated using non relativistic approach (Skyrme Hartree Fock method) along with available experimental data and indeed they are found with excellent agreement. In addition, the possible locations of the proton and neutron drip lines, the (Z,N) values for the new shell closures, disappearance of traditional shell closures as suggested by the detailed analyzes of results are also discussed in detail.
Time symmetry in wave-function collapse
Bedingham, D. J.; Maroney, O. J. E.
2017-04-01
The notion of a physical collapse of the wave function is embodied in dynamical collapse models. These involve a modification of the unitary evolution of the wave function so as to give a dynamical account of collapse. The resulting dynamics is at first sight time asymmetric for the simple reason that the wave function depends on those collapse events in the past but not those in the future. Here we show that dynamical wave-function collapse models admit a general description that has no built-in direction of time. Given some simple constraints, we show that there exist empirically equivalent pictures of collapsing wave functions in both time directions, each satisfying the same dynamical rules. A preferred direction is singled out only by the asymmetric initial and final time constraints on the state of the universe.
Parameswaran, S A; Kimchi, Itamar; Turner, Ari M; Stamper-Kurn, D M; Vishwanath, Ashvin
2013-03-22
We study Bose-Hubbard models on tight-binding, non-Bravais lattices, with a filling of one boson per unit cell--and thus fractional site filling. We discuss situations where no classical bosonic insulator, which is a product state of particles on independent sites, is admitted. Nevertheless, we show that it is possible to construct a quantum Mott insulator of bosons if a trivial band insulator of fermions is possible at the same filling. The ground state wave function is simply a permanent of exponentially localized Wannier orbitals. Such a Wannier permanent wave function is featureless in that it respects all lattice symmetries and is the unique ground state of a parent Hamiltonian that we construct. Motivated by the recent experimental demonstration of a kagome optical lattice of bosons, we study this lattice at 1/3 site filling. Previous approaches to this problem have invariably produced either broken-symmetry states or topological order. Surprisingly, we demonstrate that a featureless insulator is a possible alternative and is the exact ground state of a local Hamiltonian. We briefly comment on the experimental relevance of our results to ultracold atoms as well as to 1/3 magnetization plateaus for kagome spin models in an applied field.
Auxiliary-field based trial wave functions in quantum Monte Carlo simulations
Chang, Chia-Chen; Rubenstein, Brenda; Morales, Miguel
We propose a simple scheme for generating correlated multi-determinant trial wave functions for quantum Monte Carlo algorithms. The method is based on the Hubbard-Stratonovich transformation which decouples a two-body Jastrow-type correlator into one-body projectors coupled to auxiliary fields. We apply the technique to generate stochastic representations of the Gutzwiller wave function, and present benchmark resuts for the ground state energy of the Hubbard model in one dimension. Extensions of the proposed scheme to chemical systems will also be discussed. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344, 15-ERD-013.
On the nature of the oligoacene ground state
Hachmann, Johannes; Dorando, Jonathan; Aviles, Michael; Kin-Lic Chan, Garnet
2007-03-01
The nature of the oligoacene ground state - its spin, singlet-triplet gap, and diradical character as a function of chain-length - is a question of ongoing theoretical and experimental interest with notable technological implications. Previous computational studies have given inconclusive answers to this challenging electronic structure problem (see e.g. [1]). In the present study we exploit the capabilities of the local ab initio Density Matrix Renormalization Group (DMRG) [2], which allows the numerically exact (FCI) solution of the Schr"odinger equation in a chosen 1-particle basis and active space for quasi-one-dimensional systems. We compute the singlet-triplet gap from first principles as a function of system length ranging from naphthalene to tetradecacene, correlating the full π-space (i.e. up to 58 electrons in 58 orbitals) and converging the results to a few μEh accuracy [3]. In order to study the diradical nature of the oligoacene ground state we calculate expectation values over different diradical occupation and pair-correlation operators. Furthermore we study the natural orbitals and their occupation. [1] Bendikov, Duong, Starkey, Houk, Carter, Wudl, JACS 126 (2004), 7416. [2] Hachmann, Cardoen, Chan, JCP 125 (2006), 144101. [3] Hachmann, Dorando, Avil'es, Chan, in preparation.
Sculpturing the Electron Wave Function
Shiloh, Roy; Lilach, Yigal; Arie, Ady
2014-01-01
Coherent electrons such as those in electron microscopes, exhibit wave phenomena and may be described by the paraxial wave equation. In analogy to light-waves, governed by the same equation, these electrons share many of the fundamental traits and dynamics of photons. Today, spatial manipulation of electron beams is achieved mainly using electrostatic and magnetic fields. Other demonstrations include simple phase-plates and holographic masks based on binary diffraction gratings. Altering the spatial profile of the beam may be proven useful in many fields incorporating phase microscopy, electron holography, and electron-matter interactions. These methods, however, are fundamentally limited due to energy distribution to undesired diffraction orders as well as by their binary construction. Here we present a new method in electron-optics for arbitrarily shaping of electron beams, by precisely controlling an engineered pattern of thicknesses on a thin-membrane, thereby molding the spatial phase of the electron wav...
EFFECT OF DIELECTRIC CONSTANT ON THE EXCITON GROUND STATE ENERGY OF CdSe QUANTUM DOTS
Institute of Scientific and Technical Information of China (English)
HUI PING
2000-01-01
The B-spline technique is used in the calculation of the exciton ground state energy based on the effective mass approximation (EMA) model.The exciton is confined in CdSe microspherical crystallites with a finite-height potential wall (dots).In this approach,(a) the wave function is allowed to penetrate to the outside of the dots; (b) the dielectric constants of the quantum dot and the surrounding material are considered to be different; and (c) the dielectric constant of the dots are size-dependent.The exciton energies as functions of radii of the dots in the range 0.5-3.5nm are calculated and compared with experimental and previous theoretical data.The results show that: (1) The exciton energy is convergent as the radius of the dot becomes very small.(2) A good agreement with the experimental data better than other theoretical results is achieved.(3) The penetration (or leaking) of the wave function and the difference of the dielectric constants in different regions are necessary for correcting the Coulomb interaction energy and reproducing experimental data.(4) The EMA model with B-spline technique can describe the status of excition confined in quantum dot very well.
Potential Energy Surfaces of Nitrogen Dioxide for the Ground State
Institute of Scientific and Technical Information of China (English)
SHAO Ju-Xiang; ZHU Zheng-He; CHENG Xin-Lu; YANG Xiang-Dong
2007-01-01
The potential energy function of nitrogen dioxide with the C2v symmetry in the ground state is represented using the simplified Sorbie-Murrell many-body expansion function in terms of the symmetry of NO2. Using the potential energy function, some potential energy surfaces of NO2(C2v, X2A1), such as the bond stretching contour plot for a fixed equilibrium geometry angle θ and contour for O moving around N-O (R1), in which R1 is fixed at the equilibrium bond length, are depicted. The potential energy surfaces are analysed. Moreover, the equilibrium parameters for NO2 with the C2v, Cs and D8h symmetries, such as equilibrium geometry structures and energies, are calculated by the ab initio (CBS-Q) method.
Ground state for CH2 and symmetry for methane decomposition
Institute of Scientific and Technical Information of China (English)
Zhang Li; Luo Wen-Lang; Ruan Wen; Jiang Gang; Zhu Zheng-He
2008-01-01
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 X3B1 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 X3Σ-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→CH3+H is allowed for CH4. This is similar to the decomposition of SiH4.
Au42: A possible ground-state noble metallic nanotube
Wang, Jing; Ning, Hua; Ma, Qing-Min; Liu, Ying; Li, You-Cheng
2008-10-01
A large hollow tubelike Au42 is predicted as a new ground-state configuration based on the scalar relativistic density functional theory. The shape of this new Au42 cluster is similar to a (5,5) single-wall gold nanotube, the two ends of which are capped by half of a fullerenelike Au32. In the same way, a series of Aun (n =37,42,47,52,57,62,67,72,…, Δn =5) tubelike structures has been constructed. The highest occupied molecular orbital-lowest unoccupied molecular orbital gaps suggested a significant semiconductor-conductor alternation in n ɛ[32,47]. Similar to the predictions and speculation of Daedalus [D. E. H. Jones, New Sci. 32, 245 (1966); E. Osawa, Superaromaticity (Kagaku, Kyoto, 1970), Vol. 25, pp. 854-863; Z. Yoshida and E. Osawa, Aromaticity Chemical Monograph (Kagaku Dojin, Kyoto, Japan, 1971), Vol. 22, pp. 174-176; D. A. Bochvar and E. G. Gal'pern, Dokl. Akad. Nauk SSSR 209, 610 (1973)], here a large hollow ground-state gold nanotube was predicted theoretically.
Spatial competition of the ground states in 1111 iron pnictides
Lang, G.; Veyrat, L.; Gräfe, U.; Hammerath, F.; Paar, D.; Behr, G.; Wurmehl, S.; Grafe, H.-J.
2016-07-01
Using nuclear quadrupole resonance, the phase diagram of 1111 R FeAsO1 -xFx (R =La , Ce, Sm) iron pnictides is constructed as a function of the local charge distribution in the paramagnetic state, which features low-doping-like (LD-like) and high-doping-like (HD-like) regions. Compounds based on magnetic rare earths (Ce, Sm) display a unified behavior, and comparison with La-based compounds reveals the detrimental role of static iron 3 d magnetism on superconductivity, as well as a qualitatively different evolution of the latter at high doping. It is found that the LD-like regions fully account for the orthorhombicity of the system, and are thus the origin of any static iron magnetism. Orthorhombicity and static magnetism are not hindered by superconductivity but limited by dilution effects, in agreement with two-dimensional (2D) (respectively three-dimensional) nearest-neighbor square lattice site percolation when the rare earth is nonmagnetic (respectively magnetic). The LD-like regions are not intrinsically supportive of superconductivity, contrary to the HD-like regions, as evidenced by the well-defined Uemura relation between the superconducting transition temperature and the superfluid density when accounting for the proximity effect. This leads us to propose a complete description of the interplay of ground states in 1111 pnictides, where nanoscopic regions compete to establish the ground state through suppression of superconductivity by static magnetism, and extension of superconductivity by proximity effect.
Gradual collapse of nuclear wave functions regulated by frequency tuned X-ray scattering.
Ignatova, Nina; Cruz, Vinícius V; Couto, Rafael C; Ertan, Emelie; Zimin, Andrey; Guimarães, Freddy F; Polyutov, Sergey; Ågren, Hans; Kimberg, Victor; Odelius, Michael; Gel'mukhanov, Faris
2017-03-07
As is well established, the symmetry breaking by isotope substitution in the water molecule results in localisation of the vibrations along one of the two bonds in the ground state. In this study we find that this localisation may be broken in excited electronic states. Contrary to the ground state, the stretching vibrations of HDO are delocalised in the bound core-excited state in spite of the mass difference between hydrogen and deuterium. The reason for this effect can be traced to the narrow "canyon-like" shape of the potential of the state along the symmetric stretching mode, which dominates over the localisation mass-difference effect. In contrast, the localisation of nuclear motion to one of the HDO bonds is preserved in the dissociative core-excited state . The dynamics of the delocalisation of nuclear motion in these core-excited states is studied using resonant inelastic X-ray scattering of the vibrationally excited HDO molecule. The results shed light on the process of a wave function collapse. After core-excitation into the state of HDO the initial wave packet collapses gradually, rather than instantaneously, to a single vibrational eigenstate.
The evolution of piecewise polynomial wave functions
Andrews, Mark
2017-01-01
For a non-relativistic particle, we consider the evolution of wave functions that consist of polynomial segments, usually joined smoothly together. These spline wave functions are compact (that is, they are initially zero outside a finite region), but they immediately extend over all available space as they evolve. The simplest splines are the square and triangular wave functions in one dimension, but very complicated splines have been used in physics. In general the evolution of such spline wave functions can be expressed in terms of antiderivatives of the propagator; in the case of a free particle or an oscillator, all the evolutions are expressed exactly in terms of Fresnel integrals. Some extensions of these methods to two and three dimensions are discussed.
Ground state structures and properties of small hydrogenated silicon clusters
Indian Academy of Sciences (India)
R Prasad
2003-01-01
We present results for ground state structures and properties of small hydrogenated silicon clusters using the Car–Parrinello molecular dynamics with simulated annealing. We discuss the nature of bonding of hydrogen in these clusters. We find that hydrogen can form a bridge like Si–H–Si bond connecting two silicon atoms. We find that in the case of a compact and closed silicon cluster hydrogen bonds to the silicon cluster from outside. To understand the structural evolutions and properties of silicon cluster due to hydrogenation, we have studied the cohesive energy and first excited electronic level gap of clusters as a function of hydrogenation. We find that first excited electronic level gap of Si and SiH fluctuates as function of size and this may provide a first principle basis for the short-range potential fluctuations in hydrogenated amorphous silicon. The stability of hydrogenated silicon clusters is also discussed.
Deuteron wave function and OPE potential
Righi, S.; Rosa-Clot, M.
1987-06-01
The deuteron wave function is calculated integrating from outside the Schredinger equation using as input its asymptotic behaviour. Some potentials are tested and the one pion exchange potential (OPEP) is shown to be the main responsible of the wave function structure up to distances of about 1 fm. The relevance of the short range part of the potential is analyzed and it is shown that a substantial enhancement of the OPEP central part is needed in the deuteron channel.
The Wave Function and Quantum Reality
Gao, Shan
2011-01-01
We investigate the meaning of the wave function by analyzing the mass and charge density distribution of a quantum system. According to protective measurement, a charged quantum system has mass and charge density proportional to the modulus square of its wave function. It is shown that the mass and charge density is not real but effective, and it is formed by the ergodic motion of a localized particle with the total mass and charge of the system. Moreover, it is argued that the ergodic motion is not continuous but discontinuous and random. This result suggests a new interpretation of the wave function, according to which the wave function is a description of random discontinuous motion of particles, and the modulus square of the wave function gives the probability density of the particles being in certain locations. It is shown that the suggested interpretation of the wave function disfavors the de Broglie-Bohm theory and the many-worlds interpretation but favors the dynamical collapse theories, and the rando...
Theoretical study on thermal decomposition of azoisobutyronitrile in ground state
Institute of Scientific and Technical Information of China (English)
SUN Chengke; ZHAO Hongmei; LI Zonghe
2004-01-01
The thermal decomposition mechanisms of azoisobutyronitrile (AIBN) in the ground state have been investigated systematically. Based on the potential energy surfaces (PES) of various possible dissociation paths obtained using the semiempirical AM1 method with partial optimization, the density function theory B3LYP/6-311G* method was employed to optimize the geometric parameters of the reactants, the intermediates, the products and the transition states,which were further confirmed by the vibrational analysis. The obtained results show that the reaction process of the two-bond (three-body) simultaneous cleavage Me2(CN)C-N=Nleading to the reaction proceeding in the former pathway. The calculation results were consistent with all the experimental facts.
Inversion of an Atomic Wave Packet in a Circularly Polarized Electromagnetic Wave
Institute of Scientific and Technical Information of China (English)
ZENG Gao-Jian
2001-01-01
We study behavior of an atomic wave packet in a circularly polarized electromagnetic wave, and particularly calculate the atomic inversion of the wave packet. A general method of calculation is presented. The results are interesting. For example, if the wave packet is very narrow or/and the interaction is very strong, no matter the atom is initially in its ground state or excited state, the atomic inversion approaches zero as time approaches infinity. If the atom is initially in its ground state and excited state with the probability 1/2 respectively, and if the momentum density is an even function, then the atomic inversion equals zero at any time.``
Ground-State Transition in a Two-Dimensional Frenkel-Kontorova Model
Institute of Scientific and Technical Information of China (English)
YUAN Xiao-Ping; ZHENG Zhi-Gang
2011-01-01
The ground state of a generalized Frenkel-Kontorova model with a transversaJ degree of freedom is studied. When the coupling strength, K, and the frequency of & single-Atom vibration in the transversaJ direction, ωou are increased, the ground state of the model undergoes a transition from a two-dimensional configuration to a one-dimensional one. This transition can manifest in different ways. Furthermore, we find that the prerequisite of a two-dimensionai ground state is θ≠1//q.%The ground state of a generalized Frenkel-Kontorova model with a transversal degree of freedom is studied.When the coupling strength,K,and the frequency of a single-atom vibration in the transversal direction,ωoy,are increased,the ground state of the model undergoes a transition from a two-dimensional configuration to a one-dimensional one.This transition can manifest in different ways.Furthermore,we find that the prerequisite of a two-dimensional ground state is θ ≠ 1/q.In recent years,the Frenkel-Kontorova (FK) model has been applied to a variety of physical systems,such as adsorbed monolayers,[1,2] Josephsonjunction arrays,[3-5] tribology[6-8] and charge-density waves.[9,10] Experimental and large-scale simulation data at the nanoscale have become available,and more complicated FK-type models have been investigated using simulations of molecular dynamics.[11
Solving Quantum Ground-State Problems with Nuclear Magnetic Resonance
Li, Zhaokai; Chen, Hongwei; Lu, Dawei; Whitfield, James D; Peng, Xinhua; Aspuru-Guzik, Alán; Du, Jiangfeng
2011-01-01
Quantum ground-state problems are computationally hard problems; for general many-body Hamiltonians, there is no classical or quantum algorithm known to be able to solve them efficiently. Nevertheless, if a trial wavefunction approximating the ground state is available, as often happens for many problems in physics and chemistry, a quantum computer could employ this trial wavefunction to project the ground state by means of the phase estimation algorithm (PEA). We performed an experimental realization of this idea by implementing a variational-wavefunction approach to solve the ground-state problem of the Heisenberg spin model with an NMR quantum simulator. Our iterative phase estimation procedure yields a high accuracy for the eigenenergies (to the 10^-5 decimal digit). The ground-state fidelity was distilled to be more than 80%, and the singlet-to-triplet switching near the critical field is reliably captured. This result shows that quantum simulators can better leverage classical trial wavefunctions than c...
Symmetry and the critical phase of the two-bath spin-boson model: Ground-state properties
Zhou, Nengji; Chen, Lipeng; Xu, Dazhi; Chernyak, Vladimir; Zhao, Yang
2015-05-01
A generalized trial wave function termed as the "multi-D1 ansatz" has been developed to study the ground state of the spin-boson model with simultaneous diagonal and off-diagonal coupling in the sub-Ohmic regime. Ground-state properties including energy and spin polarization are investigated, and the results are consistent with those from exact diagonalization and density matrix renormalization group approaches for the cases involving two oscillators and two baths described by a continuous spectral density function. Breakdown of the rotational and parity symmetries along the continuous quantum phase transition separating the localized phase from the critical phase has been uncovered. Moreover, the phase boundary is determined accurately with the corresponding rotational- and parity-symmetry parameters. A critical value of the spectral exponent s*=0.49 (1 ) is predicted in the weak coupling limit, which is in agreement with the mean-field prediction of 1 /2 , but much smaller than the earlier literature estimate of 0.75 (1 ) .
Institute of Scientific and Technical Information of China (English)
E.Javadimanesh; H.Hassanabadi; A.A.Rajabi; H.Rahimov; S.Zarrinkamar
2012-01-01
We study the half-lives of some nuclei via the alpha-decay process from ground state to ground state. To go through the problem, we have considered a potential model with Yukawa proximity potential and have thereby calculated the half-lives. The comparison with the existing data is motivating.
Meaning of the nuclear wave function
Terry, John D
2016-01-01
Background The intense current experimental interest in studying the structure of the deuteron and using it to enable accurate studies of neutron structure motivate us to examine the four-dimensional space-time nature of the nuclear wave function, and the various approximations used to reduce it to an object that depends only on three spatial variables. Purpose: The aim is to determine if the ability to understand and analyze measured experimental cross sections is compromised by making the reduction from four to three dimensions. Method: Simple, exactly-calculable, covariant models of a bound-state wave state wave function (a scalar boson made of two constituent-scalar bosons) with parameters chosen to represent a deuteron are used to investigate the accuracy of using different approximations to the nuclear wave function to compute the quasi-elastic scattering cross section. Four different versions of the wave function are defined (light-front spectator, light-front, light-front with scaling and non-relativi...
Zeh, H D
2002-01-01
Schroedinger's wave function shows many aspects of a state of incomplete knowledge or information ("bit"): (1) it is defined on a space of classical configurations, (2) its generic entanglement is, therefore, analogous to statistical correlations, and (3) it determines probabilites of measurement outcomes. Nonetheless, quantum superpositions (such as represented by a wave function) also define individual physical states ("it"). This conceptual dilemma may have its origin in the conventional operational foundation of physical concepts, successful in classical physics, but inappropriate in quantum theory because of the existence of mutually exclusive operations (used for the definition of concepts). In contrast, a hypothetical realism, based on concepts that are justified only by their universal and consistent applicability, favors the wave function as a description of (thus nonlocal) physical reality. The (conceptually local) classical world then appears as an illusion, facilitated by the phenomenon of decoher...
Estimating the ground-state probability of a quantum simulation with product-state measurements
Directory of Open Access Journals (Sweden)
Bryce eYoshimura
2015-10-01
Full Text Available .One of the goals in quantum simulation is to adiabatically generate the ground state of a complicated Hamiltonian by starting with the ground state of a simple Hamiltonian and slowly evolving the system to the complicated one. If the evolution is adiabatic and the initial and final ground states are connected due to having the same symmetry, then the simulation will be successful. But in most experiments, adiabatic simulation is not possible because it would take too long, and the system has some level of diabatic excitation. In this work, we quantify the extent of the diabatic excitation even if we do not know {it a priori} what the complicated ground state is. Since many quantum simulator platforms, like trapped ions, can measure the probabilities to be in a product state, we describe techniques that can employ these simple measurements to estimate the probability of being in the ground state of the system after the diabatic evolution. These techniques do not require one to know any properties about the Hamiltonian itself, nor to calculate its eigenstate properties. All the information is derived by analyzing the product-state measurements as functions of time.
Spontaneous symmetry breaking in correlated wave functions
Kaneko, Ryui; Tocchio, Luca F.; Valentí, Roser; Becca, Federico; Gros, Claudius
2016-03-01
We show that Jastrow-Slater wave functions, in which a density-density Jastrow factor is applied onto an uncorrelated fermionic state, may possess long-range order even when all symmetries are preserved in the wave function. This fact is mainly related to the presence of a sufficiently strong Jastrow term (also including the case of full Gutzwiller projection, suitable for describing spin models). Selected examples are reported, including the spawning of Néel order and dimerization in spin systems, and the stabilization of charge and orbital order in itinerant electronic systems.
Tree based machine learning framework for predicting ground state energies of molecules
Himmetoglu, Burak
2016-10-01
We present an application of the boosted regression tree algorithm for predicting ground state energies of molecules made up of C, H, N, O, P, and S (CHNOPS). The PubChem chemical compound database has been incorporated to construct a dataset of 16 242 molecules, whose electronic ground state energies have been computed using density functional theory. This dataset is used to train the boosted regression tree algorithm, which allows a computationally efficient and accurate prediction of molecular ground state energies. Predictions from boosted regression trees are compared with neural network regression, a widely used method in the literature, and shown to be more accurate with significantly reduced computational cost. The performance of the regression model trained using the CHNOPS set is also tested on a set of distinct molecules that contain additional Cl and Si atoms. It is shown that the learning algorithms lead to a rich and diverse possibility of applications in molecular discovery and materials informatics.
Tree based machine learning framework for predicting ground state energies of molecules
Himmetoglu, Burak
2016-01-01
We present an application of the boosted regression tree algorithm for predicting ground state energies of molecules made up of C, H, N, O, P, and S (CHNOPS). The PubChem chemical compound database has been incorporated to construct a dataset of 16,242 molecules, whose electronic ground state energies have been computed using density functional theory. This dataset is used to train the boosted regression tree algorithm, which allows a computationally efficient and accurate prediction of molecular ground state energies. Predictions from boosted regression trees are compared with neural network regression, a widely used method in the literature, and shown to be more accurate with significantly reduced computational cost. The performance of the regression model trained using the CHNOPS set is also tested on a set of distinct molecules that contain additional Cl and Si atoms. It is shown that the learning algorithms lead to a rich and diverse possibility of applications in molecular discovery and materials inform...
Surface Gap Soliton Ground States for the Nonlinear Schr\\"{o}dinger Equation
Dohnal, Tomáš; Reichel, Wolfgang
2010-01-01
We consider the nonlinear Schr\\"{o}dinger equation $(-\\Delta +V(x))u = \\Gamma(x) |u|^{p-1}u$, $x\\in \\R^n$ with $V(x) = V_1(x) \\chi_{\\{x_1>0\\}}(x)+V_2(x) \\chi_{\\{x_10\\}}(x)+\\Gamma_2(x) \\chi_{\\{x_1<0\\}}(x)$ and with $V_1, V_2, \\Gamma_1, \\Gamma_2$ periodic in each coordinate direction. This problem describes the interface of two periodic media, e.g. photonic crystals. We study the existence of ground state $H^1$ solutions (surface gap soliton ground states) for $0<\\min \\sigma(-\\Delta +V)$. Using a concentration compactness argument, we provide an abstract criterion for the existence based on ground state energies of each periodic problem (with $V\\equiv V_1, \\Gamma\\equiv \\Gamma_1$ and $V\\equiv V_2, \\Gamma\\equiv \\Gamma_2$) as well as a more practical criterion based on ground states themselves. Examples of interfaces satisfying these criteria are provided. In 1D it is shown that, surprisingly, the criteria can be reduced to conditions on the linear Bloch waves of the operators $-\\tfrac{d^2}{dx^2} +V_1(x)$ an...
First-principles prediction of a ground state crystal structure of magnesium borohydride.
Ozolins, V; Majzoub, E H; Wolverton, C
2008-04-04
Mg(BH(4))(2) contains a large amount of hydrogen by weight and by volume, but its promise as a candidate for hydrogen storage is dependent on the currently unknown thermodynamics of H2 release. Using first-principles density-functional theory calculations and a newly developed prototype electrostatic ground state search strategy, we predict a new T=0 K ground state of Mg(BH(4))(2) with I4[over ]m2 symmetry, which is 5 kJ/mol lower in energy than the recently proposed P6(1) structure. The calculated thermodynamics of H(2) release are within the range required for reversible storage.
Universal crossover from ground-state to excited-state quantum criticality
Kang, Byungmin; Potter, Andrew C.; Vasseur, Romain
2017-01-01
We study the nonequilibrium properties of a nonergodic random quantum chain in which highly excited eigenstates exhibit critical properties usually associated with quantum critical ground states. The ground state and excited states of this system belong to different universality classes, characterized by infinite-randomness quantum critical behavior. Using strong-disorder renormalization group techniques, we show that the crossover between the zero and finite energy density regimes is universal. We analytically derive a flow equation describing the unitary dynamics of this isolated system at finite energy density from which we obtain universal scaling functions along the crossover.
Yang, Yonggang
2008-01-01
We investigated the effect of deuteration on the vibrational ground state of the hydrated hydroxide anion using a nine-dimensional quantum dynamical model for the case of J=0. The propagation of the nuclear wave function has been performed with the multi-configuration time-dependent Hartree method which yielded zero-point energies for the normal and fully deuterated species in quantitative agreement with previous diffusion Monte Carlo calculations. According to the zero-point energy the isotopomers having the hydrogen atom in the bridging position are more stable by about 1 kJ/mol as compared to the deuterium case. This holds irrespective of the deuteration state of the two OH groups. We also report the secondary geometric H/D isotope effect on the O--O distance which amounts to an elongation of about 0.005 A for the symmetric isotopomers and 0.009 A in the asymmetric case. Finally, we explore the isotopomer sensitivity of the ground state tunneling splitting due to the torsional motion of the two OH groups.
Exchange field effect in the crystal field ground state of CeMAl{sub 4}Si{sub 2}
Energy Technology Data Exchange (ETDEWEB)
Chen, Kai; Strigari, Fabio; Sundermann, Martin; Severing, Andrea [University of Cologne, Cologne (Germany); Agrestini, Stefano [Max Planck Institute for Chemical Physics of Solids, Dresden (Germany); Bauer, Eric D.; Sarrao, John L.; Thompson, Joe D. [Los Alamos National Laboratory, Los Alamos, NM (United States); Otero, Edwige [Synchrotron Soleil, Gif-sur-Yvette (France); Tanaka, Arata [Hiroshima University, Higashi-Hiroshima (Japan)
2016-07-01
The crystal-field ground state wave functions of the tetragonal Kondo lattice materials CeMAl{sub 4}Si{sub 2}(M = Rh, Ir and Pt), as well as the crystal-field splittings, are determined with low temperature linear polarized soft x-ray absorption spectroscopy. Surprisingly, at T < 20 K, which is far below the first excited crystal-field level at 200 K, a change in linear dichroism was observed that cannot be accounted for by population of crystal-field states. Adding an exchange field to the ionic full multiplet calculations below 20 K leads to a splitting to the ground state doublet and modification of J{sub z} admixture, thus accounting for the change in low temperature linear dichroism. The direction of the required exchange field is parallel along c-axis for the antiferromagnetic Rh and Ir compounds, and perpendicular to c-axis for ferromagnetic CePtAl{sub 4}Si{sub 2}.
Ab initio quantum Monte Carlo calculations of ground-state properties of manganese's oxides
Sharma, Vinit; Krogel, Jaron T.; Kent, P. R. C.; Reboredo, Fernando A.
One of the critical scientific challenges of contemporary research is to obtain an accurate theoretical description of the electronic properties of strongly correlated systems such as transition metal oxides and rare-earth compounds, since state-of-art ab-initio methods based on approximate density functionals are not always sufficiently accurate. Quantum Monte Carlo (QMC) methods, which use statistical sampling to evaluate many-body wave functions, have the potential to answer this challenge. Owing to the few fundamental approximations made and the direct treatment of electron correlation, QMC methods are among the most accurate electronic structure methods available to date. We assess the accuracy of the diffusion Monte Carlo method in the case of rocksalt manganese oxide (MnO). We study the electronic properties of this strongly-correlated oxide, which has been identified as a suitable candidate for many applications ranging from catalysts to electronic devices. ``This work was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division.'' Ab initio quantum Monte Carlo calculations of ground-state properties of manganese's oxides.
Energy Technology Data Exchange (ETDEWEB)
Booth, Corwin H.; Walter, Marc D.; Kazhdan, Daniel; Hu, Yung-Jin; Lukens, Wayne W.; Bauer, Eric D.; Maron, Laurent; Eisenstein, Odile; Andersen, Richard A.
2009-04-22
Partial ytterbium f-orbital occupancy (i.e., intermediate valence) and open-shell singlet formation are established for a variety of bipyridine and diazabutadiene adducts with decamethylytterbocene, (C5Me5)2Yb, abbreviated as Cp*2Yb. Data used to support this claim include ytterbium valence measurements using Yb LIII-edge X-ray absorption near-edge structure spectroscopy, magnetic susceptibility, and complete active space self-consistent field (CASSCF) multiconfigurational calculations, as well as structural measurements compared to density functional theory calculations. The CASSCF calculations indicate that the intermediate valence is the result of a multiconfigurational ground-state wave function that has both an open-shell singlet f13(?*)1, where pi* is the lowest unoccupied molecular orbital of the bipyridine or dpiazabutadiene ligands, and a closed-shell singlet f14 component. A number of other competing theories for the unusual magnetism in these materials are ruled out by the lack of temperature dependence of the measured intermediate valence. These results have implications for understanding chemical bonding not only in organolanthanide complexes but also for f-element chemistry in general, as well as understanding magnetic interactions in nanoparticles and devices.
Energy Technology Data Exchange (ETDEWEB)
Bauer, Eric D [Los Alamos National Laboratory; Booth, C H [LBNL; Walter, M D [LBNL; Kazhdan, D [LBNL; Hu, Y - J [LBNL; Lukens, Wayne [LBNL; Maron, Laurent [INSA TOULOUSE; Eisentein, Odile [UNIV MONTPELLIER 2; Anderson, Richard [LBNL
2009-01-01
Partial ytterbium f-orbital occupancy (i.e. intermediate valence) and open-shell singlet Draft 12/formation are established for a variety of bipyridine and diazabutadiene adducts to decamethylytterbocene, (C{sub 5}Me{sub 5}){sub 2}Yb or Cp*{sub 2}Yb. Data used to support this claim includes ytterbium valence measurements using Yb Lm-edge x-ray absorption near-edge structure (XANES) spectroscopy, magnetic susceptibility and Complete Active Space Self-Consistent Field (CASSCF) multi configurational calculations, as well as structural measurements compared to density-functional theory (DFT) calculations. The CASSCF calculations indicate that the intermediate valence is the result of a multiconfigurational ground state wave function that has both an open-shell singlet f{sup 13} and a closed-shell singlet f{sup 14} component. A number of other competing theories for the unusual magnetism in these materials are ruled out by the presence of intermediate valence and its lack of any significant temperature dependence. These results have implications for understanding chemical bonding not only in organolanthanide complexes, but also for organometallic chemistry in general, as well as understanding magnetic interactions in nanopartic1es and devices.
Constructibility of the Universal Wave Function
Bolotin, Arkady
2016-10-01
This paper focuses on a constructive treatment of the mathematical formalism of quantum theory and a possible role of constructivist philosophy in resolving the foundational problems of quantum mechanics, particularly, the controversy over the meaning of the wave function of the universe. As it is demonstrated in the paper, unless the number of the universe's degrees of freedom is fundamentally upper bounded (owing to some unknown physical laws) or hypercomputation is physically realizable, the universal wave function is a non-constructive entity in the sense of constructive recursive mathematics. This means that even if such a function might exist, basic mathematical operations on it would be undefinable and subsequently the only content one would be able to deduce from this function would be pure symbolical.
Koh, Yang Wei
2016-04-01
We present an extensive numerical study of the Sherrington-Kirkpatrick model in a transverse field. Recent numerical studies of quantum spin glasses have focused on exact diagonalization of the full Hamiltonian for small systems (≈20 spins). However, such exact numerical treatments are difficult to apply on larger systems. We propose making an approximation by using only a subspace of the full Hilbert space spanned by low-lying excitations consisting of one-spin-flipped and two-spin-flipped states. The approximation procedure is carried out within the theoretical framework of the Hartree-Fock approximation and configuration interaction. Although not exact, our approach allows us to study larger system sizes comparable to that achievable by state-of-the-art quantum Monte Carlo simulations. We calculate two quantities of interest due to recent advances in quantum annealing, the ground-state energy and the energy gap between the ground and first excited states. For the energy gap, we derive a formula that enables it to be calculated using just the ground-state wave function, thereby circumventing the need to diagonalize the Hamiltonian. We calculate the scalings of the energy gap and the leading correction to the extensive part of the ground-state energy with system size, which are difficult to obtain with current methods.
Ground states for a modified capillary surface equation in weighted Orlicz-Sobolev space
Directory of Open Access Journals (Sweden)
Guoqing Zhang
2015-03-01
Full Text Available In this article, we prove a compact embedding theorem for the weighted Orlicz-Sobolev space of radially symmetric functions. Using the embedding theorem and critical points theory, we prove the existence of multiple radial solutions and radial ground states for the following modified capillary surface equation $$\\displaylines{ -\\operatorname{div}\\Big(\\frac{|\
The ground state energy of the mean field spin glass model
Koukiou, Flora
2008-01-01
From the study of a functional equation of Gibbs measures we calculate the limiting free energy of the Sherrington-Kirkpatrick spin glass model at a particular value of (low) temperature. This implies the following lower bound for the ground state energy $\\epsilon_0$ \\[\\epsilon_0\\geq -0.7833...,\\] close to the replica symmetry breaking and numerical simulations values.
Comparison of two approaches for the treatment of Gutzwiller variational wave functions
Kaczmarczyk, J.
2015-02-01
In this work, we analyse the variational problem emerging from the Gutzwiller approach to strongly correlated systems. This problem comprises two main steps: evaluation and minimization of the ground state energy ? for the postulated Gutzwiller Wave Function. We discuss the available methods for evaluating ?, in particular the recently proposed diagrammatic expansion method. We compare the two existing approaches to minimize ?: the standard approach based on the effective single-particle Hamiltonian and the so-called Statistically-consistent Gutzwiller Approximation (SGA). On the example of the superconducting phase analysis, we show that these approaches lead to the same minimum as it should be. However, the calculations within the SGA method are easier to perform and the two approaches allow for a simple cross-check of the obtained results. Finally, we show two ways of solving the equations resulting from the variational procedure, as well as how to incorporate the condition for a fixed number of particles.
ON GROUND STATE SOLUTIONS FOR SUPERLINEAR DIRAC EQUATION
Institute of Scientific and Technical Information of China (English)
张建; 唐先华; 张文
2014-01-01
This article is concerned with the nonlinear Dirac equations Under suitable assumptions on the nonlinearity, we establish the existence of ground state solutions by the generalized Nehari manifold method developed recently by Szulkin and Weth.
Classical ground states of symmetric Heisenberg spin systems
Schmidt, H J
2003-01-01
We investigate the ground states of classical Heisenberg spin systems which have point group symmetry. Examples are the regular polygons (spin rings) and the seven quasi-regular polyhedra including the five Platonic solids. For these examples, ground states with special properties, e.g. coplanarity or symmetry, can be completely enumerated using group-theoretical methods. For systems having coplanar (anti-) ground states with vanishing total spin we also calculate the smallest and largest energies of all states having a given total spin S. We find that these extremal energies depend quadratically on S and prove that, under certain assumptions, this happens only for systems with coplanar S = 0 ground states. For general systems the corresponding parabolas represent lower and upper bounds for the energy values. This provides strong support and clarifies the conditions for the so-called rotational band structure hypothesis which has been numerically established for many quantum spin systems.
Seth, Michael; Ziegler, Tom
2005-10-08
A method for calculating the UV-vis spectra of molecules with spatially degenerate ground states using time-dependent density-functional theory (TDDFT) is proposed. The new transformed reference via an intermediate configuration Kohn-Sham TDDFT (TRICKS-TDDFT) method avoids the difficulties caused by the multireference nature of spatially degenerate states by rather than utilizing the ground state instead taking a nondegenerate excited state with desirable properties as the reference for the TDDFT calculation. The scope and practical application of the method are discussed. Like all open-shell TDDFT calculations this method at times suffers from the inability to produce transitions to states that are eigenfunctions of the total spin operator. A technique for alleviating this difficulty to some extent is proposed. The applicability and accuracy of the TRICKS-TDDFT method is demonstrated through example calculations of several d(1) and d(2) transition metal complexes with tetrahedral and octahedral symmetries. For the most part, the results of these calculations are similar in quality to to those obtained from standard TDDFT calculations.
Theory of ground state factorization in quantum cooperative systems.
Giampaolo, Salvatore M; Adesso, Gerardo; Illuminati, Fabrizio
2008-05-16
We introduce a general analytic approach to the study of factorization points and factorized ground states in quantum cooperative systems. The method allows us to determine rigorously the existence, location, and exact form of separable ground states in a large variety of, generally nonexactly solvable, spin models belonging to different universality classes. The theory applies to translationally invariant systems, irrespective of spatial dimensionality, and for spin-spin interactions of arbitrary range.
Quasiparticle Random Phase Approximation with an optimal Ground State
Simkovic, F; Raduta, A A
2001-01-01
A new Quasiparticle Random Phase Approximation approach is presented. The corresponding ground state is variationally determined and exhibits a minimum energy. New solutions for the ground state, some with spontaneously broken symmetry, of a solvable Hamiltonian are found. A non-iterative procedure to solve the non-linear QRPA equations is used and thus all possible solutions are found. These are compared with the exact results as well as with the solutions provided by other approaches.
Buchman, Omri; Baer, Roi
2017-09-01
The one-body density matrix (OBDM) is a fundamental contraction of the Bose-Einstein condensate wave function, encapsulating its one-body properties. It serves as a major analysis tool with which the condensed component of the density can be identified. Despite its cardinal importance, calculating the ground-state OBDM of trapped interacting bosons is a challenge and to date OBDM calculations have been published only for homogeneous systems or for trapped weakly interacting bosons. In this paper we discuss an approach for computing the OBDM based on a double-walker diffusion Monte Carlo random walk coupled with a stochastic permanent calculation. We here describe the method and study some of its statistical convergence and properties applying it to some model systems.
Lapierre, David; Kochanov, Roman; Kokoouline, Viatcheslav; Tyuterev, Vladimir
2016-01-01
Energies and lifetimes (widths) of vibrational states above the lowest dissociation limit of $^{16}$O$_3$ were determined using a previously-developed efficient approach, which combines hyperspherical coordinates and a complex absorbing potential. The calculations are based on a recently-computed potential energy surface of ozone determined with a spectroscopic accuracy [J. Chem. Phys. {\\bf 139}, 134307 (2013)]. The effect of permutational symmetry on rovibrational dynamics and the density of resonance states in O$_3$ is discussed in detail. Correspondence between quantum numbers appropriate for short- and long-range parts of wave functions of the rovibrational continuum is established. It is shown, by symmetry arguments, that the allowed purely vibrational ($J=0$) levels of $^{16}$O$_3$ and $^{18}$O$_3$, both made of bosons with zero nuclear spin, cannot dissociate on the ground state potential energy surface. Energies and wave functions of bound states of the ozone isotopologue $^{16}$O$_3$ with rotational ...
Institute of Scientific and Technical Information of China (English)
Gongming WEI
2008-01-01
A 2-coupled nonlinear Schr(o)dinger equations with bounded varying potentials and strongly attractive interactions is considered.When the attractive interaction is strong enough,the existence of a ground state for sufficiently small Planck constant is proved.As the Planck constant approaches zero,it is proved that one of the components concentrates at a minimum point of the ground state energy function which is defined in Section 4.
Mandrà, Salvatore; Katzgraber, Helmut G
2016-01-01
We study the performance of the D-Wave 2X quantum annealing machine on systems with well-controlled ground-state degeneracy. While obtaining the ground-state of a spin-glass benchmark instance represents a difficult task, the gold standard for any optimization algorithm or machine is to sample all solutions that minimize the Hamiltonian with more or less equal probability. Our results show that while naive transverse-field quantum annealing on the D-Wave 2X device can find the ground-state energy of the problems, it is not well suited in identifying all degenerate ground-state configurations associated to a particular instance. Even worse, some states are exponentially suppressed, in agreement with previous studies on toy model problems [New J. Phys. 11, 073021 (2009)]. These results suggest that more complex driving Hamiltonians, which introduce transitions between all states with equal weights, are needed in future quantum annealing machines to ensure a fair sampling of the ground-state manifold.
Continuous Observations and the Wave Function Collapse
Marchewka, A
2011-01-01
We propose to modify the collapse axiom of quantum measurement theory by replacing the instantaneous with a continuous collapse of the wave function in finite time $\\tau$. We apply it to coordinate measurement of a free quantum particle that is initially confined to a domain $D\\subset\\rR^d$ and is observed continuously by illuminating $\\rR^d-D$. The continuous collapse axiom (CCA) defines the post-measurement wave function (PMWF)in $D$ after a negative measurement as the solution of Schr\\"odinger's equation at time $\\tau$ with instantaneously collapsed initial condition and homogeneous Dirichlet condition on the boundary of $D$. The CCA applies to all cases that exhibit the Zeno effect. It rids quantum mechanics of the unphysical artifacts caused by instantaneous collapse and introduces no new artifacts.
Primordial gravitational waves and the collapse of the wave function
Leon, Gabriel; Landau, Susana J
2015-01-01
"The self-induced collapse hypothesis'' has been introduced by D. Sudarsky and collaborators to explain the origin of cosmic structure from a perfect isotropic and homogeneous universe during the inflationary regime. In this paper, we calculate the power spectrum for the tensor modes, within the semiclassical gravity approximation, with the additional hypothesis of a generic self-induced collapse of the inflaton's wave function; we also compute an estimate for the tensor-to-scalar ratio. Based on this calculation, we show that the considered proposal exhibits a strong suppression of the tensor modes amplitude; nevertheless, the corresponding amplitude is still consistent with the joint BICEP/KECK and Planck collaborations limit on the tensor-to-scalar ratio.
Quench of a symmetry-broken ground state
Giampaolo, S. M.; Zonzo, G.
2017-01-01
We analyze the problem of how different ground states associated with the same set of Hamiltonian parameters evolve after a sudden quench. To realize our analysis we define a quantitative approach to the local distinguishability between different ground states of a magnetically ordered phase in terms of the trace distance between the reduced density matrices obtained by projecting two ground states in the same subset. Before the quench, regardless of the particular choice of subset, any system in a magnetically ordered phase is characterized by ground states that are locally distinguishable. On the other hand, after the quench, the maximum distinguishability shows an exponential decay in time. Hence, in the limit of very long times, all the information about the particular initial ground state is lost even if the systems are integrable. We prove our claims in the framework of the magnetically ordered phases that characterize both the X Y and the N -cluster Ising models. The fact that we find similar behavior in models within different classes of symmetry makes us confident about the generality of our results.
Effect of spin-orbit coupling on the ground state structure of mercury
Mishra, Vinayak; Gyanchandani, Jyoti; Chaturvedi, Shashank; Sikka, S. K.
2014-05-01
Near zero kelvin ground state structure of mercury is the body centered tetragonal (BCT) structure (β Hg). However, in all previously reported density functional theory (DFT) calculations, either the rhombohedral or the HCP structure has been found to be the ground state structure. Based on the previous calculations it was predicted that the correct treatment of the SO effects would improve the result. We have performed FPLAPW calculations, with and without inclusion of the SO coupling, for determining the ground state structure. These calculations determine rhombohedral structure as the ground state structure instead of BCT structure. The calculations, without inclusion of SO effect, predict that the energies of rhombohedral and BCT structures are very close to each other but the energy of rhombohedral structure is lower than that of BCT structure at ambient as well as high pressure. On the contrary, the SO calculations predict that though at ambient conditions the rhombohedral structure is the stable structure but on applying a pressure of 3.2 GPa, the BCT structure becomes stable. Hence, instead of predicting the stability of BCT structure at zero pressure, the SO calculations predict its stability at 3.2 GPa. This small disagreement is expected when the energy differences between the structures are small.
Rabanal-León, Walter A; Murillo-López, Juliana A; Páez-Hernández, Dayán; Arratia-Pérez, Ramiro
2015-09-24
The high interest in lanthanide chemistry, and particularly in their luminescence, has been encouraged by the need of understanding the lanthanide chemical coordination and how the design of new luminescent materials can be affected by this. This work is focused on the understanding of the electronic structure, bonding nature, and optical properties of a set of lanthanide hexaaza macrocyclic complexes, which can lead to potential optical applications. Here we found that the DFT ground state of the open-shell complexes are mainly characterized by the manifold of low lying f states, having small HOMO-LUMO energy gaps. The results obtained from the wave function theory calculations (SO-RASSI) put on evidence the multiconfigurational character of their ground state and it is observed that the large spin-orbit coupling and the weak crystal field produce a strong mix of the ground and the excited states. The electron localization function (ELF) and the energy decomposition analysis (EDA) support the idea of a dative interaction between the macrocyclic ligand and the lanthanide center for all the studied systems; noting that, this interaction has a covalent character, where the d-orbital participation is evidenced from NBO analysis, leaving the f shell completely noninteracting in the chemical bonding. From the optical part we observed in all cases the characteristic intraligand (IL) (π-π*) and ligand to metal charge-transfer (LMCT) bands that are present in the ultraviolet and visible regions, and for the open-shell complexes we found the inherent f-f electronic transitions on the visible and near-infrared region.
Evolution of the Hox gene complex from an evolutionary ground state.
Gehring, Walter J; Kloter, Urs; Suga, Hiroshi
2009-01-01
In this chapter, we consider the question of how the ordered clusters of Hox genes arose during evolution. Since ordered Hox clusters are found in all major superphyla, we have to assume that the Hox clusters arose before the Cambrian "explosion" giving rise to all of these taxa. Based on his studies of the bithorax complex (BX-C) in Drosophila Lewis considered the ground state to be the mesothoracic segment (T2) since the deletion of all of the genes of the BX-C leads to a transformation of all segments from T3 to A8/9 (the last abdominal segment) into T2 segments. We define the developmental ground state genetically, by assuming that loss-of-function mutants lead to transformations toward the ground state, whereas gain-of-function mutants lead to homeotic transformations away from the ground state. By this definition, T2 also represents the developmental ground state, if one includes the anterior genes, that is, those of the Antennapedia complex. We have reconstructed the evolution of the Hox cluster on the basis of known genetic mechanisms which involve unequal crossover and lead from an urhox gene, first to an anterior and a posterior gene and subsequently to intermediate genes which are progressively inserted, between the anterior and posterior genes. These intermediate genes are recombinant due to unequal crossover, whereas the anterior and posterior genes are not affected and therefore had the longest time to diverge from the urhox gene. The molecular phylogenetic analysis strongly supports this model. We consider the ground state to be both developmental and evolutionary and to represent the prototypic body segment. It corresponds to T2 and is specified by Antennapedia or Hox6, respectively. Experiments in the mouse also suggest that the ground state is a thoracic segment. Evolution leads from the prototypic segment to segmental divergence in both the anterior and posterior direction. The most anterior head and tail segments are specified by homeobox genes
Probing quantum frustrated systems via factorization of the ground state.
Giampaolo, Salvatore M; Adesso, Gerardo; Illuminati, Fabrizio
2010-05-21
The existence of definite orders in frustrated quantum systems is related rigorously to the occurrence of fully factorized ground states below a threshold value of the frustration. Ground-state separability thus provides a natural measure of frustration: strongly frustrated systems are those that cannot accommodate for classical-like solutions. The exact form of the factorized ground states and the critical frustration are determined for various classes of nonexactly solvable spin models with different spatial ranges of the interactions. For weak frustration, the existence of disentangling transitions determines the range of applicability of mean-field descriptions in biological and physical problems such as stochastic gene expression and the stability of long-period modulated structures.
Analysis of ground state in random bipartite matching
Shi, Gui-Yuan; Liao, Hao; Zhang, Yi-Cheng
2015-01-01
In human society, a lot of social phenomena can be concluded into a mathematical problem called the bipartite matching, one of the most well known model is the marriage problem proposed by Gale and Shapley. In this article, we try to find out some intrinsic properties of the ground state of this model and thus gain more insights and ideas about the matching problem. We apply Kuhn-Munkres Algorithm to find out the numerical ground state solution of the system. The simulation result proves the previous theoretical analysis using replica method. In the result, we also find out the amount of blocking pairs which can be regarded as a representative of the system stability. Furthermore, we discover that the connectivity in the bipartite matching problem has a great impact on the stability of the ground state, and the system will become more unstable if there were more connections between men and women.
Bishop, Michael
2011-01-01
In this paper, we show the that the ground state energy of the one-dimensional Discrete Random Schr\\"{o}dinger Operator with Bernoulli Potential is controlled asymptotically as the system size N goes to infinity by the random variable, $\\ell_N$ the length the longest consecutive sequence of sites on the lattice with potential equal to zero. Specifically, we will show that with probability one the limit as the system size goes to infinity the ratio of the ground state energy with the energy of a half-sine wave converges to one.
Competing ground states of strongly correlated bosons in the Harper-Hofstadter-Mott model
Natu, Stefan S.; Mueller, Erich J.; Das Sarma, S.
2016-06-01
Using an efficient cluster approach, we study the physics of two-dimensional lattice bosons in a strong magnetic field in the regime where the tunneling is much weaker than the on-site interaction strength. We study both the dilute, hard-core bosons at filling factors much smaller than unity occupation per site and the physics in the vicinity of the superfluid-Mott lobes as the density is tuned away from unity. For hard-core bosons, we carry out extensive numerics for a fixed flux per plaquette ϕ =1 /5 and ϕ =1 /3 . At large flux, the lowest-energy state is a strongly correlated superfluid, analogous to He-4, in which the order parameter is dramatically suppressed, but nonzero. At filling factors ν =1 /2 ,1 , we find competing incompressible states which are metastable. These appear to be commensurate density wave states. For small flux, the situation is reversed and the ground state at ν =1 /2 is an incompressible density wave solid. Here, we find a metastable lattice supersolid phase, where superfluidity and density wave order coexist. We then perform careful numerical studies of the physics near the vicinity of the Mott lobes for ϕ =1 /2 and ϕ =1 /4 . At ϕ =1 /2 , the superfluid ground state has commensurate density wave order. At ϕ =1 /4 , incompressible phases appear outside the Mott lobes at densities n =1.125 and n =1.25 , corresponding to filling fractions ν =1 /2 and 1, respectively. These phases, which are absent in single-site mean-field theory, are metastable and have slightly higher energy than the superfluid, but the energy difference between them shrinks rapidly with increasing cluster size, suggestive of an incompressible ground state. We thus explore the interplay between Mott physics, magnetic Landau levels, and superfluidity, finding a rich phase diagram of competing compressible and incompressible states.
Projector augmented wave method: ab initio molecular dynamics with full wave functions
Indian Academy of Sciences (India)
Peter E Blöchl; Clemens J Först; Johannes Schimpl
2003-01-01
A brief introduction to the projector augmented wave method is given and recent developments are reviewed. The projector augmented wave method is an all-electron method for efficient ab initio molecular dynamics simulations with full wave functions. It extends and combines the traditions of existing augmented wave methods and the pseudopotential approach. Without sacrificing efficiency, the PAW method avoids transferability problems of the pseudopotential approach and it has been valuable to predict properties that depend on the full wave functions.
Ground state phase diagram of the half-filled bilayer Hubbard model
Golor, Michael; Reckling, Timo; Classen, Laura; Scherer, Michael M.; Wessel, Stefan
2014-01-01
Employing a combination of functional renormalization group calculations and projective determinantal quantum Monte Carlo simulations, we examine the Hubbard model on the square lattice bilayer at half filling. From this combined analysis, we obtain a comprehensive account on the ground state phase diagram with respect to the extent of the system's metallic and (antiferromagnetically ordered) Mott-insulating as well as band-insulating regions. By means of an unbiased functional renormalizatio...
A Test of Nuclear Wave Functions for Pseudospin Symmetry
Ginocchio, J N
2001-01-01
Using the fact that pseudospin is an approximate symmetry of the Dirac Hamiltonian with realistic scalar and vector mean fields, we derive the wave functions of the pseudospin partners of eigenstates of a realistic Dirac Hamiltonian and compare these wave functions with the wave functions of the Dirac eigenstates.
Test of nuclear wave functions for pseudospin symmetry.
Ginocchio, J N; Leviatan, A
2001-08-13
Using the fact that pseudospin is an approximate symmetry of the Dirac Hamiltonian with realistic scalar and vector mean fields, we derive the wave functions of the pseudospin partners of eigenstates of a realistic Dirac Hamiltonian and compare these wave functions with the wave functions of the Dirac eigenstates.
Test of Nuclear Wave Functions for Pseudospin Symmetry
Energy Technology Data Exchange (ETDEWEB)
Ginocchio, J. N.; Leviatan, A.
2001-08-13
Using the fact that pseudospin is an approximate symmetry of the Dirac Hamiltonian with realistic scalar and vector mean fields, we derive the wave functions of the pseudospin partners of eigenstates of a realistic Dirac Hamiltonian and compare these wave functions with the wave functions of the Dirac eigenstates.
Ground states of the SU(N) Heisenberg model.
Kawashima, Naoki; Tanabe, Yuta
2007-02-02
The SU(N) Heisenberg model with various single-row representations is investigated by quantum Monte Carlo simulations. While the zero-temperature phase boundary agrees qualitatively with the theoretical predictions based on the 1/N expansion, some unexpected features are also observed. For N> or =5 with the fundamental representation, for example, it is suggested that the ground states possess exact or approximate U(1) degeneracy. In addition, for the representation of Young tableau with more than one column, the ground state shows no valence-bond-solid order even at N greater than the threshold value.
Toward Triplet Ground State NaLi Molecules
Ebadi, Sepehr; Jamison, Alan; Rvachov, Timur; Jing, Li; Son, Hyungmok; Jiang, Yijun; Zwierlein, Martin; Ketterle, Wolfgang
2016-05-01
The NaLi molecule is expected to have a long lifetime in the triplet ground-state due to its fermionic nature, large rotational constant, and weak spin-orbit coupling. The triplet state has both electric and magnetic dipole moments, affording unique opportunities in quantum simulation and ultracold chemistry. We have mapped the excited state NaLi triplet potential by means of photoassociation spectroscopy. We report on this and our further progress toward the creation of the triplet ground-state molecules using STIRAP. NSF, ARO-MURI, Samsung, NSERC.
Ground state properties of graphene in Hartree-Fock theory
Hainzl, Christian; Sparber, Christof
2012-01-01
We study the Hartree-Fock approximation of graphene in infinite volume, with instantaneous Coulomb interactions. First we construct its translation-invariant ground state and we recover the well-known fact that, due to the exchange term, the effective Fermi velocity is logarithmically divergent at zero momentum. In a second step we prove the existence of a ground state in the presence of local defects and we discuss some properties of the linear response to an external electric field. All our results are non perturbative.
Delin, A
2002-01-01
We have performed a systematic density-functional study of the mercury chalcogenide compounds $\\beta$-HgS, HgSe, and HgTe using an all-electron full-potential linear muffin-tin orbital (FP-LMTO) method. We find that, in the zinc-blende structure, both HgSe and HgTe are semimetals whereas $\\beta$-HgS has a small spin-orbit induced band gap. Our calculated relativistic photoemission and inverse photoemission spectra (PES and IPES, respectively) reproduce very well the most recently measured spectra, as do also our theoretical optical spectra. In contrast to the normal situation, we find that the local density approximation (LDA) to the density functional gives calculated equilibrium volumes in much better agreement with experiment than does the generalized gradient corrected functional (GGA). We also address the problem of treating relativistic $p$ electrons with methods based on a scalar-relativistic basis set, and show that the effect is rather small for the present systems.
How fast is the wave function collapse?
Ignatiev, A Yu
2012-01-01
Using complex quantum Hamilton-Jacobi formulation, a new kind of non-linear equations is proposed that have almost classical structure and extend the Schroedinger equation to describe the collapse of the wave function as a finite-time process. Experimental bounds on the collapse time are reported (of order 0.1 ms to 0.1 ps) and its convenient dimensionless measure is introduced. This parameter helps to identify the areas where sensitive probes of the possible collapse dynamics can be done. Examples are experiments with Bose-Einstein condensates, ultracold neutrons or ultrafast optics.
Ground state and orbital stability for the NLS equation on a general starlike graph with potentials
Cacciapuoti, Claudio; Finco, Domenico; Noja, Diego
2017-08-01
We consider a nonlinear Schrödinger equation (NLS) posed on a graph (or network) composed of a generic compact part to which a finite number of half-lines are attached. We call this structure a starlike graph. At the vertices of the graph interactions of δ-type can be present and an overall external potential is admitted. Under general assumptions on the potential, we prove that the NLS is globally well-posed in the energy domain. We are interested in minimizing the energy of the system on the manifold of constant mass (L 2-norm). When existing, the minimizer is called ground state and it is the profile of an orbitally stable standing wave for the NLS evolution. We prove that a ground state exists for sufficiently small masses whenever the quadratic part of the energy admits a simple isolated eigenvalue at the bottom of the spectrum (the linear ground state). This is a wide generalization of a result previously obtained for a star-graph with a single vertex. The main part of the proof is devoted to prove the concentration compactness principle for starlike structures; this is non trivial due to the lack of translation invariance of the domain. Then we show that a minimizing, bounded, H 1 sequence for the constrained NLS energy with external linear potentials is in fact convergent if its mass is small enough. Moreover we show that the ground state bifurcates from the vanishing solution at the bottom of the linear spectrum. Examples are provided with a discussion of the hypotheses on the linear part.
Entanglement of two ground state neutral atoms using Rydberg blockade
DEFF Research Database (Denmark)
Miroshnychenko, Yevhen; Browaeys, Antoine; Evellin, Charles
2011-01-01
We report on our recent progress in trapping and manipulation of internal states of single neutral rubidium atoms in optical tweezers. We demonstrate the creation of an entangled state between two ground state atoms trapped in separate tweezers using the effect of Rydberg blockade. The quality of...
Borromean ground state of fermions in two dimensions
DEFF Research Database (Denmark)
G. Volosniev, A.; V. Fedorov, D.; S. Jensen, A.;
2014-01-01
-body threshold. They are the lowest in a possible sequence of so-called super-Efimov states. While the observation of the super-Efimov scaling could be very difficult, the borromean ground state should be observable in cold atomic gases and could be the basis for producing a quantum gas of three-body states...
Observation of Hyperfine Transitions in Trapped Ground-State Antihydrogen
Olin, Arthur
2015-01-01
This paper discusses the first observation of stimulated magnetic resonance transitions between the hyperfine levels of trapped ground state atomic antihydrogen, confirming its presence in the ALPHA apparatus. Our observations show that these transitions are consistent with the values in hydrogen to within 4~parts~in~$10^3$. Simulations of the trapped antiatoms in a microwave field are consistent with our measurements.
Advantages of Unfair Quantum Ground-State Sampling.
Zhang, Brian Hu; Wagenbreth, Gene; Martin-Mayor, Victor; Hen, Itay
2017-04-21
The debate around the potential superiority of quantum annealers over their classical counterparts has been ongoing since the inception of the field. Recent technological breakthroughs, which have led to the manufacture of experimental prototypes of quantum annealing optimizers with sizes approaching the practical regime, have reignited this discussion. However, the demonstration of quantum annealing speedups remains to this day an elusive albeit coveted goal. We examine the power of quantum annealers to provide a different type of quantum enhancement of practical relevance, namely, their ability to serve as useful samplers from the ground-state manifolds of combinatorial optimization problems. We study, both numerically by simulating stoquastic and non-stoquastic quantum annealing processes, and experimentally, using a prototypical quantum annealing processor, the ability of quantum annealers to sample the ground-states of spin glasses differently than thermal samplers. We demonstrate that (i) quantum annealers sample the ground-state manifolds of spin glasses very differently than thermal optimizers (ii) the nature of the quantum fluctuations driving the annealing process has a decisive effect on the final distribution, and (iii) the experimental quantum annealer samples ground-state manifolds significantly differently than thermal and ideal quantum annealers. We illustrate how quantum annealers may serve as powerful tools when complementing standard sampling algorithms.
^{66}Ga ground state β spectrum
DEFF Research Database (Denmark)
Severin, Gregory; Knutson, L. D.; Voytas, P. A.;
2014-01-01
The ground state branch of the β decay of 66Ga is an allowed Fermi (0+ → 0+) transition with a relatively high f t value. The large f t and the isospin-forbidden nature of the transition indicates that the shape of the β spectrum of this branch may be sensitive to higher order contributions...
Structure of the Particle-Hole Amplitudes in No-core Shell Model Wave Functions
Hayes, A C
2009-01-01
We study the structure of the no-core shell model wave functions for $^6$Li and $^{12}$C by investigating the ground state and first excited state electron scattering charge form factors. In both nuclei, large particle-hole ($ph$) amplitudes in the wave functions appear with the opposite sign to that needed to reproduce the shape of the $(e,e')$ form factors, the charge radii, and the B(E2) values for the lowest two states. The difference in sign appears to arise mainly from the monopole $\\Delta\\hbar\\omega=2$ matrix elements of the kinetic and potential energy (T+V) that transform under the harmonic oscillator SU(3) symmetries as $(\\lambda,\\mu)=(2,0)$. These are difficult to determine self-consistently, but they have a strong effect on the structure of the low-lying states and on the giant monopole and quadrupole resonances. The Lee-Suzuki transformation, used to account for the restricted nature of the space in terms of an effective interaction, introduces large higher-order $\\Delta\\hbar\\omega=n, n>$2, $ph$ ...
On the ground state of a model for compressed helium
Seldam, C.A. ten; Groot, S.R. de
1952-01-01
In the problem of the “compressed helium atom”, the boundary condition that the wave function ψ must vanish at infinity (r = ∞), is replaced by: ψ = 0 at a finite r = r0. This problem is solved by a variational method, which for the limiting case of the free atom (r0 → ∞) coincides with one of Hylle
Calculation of the α-Particle Ground State
Viviani, M.; Kievsky, A.; Rosati, S.
1995-01-01
The correlated hyperspherical harmonic expansion method is used to calculate α-particle properties with a realistic Hamiltonian consisting of the Argonne V14 two-nucleon and Urbana model VIII three-nucleon potentials. The calculated binding energy, mass radius and wave percentages are close to the corresponding quantities obtained with Green's-function Monte-Carlo and Faddeev-Yakubovsky techniques.
Uniqueness of non-linear ground states for fractional Laplacians in R
DEFF Research Database (Denmark)
Frank, Rupert L.; Lenzmann, Enno
2013-01-01
We prove uniqueness of ground state solutions Q = Q(|x|) ≥ 0 of the non-linear equation (−Δ)sQ+Q−Qα+1=0inR,where 0 ... recently raised by Kenig–Martel–Robbiano and we generalize (by completely different techniques) the specific uniqueness result obtained by Amick and Toland for s=12 and α = 1 in [5] for the Benjamin–Ono equation. As a technical key result in this paper, we show that the associated linearized operator L...... Benjamin–Ono (BO) and Benjamin–Bona–Mahony (BBM) water wave equations....
Comparative study on spreading function for directional wave spectra
Digital Repository Service at National Institute of Oceanography (India)
Bhat, S.S.; Anand, N.M.; Nayak, B.U.
-dimensional wave energy S(f) and the directional spreading function D(f, theta). This paper reviews various spreading functions proposed in the past for estimating the directional wave energy and presents their application to the Indian wave condition. It is found...
A Scheme of Interferometric Measurement of an Atomic Wave Function
Institute of Scientific and Technical Information of China (English)
LIU Zheng-Dong; LIN Yu; ZENG Liang; PAN Qin-Min
2000-01-01
A new method to measure an atomic wave function is discussed. It effectively solves the problem of an initially random phase of a travelling-wave laser beam. The relationship between the measured data and the atomic wavefunction is presented, and the wave function's reconstruction procedure is also analyzed.PACS: 03.65. Bz, 03. 75. Dg
Interfaces Supporting Surface Gap Soliton Ground States in the 1D Nonlinear Schroedinger Equation
Dohnal, Tomas; Plum, Michael; Reichel, Wolfgang
2012-01-01
We consider the problem of verifying the existence of $H^1$ ground states of the 1D nonlinear Schr\\"odinger equation for an interface of two periodic structures: $$-u" +V(x)u -\\lambda u = \\Gamma(x) |u|^{p-1}u \\ {on} \\R$$ with $V(x) = V_1(x), \\Gamma(x)=\\Gamma_1(x)$ for $x\\geq 0$ and $V(x) = V_2(x), \\Gamma(x)=\\Gamma_2(x)$ for $x1$. The article [T. Dohnal, M. Plum and W. Reichel, "Surface Gap Soliton Ground States for the Nonlinear Schr\\"odinger Equation," \\textit{Comm. Math. Phys.} \\textbf{308}, 511-542 (2011)] provides in the 1D case an existence criterion in the form of an integral inequality involving the linear potentials $V_{1},V_2$ and the Bloch waves of the operators $-\\tfrac{d^2}{dx^2}+V_{1,2}-\\lambda$. We choose here the classes of piecewise constant and piecewise linear potentials $V_{1,2}$ and check this criterion for a set of parameter values. In the piecewise constant case the Bloch waves are calculated explicitly and in the piecewise linear case verified enclosures of the Bloch waves are computed ...
Ground State of the Universe and the Cosmological Constant. A Nonperturbative Analysis.
Husain, Viqar; Qureshi, Babar
2016-02-12
The physical Hamiltonian of a gravity-matter system depends on the choice of time, with the vacuum naturally identified as its ground state. We study the expanding Universe with scalar field in the volume time gauge. We show that the vacuum energy density computed from the resulting Hamiltonian is a nonlinear function of the cosmological constant and time. This result provides a new perspective on the relation between time, the cosmological constant, and vacuum energy.
Ground-state energy of the electron liquid in ultrathin wires.
Fogler, Michael M
2005-02-11
The ground-state energy and the density correlation function of the electron liquid in a thin one-dimensional wire are computed. The calculation is based on an approximate mapping of the problem with a realistic Coulomb interaction law onto exactly solvable models of mathematical physics. This approach becomes asymptotically exact in the limit of a small wire radius but remains numerically accurate even for modestly thin wires.
Observation of a kilogram-scale oscillator near its quantum ground state
Abbott, B.; Abbott, R.; Adhikari, R.; Ajith, P.; Allen, B.; Allen, G.; Amin, R.; Anderson, S. B.; Anderson, W. G.; Arain, M. A.; Araya, M.; Armandula, H.; Armor, P.; Aso, Y.; Aston, S.; Aufmuth, P.; Aulbert, C.; Babak, S.; Ballmer, S.; Bantilan, H.; Barish, B. C.; Barker, C.; Barker, D.; Barr, B.; Barriga, P.; Barton, M. A.; Bastarrika, M.; Bayer, K.; Betzwieser, J.; Beyersdorf, P. T.; Bilenko, I. A.; Billingsley, G.; Biswas, R.; Black, E.; Blackburn, K.; Blackburn, L.; Blair, D.; Bland, B.; Bodiya, T. P.; Bogue, L.; Bork, R.; Boschi, V.; Bose, S.; Brady, P. R.; Braginsky, V. B.; Brau, J. E.; Brinkmann, M.; Brooks, A.; Brown, D. A.; Brunet, G.; Bullington, A.; Buonanno, A.; Burmeister, O.; Byer, R. L.; Cadonati, L.; Cagnoli, G.; Camp, J. B.; Cannizzo, J.; Cannon, K.; Cao, J.; Cardenas, L.; Casebolt, T.; Castaldi, G.; Cepeda, C.; Chalkley, E.; Charlton, P.; Chatterji, S.; Chelkowski, S.; Chen, Y.; Christensen, N.; Clark, D.; Clark, J.; Cokelaer, T.; Conte, R.; Cook, D.; Corbitt, T.; Coyne, D.; Creighton, J. D. E.; Cumming, A.; Cunningham, L.; Cutler, R. M.; Dalrymple, J.; Danilishin, S.; Danzmann, K.; Davies, G.; DeBra, D.; Degallaix, J.; Degree, M.; Dergachev, V.; Desai, S.; DeSalvo, R.; Dhurandhar, S.; Díaz, M.; Dickson, J.; Dietz, A.; Donovan, F.; Dooley, K. L.; Doomes, E. E.; Drever, R. W. P.; Duke, I.; Dumas, J.-C.; Dupuis, R. J.; Dwyer, J. G.; Echols, C.; Effler, A.; Ehrens, P.; Espinoza, E.; Etzel, T.; Evans, T.; Fairhurst, S.; Fan, Y.; Fazi, D.; Fehrmann, H.; Fejer, M. M.; Finn, L. S.; Flasch, K.; Fotopoulos, N.; Freise, A.; Frey, R.; Fricke, T.; Fritschel, P.; Frolov, V. V.; Fyffe, M.; Garofoli, J.; Gholami, I.; Giaime, J. A.; Giampanis, S.; Giardina, K. D.; Goda, K.; Goetz, E.; Goggin, L.; González, G.; Gossler, S.; Gouaty, R.; Grant, A.; Gras, S.; Gray, C.; Gray, M.; Greenhalgh, R. J. S.; Gretarsson, A. M.; Grimaldi, F.; Grosso, R.; Grote, H.; Grunewald, S.; Guenther, M.; Gustafson, E. K.; Gustafson, R.; Hage, B.; Hallam, J. M.; Hammer, D.; Hanna, C.; Hanson, J.; Harms, J.; Harry, G.; Harstad, E.; Hayama, K.; Hayler, T.; Heefner, J.; Heng, I. S.; Hennessy, M.; Heptonstall, A.; Hewitson, M.; Hild, S.; Hirose, E.; Hoak, D.; Hosken, D.; Hough, J.; Huttner, S. H.; Ingram, D.; Ito, M.; Ivanov, A.; Johnson, B.; Johnson, W. W.; Jones, D. I.; Jones, G.; Jones, R.; Ju, L.; Kalmus, P.; Kalogera, V.; Kamat, S.; Kanner, J.; Kasprzyk, D.; Katsavounidis, E.; Kawabe, K.; Kawamura, S.; Kawazoe, F.; Kells, W.; Keppel, D. G.; Khalili, F. Ya; Khan, R.; Khazanov, E.; Kim, C.; King, P.; Kissel, J. S.; Klimenko, S.; Kokeyama, K.; Kondrashov, V.; Kopparapu, R. K.; Kozak, D.; Kozhevatov, I.; Krishnan, B.; Kwee, P.; Lam, P. K.; Landry, M.; Lang, M. M.; Lantz, B.; Lazzarini, A.; Lei, M.; Leindecker, N.; Leonhardt, V.; Leonor, I.; Libbrecht, K.; Lin, H.; Lindquist, P.; Lockerbie, N. A.; Lodhia, D.; Lormand, M.; Lu, P.; Lubinski, M.; Lucianetti, A.; Lück, H.; Machenschalk, B.; MacInnis, M.; Mageswaran, M.; Mailand, K.; Mandic, V.; Márka, S.; Márka, Z.; Markosyan, A.; Markowitz, J.; Maros, E.; Martin, I.; Martin, R. M.; Marx, J. N.; Mason, K.; Matichard, F.; Matone, L.; Matzner, R.; Mavalvala, N.; McCarthy, R.; McClelland, D. E.; McGuire, S. C.; McHugh, M.; McIntyre, G.; McIvor, G.; McKechan, D.; McKenzie, K.; Meier, T.; Melissinos, A.; Mendell, G.; Mercer, R. A.; Meshkov, S.; Messenger, C. J.; Meyers, D.; Miao, H.; Miller, J.; Minelli, J.; Mitra, S.; Mitrofanov, V. P.; Mitselmakher, G.; Mittleman, R.; Miyakawa, O.; Moe, B.; Mohanty, S.; Moreno, G.; Mossavi, K.; Mow-Lowry, C.; Mueller, G.; Mukherjee, S.; Mukhopadhyay, H.; Müller-Ebhardt, H.; Munch, J.; Murray, P.; Myers, E.; Myers, J.; Nash, T.; Nelson, J.; Newton, G.; Nishizawa, A.; Numata, K.; O'Dell, J.; Ogin, G.; O'Reilly, B.; O'Shaughnessy, R.; Ottaway, D. J.; Ottens, R. S.; Overmier, H.; Owen, B. J.; Pan, Y.; Pankow, C.; Papa, M. A.; Parameshwaraiah, V.; Patel, P.; Pedraza, M.; Penn, S.; Perreca, A.; Petrie, T.; Pinto, I. M.; Pitkin, M.; Pletsch, H. J.; Plissi, M. V.; Postiglione, F.; Principe, M.; Prix, R.; Quetschke, V.; Raab, F.; Rabeling, D. S.; Radkins, H.; Rainer, N.; Rakhmanov, M.; Ramsunder, M.; Rehbein, H.; Reid, S.; Reitze, D. H.; Riesen, R.; Riles, K.; Rivera, B.; Robertson, N. A.; Robinson, C.; Robinson, E. L.; Roddy, S.; Rodriguez, A.; Rogan, A. M.; Rollins, J.; Romano, J. D.; Romie, J.; Route, R.; Rowan, S.; Rüdiger, A.; Ruet, L.; Russell, P.; Ryan, K.; Sakata, S.; Samidi, M.; Sancho de la Jordana, L.; Sandberg, V.; Sannibale, V.; Saraf, S.; Sarin, P.; Sathyaprakash, B. S.; Sato, S.; Saulson, P. R.; Savage, R.; Savov, P.; Schediwy, S. W.; Schilling, R.; Schnabel, R.; Schofield, R.; Schutz, B. F.; Schwinberg, P.; Scott, S. M.; Searle, A. C.; Sears, B.; Seifert, F.; Sellers, D.; Sengupta, A. S.; Shawhan, P.; Shoemaker, D. H.; Sibley, A.; Siemens, X.; Sigg, D.; Sinha, S.
2009-07-01
We introduce a novel cooling technique capable of approaching the quantum ground state of a kilogram-scale system—an interferometric gravitational wave detector. The detectors of the Laser Interferometer Gravitational-wave Observatory (LIGO) operate within a factor of 10 of the standard quantum limit (SQL), providing a displacement sensitivity of 10-18 m in a 100 Hz band centered on 150 Hz. With a new feedback strategy, we dynamically shift the resonant frequency of a 2.7 kg pendulum mode to lie within this optimal band, where its effective temperature falls as low as 1.4 μK, and its occupation number reaches about 200 quanta. This work shows how the exquisite sensitivity necessary to detect gravitational waves can be made available to probe the validity of quantum mechanics on an enormous mass scale.
Configuration space Faddeev calculations. I. Triton ground state properties
Payne, G. L.; Friar, J. L.; Gibson, B. F.; Afnan, I. R.
1980-08-01
The formulation of Faddeev-type equations in configuration space is discussed. Numerical solutions are obtained using splines and the method of orthogonal collocation. Triton observables and wave-function probabilities are calculated for s-wave NN interaction models of Malfliet and Tjon and the tensor force model of Reid. Comparison with previously published triton results is made; our full five-channel results for the Reid soft-core potential are in excellent agreement with those obtained by Afnan and Birrell using separable expansion methods. NUCLEAR STRUCTURE 3H, Faddeev calculations configuration space.
Configuration space Faddeev calculations. I. Triton ground-state properties
Energy Technology Data Exchange (ETDEWEB)
Payne, G.L.; Friar, J.L.; Gibson, B.F.; Afnan, I.R.
1980-08-01
The formulation of Faddeev-type equations in configuration space is discussed. Numerical solutions are obtained using splines and the method of orthogonal collocation. Triton observables and wave-function probabilities are calculated for s-wave NN interaction models of Malfliet and Tjon and the tensor force model of Reid. Comparison with previously published triton results is made; our full five-channel results for the Reid soft-core potential are in excellent agreement with those obtained by Afnan and Birrell using separable expansion methods.
Energy Technology Data Exchange (ETDEWEB)
Khan, Shehryar, E-mail: sherkhan@fysik.su.se; Odelius, Michael, E-mail: odelius@fysik.su.se [Department of Physics, Stockholm University, AlbaNova University Center, S-106 91 Stockholm (Sweden); Kubica-Misztal, Aleksandra [Institute of Physics, Jagiellonian University, ul. Reymonta 4, PL-30-059 Krakow (Poland); Kruk, Danuta [Faculty of Mathematics and Computer Science, University of Warmia and Mazury in Olsztyn, Sloneczna 54, Olsztyn PL-10710 (Poland); Kowalewski, Jozef [Department of Materials and Environmental Chemistry, Arrhenius Laboratory, Stockholm University, S-106 91 Stockholm (Sweden)
2015-01-21
The zero-field splitting (ZFS) of the electronic ground state in paramagnetic ions is a sensitive probe of the variations in the electronic and molecular structure with an impact on fields ranging from fundamental physical chemistry to medical applications. A detailed analysis of the ZFS in a series of symmetric Gd(III) complexes is presented in order to establish the applicability and accuracy of computational methods using multiconfigurational complete-active-space self-consistent field wave functions and of density functional theory calculations. The various computational schemes are then applied to larger complexes Gd(III)DOTA(H{sub 2}O){sup −}, Gd(III)DTPA(H{sub 2}O){sup 2−}, and Gd(III)(H{sub 2}O){sub 8}{sup 3+} in order to analyze how the theoretical results compare to experimentally derived parameters. In contrast to approximations based on density functional theory, the multiconfigurational methods produce results for the ZFS of Gd(III) complexes on the correct order of magnitude.
Superoscillating electron wave functions with subdiffraction spots
Remez, Roei; Tsur, Yuval; Lu, Peng-Han; Tavabi, Amir H.; Dunin-Borkowski, Rafal E.; Arie, Ady
2017-03-01
Almost one and a half centuries ago, Abbe [Arch. Mikrosk. Anat. 9, 413 (1873), 10.1007/BF02956173] and shortly after Lord Rayleigh [Philos. Mag. Ser. 5 8, 261 (1879), 10.1080/14786447908639684] showed that, when an optical lens is illuminated by a plane wave, a diffraction-limited spot with radius 0.61 λ /sinα is obtained, where λ is the wavelength and α is the semiangle of the beam's convergence cone. However, spots with much smaller features can be obtained at the focal plane when the lens is illuminated by an appropriately structured beam. Whereas this concept is known for light beams, here, we show how to realize it for a massive-particle wave function, namely, a free electron. We experimentally demonstrate an electron central spot of radius 106 pm, which is more than two times smaller than the diffraction limit of the experimental setup used. In addition, we demonstrate that this central spot can be structured by adding orbital angular momentum to it. The resulting superoscillating vortex beam has a smaller dark core with respect to a regular vortex beam. This family of electron beams having hot spots with arbitrarily small features and tailored structures could be useful for studying electron-matter interactions with subatomic resolution.
Relativistic analysis of nuclear ground state densities at 135 to 200 MeV
Indian Academy of Sciences (India)
M A Suhail; N Neeloffer; Z A Khan
2005-12-01
A relativistic analysis of p + 40Ca elastic scattering with different nuclear ground state target densities at 135 to 200 MeV is presented in this paper. It is found that the IGO densities are more consistent in reproducing the data over the energy range considered here. The reproduction of spin-rotation-function data with the simultaneous fitting of differential cross-section and analyzing power, and the appearance of wine-bottle-bottom shaped Re eff() in the transition energy region, sensitively depends on the input nuclear ground state densities and are not solely the relativistic characteristic signatures. We also found that the wine-bottle-bottom shaped Re eff() is preferred by the spin observables in the transition energy region (i.e. 181 MeV to 200 MeV).
Ground State Density Distribution of Bose-Fermi Mixture in a One-Dimensional Harmonic Trap
Institute of Scientific and Technical Information of China (English)
HAO Ya-Jiang
2011-01-01
By the density-functional calculation we investigate the ground-state properties of Bose-Fermi mixture confined in one-dimensional harmonic traps. The homogeneous mixture of bosons and polarized fermions with contact interaction can be exactly solved by the Bethe-ansatz method. After giving the exact formula of ground state energy density, we employ the local-density approximation to determine the density distribution of each component. It is shown that with the increase in interaction, the total density distribution evolves to Fermi-like distribution and the system exhibits phase separation between two components when the interaction is strong enough but finite. While in the infinite interaction limit both bosons and fermions display the completely same Fermi-like distributions and phase separation disappears.
The ground state of medium-heavy nuclei with non central forces
Fabrocini, A
1997-01-01
We study microscopically the ground state properties of 16O and 40Ca nuclei within correlated basis function theory. A truncated version of the realistic Urbana v14 (U14) potential, without momentum dependent terms, is adopted with state dependent correlations having spin, isospin and tensor components. Fermi hypernetted chain integral equations and single operator chain approximation are used to evaluate one- and two-body densities and ground state energy. The results are in good agreement with the available variational MonteCarlo data, providing a first substantial check for the accuracy of the cluster expansion method with state dependent correlations. The finite nuclei treatment of non central interactions and correlations has, at least, the same level of accuracy as in infinite nuclear matter. The binding energy for the full U14+TNI interaction is computed, addressing its small momentum dependent contributions in local density approximation. The nuclei are underbound by about 1 MeV per nucleon. Further e...
Derivation of novel human ground state naive pluripotent stem cells.
Gafni, Ohad; Weinberger, Leehee; Mansour, Abed AlFatah; Manor, Yair S; Chomsky, Elad; Ben-Yosef, Dalit; Kalma, Yael; Viukov, Sergey; Maza, Itay; Zviran, Asaf; Rais, Yoach; Shipony, Zohar; Mukamel, Zohar; Krupalnik, Vladislav; Zerbib, Mirie; Geula, Shay; Caspi, Inbal; Schneir, Dan; Shwartz, Tamar; Gilad, Shlomit; Amann-Zalcenstein, Daniela; Benjamin, Sima; Amit, Ido; Tanay, Amos; Massarwa, Rada; Novershtern, Noa; Hanna, Jacob H
2013-12-12
Mouse embryonic stem (ES) cells are isolated from the inner cell mass of blastocysts, and can be preserved in vitro in a naive inner-cell-mass-like configuration by providing exogenous stimulation with leukaemia inhibitory factor (LIF) and small molecule inhibition of ERK1/ERK2 and GSK3β signalling (termed 2i/LIF conditions). Hallmarks of naive pluripotency include driving Oct4 (also known as Pou5f1) transcription by its distal enhancer, retaining a pre-inactivation X chromosome state, and global reduction in DNA methylation and in H3K27me3 repressive chromatin mark deposition on developmental regulatory gene promoters. Upon withdrawal of 2i/LIF, naive mouse ES cells can drift towards a primed pluripotent state resembling that of the post-implantation epiblast. Although human ES cells share several molecular features with naive mouse ES cells, they also share a variety of epigenetic properties with primed murine epiblast stem cells (EpiSCs). These include predominant use of the proximal enhancer element to maintain OCT4 expression, pronounced tendency for X chromosome inactivation in most female human ES cells, increase in DNA methylation and prominent deposition of H3K27me3 and bivalent domain acquisition on lineage regulatory genes. The feasibility of establishing human ground state naive pluripotency in vitro with equivalent molecular and functional features to those characterized in mouse ES cells remains to be defined. Here we establish defined conditions that facilitate the derivation of genetically unmodified human naive pluripotent stem cells from already established primed human ES cells, from somatic cells through induced pluripotent stem (iPS) cell reprogramming or directly from blastocysts. The novel naive pluripotent cells validated herein retain molecular characteristics and functional properties that are highly similar to mouse naive ES cells, and distinct from conventional primed human pluripotent cells. This includes competence in the generation
Gamiz-Hernandez, Ana P; Magomedov, Artiom; Hummer, Gerhard; Kaila, Ville R I
2015-02-12
Proton-coupled electron transfer (PCET) processes are elementary chemical reactions involved in a broad range of radical and redox reactions. Elucidating fundamental PCET reaction mechanisms are thus of central importance for chemical and biochemical research. Here we use quantum chemical density functional theory (DFT), time-dependent density functional theory (TDDFT), and the algebraic diagrammatic-construction through second-order (ADC(2)) to study the mechanism, thermodynamic driving force effects, and reaction barriers of both ground state proton transfer (pT) and photoinduced proton-coupled electron transfer (PCET) between nitrosylated phenyl-phenol compounds and hydrogen-bonded t-butylamine as an external base. We show that the obtained reaction barriers for the ground state pT reactions depend linearly on the thermodynamic driving force, with a Brønsted slope of 1 or 0. Photoexcitation leads to a PCET reaction, for which we find that the excited state reaction barrier depends on the thermodynamic driving force with a Brønsted slope of 1/2. To support the mechanistic picture arising from the static potential energy surfaces, we perform additional molecular dynamics simulations on the excited state energy surface, in which we observe a spontaneous PCET between the donor and the acceptor groups. Our findings suggest that a Brønsted analysis may distinguish the ground state pT and excited state PCET processes.
Interpreting the wave function of the Universe.
Tipler, F. J.
The Many-Worlds Interpretation of quantum mechanics is used to determine the meaning of the universal wave function of quantum cosmology. More precisely, the Many-Worlds Interpretation is used to distinguish those quantities in quantum cosmology which are measureable, and hence physically meaningful, from those which are not. A number of rather surprising conclusions are drawn from the analysis. All conclusions are illustrated with a closed Friedmann universe quantized in conformal time. The author's quantization procedure allows only one solution to Schrödinger's equation, and this solution solves the Flatness Problem. He shows that the ADM quantization method plus the Hartle-Hawking initial foundary condition gives the same result.
Intercellular Ca2+ Waves: Mechanisms and Function
Sanderson, Michael J.
2012-01-01
Intercellular calcium (Ca2+) waves (ICWs) represent the propagation of increases in intracellular Ca2+ through a syncytium of cells and appear to be a fundamental mechanism for coordinating multicellular responses. ICWs occur in a wide diversity of cells and have been extensively studied in vitro. More recent studies focus on ICWs in vivo. ICWs are triggered by a variety of stimuli and involve the release of Ca2+ from internal stores. The propagation of ICWs predominately involves cell communication with internal messengers moving via gap junctions or extracellular messengers mediating paracrine signaling. ICWs appear to be important in both normal physiology as well as pathophysiological processes in a variety of organs and tissues including brain, liver, retina, cochlea, and vascular tissue. We review here the mechanisms of initiation and propagation of ICWs, the key intra- and extracellular messengers (inositol 1,4,5-trisphosphate and ATP) mediating ICWs, and the proposed physiological functions of ICWs. PMID:22811430
Tunnelling matrix elements with Gutzwiller wave functions
Energy Technology Data Exchange (ETDEWEB)
Di Ciolo, Andrea; Tocchio, Luca F.; Gros, Claudius [Institut fuer Theoretische Physik, Goethe Universitaet Frankfurt, Frankfurt Am Main (Germany)
2011-07-01
We use a generalized Gutzwiller approach, in order to study projected particle (hole) excitations for superconducting systems and systems with antiferromagnetic (AFM) order. As in the standard Gutzwiller scheme the effects of the strong electronic correlations are given via the suppression of the site double occupancy; for our computations it is helpful to consider a lattice with a reservoir site unaffected by this suppression of the double occupancy. In this approach we obtain the probabilities for the tunnelling of a particle (hole) into the projected state. Our results are due only to the physical properties of the trial state and not to the choice of a specifical Hamiltonian: in this sense, they are model-independent but not universal, because they rely on the features of the chosen Gutzwiller wave function (projected Fermi Sea, BCS superconductor, AFM..) The accuracy and the reliability of our analytical approximation is tested using the Variational Monte Carlo. Possible comparisons with tunnelling experiments are discussed.
Computer network defense through radial wave functions
Malloy, Ian J.
The purpose of this research is to synthesize basic and fundamental findings in quantum computing, as applied to the attack and defense of conventional computer networks. The concept focuses on uses of radio waves as a shield for, and attack against traditional computers. A logic bomb is analogous to a landmine in a computer network, and if one was to implement it as non-trivial mitigation, it will aid computer network defense. As has been seen in kinetic warfare, the use of landmines has been devastating to geopolitical regions in that they are severely difficult for a civilian to avoid triggering given the unknown position of a landmine. Thus, the importance of understanding a logic bomb is relevant and has corollaries to quantum mechanics as well. The research synthesizes quantum logic phase shifts in certain respects using the Dynamic Data Exchange protocol in software written for this work, as well as a C-NOT gate applied to a virtual quantum circuit environment by implementing a Quantum Fourier Transform. The research focus applies the principles of coherence and entanglement from quantum physics, the concept of expert systems in artificial intelligence, principles of prime number based cryptography with trapdoor functions, and modeling radio wave propagation against an event from unknown parameters. This comes as a program relying on the artificial intelligence concept of an expert system in conjunction with trigger events for a trapdoor function relying on infinite recursion, as well as system mechanics for elliptic curve cryptography along orbital angular momenta. Here trapdoor both denotes the form of cipher, as well as the implied relationship to logic bombs.
Simulation of the hydrogen ground state in stochastic electrodynamics
Nieuwenhuizen, Theo M.; Liska, Matthew T. P.
2015-10-01
Stochastic electrodynamics is a classical theory which assumes that the physical vacuum consists of classical stochastic fields with average energy \\frac{1}{2}{{\\hslash }}ω in each mode, i.e., the zero-point Planck spectrum. While this classical theory explains many quantum phenomena related to harmonic oscillator problems, hard results on nonlinear systems are still lacking. In this work the hydrogen ground state is studied by numerically solving the Abraham-Lorentz equation in the dipole approximation. First the stochastic Gaussian field is represented by a sum over Gaussian frequency components, next the dynamics is solved numerically using OpenCL. The approach improves on work by Cole and Zou 2003 by treating the full 3d problem and reaching longer simulation times. The results are compared with a conjecture for the ground state phase space density. Though short time results suggest a trend towards confirmation, in all attempted modellings the atom ionises at longer times.
Collective excitations, instabilities, and ground state in dense quark matter
Gorbar, E V; Miransky, V A; Shovkovy, I A; Hashimoto, Michio
2006-01-01
We study the spectrum of light plasmons in the (gapped and gapless) two-flavor color superconducting phases and its connection with the chromomagnetic instabilities and the structure of the ground state. It is revealed that the chromomagnetic instabilities in the 4-7th and 8th gluonic channels correspond to two very different plasmon spectra. These spectra lead us to the unequivocal conclusion about the existence of gluonic condensates (some of which can be spatially inhomogeneous) in the ground state. We also argue that spatially inhomogeneous gluonic condensates should exist in the three-flavor quark matter with the values of the mass of strange quark corresponding to the gapless color-flavor locked state.
Ground-State Phase Diagram of S = 1 Diamond Chains
Hida, Kazuo; Takano, Ken'ichi
2017-03-01
We investigate the ground-state phase diagram of a spin-1 diamond chain. Owing to a series of conservation laws, any eigenstate of this system can be expressed using the eigenstates of finite odd-length chains or infinite chains with spins 1 and 2. The ground state undergoes quantum phase transitions with varying λ, a parameter that controls frustration. Exact upper and lower bounds for the phase boundaries between these phases are obtained. The phase boundaries are determined numerically in the region not explored in a previous work [Takano et al., https://doi.org/10.1088/0953-8984/8/35/009" xlink:type="simple">J. Phys.: Condens. Matter 8, 6405 (1996)].
Borromean ground state of fermions in two dimensions
Volosniev, A. G.; Fedorov, D. V.; Jensen, A. S.; Zinner, N. T.
2014-09-01
The study of quantum mechanical bound states is as old as quantum theory itself. Yet, it took many years to realize that three-body Borromean systems that are bound when any two-body subsystem is unbound are abundant in nature. Here we demonstrate the existence of Borromean systems of spin-polarized (spinless) identical fermions in two spatial dimensions. The ground state with zero orbital (planar) angular momentum exists in a Borromean window between critical two- and three-body strengths. The doubly degenerate first excited states of angular momentum one appears only very close to the two-body threshold. They are the lowest in a possible sequence of so-called super-Efimov states. While the observation of the super-Efimov scaling could be very difficult, the Borromean ground state should be observable in cold atomic gases and could be the basis for producing a quantum gas of three-body states in two dimensions.
Coherent Control of Ground State NaK Molecules
Yan, Zoe; Park, Jee Woo; Loh, Huanqian; Will, Sebastian; Zwierlein, Martin
2016-05-01
Ultracold dipolar molecules exhibit anisotropic, tunable, long-range interactions, making them attractive for the study of novel states of matter and quantum information processing. We demonstrate the creation and control of 23 Na40 K molecules in their rovibronic and hyperfine ground state. By applying microwaves, we drive coherent Rabi oscillations of spin-polarized molecules between the rotational ground state (J=0) and J=1. The control afforded by microwave manipulation allows us to pursue engineered dipolar interactions via microwave dressing. By driving a two-photon transition, we are also able to observe Ramsey fringes between different J=0 hyperfine states, with coherence times as long as 0.5s. The realization of long coherence times between different molecular states is crucial for applications in quantum information processing. NSF, AFOSR- MURI, Alfred P. Sloan Foundation, DARPA-OLE
Non-uniform ground state for the Bose gas
2000-01-01
We study the ground state, sum a_X |X>, of N hard-core bosons on a finite lattice in configuration space, X={x_1,...,x_N}. All a_X being positive, the ratios a_X / sum a_Y can be interpreted as probabilities P_a (X). Let E denote the energy of the ground state and B_X the number of nearest-neighbor particle-hole pairs in the configuration X. We prove the concentration of P_a to X's with B_X in a sqrt(|E|)-neighborhood of |E|, show that the average of a_X over configurations with B_X=n increas...
The ground state in a spin-one color superconductor
Schmitt, A
2004-01-01
Color superconductors in which quarks of the same flavor form Cooper pairs are investigated. These Cooper pairs carry total spin one. A systematic group-theoretical classification of possible phases in a spin-one color superconductor is presented, revealing parallels and differences to the theory of superfluid $^3$He. General expressions for the gap parameter, the critical temperature, and the pressure are derived and evaluated for several spin-one phases, with special emphasis on the angular structure of the gap equation. It is shown that, in a spin-one color superconductor, the (transverse) A phase is expected to be the ground state. This is in contrast to $^3$He, where the ground state is in the B phase.
EIT ground-state cooling of long ion strings
Lechner, R; Hempel, C; Jurcevic, P; Lanyon, B P; Monz, T; Brownnutt, M; Blatt, R; Roos, C F
2016-01-01
Electromagnetically-induced-transparency (EIT) cooling is a ground-state cooling technique for trapped particles. EIT offers a broader cooling range in frequency space compared to more established methods. In this work, we experimentally investigate EIT cooling in strings of trapped atomic ions. In strings of up to 18 ions, we demonstrate simultaneous ground state cooling of all radial modes in under 1 ms. This is a particularly important capability in view of emerging quantum simulation experiments with large numbers of trapped ions. Our analysis of the EIT cooling dynamics is based on a novel technique enabling single-shot measurements of phonon numbers, by rapid adiabatic passage on a vibrational sideband of a narrow transition.
Room temperature skyrmion ground state stabilized through interlayer exchange coupling
Energy Technology Data Exchange (ETDEWEB)
Chen, Gong, E-mail: gchenncem@gmail.com; Schmid, Andreas K. [NCEM, Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, California 94720 (United States); Mascaraque, Arantzazu [Depto. Física de Materiales, Universidad Complutense de Madrid, 28040 Madrid (Spain); Unidad Asociada IQFR (CSIC) - UCM, 28040 Madrid (Spain); N' Diaye, Alpha T. [Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California 94720 (United States)
2015-06-15
Possible magnetic skyrmion device applications motivate the search for structures that extend the stability of skyrmion spin textures to ambient temperature. Here, we demonstrate an experimental approach to stabilize a room temperature skyrmion ground state in chiral magnetic films via exchange coupling across non-magnetic spacer layers. Using spin polarized low-energy electron microscopy to measure all three Cartesian components of the magnetization vector, we image the spin textures in Fe/Ni films. We show how tuning the thickness of a copper spacer layer between chiral Fe/Ni films and perpendicularly magnetized Ni layers permits stabilization of a chiral stripe phase, a skyrmion phase, and a single domain phase. This strategy to stabilize skyrmion ground states can be extended to other magnetic thin film systems and may be useful for designing skyrmion based spintronics devices.
Terahertz spectroscopy of ground state HD18O
Yu, Shanshan; Pearson, John C.; Drouin, Brian J.; Miller, Charles E.; Kobayashi, Kaori; Matsushima, Fusakazu
2016-10-01
Terahertz absorption spectroscopy was employed to measure the ground state pure rotational transitions of the water isotopologue HD18O . A total of 105 pure rotational transitions were observed in the 0.5-5.0 THz region with ∼ 100 kHz accuracy for the first time. The observed positions were fit to experimental accuracy using the Euler series expansion of the asymmetric-top Hamiltonian together with the literature Microwave, Far-IR and IR data in the ground state and ν2 . The new measurements and predictions reported here support the analysis of astronomical observations by high-resolution spectroscopic telescopes such as SOFIA and ALMA where laboratory rest frequencies with uncertainties of 1 MHz or less are required for proper analysis of velocity resolved astrophysical data.
Ground state solutions for non-local fractional Schrodinger equations
Directory of Open Access Journals (Sweden)
Yang Pu
2015-08-01
Full Text Available In this article, we study a time-independent fractional Schrodinger equation with non-local (regional diffusion $$ (-\\Delta^{\\alpha}_{\\rho}u + V(xu = f(x,u \\quad \\text{in }\\mathbb{R}^{N}, $$ where $\\alpha \\in (0,1$, $N > 2\\alpha$. We establish the existence of a non-negative ground state solution by variational methods.
0{sup +} ground state dominance in many-body systems
Energy Technology Data Exchange (ETDEWEB)
Zhao, Yu-Min [Southeast Univ., Dept. of Physics, Nanjing (China); Arima, Akito [The House of Councilors, Tokyo (Japan); Yoshinaga, Naotaka [Saitama Univ., Physics Dept., Saitama (Japan)
2002-12-01
We propose a simple approach to predict the angular momentum I ground states (Ig.s.) probabilities of many-body systems without diagonalization of the hamiltonian using random interactions. It is suggested that the 0g.s. dominance in boson systems and even valence nucleon systems is not given by the model space as previously assumed, but by specific two-body interactions. (author)
Striped spin liquid crystal ground state instability of kagome antiferromagnets.
Clark, Bryan K; Kinder, Jesse M; Neuscamman, Eric; Chan, Garnet Kin-Lic; Lawler, Michael J
2013-11-01
The Dirac spin liquid ground state of the spin 1/2 Heisenberg kagome antiferromagnet has potential instabilities. This has been suggested as the reason why it does not emerge as the ground state in large-scale numerical calculations. However, previous attempts to observe these instabilities have failed. We report on the discovery of a projected BCS state with lower energy than the projected Dirac spin liquid state which provides new insight into the stability of the ground state of the kagome antiferromagnet. The new state has three remarkable features. First, it breaks spatial symmetry in an unusual way that may leave spinons deconfined along one direction. Second, it breaks the U(1) gauge symmetry down to Z(2). Third, it has the spatial symmetry of a previously proposed "monopole" suggesting that it is an instability of the Dirac spin liquid. The state described herein also shares a remarkable similarity to the distortion of the kagome lattice observed at low Zn concentrations in Zn-paratacamite and in recently grown single crystals of volborthite suggesting it may already be realized in these materials.
Mixed configuration ground state in iron(II) phthalocyanine
Energy Technology Data Exchange (ETDEWEB)
Fernandez-Rodriguez, Javier; Toby, Brian; van Veenendaal, Michel
2015-06-23
We calculate the angular dependence of the x-ray linear and circular dichroism at the L2,3 edges of α-Fe(II) Phthalocyanine (FePc) thin films using a ligand-field model with full configuration interaction. We find the best agreement with the experimental spectra for a mixed ground state of 3E (a2 e3b1 ) and 3B (a1 e4b1 ) g 1g g 2g 2g 1g g 2g with the two configurations coupled by the spin-orbit interaction. The 3Eg(b) and 3B2g states have easy-axis and easy-plane anisotropies, respectively. Our model accounts for an easy-plane magnetic anisotropy and the measured magnitudes of the in-plane orbital and spin moments. The proximity in energy of the two configurations allows a switching of the magnetic anisotropy from easy plane to easy axis with a small change in the crystal field, as recently observed for FePc adsorbed on an oxidized Cu surface. We also discuss the possibility of a quintet ground state (5A1g is 250 meV above the ground state) with planar anisotropy by manipulation of the Fe-C bond length by depositing the complex on a substrate that is subjected to a mechanical strain.
Nuclear ground-state masses and deformations: FRDM(2012)
Moller, P; Ichikawa, T; Sagawa, H
2015-01-01
We tabulate the atomic mass excesses and binding energies, ground-state shell-plus-pairing corrections, ground-state microscopic corrections, and nuclear ground-state deformations of 9318 nuclei ranging from $^{16}$O to $A=339$. The calculations are based on the finite-range droplet macroscopic model and the folded-Yukawa single-particle microscopic model. Relative to our FRDM(1992) mass table in {\\sc Atomic Data and Nuclear Data Tables} [{\\bf 59} 185 (1995)], the results are obtained in the same model, but with considerably improved treatment of deformation and fewer of the approximations that were necessary earlier, due to limitations in computer power. The more accurate execution of the model and the more extensive and more accurate experimental mass data base now available allows us to determine one additional macroscopic-model parameter, the density-symmetry coefficient $L$, which was not varied in the previous calculation, but set to zero. Because we now realize that the FRDM is inaccurate for some high...
Approximate Stream Function wavemaker theory for highly non-linear waves in wave flumes
DEFF Research Database (Denmark)
Zhang, H.W.; Schäffer, Hemming Andreas
2007-01-01
An approximate Stream Function wavemaker theory for highly non-linear regular waves in flumes is presented. This theory is based on an ad hoe unified wave-generation method that combines linear fully dispersive wavemaker theory and wave generation for non-linear shallow water waves. This is done...... by applying a dispersion correction to the paddle position obtained for non-linear long waves. The method is validated by a number of wave flume experiments while comparing with results of linear wavemaker theory, second-order wavemaker theory and Cnoidal wavemaker theory within its range of application....
Increasing Radical Character of Large [n]cyclacenes Unveiled by Wave Function Theory.
Battaglia, Stefano; Faginas-Lago, Noelia; Andrae, Dirk; Evangelisti, Stefano; Leininger, Thierry
2017-05-18
We have investigated the radicality and the vertical singlet-triplet energy gap of [n]cyclacenes (cyclic polyacenes) as a function of the system size for n even, from 6 to 22. The calculations are performed using the complete active space self-consistent field method and second-order n-electron valence perturbation theory. We present a systematic way for the selection of the active space in order to have a balanced description of the wave function as the size of the system increases. Moreover, we provide didactic insight into the failure of an approach based on a minimal active space. We find that the ground state is an open-shell singlet and its multireference character increases progressively with n. The singlet-triplet gap decreases as a function of the system size and approaches a finite positive value for the limit n → ∞. Finally, an analysis based on the one-particle reduced density matrix suggests a polyradical character for the largest cyclacenes.
Hubbard models with nearly flat bands: Ground-state ferromagnetism driven by kinetic energy
Müller, Patrick; Richter, Johannes; Derzhko, Oleg
2016-04-01
We consider the standard repulsive Hubbard model with a flat lowest-energy band for two one-dimensional lattices (diamond chain and ladder) as well as for a two-dimensional lattice (bilayer) at half filling of the flat band. The considered models do not fall in the class of Mielke-Tasaki flat-band ferromagnets, since they do not obey the connectivity conditions. However, the ground-state ferromagnetism can emerge, if the flat band becomes dispersive. To study this kinetic-energy-driven ferromagnetism we use perturbation theory and exact diagonalization of finite lattices. We find as a typical scenario that small and moderate dispersion may lead to a ferromagnetic ground state for sufficiently large on-site Hubbard repulsion U >Uc , where Uc increases monotonically with the acquired bandwidth. However, we also observe for some specific parameter cases, that (i) ferromagnetism appears at already very small Uc, (ii) ferromagnetism does not show up at all, (iii) the critical on-site repulsion Uc is a nonmonotonic function of the bandwidth, or that (iv) a critical bandwidth is needed to open the window for ground-state ferromagnetism.
Energy Technology Data Exchange (ETDEWEB)
Kato, Tsuyoshi; Ide, Yoshihiro; Yamanouchi, Kaoru [Department of Chemistry, School of Science, The University of Tokyo, 7-3-1, Hongo Bunkyo-ku, Tokyo, 113-0033 (Japan)
2015-12-31
We first calculate the ground-state molecular wave function of 1D model H{sub 2} molecule by solving the coupled equations of motion formulated in the extended multi-configuration time-dependent Hartree-Fock (MCTDHF) method by the imaginary time propagation. From the comparisons with the results obtained by the Born-Huang (BH) expansion method as well as with the exact wave function, we observe that the memory size required in the extended MCTDHF method is about two orders of magnitude smaller than in the BH expansion method to achieve the same accuracy for the total energy. Second, in order to provide a theoretical means to understand dynamical behavior of the wave function, we propose to define effective adiabatic potential functions and compare them with the conventional adiabatic electronic potentials, although the notion of the adiabatic potentials is not used in the extended MCTDHF approach. From the comparison, we conclude that by calculating the effective potentials we may be able to predict the energy differences among electronic states even for a time-dependent system, e.g., time-dependent excitation energies, which would be difficult to be estimated within the BH expansion approach.
Bourhill, G.; Bredas, J-L.; Cheng, L-T.; Marder, S. R.; Meyers, F.; Perry, J. W.; Tiemann, B. G.
1993-01-01
The dependence of the product of the first hyperpolarizability, beta, and the ground-state dipole moment, mu, for a series of donor-acceptor polyenes with a large range of ground-state polarization, was measured in a variety of solvents by electric field induced second harmonic generation. The observed behavior of mu times beta as a function of ground-state polarization agrees well with theoretical predictions. In particular, as a function of increasing polarization, mu times beta was found to first increase, peak in a positive sense, decrease, pass through zero, become large and negative, and eventually peak in a negative sense.
Energy Technology Data Exchange (ETDEWEB)
Szybisz, L. (Lab. TANDAR, Comision Nacional de Energia Atomica, Buenos Aires (Argentina))
1989-11-01
The long-wavelength behavior of the two-body correlation factor, u(k), of the ground-state wave function for an homogeneous liquid {sup 4}He at zero temperature is studied. The solutions are obtained from a paired-phonon-analysis within the HNC/O approximation. The cut-off for the phonons is investigated analyzing u(k) at small momenta. It is shown that the numerical results: 1. rule out a pure gaussian cut-off and 2. are in good agreement with the exponential cut-off suggested by Chester and Reatto. The first-sound velocity c{sub 1} and the cut-off momentum k{sub c} are determined at several densities in the range 0.016-0.025 A{sup -3}. In addition, a parametrization of these quantities as a function of the density is provided. (orig.).
Nishimura, Kohji; Nishimori, Hidetoshi; Ochoa, Andrew J.; Katzgraber, Helmut G.
2016-09-01
We study the problem to infer the ground state of a spin-glass Hamiltonian using data from another Hamiltonian with interactions disturbed by noise from the original Hamiltonian, motivated by the ground-state inference in quantum annealing on a noisy device. It is shown that the average Hamming distance between the inferred spin configuration and the true ground state is minimized when the temperature of the noisy system is kept at a finite value, and not at zero temperature. We present a spin-glass generalization of a well-established result that the ground state of a purely ferromagnetic Hamiltonian is best inferred at a finite temperature in the sense of smallest Hamming distance when the original ferromagnetic interactions are disturbed by noise. We use the numerical transfer-matrix method to establish the existence of an optimal finite temperature in one- and two-dimensional systems. Our numerical results are supported by mean-field calculations, which give an explicit expression of the optimal temperature to infer the spin-glass ground state as a function of variances of the distributions of the original interactions and the noise. The mean-field prediction is in qualitative agreement with numerical data. Implications on postprocessing of quantum annealing on a noisy device are discussed.
Energy Technology Data Exchange (ETDEWEB)
Singh, T.S.C. [Thoubal Coll., Manipur (India). Dept. of Phys.; Choudhury, K.B. [B.K.C. Coll., Calcutta (India). Dept. of Phys.; Singh, M.B. [Manipur Univ. (India). Sch. of Sci.; Deb, N.C. [Indian Association for the Cultivation of Science, Calcutta (India). Dept. of Theoretical Physics; Mukherjee, S.C. [Indian Association for the Cultivation of Science, Calcutta (India). Dept. of Theoretical Physics; Mazumdar, P.S. [Manipur Univ. (India). Sch. of Sci.
1997-04-01
Total cross sections (TCS) and single differential cross sections (SDCS) have been computed for the single ionization of the ground state of helium by electron impact in a distorted wave formalism which takes into account the effects of the initial and final channel distortions. The present TCS and SDCS results are in fair agreement with the measured values and other theoretical predictions for the incident electron energy E{sub i} > 150 eV. (orig.).
ON THE RADIAL GROUND STATE OF P-LAPLACIAN EQUATION INVOLVING SUPER-CRITICAL OR CRITICAL EXPONENTS
Institute of Scientific and Technical Information of China (English)
Xuan Benjin; Chen Zuchi
2000-01-01
In this paper, we consider the existence and uniqueness of the radial ground state to the following p-Laplacian equation involving super-critical or critical exponents: Δpu + uq - |Du|σ = 0, x ∈ Rn, 2 ＜ p ＜ n, q _＞ [n(p - 1) + p]/(n - p), σ ＞ 0. Applying the shooting argument, the Schauder's fixed point theorem and some delicate estimates of auxiliary functions, we study the influence of the parameters n, p, q, σ on the existence and uniqueness of the radial ground state to the above p-Laplacian equation.
Influence of Generalized (r, q) Distribution Function on Electrostatic Waves
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Non-Maxwellian particle distribution functions possessing high energy tail and shoulder in the profile of distribution function considerably change the damping characteristics of the waves. In the present paper Landau damping ofelectron plasma (Langmuir) waves and ion-acoustic waves in a hot, isotropic, unmagnetized plasma is studied with the generalized (r, q) distribution function. The results show that for the Langmuir oscillations Landau damping becomes severe as the spectral index r or q reduces. However, for the ion-acoustic waves Landau damping is more sensitive to the ion temperature than the spectral indices.
Functional evolution of quantum cylindrical waves
Cho, D H J; Cho, Demian H.J.; Varadarajan, Madhavan
2006-01-01
Kucha{\\v{r}} showed that the quantum dynamics of (1 polarization) cylindrical wave solutions to vacuum general relativity is determined by that of a free axially-symmetric scalar field along arbitrary axially-symmetric foliations of a fixed flat 2+1 dimensional spacetime. We investigate if such a dynamics can be defined {\\em unitarily} within the standard Fock space quantization of the scalar field. Evolution between two arbitrary slices of an arbitrary foliation of the flat spacetime can be built out of a restricted class of evolutions (and their inverses). The restricted evolution is from an initial flat slice to an arbitrary (in general, curved) slice of the flat spacetime and can be decomposed into (i) `time' evolution in which the spatial Minkowskian coordinates serve as spatial coordinates on the initial and the final slice, followed by (ii) the action of a spatial diffeomorphism of the final slice on the data obtained from (i). We show that although the functional evolution of (i) is unitarily implemen...
Chameleonic equivalence postulate and wave function collapse
Zanzi, Andrea
2014-01-01
A chameleonic solution to the cosmological constant problem and the non-equivalence of different conformal frames at the quantum level have been recently suggested [Phys. Rev. D82 (2010) 044006]. In this article we further discuss the theoretical grounds of that model and we are led to a chameleonic equivalence postulate (CEP). Whenever a theory satisfies our CEP (and some other additional conditions), a density-dependence of the mass of matter fields is naturally present. Let us summarize the main results of this paper. 1) The CEP can be considered the microscopic counterpart of the Einstein's Equivalence Principle and, hence, a chameleonic description of quantum gravity is obtained: in our model, (quantum) gravitation is equivalent to a conformal anomaly. 2) To illustrate one of the possible applications of the CEP, we point out a connection between chameleon fields and quantum-mechanical wave function collapse. The collapse is induced by the chameleonic nature of the theory. We discuss the collapse for a S...
Wave-function reconstruction in a graded semiconductor superlattice
DEFF Research Database (Denmark)
Lyssenko, V. G.; Hvam, Jørn Märcher; Meinhold, D.
2004-01-01
We reconstruct a test wave function in a strongly coupled, graded well-width superlattice by resolving the spatial extension of the interband polarisation and deducing the wave function employing non-linear optical spectroscopy. The graded gap superlattice allows us to precisely control the dista...
On quantum mechanical phase-space wave functions
DEFF Research Database (Denmark)
Wlodarz, Joachim J.
1994-01-01
An approach to quantum mechanics based on the notion of a phase-space wave function is proposed within the Weyl-Wigner-Moyal representation. It is shown that the Schrodinger equation for the phase-space wave function is equivalent to the quantum Liouville equation for the Wigner distribution...
Real no-boundary wave function in Lorentzian quantum cosmology
Dorronsoro, J. Diaz; Halliwell, J. J.; Hartle, J. B.; Hertog, T.; Janssen, O.
2017-08-01
It is shown that the standard no-boundary wave function has a natural expression in terms of a Lorentzian path integral with its contour defined by Picard-Lefschetz theory. The wave function is real, satisfies the Wheeler-DeWitt equation and predicts an ensemble of asymptotically classical, inflationary universes with nearly-Gaussian fluctuations and with a smooth semiclassical origin.
Trial wave functions for High-Pressure Metallic Hydrogen
Pierleoni, Carlo; Morales, Miguel A; Ceperley, David M; Holzmann, Markus
2007-01-01
Many body trial wave functions are the key ingredient for accurate Quantum Monte Carlo estimates of total electronic energies in many electron systems. In the Coupled Electron-Ion Monte Carlo method, the accuracy of the trial function must be conjugated with the efficiency of its evaluation. We report recent progress in trial wave functions for metallic hydrogen implemented in the Coupled Electron-Ion Monte Carlo method. We describe and characterize several types of trial functions of increasing complexity in the range of the coupling parameter $1.0 \\leq r_s \\leq1.55$. We report wave function comparisons for disordered protonic configurations and preliminary results for thermal averages.
Ground-state spin of {sup 59}Mn
Energy Technology Data Exchange (ETDEWEB)
Oinonen, M.; Koester, U.; Aeystoe, J. [CERN, Geneva (Switzerland). EP Div.; Fedoseyev, V.; Mishin, V. [Rossijskaya Akademiya Nauk, Troitsk (Russian Federation). Inst. Spektroskopii; Huikari, J.; Jokinen, A.; Nieminen, A.; Peraejaervi, K. [Jyvaeskylae Univ. (Finland). Dept. of Physics; Knipper, A.; Walter, G. [Institute de Recherches Subatomiques, 67 - Strasbourg (France)
2001-02-01
Beta-decay of {sup 59}Mn has been studied at PSB-ISOLDE, CERN. The intense and pure Mn beam was produced using the Resonance Ionization Laser Ion Source (RILIS). Based on the measured {beta}-decay rates the ground-state spin and parity are proposed to be J{sup {pi}} = 5/2{sup -}. This result is consistent with the systematic trend of the odd-A Mn nuclei and extends the systematics one step further towards the neutron drip line. (orig.)
Triaxiality near the 110Ru ground state from Coulomb excitation
Doherty, D. T.; Allmond, J. M.; Janssens, R. V. F.; Korten, W.; Zhu, S.; Zielińska, M.; Radford, D. C.; Ayangeakaa, A. D.; Bucher, B.; Batchelder, J. C.; Beausang, C. W.; Campbell, C.; Carpenter, M. P.; Cline, D.; Crawford, H. L.; David, H. M.; Delaroche, J. P.; Dickerson, C.; Fallon, P.; Galindo-Uribarri, A.; Kondev, F. G.; Harker, J. L.; Hayes, A. B.; Hendricks, M.; Humby, P.; Girod, M.; Gross, C. J.; Klintefjord, M.; Kolos, K.; Lane, G. J.; Lauritsen, T.; Libert, J.; Macchiavelli, A. O.; Napiorkowski, P. J.; Padilla-Rodal, E.; Pardo, R. C.; Reviol, W.; Sarantites, D. G.; Savard, G.; Seweryniak, D.; Srebrny, J.; Varner, R.; Vondrasek, R.; Wiens, A.; Wilson, E.; Wood, J. L.; Wu, C. Y.
2017-03-01
A multi-step Coulomb excitation measurement with the GRETINA and CHICO2 detector arrays was carried out with a 430-MeV beam of the neutron-rich 110Ru (t1/2 = 12 s) isotope produced at the CARIBU facility. This represents the first successful measurement following the post-acceleration of an unstable isotope of a refractory element. The reduced transition probabilities obtained for levels near the ground state provide strong evidence for a triaxial shape; a conclusion confirmed by comparisons with the results of beyond-mean-field and triaxial rotor model calculations.
Evidence for the ground-state resonance of 26O
Lunderberg, E; Kohley, Z; Attanayake, H; Baumann, T; Bazin, D; Christian, G; Divaratne, D; Grimes, S M; Haagsma, A; Finck, J E; Frank, N; Luther, B; Mosby, S; Nagy, T; Peaslee, G F; Schiller, A; Snyder, J; Spyrou, A; Strongman, M J; Thoennessen, M
2012-01-01
Evidence for the ground state of the neutron-unbound nucleus 26O was observed for the first time in the single proton-knockout reaction from a 82 MeV/u 27F beam. Neutrons were measured in coincidence with 24O fragments. 26O was determined to be unbound by 150+50-150 keV from the observation of low-energy neutrons. This result agrees with recent shell model calculations based on microscopic two- and three-nucleon forces.
First Observation of Ground State Dineutron Decay: Be16
Spyrou, A.; Kohley, Z.; Baumann, T.; Bazin, D.; Brown, B. A.; Christian, G.; Deyoung, P. A.; Finck, J. E.; Frank, N.; Lunderberg, E.; Mosby, S.; Peters, W. A.; Schiller, A.; Smith, J. K.; Snyder, J.; Strongman, M. J.; Thoennessen, M.; Volya, A.
2012-03-01
We report on the first observation of dineutron emission in the decay of Be16. A single-proton knockout reaction from a 53MeV/u B17 beam was used to populate the ground state of Be16. Be16 is bound with respect to the emission of one neutron and unbound to two-neutron emission. The dineutron character of the decay is evidenced by a small emission angle between the two neutrons. The two-neutron separation energy of Be16 was measured to be 1.35(10) MeV, in good agreement with shell model calculations, using standard interactions for this mass region.
Ground state of a confined Yukawa plasma including correlation effects
Henning, C; Filinov, A; Piel, A; Bonitz, M
2007-01-01
The ground state of an externally confined one-component Yukawa plasma is derived analytically using the local density approximation (LDA). In particular, the radial density profile is computed. The results are compared with the recently obtained mean-field (MF) density profile \\cite{henning.pre06}. While the MF results are more accurate for weak screening, LDA with correlations included yields the proper description for large screening. By comparison with first-principle simulations for three-dimensional spherical Yukawa crystals we demonstrate that both approximations complement each other. Together they accurately describe the density profile in the full range of screening parameters.
Fate of the Superconducting Ground State on the Moyal Plane
Basu, Prasad; Vaidya, Sachindeo
2009-01-01
It is known that Berry curvature of the band structure of certain crystals can lead to effective noncommutativity between spatial coordinates. Using the techniques of twisted quantum field theory, we investigate the question of the formation of a paired state of twisted fermions in such a system. We find that to leading order in the noncommutativity parameter, the gap between the non-interacting ground state and the paired state is {\\it smaller} compared to its commutative counterpart. This suggests that BCS type superconductivity, if present in such systems, is more fragile and easier to disrupt.
Tetraphenylhexaazaanthracenes: 16π Weakly Antiaromatic Species with Singlet Ground States.
Constantinides, Christos P; Zissimou, Georgia A; Berezin, Andrey A; Ioannou, Theodosia A; Manoli, Maria; Tsokkou, Demetra; Theodorou, Eleni; Hayes, Sophia C; Koutentis, Panayiotis A
2015-08-21
Tetraphenylhexaazaanthracene, TPHA-1, is a fluorescent zwitterionic biscyanine with a closed-shell singlet ground state. TPHA-1 overcomes its weak 16π antiaromaticity by partitioning its π system into 6π positive and 10π negative cyanines. The synthesis of TPHA-1 is low yielding and accompanied by two analogous TPHA isomers: the deep red, non-charge-separated, quinoidal TPHA-2, and the deep green TPHA-3 that partitions into two equal but oppositely charged 8π cyanines. The three TPHA isomers are compared.
Ground state hyperfine splitting of high Z hydrogenlike ions
Shabaev, V M; Kühl, T; Artemiev, A N; Yerokhin, V A
1997-01-01
The ground state hyperfine splitting values of high Z hydrogenlike ions are calculated. The relativistic, nuclear and QED corrections are taken into account. The nuclear magnetization distribution correction (the Bohr-Weisskopf effect) is evaluated within the single particle model with the g_{S}-factor chosen to yield the observed nuclear moment. An additional contribution caused by the nuclear spin-orbit interaction is included in the calculation of the Bohr-Weisskopf effect. It is found that the theoretical value of the wavelength of the transition between the hyperfine splitting components in ^{165}Ho^{66+} is in good agreement with experiment.
Photoabsorption by ground-state alkali-metal atoms.
Weisheit, J. C.
1972-01-01
Principal-series oscillator strengths and ground-state photoionization cross sections are computed for sodium, potassium, rubidium, and cesium. The degree of polarization of the photoelectrons is also predicted for each atom. The core-polarization correction to the dipole transition moment is included in all of the calculations, and the spin-orbit perturbation of valence-p-electron orbitals is included in the calculations of the Rb and Cs oscillator strengths and of all the photoionization cross sections. The results are compared with recent measurements.
Two-state model based on the block-localized wave function method
Mo, Yirong
2007-06-01
The block-localized wave function (BLW) method is a variant of ab initio valence bond method but retains the efficiency of molecular orbital methods. It can derive the wave function for a diabatic (resonance) state self-consistently and is available at the Hartree-Fock (HF) and density functional theory (DFT) levels. In this work we present a two-state model based on the BLW method. Although numerous empirical and semiempirical two-state models, such as the Marcus-Hush two-state model, have been proposed to describe a chemical reaction process, the advantage of this BLW-based two-state model is that no empirical parameter is required. Important quantities such as the electronic coupling energy, structural weights of two diabatic states, and excitation energy can be uniquely derived from the energies of two diabatic states and the adiabatic state at the same HF or DFT level. Two simple examples of formamide and thioformamide in the gas phase and aqueous solution were presented and discussed. The solvation of formamide and thioformamide was studied with the combined ab initio quantum mechanical and molecular mechanical Monte Carlo simulations, together with the BLW-DFT calculations and analyses. Due to the favorable solute-solvent electrostatic interaction, the contribution of the ionic resonance structure to the ground state of formamide and thioformamide significantly increases, and for thioformamide the ionic form is even more stable than the covalent form. Thus, thioformamide in aqueous solution is essentially ionic rather than covalent. Although our two-state model in general underestimates the electronic excitation energies, it can predict relative solvatochromic shifts well. For instance, the intense π →π* transition for formamide upon solvation undergoes a redshift of 0.3eV, compared with the experimental data (0.40-0.5eV).
Flavour Mixing, Gauge Invariance and Wave-function Renormalisation
Espriu, Doménec; Talavera, P
2002-01-01
We clarify some aspects of the LSZ formalism and wave function renormalisation for unstable particles in the presence of electroweak interactions when mixing and CP violation are considered. We also analyse the renormalisation of the CKM mixing matrix which is closely related to wave function renormalisation. We critically review earlier attempts to define a set of "on-shell" wave function renormalisation constants. With the aid of an extensive use of the Nielsen identities complemented by explicit calculations we corroborate that the counter term for the CKM mixing matrix must be explicitly gauge independent and demonstrate that the commonly used prescription for the wave function renormalisation constants leads to gauge parameter dependent amplitudes, even if the CKM counter term is gauge invariant as required. We show that a proper LSZ-compliant prescription leads to gauge independent amplitudes. The resulting wave function renormalisation constants necessarily possess absorptive parts, but we verify that ...
Separation of different wave components in the Bethe–Salpeter wave function
Indian Academy of Sciences (India)
Jiao-Kai Chen
2011-03-01
The scalar products of polarization tensor and unit vectors are presented explicitly in spherical coordinate system expanded in terms of spherical harmonic functions. By applying the obtained formulae, different wave components in the Salpeter wave function can be shown explicitly, and the results are consistent with the results obtained by - coupling analysis. The cancelation formula is given, by which the terms with pure = + 1 wave components in the Salpeter wave function for the bound state with = (-1) can be obtained by separating the = - 1 wave components from mixing terms. This separation provides the basis for studying higher-order contributions from the coupling of = - 1 and + 1 wave states, and for solving the Salpeter equation exactly without approximation.
Ground-state ammonia and water in absorption towards Sgr B2
Wirström, E S; Black, J H; Hjalmarson, Å; Larsson, B; Olofsson, A O H; Encrenaz, P J; Falgarone, E; Frisk, U; Olberg, M; Sandqvist, Aa
2010-01-01
We have used the Odin submillimetre-wave satellite telescope to observe the ground state transitions of ortho-ammonia and ortho-water, including their 15N, 18O, and 17O isotopologues, towards Sgr B2. The extensive simultaneous velocity coverage of the observations, >500 km/s, ensures that we can probe the conditions of both the warm, dense gas of the molecular cloud Sgr B2 near the Galactic centre, and the more diffuse gas in the Galactic disk clouds along the line-of-sight. We present ground-state NH3 absorption in seven distinct velocity features along the line-of-sight towards Sgr B2. We find a nearly linear correlation between the column densities of NH3 and CS, and a square-root relation to N2H+. The ammonia abundance in these diffuse Galactic disk clouds is estimated to be about (0.5-1)e-8, similar to that observed for diffuse clouds in the outer Galaxy. On the basis of the detection of H218O absorption in the 3 kpc arm, and the absence of such a feature in the H217O spectrum, we conclude that the water...
Laboratory rotational ground state transitions of NH$_3$D$^+$ and CF$^+$
Stoffels, Alexander; Schlemmer, Stephan; Brünken, Sandra
2016-01-01
Aims. This paper reports accurate laboratory frequencies of the rotational ground state transitions of two astronomically relevant molecular ions, NH3D+ and CF+. Methods. Spectra in the millimeter-wave band were recorded by the method of rotational state-selective attachment of He-atoms to the molecular ions stored and cooled in a cryogenic ion trap held at 4 K. The lowest rotational transition in the A state (ortho state) of NH$_3$D$^+$ ($J_K = 1_0 - 0_0$), and the two hyperfine components of the ground state transition of CF$^+$($J = 1 - 0$) were measured with a relative precision better than $10^{-7}$. Results. For both target ions the experimental transition frequencies agree with recent observations of the same lines in different astronomical environments. In the case of NH$_3$D$^+$ the high-accuracy laboratory measurements lend support to its tentative identification in the interstellar medium. For CF$^+$ the experimentally determined hyperfine splitting confirms previous quantum-chemical calculations a...
Tkalya, E V
2016-01-01
The magnetic hyperfine (MHF) structure of the $5/2^+$(0.0 eV) ground state and the low-lying $3/2^+$(7.8 eV) isomeric state of the $^{229}$Th nucleus in highly charged ions Th$^{89+}$ and Th$^{87+}$ is calculated. The distribution of the nuclear magnetization (the Bohr-Weisskopf effect) is accounted for in the framework of the collective nuclear model with the wave functions of the Nilsson model for the unpaired neutron. The deviations of the MHF structure for the ground and isomeric states from their values in the model of point-like nuclear magnetic dipole are calculated. The influence of the mixing of the states with the same quantum number $F$ on the energy of sublevels is studied. Taking into account the mixing of states, the probabilities of the transitions between the components of MHF structure are found.
Uniqueness of ground states of some coupled nonlinear Schrodinger systems and their application
MA,LI; Lin ZHAO
2007-01-01
We establish the uniqueness of ground states of some coupled nonlinear Schrodinger systems in the whole space. We firstly use Schwartz symmetrization to obtain the existence of ground states for a more general case. To prove the uniqueness of ground states, we use the radial symmetry of the ground states to transform the systems into an ordinary differential system, and then we use the integral forms of the system. More interestingly, as an application of our uniqueness results, we derive a s...
Ground-state electronic structure of actinide monocarbides and mononitrides
DEFF Research Database (Denmark)
Petit, Leon; Svane, Axel; Szotek, Z.
2009-01-01
The self-interaction corrected local spin-density approximation is used to investigate the ground-state valency configuration of the actinide ions in the actinide monocarbides, AC (A=U,Np,Pu,Am,Cm), and the actinide mononitrides, AN. The electronic structure is characterized by a gradually...... increasing degree of f electron localization from U to Cm, with the tendency toward localization being slightly stronger in the (more ionic) nitrides compared to the (more covalent) carbides. The itinerant band picture is found to be adequate for UC and acceptable for UN, while a more complex manifold...... of competing localized and delocalized f-electron configurations underlies the ground states of NpC, PuC, AmC, NpN, and PuN. The fully localized 5f-electron configuration is realized in CmC (f7), CmN (f7), and AmN (f6). The observed sudden increase in lattice parameter from PuN to AmN is found to be related...
Ground state energies from converging and diverging power series expansions
Lisowski, C.; Norris, S.; Pelphrey, R.; Stefanovich, E.; Su, Q.; Grobe, R.
2016-10-01
It is often assumed that bound states of quantum mechanical systems are intrinsically non-perturbative in nature and therefore any power series expansion methods should be inapplicable to predict the energies for attractive potentials. However, if the spatial domain of the Schrödinger Hamiltonian for attractive one-dimensional potentials is confined to a finite length L, the usual Rayleigh-Schrödinger perturbation theory can converge rapidly and is perfectly accurate in the weak-binding region where the ground state's spatial extension is comparable to L. Once the binding strength is so strong that the ground state's extension is less than L, the power expansion becomes divergent, consistent with the expectation that bound states are non-perturbative. However, we propose a new truncated Borel-like summation technique that can recover the bound state energy from the diverging sum. We also show that perturbation theory becomes divergent in the vicinity of an avoided-level crossing. Here the same numerical summation technique can be applied to reproduce the energies from the diverging perturbative sums.
EVANS FUNCTIONS AND ASYMPTOTIC STABILITY OF TRAVELING WAVE SOLUTIONS
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
This paper studies the asymptotic stability of traveling wave solutions of nonlinear systems of integral-differential equations. It has been established that linear stability of traveling waves is equivalent to nonlinear stability and some “nice structure” of the spectrum of an associated operator implies the linear stability. By using the method of variation of parameter, the author defines some complex analytic function, called the Evans function. The zeros of the Evans function corresponds to the eigenvalues of the associated linear operator. By calculating the zeros of the Evans function, the asymptotic stability of the travling wave solutions is established.
Positive ground state solutions to Schrodinger-Poisson systems with a negative non-local term
Directory of Open Access Journals (Sweden)
Yan-Ping Gao
2015-04-01
Full Text Available In this article, we study the Schrodinger-Poisson system $$\\displaylines{ -\\Delta u+u-\\lambda K(x\\phi(xu=a(x|u|^{p-1}u, \\quad x\\in\\mathbb{R}^3, \\cr -\\Delta\\phi=K(xu^{2},\\quad x\\in\\mathbb{R}^3, }$$ with $p\\in(1,5$. Assume that $a:\\mathbb{R}^3\\to \\mathbb{R^{+}}$ and $K:\\mathbb{R}^3\\to \\mathbb{R^{+}}$ are nonnegative functions and satisfy suitable assumptions, but not requiring any symmetry property on them, we prove the existence of a positive ground state solution resolved by the variational methods.
E2 transitions between excited single-phonon states: Role of ground-state correlations
Energy Technology Data Exchange (ETDEWEB)
Kamerdzhiev, S. P. [National Research Centre Kurchatov Institute (Russian Federation); Voitenkov, D. A., E-mail: dvoytenkov@ippe.ru [Institute for Physics and Power Engineering (Russian Federation)
2016-11-15
The probabilities for E2 transitions between low-lying excited 3{sup −} and 5{sup −} single-phonon states in the {sup 208}Pb and {sup 132}Sn magic nuclei are estimated on the basis of the theory of finite Fermi systems. The approach used involves a new type of ground-state correlations, that which originates from integration of three (rather than two, as in the random-phase approximation) single-particle Green’s functions. These correlations are shown to make a significant contribution to the probabilities for the aforementioned transitions.
Ground State Transitions of Four-Electron Quantum Dots in Zero Magnetic Field
Institute of Scientific and Technical Information of China (English)
KANG Shuai; XIE Wen-Fang; LIU Yi-Ming; SHI Ting-Yun
2008-01-01
In this paper, we study four electrons confined in a parabolic quantum dot in the absence of magnetic field, by the exact diagonalization method. The ground-state electronic structures and orbital and spin angular momenta transitions as a function of the confined strength are investigated. We find that the confinement may cause accidental degeneracies between levels with different low-lying states and the inversion of the energy values. The present results are useful to understand the optical properties and internal electron-electron correlations of quantum dot materials.
Ground-state properties of 4He and 16O extrapolated from lattice QCD with pionless EFT
Contessi, L.; Lovato, A.; Pederiva, F.; Roggero, A.; Kirscher, J.; van Kolck, U.
2017-09-01
We extend the prediction range of Pionless Effective Field Theory with an analysis of the ground state of 16O in leading order. To renormalize the theory, we use as input both experimental data and lattice QCD predictions of nuclear observables, which probe the sensitivity of nuclei to increased quark masses. The nuclear many-body Schrödinger equation is solved with the Auxiliary Field Diffusion Monte Carlo method. For the first time in a nuclear quantum Monte Carlo calculation, a linear optimization procedure, which allows us to devise an accurate trial wave function with a large number of variational parameters, is adopted. The method yields a binding energy of 4He which is in good agreement with experiment at physical pion mass and with lattice calculations at larger pion masses. At leading order we do not find any evidence of a 16O state which is stable against breakup into four 4He, although higher-order terms could bind 16O.
Special software for computing the special functions of wave catastrophes
Directory of Open Access Journals (Sweden)
Andrey S. Kryukovsky
2015-01-01
Full Text Available The method of ordinary differential equations in the context of calculating the special functions of wave catastrophes is considered. Complementary numerical methods and algorithms are described. The paper shows approaches to accelerate such calculations using capabilities of modern computing systems. Methods for calculating the special functions of wave catastrophes are considered in the framework of parallel computing and distributed systems. The paper covers the development process of special software for calculating of special functions, questions of portability, extensibility and interoperability.
Energy Technology Data Exchange (ETDEWEB)
Boda, Aalu, E-mail: aaluphd@gmail.com; Kumar, D. Sanjeev; Chatterjee, Ashok [School of Physics, University of Hyderabad, Hyderabad-500046, Telangana (India); Mukhopadhyay, Soma [Department of Physics, DVR College of Engineering and Technology, Sangareddy Mandal, Hyderabad 502285 (India)
2015-06-24
The ground state energy of a hydrogenic D{sup 0} complex trapped in a three-dimensional GaAs quantum dot with Gaussian confinement is calculated variationally incorporating the effect of Rashba spin-orbit interaction. The results are obtained as a function of the quantum dot size and the Rashba spin-orbit interaction. The results show that the Rashba interaction reduces the ground state energy of the system.
Ground state configurations in antiferromagnetic ultrathin films with dipolar anisotropy
Energy Technology Data Exchange (ETDEWEB)
Leon, H., E-mail: hleon@imre.oc.uh.cu [Instituto de Ciencia y Tecnologia de Materiales, Universidad de La Habana, Zapata e/ Mazon y G. Vedado, 10400 La Habana (Cuba)
2013-02-15
The formalism developed in a previous work to calculate the dipolar energy in quasi-two-dimensional crystals with ferromagnetic order is now extended to collinear antiferromagnetic order. Numerical calculations of the dipolar energy are carried out for systems with tetragonally distorted fcc [001] structures, the case of NiO and MnO ultrathin film grown in non-magnetic substrates, where the magnetic phase is a consequence of superexchange and dipolar interactions. The employed approximation allows to demonstrate that dipolar coupling between atomic layers is responsible for the orientation of the magnetization when it differs from the one in a single layer. The ground state energy of a given NiO or MnO film is found to depend not only on the strain, but also on how much the interlayer separation and the 2D lattice constant are changed with respect to the ideal values corresponding to the non-distorted cubic structure. Nevertheless, it is shown that the orientation of the magnetization in the magnetic phase of any of these films is determined by the strain exclusively. A striped phase with the magnetization along the [112{sup Macron }] direction appears as the ground state configuration of NiO and MnO ultrathin films. In films with equally oriented stripes along the layers this magnetic phase is twofold degenerate, while in films with multidomain layers it is eightfold degenerate. These results are not in contradiction with experimentally observed out-of-plane or in-plane magnetization of striped phases in NiO and MnO ultrathin films. - Highlights: Black-Right-Pointing-Pointer Dipolar energy in collinear antiferromagnetic ultrathin films is calculated. Black-Right-Pointing-Pointer Numerical results are presented for distorted fcc [001] structures. Black-Right-Pointing-Pointer The lowest energy of a system depends on how the tetragonal distortion is achieved. Black-Right-Pointing-Pointer A striped phase with magnetization in the [112{sup Macron }] direction is the
Dynamics Near the Ground State for the Energy Critical Nonlinear Heat Equation in Large Dimensions
Collot, Charles; Merle, Frank; Raphaël, Pierre
2016-11-01
We consider the energy critical semilinear heat equation partial_tu = Δ u + |u|^{4/d-2}u, quad x in R^d and give a complete classification of the flow near the ground state solitary wave Q(x) = 1/(1+{|x|^2/{d(d-2)})^{d-2/2}} in dimension {d ≥ 7} , in the energy critical topology and without radial symmetry assumption. Given an initial data {Q + ɛ_0} with {|nabla ɛ_0|_{L^2} ≪ 1} , the solution either blows up in the ODE type I regime, or dissipates, and these two open sets are separated by a codimension one set of solutions asymptotically attracted by the solitary wave. In particular, non self similar type II blow up is ruled out in dimension {d ≥ 7} near the solitary wave even though it is known to occur in smaller dimensions (Schweyer, J Funct Anal 263(12):3922-3983, 2012). Our proof is based on sole energy estimates deeply connected to Martel et al. (Acta Math 212(1):59-140, 2014) and draws a route map for the classification of the flow near the solitary wave in the energy critical setting. A by-product of our method is the classification of minimal elements around Q belonging to the unstable manifold.
On the interpretation of wave function overlaps in quantum dots
DEFF Research Database (Denmark)
Stobbe, Søren; Hvam, Jørn Märcher; Lodahl, Peter
2011-01-01
that the electron and the hole are located at the same point or region in space, i.e., they must coincide spatially to recombine. Here, we show that this interpretation is not correct even loosely speaking. By general mathematical considerations we compare the envelope wave function overlap, the exchange overlap......The spontaneous emission rate of excitons strongly confined in quantum dots (QDs) is proportional to the overlap integral of electron and hole envelope wave functions. A common and intuitive interpretation of this result is that the spontaneous emission rate is proportional to the probability...... compare our qualitative predictions with recent measurements of the wave function overlap and find good agreement....
Energy Technology Data Exchange (ETDEWEB)
Samuel Millan, J. [Facultad de Ingenieria, Universidad Autonoma del Carmen, Cd. del Carmen, C.P. 24180, Campeche (Mexico); Perez, Luis A. [Instituto de Fisica, Universidad Nacional Autonoma de Mexico (UNAM), A.P. 20-364, C.P. 01000, Mexico D.F. (Mexico)], E-mail: lperez@fisica.unam.mx; Shelomov, Evgen [Facultad de Ingenieria, Universidad Autonoma del Carmen, Cd. del Carmen, C.P. 24180, Campeche (Mexico); Wang, Chumin [Instituto de Investigaciones en Materiales, UNAM, A.P. 70-360, C.P. 04510, Mexico D.F. (Mexico)
2007-09-01
The formation of p- and d-wave superconducting ground states on a square lattice is studied within the BCS formalism and a generalized Hubbard model, in which a second-neighbor correlated hopping ({delta}t{sub 3}) is included in addition to the on site and nearest neighbor repulsions. The triplet superconductivity is obtained when a small distortion of the right angles in the square lattice is introduced. This distortion can be characterized by the difference between the values of {delta}t{sub 3}{sup {+-}} in the x {+-} y directions, i.e., {delta}{sub 3}=({delta}t{sub 3}{sup +}-{delta}t{sub 3}{sup -})/2. The phase diagram is analyzed in the space of the electron density (n) and {delta}{sub 3}. The results show that the p- and d-channel superconductivities are respectively enhanced in the low and high electron density regions.
Boundary conditions on internal three-body wave functions
Energy Technology Data Exchange (ETDEWEB)
Mitchell, Kevin A.; Littlejohn, Robert G.
1999-10-01
For a three-body system, a quantum wave function {Psi}{sub m}{sup {ell}} with definite {ell} and m quantum numbers may be expressed in terms of an internal wave function {chi}{sub k}{sup {ell}} which is a function of three internal coordinates. This article provides necessary and sufficient constraints on {chi}{sub k}{sup {ell}} to ensure that the external wave function {Psi}{sub k}{sup {ell}} is analytic. These constraints effectively amount to boundary conditions on {chi}{sub k}{sup {ell}} and its derivatives at the boundary of the internal space. Such conditions find similarities in the (planar) two-body problem where the wave function (to lowest order) has the form r{sup |m|} at the origin. We expect the boundary conditions to prove useful for constructing singularity free three-body basis sets for the case of nonvanishing angular momentum.
Charge transfer to ground-state ions produces free electrons
You, D.; Fukuzawa, H.; Sakakibara, Y.; Takanashi, T.; Ito, Y.; Maliyar, G. G.; Motomura, K.; Nagaya, K.; Nishiyama, T.; Asa, K.; Sato, Y.; Saito, N.; Oura, M.; Schöffler, M.; Kastirke, G.; Hergenhahn, U.; Stumpf, V.; Gokhberg, K.; Kuleff, A. I.; Cederbaum, L. S.; Ueda, K.
2017-01-01
Inner-shell ionization of an isolated atom typically leads to Auger decay. In an environment, for example, a liquid or a van der Waals bonded system, this process will be modified, and becomes part of a complex cascade of relaxation steps. Understanding these steps is important, as they determine the production of slow electrons and singly charged radicals, the most abundant products in radiation chemistry. In this communication, we present experimental evidence for a so-far unobserved, but potentially very important step in such relaxation cascades: Multiply charged ionic states after Auger decay may partially be neutralized by electron transfer, simultaneously evoking the creation of a low-energy free electron (electron transfer-mediated decay). This process is effective even after Auger decay into the dicationic ground state. In our experiment, we observe the decay of Ne2+ produced after Ne 1s photoionization in Ne-Kr mixed clusters.
Charge transfer to ground-state ions produces free electrons
You, D.; Fukuzawa, H.; Sakakibara, Y.; Takanashi, T.; Ito, Y.; Maliyar, G. G.; Motomura, K.; Nagaya, K.; Nishiyama, T.; Asa, K.; Sato, Y.; Saito, N.; Oura, M.; Schöffler, M.; Kastirke, G.; Hergenhahn, U.; Stumpf, V.; Gokhberg, K.; Kuleff, A. I.; Cederbaum, L. S.; Ueda, K
2017-01-01
Inner-shell ionization of an isolated atom typically leads to Auger decay. In an environment, for example, a liquid or a van der Waals bonded system, this process will be modified, and becomes part of a complex cascade of relaxation steps. Understanding these steps is important, as they determine the production of slow electrons and singly charged radicals, the most abundant products in radiation chemistry. In this communication, we present experimental evidence for a so-far unobserved, but potentially very important step in such relaxation cascades: Multiply charged ionic states after Auger decay may partially be neutralized by electron transfer, simultaneously evoking the creation of a low-energy free electron (electron transfer-mediated decay). This process is effective even after Auger decay into the dicationic ground state. In our experiment, we observe the decay of Ne2+ produced after Ne 1s photoionization in Ne–Kr mixed clusters. PMID:28134238
Ground-state rotational constants of 12CH 3D
Chackerian, C.; Guelachvili, G.
1980-12-01
An analysis of ground-state combination differences in the ν2( A1) fundamental band of 12CH 3D ( ν0 = 2200.03896 cm -1) has been made to yield values for the rotational constants B0, D0J, D0JK, H0JJJ, H0JJK, H0JKK, LJJJJ, L0JJJK, and order of magnitude values for L0JJKK and L0JKKK. These constants should be useful in assisting radio searches for this molecule in astrophysical sources. In addition, splittings of A1A2 levels ( J ≥ 17, K = 3) have been measured in both the ground and excited vibrational states of this band.
LABS problem and ground state spin glasses system
Leukhin, A. N.; Bezrodnyi, V. I.; Kozlova, Yu. A.
2016-12-01
In our work we demonstrate the new results of an exhaustive search for optimal binary sequences with minimum peak sidelobe (MPS) up to length N=85. The design problem for law autocorrelation binary sequences (LABS) is a notoriously difficult computational problem which is numbered as the problem number 005 in CSPLib. In statistical physics LABS problem can be interrepted as the energy of N iteracting Ising spins. This is a Bernasconi model. Due to this connection to physics we refer a binary sequence as one-dimensional spin lattice. At this assumption optimal binary sequences by merit factor (MF) criteria are the ground-state spin system without disorder which exhibits a glassy regime.
Ground-state correlations within a nonperturbative approach
De Gregorio, G.; Herko, J.; Knapp, F.; Lo Iudice, N.; Veselý, P.
2017-02-01
The contribution of the two-phonon configurations to the ground state of 4He and 16O is evaluated nonperturbatively using a Hartree-Fock basis within an equation-of-motion phonon method using a nucleon-nucleon optimized chiral potential. Convergence properties of energies and root-mean-square radii versus the harmonic oscillator frequency and space dimensions are investigated. The comparison with the second-order perturbation theory calculations shows that the higher-order terms have an appreciable repulsive effect and yield too-small binding energies and nuclear radii. It is argued that four-phonon configurations, through their strong coupling to two phonons, may provide most of the attractive contribution necessary for filling the gap between theoretical and experimental quantities. Possible strategies for accomplishing such a challenging task are discussed.
Eigenvectors in the superintegrable model II: ground-state sector
Energy Technology Data Exchange (ETDEWEB)
Au-Yang, Helen; Perk, Jacques H H [Department of Physics, Oklahoma State University, 145 Physical Sciences, Stillwater, OK 74078-3072 (United States)], E-mail: helenperk@yahoo.com, E-mail: perk@okstate.edu
2009-09-18
In 1993, Baxter gave 2{sup m{sub Q}} eigenvalues of the transfer matrix of the N-state superintegrable chiral Potts model with the spin-translation quantum number Q, where m{sub Q} = lfloor(NL - L - Q)/Nrfloor. In our previous paper we studied the Q = 0 ground-state sector, when the size L of the transfer matrix is chosen to be a multiple of N. It was shown that the corresponding {tau}{sub 2} matrix has a degenerate eigenspace generated by the generators of r = m{sub 0} simple sl{sub 2} algebras. These results enable us to express the transfer matrix in the subspace in terms of these generators E{sup {+-}}{sub m} and H{sub m} for m = 1, ..., r. Moreover, the corresponding 2{sup r} eigenvectors of the transfer matrix are expressed in terms of rotated eigenvectors of H{sub m}.
Sympathetic cooling of molecular ion motion to the ground state
Rugango, Rene; Dixon, Thomas H; Gray, John M; Khanyile, Ncamiso; Shu, Gang; Clark, Robert J; Brown, Kenneth R
2014-01-01
We demonstrate sympathetic sideband cooling of a $^{40}$CaH$^{+}$ molecular ion co-trapped with a $^{40}$Ca$^{+}$ atomic ion in a linear Paul trap. Both axial modes of the two-ion chain are simultaneously cooled to near the ground state of motion. The center of mass mode is cooled to an average quanta of harmonic motion $\\overline{n}_{\\mathrm{COM}} = 0.13 \\pm 0.03$, corresponding to a temperature of $12.47 \\pm 0.03 ~\\mu$K. The breathing mode is cooled to $\\overline{n}_{\\mathrm{BM}} = 0.05 \\pm 0.02$, corresponding to a temperature of $15.36 \\pm 0.01~\\mu$K.
Ground-state properties of neutron magic nuclei
Energy Technology Data Exchange (ETDEWEB)
Saxena, G., E-mail: gauravphy@gmail.com [Govt. Women Engineering College, Department of Physics (India); Kaushik, M. [Shankara Institute of Technology, Department of Physics (India)
2017-03-15
A systematic study of the ground-state properties of the entire chains of even–even neutron magic nuclei represented by isotones of traditional neutron magic numbers N = 8, 20, 40, 50, 82, and 126 has been carried out using relativistic mean-field plus Bardeen–Cooper–Schrieffer approach. Our present investigation includes deformation, binding energy, two-proton separation energy, single-particle energy, rms radii along with proton and neutron density profiles, etc. Several of these results are compared with the results calculated using nonrelativistic approach (Skyrme–Hartree–Fock method) along with available experimental data and indeed they are found with excellent agreement. In addition, the possible locations of the proton and neutron drip-lines, the (Z, N) values for the new shell closures, disappearance of traditional shell closures as suggested by the detailed analyzes of results are also discussed in detail.
Zamudio-Bayer, V; Langenberg, A; Lawicki, A; Terasaki, A; Issendorff, B v; Lau, J T
2015-01-01
The $^6\\Delta$ electronic ground state of the Co$_2^+$ diatomic molecular cation has been assigned experimentally by x-ray absorption and x-ray magnetic circular dichroism spectroscopy in a cryogenic ion trap. Three candidates, $^6\\Phi$, $^6\\Gamma$, and $^8\\Gamma$, for the electronic ground state of Fe$_2^+$ have been identified. These states carry sizable ground-state orbital angular momenta that disagree with theoretical predictions from multireference configuration interaction and density functional theory. Our results show that the ground states of neutral and cationic diatomic molecules of $3d$ elements cannot be assumed to be connected by a one-electron process.
The Green-function transform and wave propagation
Directory of Open Access Journals (Sweden)
Colin eSheppard
2014-11-01
Full Text Available Fourier methods well known in signal processing are applied to three-dimensional wave propagation problems. The Fourier transform of the Green function, when written explicitly in terms of a real-valued spatial frequency, consists of homogeneous and inhomogeneous components. Both parts are necessary to result in a pure out-going wave that satisfies causality. The homogeneous component consists only of propagating waves, but the inhomogeneous component contains both evanescent and propagating terms. Thus we make a distinction between inhomogeneous waves and evanescent waves. The evanescent component is completely contained in the region of the inhomogeneous component outside the k-space sphere. Further, propagating waves in the Weyl expansion contain both homogeneous and inhomogeneous components. The connection between the Whittaker and Weyl expansions is discussed. A list of relevant spherically symmetric Fourier transforms is given.
The Green-function transform and wave propagation
Sheppard, Colin J R; Lin, Jiao
2014-01-01
Fourier methods well known in signal processing are applied to three-dimensional wave propagation problems. The Fourier transform of the Green function, when written explicitly in terms of a real-valued spatial frequency, consists of homogeneous and inhomogeneous components. Both parts are necessary to result in a pure out-going wave that satisfies causality. The homogeneous component consists only of propagating waves, but the inhomogeneous component contains both evanescent and propagating terms. Thus we make a distinction between inhomogenous waves and evanescent waves. The evanescent component is completely contained in the region of the inhomogeneous component outside the k-space sphere. Further, propagating waves in the Weyl expansion contain both homogeneous and inhomogeneous components. The connection between the Whittaker and Weyl expansions is discussed. A list of relevant spherically symmetric Fourier transforms is given.
General Green's function formalism for layered systems: Wave function approach
Zhang, Shu-Hui; Yang, Wen; Chang, Kai
2017-02-01
The single-particle Green's function (GF) of mesoscopic structures plays a central role in mesoscopic quantum transport. The recursive GF technique is a standard tool to compute this quantity numerically, but it lacks physical transparency and is limited to relatively small systems. Here we present a numerically efficient and physically transparent GF formalism for a general layered structure. In contrast to the recursive GF that directly calculates the GF through the Dyson equations, our approach converts the calculation of the GF to the generation and subsequent propagation of a scattering wave function emanating from a local excitation. This viewpoint not only allows us to reproduce existing results in a concise and physically intuitive manner, but also provides analytical expressions of the GF in terms of a generalized scattering matrix. This identifies the contributions from each individual scattering channel to the GF and hence allows this information to be extracted quantitatively from dual-probe STM experiments. The simplicity and physical transparency of the formalism further allows us to treat the multiple reflection analytically and derive an analytical rule to construct the GF of a general layered system. This could significantly reduce the computational time and enable quantum transport calculations for large samples. We apply this formalism to perform both analytical analysis and numerical simulation for the two-dimensional conductance map of a realistic graphene p -n junction. The results demonstrate the possibility of observing the spatially resolved interference pattern caused by negative refraction and further reveal a few interesting features, such as the distance-independent conductance and its quadratic dependence on the carrier concentration, as opposed to the linear dependence in uniform graphene.
Improved Wave-vessel Transfer Functions by Uncertainty Modelling
DEFF Research Database (Denmark)
Nielsen, Ulrik Dam; Fønss Bach, Kasper; Iseki, Toshio
2016-01-01
This paper deals with uncertainty modelling of wave-vessel transfer functions used to calculate or predict wave-induced responses of a ship in a seaway. Although transfer functions, in theory, can be calculated to exactly reflect the behaviour of the ship when exposed to waves, uncertainty in input...... variables, notably speed, draft and relative wave eading, often compromises results. In this study, uncertling is applied to improve theoretically calculated transfer functions, so they better fit the corresponding experimental, full-scale ones. Based on a vast amount of full-scale measurements data......, it is shown that uncertainty modelling can be successfully used to improve accuracy (and reliability) of theoretical transfer functions....
Alignment of wave functions for angular momentum projection
Taniguchi, Yasutaka
2016-01-01
Angular momentum projection is used to obtain eigen states of angular momentum from general wave functions. Multi-configuration mixing calculation with angular momentum projection is an important microscopic method in nuclear physics. For accurate multi-configuration mixing calculation with angular momentum projection, concentrated distribution of $z$ components $K$ of angular momentum in the body-fixed frame ($K$-distribution) is favored. Orientation of wave functions strongly affects $K$-distribution. Minimization of variance of $\\hat{J}_z$ is proposed as an alignment method to obtain wave functions that have concentrated $K$-distribution. Benchmark calculations are performed for $\\alpha$-$^{24}$Mg cluster structure, triaxially superdeformed states in $^{40}$Ar, and Hartree-Fock states of some nuclei. The proposed alignment method is useful and works well for various wave functions to obtain concentrated $K$-distribution.
Ground-State Behavior of the Quantum Compass Model in an External Field
Institute of Scientific and Technical Information of China (English)
SUN Ke-Wei; CHEN Qing-Hu
2011-01-01
@@ Ground-state(GS)properties of the two-dimensional(2D)quantum compass model in an external field on a square 5×5 lattice are investigated by using the exact diagonalization(ED)method.We obtain the GS energy and evaluate quantities such as its correlation functions,nearest-neighbor entanglement and local order parameter.As the external field is presented,the first-order quantum phase point is absent and the system exhibits the behaviors of the second-order phase transition.%Ground-state (GS) properties of the two-dimensional (2D) quantum compass model in an external Geld on a square 5x5 lattice are investigated by using the exact diagonalization (ED) method. We obtain the GS energy and evaluate quantities such as its correlation functions, nearest-neighbor entanglement and local order parameter. As the external Geld is presented, the first-order quantum phase point is absent and the system exhibits the behaviors of the second-order phase transition.
Ground-state properties of two-dimensional quantum fluid helium and hydrogen mixtures
Um, C I; Oh, H G
1998-01-01
Using a variational Jastrow wavefunction extended to include a three-body correlation function and a hypernetted chain scheme with the contributions of elementary diagrams, we analyze the ground-state energies and the structural properties of two-dimensional H- sup 4 He and H sub 2 - sup 4 He mixtures. The mixtures are in equilibrium at a lower density compared to a pure sup 4 He system because of the large zero-point energies of the hydrogen atom and molecule. We evaluate the lowering of the ground-state energies as a function of the impurity concentration and total density of mixtures. Comparing the result with boson sup 3 He- sup 4 He mixtures, we show that the shifts of energy mainly come from the difference of the zero-point energies of the impurities rather than from the interatomic potentials.We also analyze the enthalpies to study the miscibility and conclude that boson-boson mixtures are completely phase separated in their equilibria.
Do Neutrino Wave Functions Overlap and Does it Matter?
Li, Cheng-Hsien
2016-01-01
Studies of neutrinos commonly ignore anti-symmetrization of their wave functions. This implicitly assumes that either spatial wave functions for neutrinos with approximately the same momentum do not overlap or their overlapping has no measurable consequences. We examine these assumptions by considering the evolution of three-dimensional neutrino wave packets (WPs). We find that it is perfectly adequate to treat accelerator and reactor neutrinos as separate WPs for typical experimental setup. While solar and supernova neutrinos correspond to overlapping WPs, they can be treated effectively as non-overlapping for analyses of their detection.
Ran, Shi-Ju
2016-05-01
In this work, a simple and fundamental numeric scheme dubbed as ab initio optimization principle (AOP) is proposed for the ground states of translational invariant strongly correlated quantum lattice models. The idea is to transform a nondeterministic-polynomial-hard ground-state simulation with infinite degrees of freedom into a single optimization problem of a local function with finite number of physical and ancillary degrees of freedom. This work contributes mainly in the following aspects: (1) AOP provides a simple and efficient scheme to simulate the ground state by solving a local optimization problem. Its solution contains two kinds of boundary states, one of which play the role of the entanglement bath that mimics the interactions between a supercell and the infinite environment, and the other gives the ground state in a tensor network (TN) form. (2) In the sense of TN, a novel decomposition named as tensor ring decomposition (TRD) is proposed to implement AOP. Instead of following the contraction-truncation scheme used by many existing TN-based algorithms, TRD solves the contraction of a uniform TN in an opposite way by encoding the contraction in a set of self-consistent equations that automatically reconstruct the whole TN, making the simulation simple and unified; (3) AOP inherits and develops the ideas of different well-established methods, including the density matrix renormalization group (DMRG), infinite time-evolving block decimation (iTEBD), network contractor dynamics, density matrix embedding theory, etc., providing a unified perspective that is previously missing in this fields. (4) AOP as well as TRD give novel implications to existing TN-based algorithms: A modified iTEBD is suggested and the two-dimensional (2D) AOP is argued to be an intrinsic 2D extension of DMRG that is based on infinite projected entangled pair state. This paper is focused on one-dimensional quantum models to present AOP. The benchmark is given on a transverse Ising
Factorized molecular wave functions: Analysis of the nuclear factor
Energy Technology Data Exchange (ETDEWEB)
Lefebvre, R., E-mail: roland.lefebvre@u-psud.fr [Institut des Sciences Moléculaires d’ Orsay, Bâtiment 350, UMR8214, CNRS- Université. Paris-Sud, 91405 Orsay, France and Sorbonne Universités, UPMC Univ Paris 06, UFR925, F-75005 Paris (France)
2015-06-07
The exact factorization of molecular wave functions leads to nuclear factors which should be nodeless functions. We reconsider the case of vibrational perturbations in a diatomic species, a situation usually treated by combining Born-Oppenheimer products. It was shown [R. Lefebvre, J. Chem. Phys. 142, 074106 (2015)] that it is possible to derive, from the solutions of coupled equations, the form of the factorized function. By increasing artificially the interstate coupling in the usual approach, the adiabatic regime can be reached, whereby the wave function can be reduced to a single product. The nuclear factor of this product is determined by the lowest of the two potentials obtained by diagonalization of the potential matrix. By comparison with the nuclear wave function of the factorized scheme, it is shown that by a simple rectification, an agreement is obtained between the modified nodeless function and that of the adiabatic scheme.
Ultrarelativistic quasiclassical wave functions in strong laser and atomic fields
Di Piazza, A
2014-01-01
The problem of an ultrarelativistic charge in the presence of an atomic and a plane-wave field is investigated in the quasiclassical regime by including exactly the effects of both background fields. Starting from the quasiclassical Green's function obtained in [Phys. Lett. B \\textbf{717}, 224 (2012)], the corresponding in- and out-wave functions are derived in the experimentally relevant case of the particle initially counterpropagating with respect to the plane wave. The knowledge of these electron wave functions opens the possibility of investigating a variety of problems in strong-field QED, where both the atomic field and the laser field are strong enough to be taken into account exactly from the beginning in the calculations.
Donor wave functions in Si gauged by STM images
Saraiva, A. L.; Salfi, J.; Bocquel, J.; Voisin, B.; Rogge, S.; Capaz, Rodrigo B.; Calderón, M. J.; Koiller, Belita
2016-01-01
The triumph of effective mass theory in describing the energy spectrum of dopants does not guarantee that the model wave functions will withstand an experimental test. Such wave functions have recently been probed by scanning tunneling spectroscopy, revealing localized patterns of resonantly enhanced tunneling currents. We show that the shape of the conducting splotches resembles a cut through Kohn-Luttinger (KL) hydrogenic envelopes, which modulate the interfering Bloch states of conduction electrons. All the nonmonotonic features of the current profile are consistent with the charge density fluctuations observed between successive {001 } atomic planes, including a counterintuitive reduction of the symmetry—a heritage of the lowered point group symmetry at these planes. A model-independent analysis of the diffraction figure constrains the value of the electron wave vector to k0=(0.82 ±0.03 ) (2 π /aSi) . Unlike prior measurements, averaged over a sizable density of electrons, this estimate is obtained directly from isolated electrons. We further investigate the model-specific anisotropy of the wave function envelope, related to the effective mass anisotropy. This anisotropy appears in the KL variational wave function envelope as the ratio between Bohr radii b /a . We demonstrate that the central-cell-corrected estimates for this ratio are encouragingly accurate, leading to the conclusion that the KL theory is a valid model not only for energies but for wave functions as well.
Directional Wave Spectra Using Normal Spreading Function
1985-03-01
energy spectral density function U. g. Army Engineer Waternays Experiment Station. Coastal Engineering Research Center P. 0. lox 631, Vicksburg...Z39-18 D(f,e) = spreading function E (f,(3) = directional spectral density function f = frequency in cycles per second 8 = direction in radians...of this assumption depends on the narrow bandedness of the energy spectral density function . For fairly narrow spectra (e.g., a swell train), the
The effect of meson wave function on heavy-quark fragmentation function
Energy Technology Data Exchange (ETDEWEB)
Moosavi Nejad, S.M. [Yazd University, Faculty of Physics (Iran, Islamic Republic of); Institute for Research in Fundamental Sciences (IPM), School of Particles and Accelerators, Tehran (Iran, Islamic Republic of)
2016-05-15
We calculate the process-independent fragmentation functions (FFs) for a heavy quark to fragment into heavy mesons considering the effects of meson wave function. In all previous works, where the FFs of heavy mesons or heavy baryons were calculated, a delta function form was approximated for the wave function of hadrons. Here, for the first time, we consider a typical mesonic wave function which is different from the delta function and is the nonrelativistic limit of the solution of Bethe-Salpeter equation with the QCD kernel. We present our numerical results for the heavy FFs and show how the proposed wave function improves the previous results. As an example, we focus on the fragmentation function for c-quark to split into S-wave D{sup 0} -meson and compare our results with experimental data from BELLE and CLEO. (orig.)
The ground state of the ${\\rm H}_3^+$ molecular ion: a physics behind
Turbiner, A V
2012-01-01
Five physics mechanisms of interaction leading to binding of the ${\\rm H}_3^+$ molecular ion are identified, realized in a form of variational trial functions and their respective total energies are calculated. Each of them provides subsequently the most accurate approximation for the Born-Oppenheimer (BO) ground state energy among (two-three-seven)-parametric trial functions being correspondingly, H$_2$-molecule plus proton (two variational parameters), H$_2^+$-ion plus H-atom (three variational parameters) and generalized Guillemin-Zener (seven variational parameters). These trial functions are chosen following a criterion of physical adequacy, they include the electronic correlation in the exponential form $\\sim\\exp{(\\gamma r_{12})}$, where $\\gamma$ is a variational parameter. Superpositions of two different mechanisms of binding are investigated and a particular one, which is a generalized Guillemin-Zener plus H$_2$-molecule plus proton (ten variational parameters), provides the total energy at the equili...
Semilocal and Hybrid Density Embedding Calculations of Ground-State Charge-Transfer Complexes
Laricchia, S; Della Sala, F; 10.1063/1.4795825
2013-01-01
We apply the frozen density embedding method, using a full relaxation of embedded densities through a freeze-and-thaw procedure, to study the electronic structure of several benchmark ground-state charge-transfer complexes, in order to assess the merits and limitations of the approach for this class of systems. The calculations are performed using both semilocal and hybrid exchange-correlation (XC) functionals. The results show that embedding calculations using semilocal XC functionals yield rather large deviations with respect to the corresponding supermolecular calculations. Due to a large error cancellation effect, however, they can often provide a relatively good description of the electronic structure of charge-transfer complexes, in contrast to supermolecular calculations performed at the same level of theory. On the contrary, when hybrid XC functionals are employed, both embedding and supermolecular calculations agree very well with each other and with the reference benchmark results. In conclusion, fo...
Parametric dependence of ocean wave-radar modulation transfer functions
Plant, W. J.; Keller, W. C.; Cross, A.
1983-01-01
Microwave techniques at X and L band were used to determine the dependence of ocean-wave radar modulation transfer functions (MTFs) on various environmental and radar parameters during the Marine Remote Sensing experiment of 1979 (MARSEN 79). These MIF are presented, as are coherence functions between the AM and FM parts of the backscattered microwave signal. It is shown that they both depend on several of these parameters. Besides confirming many of the properties of transfer functions reported by previous authors, indications are found that MTFs decrease with increasing angle between wave propagation and antenna-look directions but are essentially independent of small changes in air-sea temperature difference. However, coherence functions are much smaller when the antennas are pointed perpendicular to long waves. It is found that X band transfer functions measured with horizontally polarized microwave radiation have larger magnitudes than those obtained by using vertical polarization.
Dynamics of a Ground-State Cooled Ion Colliding with Ultracold Atoms
Meir, Ziv; Sikorsky, Tomas; Ben-shlomi, Ruti; Akerman, Nitzan; Dallal, Yehonatan; Ozeri, Roee
2016-12-01
Ultracold atom-ion mixtures are gaining increasing interest due to their potential applications in ultracold and state-controlled chemistry, quantum computing, and many-body physics. Here, we studied the dynamics of a single ground-state cooled ion during few, to many, Langevin (spiraling) collisions with ultracold atoms. We measured the ion's energy distribution and observed a clear deviation from the Maxwell-Boltzmann distribution, characterized by an exponential tail, to a power-law distribution best described by a Tsallis function. Unlike previous experiments, the energy scale of atom-ion interactions is not determined by either the atomic cloud temperature or the ion's trap residual excess-micromotion energy. Instead, it is determined by the force the atom exerts on the ion during a collision which is then amplified by the trap dynamics. This effect is intrinsic to ion Paul traps and sets the lower bound of atom-ion steady-state interaction energy in these systems. Despite the fact that our system is eventually driven out of the ultracold regime, we are capable of studying quantum effects by limiting the interaction to the first collision when the ion is initialized in the ground state of the trap.
Ground state study of the thin ferromagnetic nano-islands for artificial spin ice arrays
Energy Technology Data Exchange (ETDEWEB)
Vieira Júnior, D. S., E-mail: damiao.vieira@ifsudestemg.edu.br [Departamento Acadêmico de Matemática, Física e Estatística, Instituto Federal de Educação, Ciência e Tecnologia do Sudeste de Minas Gerais - Câmpus Rio Pomba, Rio Pomba, Minas Gerais 36180-000 (Brazil); Departamento de Física, Laboratório de Simulação Computacional, Universidade Federal de Juiz de Fora, Juiz de Fora, Minas Gerais 36036-330 (Brazil); Leonel, S. A., E-mail: sidiney@fisica.ufjf.br; Dias, R. A., E-mail: radias@fisica.ufjf.br; Toscano, D., E-mail: danilotoscano@fisica.ufjf.br; Coura, P. Z., E-mail: pablo@fisica.ufjf.br; Sato, F., E-mail: sjfsato@fisica.ufjf.br [Departamento de Física, Laboratório de Simulação Computacional, Universidade Federal de Juiz de Fora, Juiz de Fora, Minas Gerais 36036-330 (Brazil)
2014-09-07
In this work, we used numerical simulations to study the magnetic ground state of the thin elongated (elliptical) ferromagnetic nano-islands made of Permalloy. In these systems, the effects of demagnetization of dipolar source generate a strong magnetic anisotropy due to particle shape, defining two fundamental magnetic ground state configurations—vortex or type C. To describe the system, we considered a model Hamiltonian in which the magnetic moments interact through exchange and dipolar potentials. We studied the competition between the vortex states and aligned states—type C—as a function of the shape of each elliptical nano-islands and constructed a phase diagram vortex—type C state. Our results show that it is possible to obtain the elongated nano-islands in the C-state with aspect ratios less than 2, which is interesting from the technological point of view because it will be possible to use smaller islands in spin ice arrays. Generally, the experimental spin ice arrangements are made with quite elongated particles with aspect ratio approximately 3 to ensure the C-state.
Lim, Zhenglong
2015-11-12
Quinoidal π-conjugated polycyclic hydrocarbons have attracted intensive research interest due to their unique optical/electronic properties and possible magnetic activity, which arises from a thermally excited triplet state. However, there is still lack of fundamental understanding on the factors that determine the electronic ground states. Herein, by using quinoidal oligo(9,10-anthryl)s, it is demonstrated that both aromatic stabilisation and steric strain release play balanced roles in determining the ground states. Oligomers with up to four anthryl units were synthesised and their ground states were investigated by electronic absorption and electron spin resonance (ESR) spectroscopy, assisted by density functional theory (DFT) calculations. The quinoidal 9,10-anthryl dimer 1 has a closed-shell ground state, whereas the tri- (2) and tetramers (3) both have an open-shell diradical ground state with a small singlet-triplet gap. Such a difference results from competition between two driving forces: the large steric repulsion between the anthryl/phenyl units in the closed-shell quinoidal form that drives the molecule to a flexible open-shell diradical structure, and aromatic stabilisation due to the gain of more aromatic sextet rings in the closed-shell form, which drives the molecule towards a contorted quinoidal structure. The ground states of these oligomers thus depend on the overall balance between these two driving forces and show chain-length dependence. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Institute of Scientific and Technical Information of China (English)
刘正东; 武强; 曾亮; 林宇; 朱诗尧
2001-01-01
The reconstruction of the atom-laser wave function is performed using an interferometric measurement with a standing-wave grating, and the results of this scheme are studied. The relations between the measurement data and the atomic wave function are also presented. This scheme is quite applicable and effectively avoids the initial random phase problem of the method that employs the laser running wave. The information which is encoded in the atom-laser wave is extracted.
Ground-state properties of neutron-rich Mg isotopes
Watanabe, Shin; Shimada, Mitsuhiro; Tagami, Shingo; Kimura, Masaaki; Takechi, Maya; Fukuda, Mitsunori; Nishimura, Daiki; Suzuki, Takeshi; Matsumoto, Takuma; Shimizu, Yoshifumi R; Yahiro, Masanobu
2014-01-01
We analyze recently-measured total reaction cross sections for 24-38Mg isotopes incident on 12C targets at 240 MeV/nucleon by using the folding model and antisymmetrized molecular dynamics(AMD). The folding model well reproduces the measured reaction cross sections, when the projectile densities are evaluated by the deformed Woods-Saxon (def-WS) model with AMD deformation. Matter radii of 24-38Mg are then deduced from the measured reaction cross sections by ?ne-tuning the parameters of the def-WS model. The deduced matter radii are largely enhanced by nuclear deformation. Fully-microscopic AMD calculations with no free parameter well reproduce the deduced matter radii for 24-36Mg, but still considerably underestimate them for 37,38Mg. The large matter radii suggest that 37,38Mg are candidates for deformed halo nucleus. AMD also reproduces other existing measured ground-state properties (spin-parity, total binding energy, and one-neutron separation energy) of Mg isotopes. Neutron-number (N) dependence of defor...
Continuous Vibrational Cooling of Ground State Rb2
Tallant, Jonathan; Marcassa, Luis
2014-05-01
The process of photoassociation generally results in a distribution of vibrational levels in the electronic ground state that is energetically close to the dissociation limit. Several schemes have appeared that aim to transfer the population from the higher vibrational levels to lower ones, especially the ground vibrational state. We demonstrate continuous production of vibrationally cooled Rb2 using optical pumping. The vibrationally cooled molecules are produced in three steps. First, we use a dedicated photoassociation laser to produce molecules in high vibrational levels of the X1Σg+ state. Second, a broadband fiber laser at 1071 nm is used to transfer the molecules to lower vibrational levels via optical pumping through the A1Σu+ state. This process transfers the molecules from vibrational levels around ν ~= 113 to a distribution of levels where ν superluminescent diode near 685 nm that has its frequency spectrum shaped. The resulting vibrational distributions are probed using resonance-enhanced multiphoton ionization with a pulsed dye laser near 670 nm. The results are presented and compared with theoretical simulations. This work was supported by Fapesp and INCT-IQ.
Tkalya, E. V.; Nikolaev, A. V.
2016-07-01
Background: The search for new opportunities to investigate the low-energy level in the 229Th nucleus, which is nowadays intensively studied experimentally, has motivated us to theoretical studies of the magnetic hyperfine (MHF) structure of the 5 /2+ (0.0 eV) ground state and the low-lying 3 /2+ (7.8 eV) isomeric state in highly charged 89+229Th and 87+229Th ions. Purpose: The aim is to calculate, with the maximal precision presently achievable, the energy of levels of the hyperfine structure of the 229Th ground-state doublet in highly charged ions and the probability of radiative transitions between these levels. Methods: The distribution of the nuclear magnetization (the Bohr-Weisskopf effect) is accounted for in the framework of the collective nuclear model with Nilsson model wave functions for the unpaired neutron. Numerical calculations using precise atomic density functional theory methods, with full account of the electron self-consistent field, have been performed for the electron structure inside and outside the nuclear region. Results: The deviations of the MHF structure for the ground and isomeric states from their values in a model of a pointlike nuclear magnetic dipole are calculated. The influence of the mixing of the states with the same quantum number F on the energy of sublevels is studied. Taking into account the mixing of states, the probabilities of the transitions between the components of the MHF structure are calculated. Conclusions: Our findings are relevant for experiments with highly ionized 229Th ions in a storage ring at an accelerator facility.
Rapidity resummation for B-meson wave functions
Directory of Open Access Journals (Sweden)
Shen Yue-Long
2014-01-01
Full Text Available Transverse-momentum dependent (TMD hadronic wave functions develop light-cone divergences under QCD corrections, which are commonly regularized by the rapidity ζ of gauge vector defining the non-light-like Wilson lines. The yielding rapidity logarithms from infrared enhancement need to be resummed for both hadronic wave functions and short-distance functions, to achieve scheme-independent calculations of physical quantities. We briefly review the recent progress on the rapidity resummation for B-meson wave functions which are the key ingredients of TMD factorization formulae for radiative-leptonic, semi-leptonic and non-leptonic B-meson decays. The crucial observation is that rapidity resummation induces a strong suppression of B-meson wave functions at small light-quark momentum, strengthening the applicability of TMD factorization in exclusive B-meson decays. The phenomenological consequence of rapidity-resummation improved B-meson wave functions is further discussed in the context of B → π transition form factors at large hadronic recoil.
Rossby wave Green's functions in an azimuthal wind
Webb, G. M.; Duba, C. T.; Hu, Q.
2016-05-01
Green's functions for Rossby waves in an azimuthal wind are obtained, in which the stream-function $\\psi$ depends on $r$, $\\phi$ and $t$, where $r$ is cylindrical radius and $\\phi$ is the azimuthal angle in the $\\beta$-plane relative to the easterly direction, in which the $x$-axis points east and the $y$-axis points north. The Rossby wave Green's function with no wind is obtained using Fourier transform methods, and is related to the previously known Green's function obtained for this case, which has a different but equivalent form to the Green's function obtained in the present paper. We emphasize the role of the wave eikonal solution, which plays an important role in the form of the solution. The corresponding Green's function for a rotating wind with azimuthal wind velocity ${\\bf u}=\\Omega r{\\bf e}_\\phi$ ($\\Omega=$const.) is also obtained by Fourier methods, in which the advective rotation operator in position space is transformed to a rotation operator in ${\\bf k}$ transform space. The finite Rossby deformation radius is included in the analysis. The physical characteristics of the Green's functions are delineated and applications are discussed. In the limit as $\\Omega\\to 0$, the rotating wind Green's function reduces to the Rossby wave Green function with no wind.
New approach to folding with the Coulomb wave function
Energy Technology Data Exchange (ETDEWEB)
Blokhintsev, L. D.; Savin, D. A. [Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow 119991 (Russian Federation); Kadyrov, A. S. [Department of Physics, Astronomy and Medical Radiation Sciences, Curtin University, GPO Box U1987, Perth 6845 (Australia); Mukhamedzhanov, A. M. [Cyclotron Institute, Texas A and M University, College Station, Texas 77843 (United States)
2015-05-15
Due to the long-range character of the Coulomb interaction theoretical description of low-energy nuclear reactions with charged particles still remains a formidable task. One way of dealing with the problem in an integral-equation approach is to employ a screened Coulomb potential. A general approach without screening requires folding of kernels of the integral equations with the Coulomb wave. A new method of folding a function with the Coulomb partial waves is presented. The partial-wave Coulomb function both in the configuration and momentum representations is written in the form of separable series. Each term of the series is represented as a product of a factor depending only on the Coulomb parameter and a function depending on the spatial variable in the configuration space and the momentum variable if the momentum representation is used. Using a trial function, the method is demonstrated to be efficient and reliable.
Zero-Point Fluctuations in the Nuclear Born-Oppenheimer Ground State
Zettili, Nouredine
The small-amplitude oscillations of rigid nuclei around the equilibrium state are described by means of the nuclear Born-Oppenheimer (NBO) method. In this limit, the method is shown to give back the random phase approximation (RPA) equations of motion. The contribution of the zero-point fluctuations to the ground state are examined, and the NBO ground state energy derived is shown to be identical to the RPA ground state energy.
Ground state properties of a Bose-Einstein condensate confined in an anharmonic external potential
Institute of Scientific and Technical Information of China (English)
Wang Deng-Long; Yan Xiao-Hong; Tang Yi
2004-01-01
In light of the interference experiment of Bose-Einstein condensates, we present an anharmonic external potential model to study ground state properties of Bose-Einstein condensates. The ground state energy and the chemical potential have been analytically obtained, which are lower than those in harmonic trap. Additionally, it is found that the anharmonic strength of the external potential has an important effect on density and velocity distributions of the ground state for the Thomas-Fermi model.
Upper Bounds on the Degeneracy of the Ground State in Quantum Field Models
Directory of Open Access Journals (Sweden)
Asao Arai
2016-01-01
Full Text Available Axiomatic abstract formulations are presented to derive upper bounds on the degeneracy of the ground state in quantum field models including massless ones. In particular, given is a sufficient condition under which the degeneracy of the ground state of the perturbed Hamiltonian is less than or equal to the degeneracy of the ground state of the unperturbed one. Applications of the abstract theory to models in quantum field theory are outlined.
Exact many-electron ground states on diamond and triangle Hubbard chains
2008-01-01
We construct exact ground states of interacting electrons on triangle and diamond Hubbard chains. The construction requires (i) a rewriting of the Hamiltonian into positive semidefinite form, (ii) the construction of a many-electron ground state of this Hamiltonian, and (iii) the proof of the uniqueness of the ground state. This approach works in any dimension, requires no integrability of the model, and only demands sufficiently many microscopic parameters in the Hamiltonian which have to fu...
Efficient wave-function matching approach for quantum transport calculations
DEFF Research Database (Denmark)
Sørensen, Hans Henrik Brandenborg; Hansen, Per Christian; Petersen, Dan Erik;
2009-01-01
The wave-function matching (WFM) technique has recently been developed for the calculation of electronic transport in quantum two-probe systems. In terms of efficiency it is comparable to the widely used Green's function approach. The WFM formalism presented so far requires the evaluation of all ...
Norris, D G; Orozco, L A; Barberis-Blostein, P; Carmichael, H J; 10.1103/PhysRevA.86.053816
2012-01-01
The spontaneous creation and persistence of ground-state coherence in an ensemble of intracavity Rb atoms has been observed as a quantum beat. Our system realizes a quantum eraser, where the detection of a first photon prepares a superposition of ground-state Zeeman sublevels, while detection of a second erases the stored information. Beats appear in the time-delayed photon-photon coincidence rate (intensity correlation function). We study the beats theoretically and experimentally as a function of system parameters, and find them remarkably robust against perturbations such as spontaneous emission. Although beats arise most simply through single-atom-mediated quantum interference, scattering pathways involving pairs of atoms interfere also in our intracavity experiment. We present a detailed model which identifies all sources of interference and accounts for experimental realities such as imperfect pre-pumping of the atomic beam, cavity birefringence, and the transit of atoms across the cavity mode.
Lower bounds for the ground-state degeneracies of frustrated systems on fractal lattices
Curado; Nobre
2000-12-01
The total number of ground states for nearest-neighbor-interaction Ising systems with frustrations, defined on hierarchical lattices, is investigated. A simple method is presented, which allows one to factorize the ground-state degeneracy, at a given hierarchy level n, in terms of contributions due to all hierarchy levels. Such a method may yield the exact ground-state degeneracy of uniformly frustrated systems, whereas it works as an approximation for randomly frustrated models. In the latter cases, it is demonstrated that such an approximation yields lower-bound estimates for the ground-state degeneracies.
Ground-State Analysis for an Exactly Solvable Coupled-Spin Hamiltonian
Directory of Open Access Journals (Sweden)
Eduardo Mattei
2013-11-01
Full Text Available We introduce a Hamiltonian for two interacting su(2 spins. We use a mean-field analysis and exact Bethe ansatz results to investigate the ground-state properties of the system in the classical limit, defined as the limit of infinite spin (or highest weight. Complementary insights are provided through investigation of the energy gap, ground-state fidelity, and ground-state entanglement, which are numerically computed for particular parameter values. Despite the simplicity of the model, a rich array of ground-state features are uncovered. Finally, we discuss how this model may be seen as an analogue of the exactly solvable p+ip pairing Hamiltonian.
Ground state solutions for asymptotically periodic Schrodinger equations with critical growth
Directory of Open Access Journals (Sweden)
Hui Zhang
2013-10-01
Full Text Available Using the Nehari manifold and the concentration compactness principle, we study the existence of ground state solutions for asymptotically periodic Schrodinger equations with critical growth.
Kawashima, Yukio; Hirao, Kimihiko
2017-02-24
We introduced two methods to correct the singularity in the calculation of long-range Hartree-Fock (HF) exchange for long-range-corrected density functional theory (LC-DFT) calculations in plane-wave basis sets. The first method introduces an auxiliary function to cancel out the singularity. The second method introduces a truncated long-range Coulomb potential, which has no singularity. We assessed the introduced methods using the LC-BLYP functional by applying it to isolated systems of naphthalene and pyridine. We first compared the total energies and the HOMO energies of the singularity-corrected and uncorrected calculations and confirmed that singularity correction is essential for LC-DFT calculations using plane-wave basis sets. The LC-DFT calculation results converged rapidly with respect to the cell size as the other functionals, and their results were in good agreement with the calculated results obtained using Gaussian basis sets. LC-DFT succeeded in obtaining accurate orbital energies and excitation energies. We next applied LC-DFT with singularity correction methods to the electronic structure calculations of the extended systems, Si and SiC. We confirmed that singularity correction is important for calculations of extended systems as well. The calculation results of the valence and conduction bands by LC-BLYP showed good convergence with respect to the number of k points sampled. The introduced methods succeeded in overcoming the singularity problem in HF exchange calculation. We investigated the effect of the singularity correction on the excitation state calculation and found that careful treatment of the singularities is required compared to ground-state calculations. We finally examined the excitonic effect on the band gap of the extended systems. We calculated the excitation energies to the first excited state of the extended systems using a supercell model at the Γ point and found that the excitonic binding energy, supposed to be small for
Analytic Beyond-Mean-Field BEC Wave Functions
Dunn, Martin; Laing, W. Blake; Watson, Deborah K.; Loeser, John G.
2006-05-01
We present analytic N-body beyond-mean-field wave functions for Bose-Einstein condensates. This extends our previous beyond-mean-field energy calculations to the substantially more difficult problem of determining correlated N-body wave functions for a confined system. The tools used to achieve this have been carefully chosen to maximize the use of symmetry and minimize the dependence on numerical computation. We handle the huge number of interactions when N is large (˜N^2/2 two-body interactions) by bringing together three theoretical methods. These are dimensional perturbation theory, the FG method of Wilson et al, and the group theory of the symmetric group. The wave function is then used to derive the density profile of a condensate in a cylindrical trap.This method makes no assumptions regarding the form or strength of the interactions and is applicable to both small-N and large-N systems.
Laws of Nature and the Reality of the Wave Function
Dorato, Mauro
2015-01-01
In this paper I review three different positions on the wave function, namely: nomological realism, dispositionalism, and configuration space realism by regarding as essential their capacity to account for the world of our experience. I conclude that the first two positions are committed to regard the wave function as an abstract entity. The third position will be shown to be a merely speculative attempt to derive a primitive ontology from a reified mathematical space. Without entering any discussion about nominalism, I conclude that an elimination of abstract entities from one's ontology commits one to instrumentalism about the wave function, a position that therefore is not as unmotivated as it has seemed to be to many philosophers.
Propagation of Vortex Electron Wave Functions in a Magnetic Field
Gallatin, Gregg M
2012-01-01
The physics of coherent beams of photons carrying axial orbital angular momentum (OAM) is well understood and such beams, sometimes known as vortex beams, have found applications in optics and microscopy. Recently electron beams carrying very large values of axial OAM have been generated. In the absence of coupling to an external electromagnetic field the propagation of such vortex electron beams is virtually identical mathematically to that of vortex photon beams propagating in a medium with a homogeneous index of refraction. But when coupled to an external electromagnetic field the propagation of vortex electron beams is distinctly different from photons. Here we use the exact path integral solution to Schrodingers equation to examine the time evolution of an electron wave function carrying axial OAM. Interestingly we find that the nonzero OAM wave function can be obtained from the zero OAM wave function, in the case considered here, simply by multipling it by an appropriate time and position dependent pref...
The nucleon wave function in light-front dynamics
Karmanov, V A
1998-01-01
The general spin structure of the relativistic nucleon wave function in the $3q$-model is found. It contains 16 spin components, in contrast to 8 ones known previously, since in a many-body system the parity conservation does not reduce the number of the components. The explicitly covariant form of the wave function automatically takes into account the relativistic spin rotations, without introducing any Melosh rotation matrices. It also reduces the calculations to the standard routine of the Dirac matrices and of the trace techniques. In examples of the proton magnetic moment and of the axial nucleon form factor, with a particular wave function, we reproduce the results of the standard approach. Calculations beyond the standard assumptions give different results.
A unified intrinsic functional expansion theory for solitary waves
Institute of Scientific and Technical Information of China (English)
Theodore Yaotsu Wu; John Kao; Jin E. Zhang
2005-01-01
A new theory is developed here for evaluating solitary waves on water, with results of high accuracy uniformly valid for waves of all heights, from the highest wave with a corner crest of 120° down to very low ones of diminishing height. Solutions are sought for the Euler model by employing a unified expansion of the logarithmic hodograph in terms of a set of intrinsic component functions analytically determined to represent all the intrinsic properties of the wave entity from the wave crest to its outskirts. The unknown coefficients in the expansion are determined by minimization of the mean-square error of the solution, with the minimization optimized so as to take as few terms as needed to attain results as high in accuracy as attainable. In this regard, Stokes's formula, F2μπ = tanμπ, relating the wave speed (the Froude number F) and the logarithmic decrement μ of its wave field in the outskirt, is generalized to establish a new criterion requiring (for minimizing solution error) the functional expansion to contain a finite power series in M terms of Stokes's basic term (singular inμ), such that 2Mμ is just somewhat beyond unity, i.e. 2Mμ (~-) 1. This fundamental criterion is fully validated by solutions for waves Dedicated to Zhemin Zheng for celebration of his Eightieth Anniversary It gives us a great pleasure to dedicate this study to Prof. Zhemin Zheng and join our distinguished colleagues and friends for the jubilant celebration of his Eightieth Anniversary. Warmest tribute is due from us, as from many others unlimited by borders and boundaries, for his contributions of great significance to science, engineering science and engineering, his tremendous influence as a source of inspiration and unerring guide to countless workers in the field, his admirable leadership in fostering the Institute of Mechanics of world renown, as well as for his untiring endeavor in promoting international interaction and cooperation between academies of various nations
Period functions for Maass wave forms and cohomology
Bruggeman, R; Zagier, D; Bruggeman, R W; Zagier, D
2015-01-01
The authors construct explicit isomorphisms between spaces of Maass wave forms and cohomology groups for discrete cofinite groups \\Gamma\\subset\\mathrm{PSL}_2({\\mathbb{R}}). In the case that \\Gamma is the modular group \\mathrm{PSL}_2({\\mathbb{Z}}) this gives a cohomological framework for the results in Period functions for Maass wave forms. I, of J. Lewis and D. Zagier in Ann. Math. 153 (2001), 191-258, where a bijection was given between cuspidal Maass forms and period functions. The authors introduce the concepts of mixed parabolic cohomology group and semi-analytic vectors in principal serie
Peterson, Michael
2009-03-01
The fractional quantum Hall effect (FQHE) in the second orbital Landau level at even-denominator filling factor 5/2 remains mysterious and is currently motivating many scientists not only because of its connection to a possible implementation of a fault tolerant topological quantum computer (Das Sarma et al., PRL 94, 166802(2005)). In this work, we theoretically consider the effect of the quasi-two-dimensional nature of the experimental fractional quantum Hall systems on a number of FQHE states in the lowest three orbital Landau levels. Our primary result is that the finite width of the quasi-two-dimensional systems produce a physical environment sufficient to stabilize the Moore-Read Pfaffian state thought to describe the FQHE at filling factor 5/2. This conclusion is based on exact calculations performed in the spherical and torus geometries, studying wave function overlap and ground state degeneracy. Furthermore, our results open the possibility of creating optimal experimental systems where the 5/2 FQHE state would more likely be described by the Moore-Read Pfaffian. We also discuss the role of the three-body interaction Hamiltonian that produces the Moore-Read Pfaffian as an exact ground state and particle-hole symmetry in the FQHE at 5/2. We acknowledge support from Microsoft Project Q. Work done in collaboration with Sankar Das Sarma, Thierry Jolicoeur, and Kwon Park.
Ground state structures and properties of Si3H ( = 1–6) clusters
Indian Academy of Sciences (India)
D Balamurugan; R Prasad
2003-01-01
The ground state structures and properties of Si3H (1 ≤ ≤ 6) clusters have been calculated using Car–Parrinello molecular dynamics with simulated annealing and steepest descent optimization methods. We have studied cohesive energy per particle and first excited electronic level gap of the clusters as a function of hydrogenation. Hydrogenation is done till all dangling bonds of silicon are saturated. Our results show that over coordination of hydrogen is favoured in Si3H clusters and the geometry of Si3 cluster does not change due to hydrogenation. Cohesive energy per particle and first excited electronic level gap study of the clusters show that Si3H6 cluster is most stable and Si3H3 cluster is most unstable among the clusters considered here.
Ground State Energy of Unitary Fermion Gas with the Thomson Problem Approach
Institute of Scientific and Technical Information of China (English)
CHEN Ji-Sheng
2007-01-01
The dimensionless universal coefficient § defines the ratio of the unitary fermions energy density to that for the ideal non-interacting ones in the non-relativistic limit with T = 0. The classical Thomson problem is taken as a nonperturbative quantum many-body arm to address the ground state energy including the Iow energy nonlinear quantum fluctuation/correlation effects. With the relativistic Dirac continuum field theory formalism, the concise expression for the energy density functional of the strongly interacting limit fermions at both finite temperature and density is obtained. Analytically, the universal factor is calculated to be § = 4/9. The energy gap is △ = 5/18 k2f/(2m).
Ground state energy of excitons in quantum dot treated variationally via Hylleraas-like wavefunction
Institute of Scientific and Technical Information of China (English)
S.(S)akiro(g)lu; (U). Do(g)an; A. Yildlz; K. Akgüng(o)r; H. Epik; Y. Ergün; H. San; (I).S(o)kmen
2009-01-01
In this work,the effects of quantum confinement on the ground state energy of a correlated electron-hole pair in a spherical and in a disc-like quantum dot have been investigated as a function of quantum dot size.Under parabolic confinement potential and within effective mass approximation Ritz's variational method is applied to Hylleraas-like trial wavefunction.An efficient method for reducing the main effort of the calculation of terms like rkeh exp(-λreh)is introduced.The main contribution of the present work is the introduction of integral transforms which provide the calculation of expectation value of energy and the related matrix elements to be done analytically over single-particle coordinates instead of Hylleraas coordinates.
Loco, Daniele; Polack, Étienne; Caprasecca, Stefano; Lagardère, Louis; Lipparini, Filippo; Piquemal, Jean-Philip; Mennucci, Benedetta
2016-08-09
A fully polarizable implementation of the hybrid quantum mechanics/molecular mechanics approach is presented, where the classical environment is described through the AMOEBA polarizable force field. A variational formalism, offering a self-consistent relaxation of both the MM induced dipoles and the QM electronic density, is used for ground state energies and extended to electronic excitations in the framework of time-dependent density functional theory combined with a state specific response of the classical part. An application to the calculation of the solvatochromism of the pyridinium N-phenolate betaine dye used to define the solvent ET(30) scale is presented. The results show that the QM/AMOEBA model not only properly describes specific and bulk effects in the ground state but it also correctly responds to the large change in the solute electronic charge distribution upon excitation.
The 75As(n,2n) Cross Sections into the 74As Isomer and Ground State
Energy Technology Data Exchange (ETDEWEB)
Younes, W; Garrett, P E; Becker, J A; Bernstein, L A; Ormand, W E; Dietrich, F S; Nelson, R O; Devlin, M; Fotiades, N
2003-06-30
The {sup 75}As(n, 2n) cross section for the population of the T{sub 1/2} = 26.8-ns isomer at E{sub x} = 259.3 keV in {sup 74}As has been measured as a function of incident neutron energy, from threshold to E{sub n} = 20 MeV. The cross section was measured using the GEANIE spectrometer at LANSCE/WNR. For convenience, the {sup 75}As(n, 2n) population cross section for the {sup 74}As ground state has been deduced as the difference between the previously-known (n, 2n) reaction cross section and the newly measured {sup 75}As(n, 2n){sup 74}As{sup m} cross section. The (n, 2n) reaction, ground-state, and isomer population cross sections are tabulated in this paper.
Directory of Open Access Journals (Sweden)
Ho-Ming Su
Full Text Available The P wave parameters measured by 12-lead electrocardiogram (ECG are commonly used as noninvasive tools to assess for left atrial enlargement. There are limited studies to evaluate whether P wave parameters are independently associated with decline in renal function. Accordingly, the aim of this study is to assess whether P wave parameters are independently associated with progression to renal end point of ≥25% decline in estimated glomerular filtration rate (eGFR. This longitudinal study included 166 patients. The renal end point was defined as ≥25% decline in eGFR. We measured two ECG P wave parameters corrected by heart rate, i.e. corrected P wave dispersion (PWdisperC and corrected P wave maximum duration (PWdurMaxC. Heart function and structure were measured from echocardiography. Clinical data, P wave parameters, and echocardiographic measurements were compared and analyzed. Forty-three patients (25.9% reached renal end point. Kaplan-Meier curves for renal end point-free survival showed PWdisperC > median (63.0 ms (log-rank P = 0.004 and PWdurMaxC > median (117.9 ms (log-rank P<0.001 were associated with progression to renal end point. Multivariate forward Cox-regression analysis identified increased PWdisperC (hazard ratio [HR], 1.024; P = 0.001 and PWdurMaxC (HR, 1.029; P = 0.001 were independently associated with progression to renal end point. Our results demonstrate that increased PWdisperC and PWdurMaxC were independently associated with progression to renal end point. Screening patients by means of PWdisperC and PWdurMaxC on 12 lead ECG may help identify a high risk group of rapid renal function decline.
Ground state solutions for nonlinear fractional Schrodinger equations involving critical growth
Directory of Open Access Journals (Sweden)
Hua Jin
2017-03-01
Full Text Available This article concerns the ground state solutions of nonlinear fractional Schrodinger equations involving critical growth. We obtain the existence of ground state solutions when the potential is not a constant and not radial. We do not use the Ambrosetti-Rabinowitz condition, or the monotonicity condition on the nonlinearity.
Ground state correlations and mean field using the exp(S) method
Heisenberg, J H; Heisenberg, Jochen H.; Mihaila, Bogdan
1999-01-01
This document gives a detailed account of the terms used in the computation of the ground state mean field and the ground state correlations. While the general approach to this description is given in a separate paper (nucl-th/9802029) we give here the explicite expressions used.
The study of magnetization of the spin systm in the ground state
Institute of Scientific and Technical Information of China (English)
Jiang Wei; Wang Xi-Kun; Zhao Qiang
2006-01-01
Within the framework of the effective-field theory with self-spin correlations and the differential operator technique,the ground state magnetizations of the biaxial crystal field spin system on the honeycomb lattices have been studied.The influences of the biaxial crystal field on the magnetization in the ground state have been investigated in detail.
Improved lower bounds on the ground-state entropy of the antiferromagnetic Potts model.
Chang, Shu-Chiuan; Shrock, Robert
2015-05-01
We present generalized methods for calculating lower bounds on the ground-state entropy per site, S(0), or equivalently, the ground-state degeneracy per site, W=e(S(0)/k(B)), of the antiferromagnetic Potts model. We use these methods to derive improved lower bounds on W for several lattices.
On the asymptotic evolution of finite energy Airy wave functions.
Chamorro-Posada, P; Sánchez-Curto, J; Aceves, A B; McDonald, G S
2015-06-15
In general, there is an inverse relation between the degree of localization of a wave function of a certain class and its transform representation dictated by the scaling property of the Fourier transform. We report that in the case of finite energy Airy wave packets a simultaneous increase in their localization in the direct and transform domains can be obtained as the apodization parameter is varied. One consequence of this is that the far-field diffraction rate of a finite energy Airy beam decreases as the beam localization at the launch plane increases. We analyze the asymptotic properties of finite energy Airy wave functions using the stationary phase method. We obtain one dominant contribution to the long-term evolution that admits a Gaussian-like approximation, which displays the expected reduction of its broadening rate as the input localization is increased.
Zethrenes, Extended p -Quinodimethanes, and Periacenes with a Singlet Biradical Ground State
Sun, Zhe
2014-08-19
ConspectusResearchers have studied polycyclic aromatic hydrocarbons (PAHs) for more than 100 years, and most PAHs in the neutral state reported so far have a closed-shell electronic configuration in the ground state. However, recent studies have revealed that specific types of polycyclic hydrocarbons (PHs) could have a singlet biradical ground state and exhibit unique electronic, optical, and magnetic activities. With the appropriate stabilization, these new compounds could prove useful as molecular materials for organic electronics, nonlinear optics, organic spintronics, organic photovoltaics, and energy storage devices. However, before researchers can use these materials to design new devices, they need better methods to synthesize these molecules and a better understanding of the fundamental relationship between the structure and biradical character of these compounds and their physical properties. Their biradical character makes these compounds difficult to synthesize. These compounds are also challenging to physically characterize and require the use of various experimental techniques and theoretic methods to comprehensively describe their unique properties.In this Account, we will discuss the chemistry and physics of three types of PHs with a significant singlet biradical character, primarily developed in our group. These structures are zethrenes, Z-shaped quinoidal hydrocarbons; hydrocarbons that include a proaromatic extended p-quinodimethane unit; and periacenes, acenes fused in a peri-Arrangement. We used a variety of synthetic methods to prepare these compounds and stabilized them using both thermodynamic and kinetic approaches. We probed their ground-state structures by electronic absorption, NMR, ESR, SQUID, Raman spectroscopy, and X-ray crystallography and also performed density functional theory calculations. We investigated the physical properties of these PHs using various experimental methods such as one-photon absorption, two-photon absorption
Nogawa, Tomoaki
2012-05-22
We investigate the ground state of the irrationally frustrated Josephson junction array with a controlling anisotropy parameter λ that is the ratio of the longitudinal Josephson coupling to the transverse one. We find that the ground state has one-dimensional periodicity whose reciprocal lattice vector depends on λ and is incommensurate with the substrate lattice. Approaching the isotropic point λ=1, the so-called hull function of the ground state exhibits analyticity breaking similar to the Aubry transition in the Frenkel-Kontorova model. We find a scaling law for the harmonic spectrum of the hull functions, which suggests the existence of a characteristic length scale diverging at the isotropic point. This critical behavior is directly connected to the jamming transition previously observed in the current-voltage characteristics by a numerical simulation. On top of the ground state there is a gapless continuous band of metastable states, which exhibit the same critical behavior as the ground state. © 2012 American Physical Society.
Local reversibility and entanglement structure of many-body ground states
Kuwahara, Tomotaka; Amico, Luigi; Vedral, Vlatko
2015-01-01
The low-temperature physics of quantum many-body systems is largely governed by the structure of their ground states. Minimizing the energy of local interactions, ground states often reflect strong properties of locality such as the area law for entanglement entropy and the exponential decay of correlations between spatially separated observables. In this letter we present a novel characterization of locality in quantum states, which we call `local reversibility'. It characterizes the type of operations that are needed to reverse the action of a general disturbance on the state. We prove that unique ground states of gapped local Hamiltonian are locally reversible. This way, we identify new fundamental features of many-body ground states, which cannot be derived from the aforementioned properties. We use local reversibility to distinguish between states enjoying microscopic and macroscopic quantum phenomena. To demonstrate the potential of our approach, we prove specific properties of ground states, which are ...
How close can we get waves to wave functions, including potential?
Faletič, Sergej
2016-05-01
In the following article we show that mechanical waves on a braced string can have the same shapes as important wave functions in introductory quantum mechanics. A braced string is a string with additional transversal springs that serve as external "potential". The aim is not to suggest teaching quantum mechanics with these analogies. Instead, the aim is to provide students with some additional relevant experience in wave mechanics before they are introduced to quantum mechanics. We show how this experience can be used in a constructivist sense as the basis for building quantum concepts. We consider energy transfer along such string and show that penetration of a wave into a region with high "potential" is not unexpected. We also consider energy transfer between two such strings and show that it can appear point-like even though the wave is an extended object. We also suggest that applying quantization of energy transfer to wave phenomena can explain some of the more difficult to accept features of quantum mechanics.
A Green's function method for surface acoustic waves in functionally graded materials.
Matsuda, Osamu; Glorieux, Christ
2007-06-01
Acoustic wave propagation in anisotropic media with one-dimensional inhomogeneity is discussed. Using a Green's function approach, the wave equation with inhomogeneous variation of elastic property and mass density is transformed into an integral equation, which is then solved numerically. The method is applied to find the dispersion relation of surface acoustic waves for a medium with continuously or discontinuously varying elastic property and mass density profiles.
Dark energy and normalization of the cosmological wave function
Energy Technology Data Exchange (ETDEWEB)
Huang, Peng [Sun Yat-Sen University, School of Astronomy and Space Science, Guangzhou (China); Huang, Yue; Li, Nan [Institute of Theoretical Physics, Chinese Academy of Sciences, State Key Laboratory of Theoretical Physics, Beijing (China); Kavli Institute for Theoretical Physics China, Chinese Academy of Sciences, Beijing (China); Li, Miao [Sun Yat-Sen University, School of Astronomy and Space Science, Guangzhou (China); Institute of Theoretical Physics, Chinese Academy of Sciences, State Key Laboratory of Theoretical Physics, Beijing (China)
2016-08-15
Dark energy is investigated from the perspective of quantum cosmology. It is found that, together with an appropriate normal ordering factor q, only when there is dark energy can the cosmological wave function be normalized. This interesting observation may require further attention. (orig.)
Wave function of the de Sitter-Schwarzchild universe
Energy Technology Data Exchange (ETDEWEB)
Nagai, Hiroyuki (Kyushu Industrial Univ., Fukuoka (Japan))
1989-08-01
The wave function of the universe with an O(3) invariant inhomogeneous 3-space metric, called the de Sitter-Schwarzschild metric, is calculated under an appropriate boundary condition in the semi-classical approximation. The calculated result suggests that the quantum birth of the inhomogeneous universe cannot be disregarded. (author).
Precanonical Quantization and the Schr\\"odinger Wave Functional Revisited
Kanatchikov, I V
2011-01-01
We address the long-standing issue of the relation between the Schr\\"odinger functional representation in quantum field theory and the approach of precanonical field quantization which requires neither a distinguished time variable nor infinite-dimensional spaces of field configurations. The functional Schr\\"odinger equation is derived in the limiting case \\varkappa \\rightarrow \\delta(0) from the Dirac-like covariant generalization of the Schr\\"odinger equation within the precanonical quantization approach, where the constant \\varkappa of the dimension of the inverse spatial volume naturally appears on dimensional grounds. An explicit expression of the Schr\\"odinger wave functional as a continuous product of precanonical wave functions on the finite-dimensional covariant configuration space of the field and space-time variables is obtained.
Linear density response function in the projector augmented wave method
DEFF Research Database (Denmark)
Yan, Jun; Mortensen, Jens Jørgen; Jacobsen, Karsten Wedel;
2011-01-01
We present an implementation of the linear density response function within the projector-augmented wave method with applications to the linear optical and dielectric properties of both solids, surfaces, and interfaces. The response function is represented in plane waves while the single......-particle eigenstates can be expanded on a real space grid or in atomic-orbital basis for increased efficiency. The exchange-correlation kernel is treated at the level of the adiabatic local density approximation (ALDA) and crystal local field effects are included. The calculated static and dynamical dielectric...... functions of Si, C, SiC, AlP, and GaAs compare well with previous calculations. While optical properties of semiconductors, in particular excitonic effects, are generally not well described by ALDA, we obtain excellent agreement with experiments for the surface loss function of graphene and the Mg(0001...
Microstructure Functional Devices-Effectively Manipulate Terahertz Waves
Institute of Scientific and Technical Information of China (English)
Fei Fan; Ji-Ning Li; Sai Chen; Sheng-Jiang Chang
2014-01-01
Terahertz (THz) technology promises important applications including imaging, spectroscopy, and communications. However, one of limitations at present for advancing THz applications is the lack of efficient devices to manipulate THz waves. Here, our recent important progresses in THz functional devices based on artificial microstructures, such as photonic crystal, metamaterial, and plasmonic structures, have been reviewed in this paper, involving the THz modulator, isolator, and sensor. These THz microstructure functional devices exhibit great promising potential in THz application systems.
Explicitly correlated wave function for a boron atom
Puchalski, Mariusz; Pachucki, Krzysztof
2015-01-01
We present results of high-precision calculations for a boron atom's properties using wave functions expanded in the explicitly correlated Gaussian basis. We demonstrate that the well-optimized 8192 basis functions enable a determination of energy levels, ionization potential, and fine and hyperfine splittings in atomic transitions with nearly parts per million precision. The results open a window to a spectroscopic determination of nuclear properties of boron including the charge radius of the proton halo in the $^8$B nucleus.
Rossby Wave Green's Functions in an Azimuthal Wind
Webb, G M; Hu, Q
2015-01-01
Green's functions for Rossby waves in an azimuthal wind are obtained, in which the stream-function $\\psi$ depends on $r$, $\\phi$ and $t$, where $r$ is cylindrical radius and $\\phi$ is the azimuthal angle in the $\\beta$-plane relative to the easterly direction, in which the $x$-axis points east and the $y$-axis points north. The Rossby wave Green's function with no wind is obtained using Fourier transform methods, and is related to the previously known Green's function obtained for this case, which has a different but equivalent form to the Green's function obtained in the present paper. We emphasize the role of the wave eikonal solution, which plays an important role in the form of the solution. The corresponding Green's function for a rotating wind with azimuthal wind velocity ${\\bf u}=\\Omega r{\\bf e}_\\phi$ ($\\Omega=$const.) is also obtained by Fourier methods, in which the advective rotation operator in position space is transformed to a rotation operator in ${\\bf k}$ transform space. The finite Rossby defo...
Li, Yuan
2012-09-12
Polycyclic aromatic hydrocarbons with an open-shell singlet biradical ground state are of fundamental interest and have potential applications in materials science. However, the inherent high reactivity makes their synthesis and characterization very challenging. In this work, a convenient synthetic route was developed to synthesize two kinetically blocked heptazethrene (HZ-TIPS) and octazethrene (OZ-TIPS) compounds with good stability. Their ground-state electronic structures were systematically investigated by a combination of different experimental methods, including steady-state and transient absorption spectroscopy, variable temperature NMR, electron spin resonance (ESR), superconducting quantum interfering device (SQUID), FT Raman, and X-ray crystallographic analysis, assisted by unrestricted symmetry-broken density functional theory (DFT) calculations. All these demonstrated that the heptazethrene derivative HZ-TIPS has a closed-shell ground state while its octazethrene analogue OZ-TIPS with a smaller energy gap exists as an open-shell singlet biradical with a large measured biradical character (y = 0.56). Large two-photon absorption (TPA) cross sections (σ(2)) were determined for HZ-TIPS (σ(2)max = 920 GM at 1250 nm) and OZ-TIPS (σ(2)max = 1200 GM at 1250 nm). In addition, HZ-TIPS and OZ-TIPS show a closely stacked 1D polymer chain in single crystals. © 2012 American Chemical Society.
Evaluation techniques for Gutzwiller wave functions in finite dimensions
Kaczmarczyk, Jan; Schickling, Tobias; Bünemann, Jörg
2015-09-01
We give a comprehensive introduction into a diagrammatic method that allows for the evaluation of Gutzwiller wave functions in finite spatial dimensions. We discuss in detail some numerical schemes that turned out to be useful in the real-space evaluation of the diagrams. The method is applied to the problem of d-wave superconductivity in a two-dimensional single-band Hubbard model. Here, we discuss in particular the role of long-range contributions in our diagrammatic expansion. We further reconsider our previous analysis on the kinetic energy gain in the superconducting state.
Properties of the {sup 7}He ground state from {sup 8}He neutron knockout
Energy Technology Data Exchange (ETDEWEB)
Aksyutina, Yu. [GSI Helmholtzzentrum fuer Schwerionenforschung GmbH, D-64291 Darmstadt (Germany); Fundamental Fysik, Chalmers Tekniska Hoegskola, S-412 96 Goeteborg (Sweden); Johansson, H.T. [Fundamental Fysik, Chalmers Tekniska Hoegskola, S-412 96 Goeteborg (Sweden); Aumann, T.; Boretzky, K. [GSI Helmholtzzentrum fuer Schwerionenforschung GmbH, D-64291 Darmstadt (Germany); Borge, M.J.G. [Instituto Estructura de la Materia, CSIC, E-28006 Madrid (Spain); Chatillon, A. [GSI Helmholtzzentrum fuer Schwerionenforschung GmbH, D-64291 Darmstadt (Germany); Chulkov, L.V. [GSI Helmholtzzentrum fuer Schwerionenforschung GmbH, D-64291 Darmstadt (Germany); Kurchatov Institute, RU-123182 Moscow (Russian Federation); Cortina-Gil, D. [GSI Helmholtzzentrum fuer Schwerionenforschung GmbH, D-64291 Darmstadt (Germany); University of Santiago de Compostela, 15706 Santiago de Compostela (Spain); Pramanik, U. Datta [Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700064 (India); Emling, H. [GSI Helmholtzzentrum fuer Schwerionenforschung GmbH, D-64291 Darmstadt (Germany); Forssen, C. [Fundamental Fysik, Chalmers Tekniska Hoegskola, S-412 96 Goeteborg (Sweden); Fynbo, H.O.U. [Department of Physics and Astronomy, University of Aarhus, DK-8000 Aarhus C (Denmark); Geissel, H.; Ickert, G. [GSI Helmholtzzentrum fuer Schwerionenforschung GmbH, D-64291 Darmstadt (Germany); Jonson, B. [Fundamental Fysik, Chalmers Tekniska Hoegskola, S-412 96 Goeteborg (Sweden)], E-mail: bjn@fy.chalmers.se; Kulessa, R. [Instytut Fizyki, Universytet Jagiellonski, PL-30-059 Krakow (Poland); Langer, C. [GSI Helmholtzzentrum fuer Schwerionenforschung GmbH, D-64291 Darmstadt (Germany); Lantz, M. [Fundamental Fysik, Chalmers Tekniska Hoegskola, S-412 96 Goeteborg (Sweden); LeBleis, T. [GSI Helmholtzzentrum fuer Schwerionenforschung GmbH, D-64291 Darmstadt (Germany); Lindahl, A.O. [Institutionen foer Fysik, University of Gothenburg, S-412 96 Goeteborg (Sweden)] (and others)
2009-08-24
The unbound nucleus {sup 7}He, produced in neutron-knockout reactions with a 240 MeV/u {sup 8}He beam in a liquid-hydrogen target, has been studied in an experiment at the ALADIN-LAND setup at GSI. From an R-matrix analysis the resonance parameters for {sup 7}He as well as the spectroscopic factor for the {sup 6}He(0{sup +}) + n configuration in its ground-state have been obtained. The spectroscopic factor is 0.61 confirming that {sup 7}He is not a pure single-particle state. An analysis of {sup 5}He data from neutron-knockout reactions of {sup 6}He in a carbon target reveals the presence of an s-wave component at low energies in the {alpha}+n relative energy spectrum. A possible low-lying exited state in {sup 7}He observed in neutron knockout data from {sup 8}He in a carbon target and tentatively interpreted as a I{sup {pi}}=1/2{sup -} state, could not be observed in the present experiment. Possible explanations of the shape difference between the {sup 7}He resonance obtained in the two knockout reactions are discussed in terms of target-dependence or different reaction mechanisms at relativistic energies.
Randall-Sundrum brane Universe as a ground state for Chern-Simons gravity
Cordonier-Tello, Fabrizio; Izaurieta, Fernando; Mella, Patricio; Rodríguez, Eduardo
2016-12-01
In stark contrast with the three-dimensional case, higher-dimensional Chern-Simons (CS) theories can have non-topological, propagating degrees of freedom. Finding those vacua that allow for the propagation of linear perturbations, however, proves to be surprisingly challenging. The simplest solutions are somehow ‘hyper-stable’, preventing the construction of realistic, four-dimensional physical models. Here, we show that a Randall-Sundrum (RS) brane Universe can be regarded as a vacuum solution of CS gravity in five-dimensional spacetime, with non vanishing torsion along the dimension perpendicular to the brane. Linearized perturbations around this solution not only exist, but behave as standard gravitational waves on a four-dimensional Minkowski background. In the non-perturbative regime, the solution leads to a four-dimensional ‘cosmological function’ {{Λ }}(x) which depends on the Euler density of the brane. Interestingly, the fact that the solution admits nontrivial linear perturbations seems to be related to an often neglected property of the RS spacetime: that it is a group manifold, or, more precisely, two identical group manifolds glued together along the brane. The gravitational theory is then built around this fact, adding the Lorentz generators and one scalar generator needed to close the algebra. In this way, a conjecture emerges: a spacetime that is also a group manifold can be regarded as the ground state of a CS theory for an appropriate Lie algebra.
Directory of Open Access Journals (Sweden)
Tobias Hacker
2012-04-01
Full Text Available The integral boundary layer system (IBL with spatially periodic coefficients arises as a long wave approximation for the flow of a viscous incompressible fluid down a wavy inclined plane. The Nusselt-like stationary solution of the IBL is linearly at best marginally stable; i.e., it has essential spectrum at least up to the imaginary axis. Nevertheless, in this stable case we show that localized perturbations of the ground state decay in a self-similar way. The proof uses the renormalization group method in Bloch variables and the fact that in the stable case the Burgers equation is the amplitude equation for long waves of small amplitude in the IBL. It is the first time that such a proof is given for a quasilinear PDE with spatially periodic coefficients.
Wind-Wave Model with an Optimized Source Function
Polnikov, Vladislav
2010-01-01
On the basis of the author's earlier results, a new source function for a numerical wind-wave model optimized by the criterion of accuracy and speed of calculation is substantiated. The proposed source function includes (a) an optimized version of the discrete interaction approximation for parametrization of the nonlinear evolution mechanism, (b) a generalized empirical form of the input term modified by adding a special block of the dynamic boundary layer of the atmosphere, and (c) a dissipation term quadratic in the wave spectrum. Particular attention is given to a theoretical substantiation of the least investigated dissipation term. The advantages of the proposed source function are discussed by its comparison to the analogues used in the widespread models of the third generation WAM and WAVEWATCH. At the initial stage of assessing the merits of the proposed model, the results of its testing by the system of academic tests are presented. In the course of testing, some principals of this procedure are form...
Ground-state characterizations of systems predicted to exhibit L11 or L13 crystal structures
Nelson, Lance J.; Hart, Gus L. W.; Curtarolo, Stefano
2012-02-01
Despite their geometric simplicity, the crystal structures L11 (CuPt) and L13 (CdPt3) do not appear as ground states experimentally, except in Cu-Pt. We investigate the possibility that these phases are ground states in other binary intermetallic systems, but overlooked experimentally. Via the synergy between high-throughput and cluster-expansion computational methods, we conduct a thorough search for systems that may exhibit these phases and calculate order-disorder transition temperatures when they are predicted. High-throughput calculations predict L11 ground states in the systems Ag-Pd, Ag-Pt, Cu-Pt, Pd-Pt, Li-Pd, Li-Pt, and L13 ground states in the systems Cd-Pt, Cu-Pt, Pd-Pt, Li-Pd, Li-Pt. Cluster expansions confirm the appearance of these ground states in some cases. In the other cases, cluster expansion predicts unsuspected derivative superstructures as ground states. The order-disorder transition temperatures for all L11/L13 ground states were found to be sufficiently high that their physical manifestation may be possible.
Electronic ground state OH(X) radical in a low-temperature atmospheric pressure plasma jet
Fuh, Che A.; Clark, Shane M.; Wu, Wei; Wang, Chuji
2016-10-01
The wide applicability of atmospheric pressure plasma jets in biomedicine stems from the presence of reactive nitrogen and oxygen species generated in these plasma jets. Knowing the absolute concentration of these reactive species is of utmost importance as it is critical, along with the particle flux obtained from the plasma feed gas flow rate to ensure that the correct dosage is applied during applications. In this study, we investigate and report the ground state OH(X) number density acquired using cavity ringdown spectroscopy, along the propagation axis (z-axis) of a cold atmospheric pressure helium plasma plume. The jet was generated by a repetitively pulsed mono-polar square wave of duration 1 μs running at a frequency of 9.9 kHz. The voltage supplied was 6.5 kV with the helium flow rate fixed at 3.6 standard liters per minute. The rotational and vibrational temperatures are simulated from the second positive system of nitrogen, N 2(C3πu-B3πg) , with the rotational temperature being spatially constant at 300 K along the propagation axis of the atmospheric pressure plasma jet while the vibrational temperature is 3620 K at the beginning of the plume and is observed to decrease downstream. The OH(A) emission intensity obtained via optical emission spectroscopy was observed to decrease downstream of the plasma jet. The OH(X) number density along the propagation axis was initially 2.2 × 1013 molecules cm-3 before increasing to a peak value of 2.4 × 1013 molecules cm-3, from which the number density was observed to decrease to 2.2 × 1013 molecules cm-3 downstream of the plasma jet. The total OH(A, X) in the plasma jet remained relatively constant along the propagation axis of the plasma jet before falling off at the tip of the jet. The increase in vibrational temperature downstream and the simultaneous measurements of both the excited state OH(A) and the ground state OH(X) reported in this study provide insights into the formation and consumption of this
A remark on ground state of boundary Izergin-Korepin model
Kojima, Takeo
2011-01-01
We study the ground state of the boundary Izergin-Korepin model. The boundary Izergin-Korepin model is defined by so-called $R$-matrix and $K$-matrix for $U_q(A_2^{(2)})$ which satisfy Yang-Baxter equation and boundary Yang-Baxter equation respectively. The ground state associated with identity $K$-matrix $K(z)=id$ was constructed in earlier study [Yang and Zhang, Nucl.Phys.B596,495-(2001)]. We construct the free field realization of the ground state associated with nontrivial diagonal $K$-matrix.
Characterization of ground state entanglement by single-qubit operations and excitation energies
Giampaolo, S M; Illuminati, F; Verrucchi, P; Giampaolo, Salvatore M.; Illuminati, Fabrizio; Siena, Silvio De; Verrucchi, Paola
2006-01-01
We consider single-qubit unitary operations and study the associated excitation energies above the ground state of interacting quantum spins. We prove that there exists a unique operation such that the vanishing of the corresponding excitation energy determines a necessary and sufficient condition for the separability of the ground state. We show that the energy difference associated to factorization exhibits a monotonic behavior with the one-tangle and the entropy of entanglement, including non analiticity at quantum critical points. The single-qubit excitation energy thus provides an independent, directly observable characterization of ground state entanglement, and a simple relation connecting two universal physical resources, energy and nonlocal quantum correlations.
Stevenson, I C; Chen, Y P; Elliott, D S
2016-01-01
We report a newly observed photoassociation resonance in $^7$Li-$^{85}$Rb, a mixed $2(1) - 4(1)$ excited state, that spontaneously decays to the rovibronic ground state. This resonance between ultracold Li and Rb is the strongest ground state molecule-forming photoassociation line observed in LiRb, and forms deeply bound $X \\: ^1\\Sigma^+$ molecules in large numbers. The production rate of the $v=0 \\ J=0$ rovibrational ground state is $\\sim 1.5 \\times 10^{4}$ molecules/s.
Configuration interaction wave functions: A seniority number approach
Energy Technology Data Exchange (ETDEWEB)
Alcoba, Diego R. [Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and Instituto de Física de Buenos Aires, Consejo Nacional de Investigaciones Científicas y Técnicas, Ciudad Universitaria, 1428 Buenos Aires (Argentina); Torre, Alicia; Lain, Luis, E-mail: qfplapel@lg.ehu.es [Departamento de Química Física, Facultad de Ciencia y Tecnología, Universidad del País Vasco, Apdo. 644, E-48080 Bilbao (Spain); Massaccesi, Gustavo E. [Departamento de Ciencias Exactas, Ciclo Básico Común, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires (Argentina); Oña, Ofelia B. [Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas, Universidad Nacional de La Plata, CCT La Plata, Consejo Nacional de Investigaciones Científicas y Técnicas, Diag. 113 y 64 (S/N), Sucursal 4, CC 16, 1900 La Plata (Argentina)
2014-06-21
This work deals with the configuration interaction method when an N-electron Hamiltonian is projected on Slater determinants which are classified according to their seniority number values. We study the spin features of the wave functions and the size of the matrices required to formulate states of any spin symmetry within this treatment. Correlation energies associated with the wave functions arising from the seniority-based configuration interaction procedure are determined for three types of molecular orbital basis: canonical molecular orbitals, natural orbitals, and the orbitals resulting from minimizing the expectation value of the N-electron seniority number operator. The performance of these bases is analyzed by means of numerical results obtained from selected N-electron systems of several spin symmetries. The comparison of the results highlights the efficiency of the molecular orbital basis which minimizes the mean value of the seniority number for a state, yielding energy values closer to those provided by the full configuration interaction procedure.
GPView: A program for wave function analysis and visualization.
Shi, Tian; Wang, Ping
2016-11-01
In this manuscript, we will introduce a recently developed program GPView, which can be used for wave function analysis and visualization. The wave function analysis module can calculate and generate 3D cubes for various types of molecular orbitals and electron density of electronic excited states, such as natural orbitals, natural transition orbitals, natural difference orbitals, hole-particle density, detachment-attachment density and transition density. The visualization module of GPView can display molecular and electronic (iso-surfaces) structures. It is also able to animate single trajectories of molecular dynamics and non-adiabatic excited state molecular dynamics using the data stored in existing files. There are also other utilities to extract and process the output of quantum chemistry calculations. The GPView provides full graphic user interface (GUI), so it very easy to use. It is available from website http://life-tp.com/gpview.
Horizon Wave-Function and the Quantum Cosmic Censorship
Casadio, Roberto; Stojkovic, Dejan
2015-01-01
We investigate the Cosmic Censorship Conjecture by means of the horizon wave-function (HWF) formalism. We consider a charged massive particle whose quantum mechanical state is represented by a spherically symmetric Gaussian wave-function, and restrict our attention to the superxtremal case (with charge-to-mass ratio $\\alpha>1$), which is the prototype of a naked singularity in the classical theory. We find that one can still obtain a normalisable HWF for $\\alpha^2 2$, and the uncertainty in the location of the horizon blows up at $\\alpha^2=2$, signalling that such an object is no more well-defined. This perhaps implies that a {\\em quantum\\/} Cosmic Censorhip might be conjectured by stating that no black holes with charge-to-mass ratio greater than a critical value (of the order of $\\sqrt{2}$) can exist.
GPView: a program for wave function analysis and visualization
Shi, Tian
2016-01-01
In this manuscript, we will introduce a recently developed program GPView, which can be used for wave function analysis and visualization. The wave function analysis module can calculate and generate 3D cubes for various types of molecular orbitals and electron density related with electronic excited states, such as natural orbitals, natural transition orbitals, natural difference orbitals, hole-particle density, detachment-attachment density and transition density. The visualization module of GPView can display molecular and electronic (iso-surfaces) structures. It is also able to animate single trajectories of molecular dynamics and non-adiabatic excited state molecular dynamics using the data stored in existing files. There are also other utilities help to extract and process the output of quantum chemistry calculations. The GPView provides full graphic user interface (GUI) which makes it very easy to use. The software, manual and tutorials are available in the website http://www.life-tp.com/gpview.
Horizon wave-function and the quantum cosmic censorship
Directory of Open Access Journals (Sweden)
Roberto Casadio
2015-07-01
Full Text Available We investigate the Cosmic Censorship Conjecture by means of the horizon wave-function (HWF formalism. We consider a charged massive particle whose quantum mechanical state is represented by a spherically symmetric Gaussian wave-function, and restrict our attention to the superextremal case (with charge-to-mass ratio α>1, which is the prototype of a naked singularity in the classical theory. We find that one can still obtain a normalisable HWF for α22, and the uncertainty in the location of the horizon blows up at α2=2, signalling that such an object is no more well-defined. This perhaps implies that a quantum Cosmic Censorship might be conjectured by stating that no black holes with charge-to-mass ratio greater than a critical value (of the order of 2 can exist.
Reactive Scattering Wave Functions by Linear Combination of Arrangement Channels
Institute of Scientific and Technical Information of China (English)
邓从豪; 冯大诚; 蔡政亭
1994-01-01
The similarity and dissimilarity of reactive scattering wave functions and molecular orbitalby linear combination of atomic orbitals(LCAOMO)are examined.Based on the similarity a method is pro-posed to construct the reactive scattering wave functions by linear combination of arrangement channel wavefunctions(LCACSW).Based on the dissimilarity,it is shown that the combination coefficients can be deter-mined by solving s set of simultaneous algebraic equations.The elements of the reactive scattering matrix areshown to be related to the combination coefficients of open arrangement channels.The differential and totalreactive scattering cross-section derived by this method agrees completely with that derived by other meth-ods.
Spin-orbit decomposition of ab initio nuclear wave functions
Johnson, Calvin W.
2015-03-01
Although the modern shell-model picture of atomic nuclei is built from single-particle orbits with good total angular momentum j , leading to j -j coupling, decades ago phenomenological models suggested that a simpler picture for 0 p -shell nuclides can be realized via coupling of the total spin S and total orbital angular momentum L . I revisit this idea with large-basis, no-core shell-model calculations using modern ab initio two-body interactions and dissect the resulting wave functions into their component L - and S -components. Remarkably, there is broad agreement with calculations using the phenomenological Cohen-Kurath forces, despite a gap of nearly 50 years and six orders of magnitude in basis dimensions. I suggest that L -S decomposition may be a useful tool for analyzing ab initio wave functions of light nuclei, for example, in the case of rotational bands.
Wave functions in SUSY cosmological models with matter
Energy Technology Data Exchange (ETDEWEB)
Ortiz, C. [Instituto de Fisica de la Universidad de Guanajuato, A.P. E-143, C.P. 37150, Leon, Guanajuato (Mexico); Rosales, J.J. [Facultad de Ingenieria Mecanica Electrica y Electronica, Universidad de Guanajuato, Prolongacion Tampico 912, Bellavista, Salamanca, Guanajuato (Mexico); Socorro, J. [Instituto de Fisica de la Universidad de Guanajuato, A.P. E-143, C.P. 37150, Leon, Guanajuato (Mexico)]. E-mail: socorro@fisica.ugto.mx; Torres, J. [Instituto de Fisica de la Universidad de Guanajuato, A.P. E-143, C.P. 37150, Leon, Guanajuato (Mexico); Tkach, V.I. [Instituto de Fisica de la Universidad de Guanajuato, A.P. E-143, C.P. 37150, Leon, Guanajuato (Mexico)
2005-06-06
In this work we consider the n=2 supersymmetric superfield approach for the FRW cosmological model and the corresponding term of matter content, perfect fluid with barotropic state equation p={gamma}{rho}. We are able to obtain a normalizable wave function (at zero energy) of the universe. Besides, the mass parameter spectrum is found for the closed FRW case in the Schrodinger picture, being similar to those obtained by other methods, using a black hole system.
Heavy quarkonia spectra using wave function with gluonic components
Bartnik, E. A.; Al-Nadary, H.
2009-01-01
We calculate the spectra of charmonium and bottomium in an approximation scheme which treats hard gluons perturbatively while soft gluons are expanded in a set of localized wave functions. Quark-antiquark and quark-antiquark-gluon sectors are included. Reasonable agreement with 2 parameters only is found but the spectra are too coulombic. Despite large coupling constant the admixture of the quark-antiquark-gluon sector is found to be remarkably small.
Two-Variable Hermite Function as Quantum Entanglement of Harmonic Oscillator's Wave Functions
Institute of Scientific and Technical Information of China (English)
LU Hai-Liang; FAN Hong-Yi
2007-01-01
We reveal that the two-variable Hermite function hm,n, which is the generalized Bargmann representation of the two-mode Fock state, involves quantum entanglement of harmonic oscillator's wave functions.The Schmidt decomposition of hm,n is derived. It also turns out that hm,n can be generated by windowed Fourier transform of the single-variable Hermite functions. As an application, the wave function of the two-variable Hermite polynomial state S(r)Hm,n(μa1+, μa2+)|00〉, which is the minimum uncertainty state for sum squeezing, in 〈η| representation is calculated.
Improved variational many-body wave function in light nuclei
Usmani, Q. N.; Singh, A.; Anwar, K.; Rawitscher, G.
2009-09-01
We propose and implement a simple method for improving the variational wave function of a many-body system. We have obtained a significant improvement in the binding energies, wave functions, and variance for the light nuclei H3, He4, and Li6, using the fully realistic Argonne (AV18) two-body and Urbana-IX (UIX) three-body interactions. The energy of He4 was improved by about 0.2 MeV and the Li6 binding energy was increased by ≈1.7 MeV compared to earlier variational Monte Carlo results. The latter result demonstrates the significant progress achieved by our method, and detailed analyses of the improved results are given. With central interactions the results are found to be in agreement with the “exact” calculations. Our study shows that the relative error in the many-body wave functions, compared to two-body pair correlations, increases rapidly at least proportionally to the number of pairs in the system. However, this error does not increase indefinitely since the pair interactions saturate owing to convergence of cluster expansion.
A Rigorous Investigation on the Ground State of the Penson-Kolb Model
Institute of Scientific and Technical Information of China (English)
YANG Kai-Hua; TIAN Guang-Shan; HAN Ru-Qi
2003-01-01
By using either numerical calculations or analytical methods, such as the bosonization technique, the ground state of the Penson-Kolb model has been previously studied by several groups. Some physicists argued that, as far as the existence of superconductivity in this model is concerned, it is canonically equivalent to the negative-U Hubbard model.However, others did not agree. In the present paper, we shall investigate this model by an independent and rigorous approach. We show that the ground state of the Penson-Kolb model is nondegenerate and has a nonvanishing overlap with the ground state of the negative-U Hubbard model. Furthermore, we also show that the ground states of both the models have the same good quantum numbers and may have superconducting long-range order at the same momentum q ＝ 0. Our results support the equivalence between these models.
Efficient sympathetic motional ground-state cooling of a molecular ion
Wan, Yong; Wolf, Fabian; Schmidt, Piet O
2015-01-01
Cold molecular ions are promising candidates in various fields ranging from precision spectroscopy and test of fundamental physics to ultra-cold chemistry. Control of internal and external degrees of freedom is a prerequisite for many of these applications. Motional ground state cooling represents the starting point for quantum logic-assisted internal state preparation, detection, and spectroscopy protocols. Robust and fast cooling is crucial to maximize the fraction of time available for the actual experiment. We optimize the cooling rate of ground state cooling schemes for single $^{25}\\mathrm{Mg}^{+}$ ions and sympathetic ground state cooling of $^{24}\\mathrm{MgH}^{+}$. In particular, we show that robust cooling is achieved by combining pulsed Raman sideband cooling with continuous quench cooling. Furthermore, we experimentally demonstrate an efficient strategy for ground state cooling outside the Lamb-Dicke regime.
Ground-state energies of the nonlinear sigma model and the Heisenberg spin chains
Zhang, Shoucheng; Schulz, H. J.; Ziman, Timothy
1989-01-01
A theorem on the O(3) nonlinear sigma model with the topological theta term is proved, which states that the ground-state energy at theta = pi is always higher than the ground-state energy at theta = 0, for the same value of the coupling constant g. Provided that the nonlinear sigma model gives the correct description for the Heisenberg spin chains in the large-s limit, this theorem makes a definite prediction relating the ground-state energies of the half-integer and the integer spin chains. The ground-state energies obtained from the exact Bethe ansatz solution for the spin-1/2 chain and the numerical diagonalization on the spin-1, spin-3/2, and spin-2 chains support this prediction.
Bott periodicity for Z2 symmetric ground states of gapped free-fermion systems
Kennedy, Ricardo
2014-01-01
Building on the symmetry classification of disordered fermions, we give a proof of the proposal by Kitaev, and others, for a "Bott clock" topological classification of free-fermion ground states of gapped systems with symmetries. Our approach differs from previous ones in that (i) we work in the standard framework of Hermitian quantum mechanics over the complex numbers, (ii) we directly formulate a mathematical model for ground states rather than spectrally flattened Hamiltonians, and (iii) we use homotopy-theoretic tools rather than K-theory. Key to our proof is a natural transformation that squares to the standard Bott map and relates the ground state of a d-dimensional system in symmetry class s to the ground state of a (d+1)-dimensional system in symmetry class s+1. This relation gives a new vantage point on topological insulators and superconductors.
Exact ground-state phase diagrams for the spin-3/2 Blume Emery Griffiths model
Canko, Osman; Deviren, Bayram; Keskin, Mustafa
2008-05-01
We have calculated the exact ground-state phase diagrams of the spin-3/2 Ising model using the method that was proposed and applied to the spin-1 Ising model by Dublenych (2005 Phys. Rev. B 71 012411). The calculated, exact ground-state phase diagrams on the diatomic and triangular lattices with the nearest-neighbor (NN) interaction have been presented in this paper. We have obtained seven and 15 topologically different ground-state phase diagrams for J>0 and Jnon-uniform phases. We have also constructed the exact ground-state phase diagrams of the model on the triangular lattice and found 20 and 59 fundamental phase diagrams for J>0 and J<0, respectively, the conditions for the existence of uniform and intermediate phases have also been found.
Vacuum polarization screening corrections to the ground state energy of two-electron ions
Artemiev, A N; Yerokhin, V A
1997-01-01
Vacuum polarization screening corrections to the ground state energy of two-electron ions are calculated in the range $Z=20-100$. The calculations are carried out for a finite nucleus charge distribution.
Hirose, Yuhei; Oguchi, Akihide; Fukumoto, Yoshiyuki
2017-01-01
We study the ground-state phase diagram of a Heisenberg model with spin S = 1/2 on a diamond-like-decorated square lattice. A diamond unit has two types of antiferromagnetic exchange interactions, and the ratio λ of the length of the diagonal bond to that of the other four edges determines the strength of frustration. It has been pointed out [https://doi.org/10.7566/JPSJ.85.033705" xlink:type="simple">J. Phys. Soc. Jpn 85, 033705 (2016)] that the so-called tetramer-dimer states, which are expected to be stabilized in an intermediate region of λc < λ < 2, are identical to the square-lattice dimer-covering states, which ignited renewed interest in high-dimensional diamond-like-decorated lattices. In order to determine the phase boundary λc, we employ the modified spin wave method to estimate the energy of the ferrimagnetic state and obtain λc = 0.974. Furthermore, our numerical diagonalization study suggests that other cluster states do not appear in the ground-state phase diagram.
Competing magnetic ground states and their coupling to the crystal lattice in CuFe2Ge2
May, Andrew F.; Calder, Stuart; Parker, David S.; Sales, Brian C.; McGuire, Michael A.
2016-01-01
Identifying and characterizing systems with coupled and competing interactions is central to the development of physical models that can accurately describe and predict emergent behavior in condensed matter systems. This work demonstrates that the metallic compound CuFe2Ge2 has competing magnetic ground states, which are shown to be strongly coupled to the lattice and easily manipulated using temperature and applied magnetic fields. Temperature-dependent magnetization M measurements reveal a ferromagnetic-like onset at 228 (1) K and a broad maximum in M near 180 K. Powder neutron diffraction confirms antiferromagnetic ordering below TN ≈ 175 K, and an incommensurate spin density wave is observed below ≈125 K. Coupled with the small refined moments (0.5–1 μB/Fe), this provides a picture of itinerant magnetism in CuFe2Ge2. The neutron diffraction data also reveal a coexistence of two magnetic phases that further highlights the near-degeneracy of various magnetic states. These results demonstrate that the ground state in CuFe2Ge2 can be easily manipulated by external forces, making it of particular interest for doping, pressure, and further theoretical studies. PMID:27739477
Ground-state entanglement in a three-spin transverse Ising model with energy current
Institute of Scientific and Technical Information of China (English)
Zhang Yong; Liu Dan; Long Gui-Lu
2007-01-01
The ground-state entanglement associated with a three-spin transverse Ising model is studied. By introducing an energy current into the system, a quantum phase transition to energy-current phase may be presented with the variation of external magnetic field; and the ground-state entanglement varies suddenly at the critical point of quantum phase transition. In our model, the introduction of energy current makes the entanglement between any two qubits become maximally robust.
Expectation values of single-particle operators in the random phase approximation ground state.
Kosov, D S
2017-02-07
We developed a method for computing matrix elements of single-particle operators in the correlated random phase approximation ground state. Working with the explicit random phase approximation ground state wavefunction, we derived a practically useful and simple expression for a molecular property in terms of random phase approximation amplitudes. The theory is illustrated by the calculation of molecular dipole moments for a set of representative molecules.
Ground-State Density Profiles of One-Dimensional Bose Gases with Anisotropic Transversal Confinement
Institute of Scientific and Technical Information of China (English)
HAO Ya-Jiang
2011-01-01
We investigate the ground-state density distributions of interacting one-dimensional Bose gases with anisotropic transversal confinement.Combining the exact ground state energy density of homogeneous bose gases with local density approximation,we determine the density distribution in each interacting regime for different anisotropic parameters.It is shown that the transversal anisotropic parameter changes the density distribution obviously,and the observed density profiles on each orientation exhibit a difference of a factor.
Hyperfine splitting of the dressed hydrogen atom ground state in non-relativistic QED
Amour, L
2010-01-01
We consider a spin-1/2 electron and a spin-1/2 nucleus interacting with the quantized electromagnetic field in the standard model of non-relativistic QED. For a fixed total momentum sufficiently small, we study the multiplicity of the ground state of the reduced Hamiltonian. We prove that the coupling between the spins of the charged particles and the electromagnetic field splits the degeneracy of the ground state.
Hyperfine splitting in non-relativistic QED: uniqueness of the dressed hydrogen atom ground state
Amour, Laurent
2011-01-01
We consider a free hydrogen atom composed of a spin-1/2 nucleus and a spin-1/2 electron in the standard model of non-relativistic QED. We study the Pauli-Fierz Hamiltonian associated with this system at a fixed total momentum. For small enough values of the fine-structure constant, we prove that the ground state is unique. This result reflects the hyperfine structure of the hydrogen atom ground state.
Institute of Scientific and Technical Information of China (English)
WU Feng; HE Pei; CHEN Zu-Yao; JIANG Wan-Quan
2000-01-01
The effect of the shape of suspension particle in electrorheological (ER) fluid on the ground state structure of ER solid is discussed. The results of computation show that the ground state structure will change with the shape of suspension particle. This phenomenon is a kind of phase transitions that takes the shape factors of suspension particle as tuning parameters. The variation-value of interaction energy of the lattice structure of ER solid with the shape factors of suspension particle is sometimes noticeable.
Expectation values of single-particle operators in the random phase approximation ground state
Kosov, D. S.
2017-02-01
We developed a method for computing matrix elements of single-particle operators in the correlated random phase approximation ground state. Working with the explicit random phase approximation ground state wavefunction, we derived a practically useful and simple expression for a molecular property in terms of random phase approximation amplitudes. The theory is illustrated by the calculation of molecular dipole moments for a set of representative molecules.
Energy Technology Data Exchange (ETDEWEB)
Szybisz, L. (Lab. TANDAR, Dept. de Fisica, Comision Nacional de Energia Atomica, Buenos Aires (Argentina))
1990-08-01
The ground-state wave function for a two-dimensional homogeneous liquid 4He at zero temperature is obtained from a paired-phonon analysis within the HNC/0 approximation. The long-wavelength behavior of the twobody correlation factor, u(q), is studied by following the procedure previously applied to three-dimensional bulk systems. It is shown that a cut-off law for the phonons can be determined by analyzing u(q) at small two-dimensional momenta q. The numerical results strongly support an exponential cut-off similar to that suggested by Chester and Reatto for the bulk liquid. The first-sound velocity c{sub 1} and the cut-off momentum q{sub c} are calculated at several densities in the range 0.028-0.080 A - 2. (orig.).
Patterns of the ground states in the presence of random interactions: nucleon systems
Zhao, Y M; Shimizu, N; Ogawa, K; Yoshinaga, N; Scholten, O
2004-01-01
We present our results on properties of ground states for nucleonic systems in the presence of random two-body interactions. In particular we present probability distributions for parity, seniority, spectroscopic (i.e., in the laboratory framework) quadrupole moments and $\\alpha$ clustering in the ground states. We find that the probability distribution for the parity of the ground states obtained by a two-body random ensemble simulates that of realistic nuclei: positive parity is dominant in the ground states of even-even nuclei while for odd-odd nuclei and odd-mass nuclei we obtain with almost equal probability ground states with positive and negative parity. In addition we find that for the ground states, assuming pure random interactions, low seniority is not favored, no dominance of positive values of spectroscopic quadrupole deformation, and no sign of $\\alpha$-cluster correlations, all in sharp contrast to realistic nuclei. Considering a mixture of a random and a realistic interaction, we observe a sec...
Ground-State Phases of Anisotropic Mixed Diamond Chains with Spins 1 and 1/2
Hida, Kazuo
2014-11-01
The ground-state phases of anisotropic mixed diamond chains with spins 1 and 1/2 are investigated. Both single-site and exchange anisotropies are considered. We find the phases consisting of an array of uncorrelated spin-1 clusters separated by singlet dimers. Except in the simplest case where the cluster consists of a single S = 1 spin, this type of ground state breaks the translational symmetry spontaneously. Although the mechanism leading to this type of ground state is the same as that in the isotropic case, it is nonmagnetic or paramagnetic depending on the competition between two types of anisotropy. We also find the Néel, period-doubled Néel, Haldane, and large-D phases, where the ground state is a single spin cluster of infinite size equivalent to the spin-1 Heisenberg chain with alternating anisotropies. The ground-state phase diagrams are determined for typical sets of parameters by numerical analysis. In various limiting cases, the ground-state phase diagrams are determined analytically. The low-temperature behaviors of magnetic susceptibility and entropy are investigated to distinguish each phase by observable quantities. The relationship of the present model with the anisotropic rung-alternating ladder with spin-1/2 is also discussed.
Computational aspects of the continuum quaternionic wave functions for hydrogen
Energy Technology Data Exchange (ETDEWEB)
Morais, J., E-mail: joao.pedro.morais@ua.pt
2014-10-15
Over the past few years considerable attention has been given to the role played by the Hydrogen Continuum Wave Functions (HCWFs) in quantum theory. The HCWFs arise via the method of separation of variables for the time-independent Schrödinger equation in spherical coordinates. The HCWFs are composed of products of a radial part involving associated Laguerre polynomials multiplied by exponential factors and an angular part that is the spherical harmonics. In the present paper we introduce the continuum wave functions for hydrogen within quaternionic analysis ((R)QHCWFs), a result which is not available in the existing literature. In particular, the underlying functions are of three real variables and take on either values in the reduced and full quaternions (identified, respectively, with R{sup 3} and R{sup 4}). We prove that the (R)QHCWFs are orthonormal to one another. The representation of these functions in terms of the HCWFs are explicitly given, from which several recurrence formulae for fast computer implementations can be derived. A summary of fundamental properties and further computation of the hydrogen-like atom transforms of the (R)QHCWFs are also discussed. We address all the above and explore some basic facts of the arising quaternionic function theory. As an application, we provide the reader with plot simulations that demonstrate the effectiveness of our approach. (R)QHCWFs are new in the literature and have some consequences that are now under investigation.
Love wave propagation in functionally graded piezoelectric material layer.
Du, Jianke; Jin, Xiaoying; Wang, Ji; Xian, Kai
2007-03-01
An exact approach is used to investigate Love waves in functionally graded piezoelectric material (FGPM) layer bonded to a semi-infinite homogeneous solid. The piezoelectric material is polarized in z-axis direction and the material properties change gradually with the thickness of the layer. We here assume that all material properties of the piezoelectric layer have the same exponential function distribution along the x-axis direction. The analytical solutions of dispersion relations are obtained for electrically open or short circuit conditions. The effects of the gradient variation of material constants on the phase velocity, the group velocity, and the coupled electromechanical factor are discussed in detail. The displacement, electric potential, and stress distributions along thickness of the graded layer are calculated and plotted. Numerical examples indicate that appropriate gradient distributing of the material properties make Love waves to propagate along the surface of the piezoelectric layer, or a bigger electromechanical coupling factor can be obtained, which is in favor of acquiring a better performance in surface acoustic wave (SAW) devices.
A quantum Monte Carlo study of the ground state chromium dimer
Hongo, Kenta
2011-01-01
We report variational and diffusion quantum Monte Carlo (VMC and DMC) studies of the binding curve of the ground-state chromium dimer. We employed various single determinant (SD) or multi-determinant (MD) wavefunctions multiplied by a Jastrow fuctor as a trial/guiding wavefunction. The molecular orbitals (MOs) in the SD were calculated using restricted or unrestricted Hartree-Fock or density functional theory (DFT) calculations where five commonly-used local (SVWN5), semi-local (PW91PW91 and BLYP), and hybrid (B1LYP and B3LYP) functionals were examined. The MD expansions were obtained from the complete-active space SCF, generalized valence bond, and unrestricted configuration interaction methods. We also adopted the UB3LYP-MOs to construct the MD expansion (UB3LYP-MD) and optimized their coefficients at the VMC level. In addition to the wavefunction dependence, we investigated the time-step bias in the DMC calculation and the effects of pseudopotentials and backflow transformation for the UB3LYP-SD case. Some...
Ground-state and dynamical properties of two-dimensional dipolar Fermi liquids
Abedinpour, Saeed H.; Asgari, Reza; Tanatar, B.; Polini, Marco
2014-01-01
We study the ground-state properties of a two-dimensional spin-polarized fluid of dipolar fermions within the Euler-Lagrange Fermi-hypernetted-chain approximation. Our method is based on the solution of a scattering Schrödinger equation for the "pair amplitude" g(r), where g(r) is the pair distribution function. A key ingredient in our theory is the effective pair potential, which includes a bosonic term from Jastrow-Feenberg correlations and a fermionic contribution from kinetic energy and exchange, which is tailored to reproduce the Hartree-Fock limit at weak coupling. Very good agreement with recent results based on quantum Monte Carlo simulations is achieved over a wide range of coupling constants up to the liquid-to-crystal quantum phase transition. Using the fluctuation-dissipation theorem and a static approximation for the effective inter-particle interactions, we calculate the dynamical density-density response function, and furthermore demonstrate that an undamped zero-sound mode exists for any value of the interaction strength, down to infinitesimally weak couplings.
Ammari, Zied; Falconi, Marco
2014-10-01
We consider the classical limit of the Nelson model, a system of stable nucleons interacting with a meson field. We prove convergence of the quantum dynamics towards the evolution of the coupled Klein-Gordon-Schrödinger equation. Also, we show that the ground state energy level of nucleons, when is large and the meson field approaches its classical value, is given by the infimum of the classical energy functional at a fixed density of particles. Our study relies on a recently elaborated approach for mean field theory and uses Wigner measures.
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
We investigate the energy spectrum of ground state and quasi-particle excitation spectrum of hard-core bosons, which behave very much like spinless noninteracting fermions, in optical lattices by means of the perturbation expansion and Bogoliubov approach. The results show that the energy spectrum has a single band structure, and the energy is lower near zero momentum; the excitation spectrum gives corresponding energy gap, and the system is in Mott-insulating state at Tonks limit. The analytic result of energy spectrum is in good agreement with that calculated in terms of Green's function at strong correlation limit.
Peng, Bo; Van Kuiken, Benjamin E; Ding, Feizhi; Li, Xiaosong
2013-09-10
A guided self-consistent field (SCF) method is presented in this paper. This method uses the eigenspace update-and-following idea to improve the SCF method for optimizing wave functions that are higher-energy solutions to the Roothaan-Hall equation. In this method, the eigenvectors of the previous SCF step are used to prediagonalize the current Fock/Kohn-Sham matrix, preserving the ordering of orbital occupations. When the subject of interest is an excited state of the same spin symmetry as the ground state, the initial guess of excited wave function is improved with a preconditioning step. The preconditioning step is an SCF iteration applied to the β spin manifold if the initial guess is generated by orbital permutation in the α spin manifold. This simple preconditioning step gives rise to more-stable SCF convergence using the algorithm presented herein. The guided SCF method is used to optimize ligand-field excited states in tetrahedral transition-metal complexes, and calculate ΔSCF excitation energies. The calculated ligand-field transition energies are compared with those obtained from orbital energy differences, linear response time-dependent density functional theory, and experiments. The excitation energies obtained using the method presented in this work show a significant improvement over orbital energy differences and linear response method.
Relativistic corrections to the ground state energies of the carbon-like atoms%类碳体系基态能量的相对论修正
Institute of Scientific and Technical Information of China (English)
马堃; 黄时中; 倪秀波; 吴长义; 胡健
2008-01-01
Based on the tensor expression for the Breit-Pauli Hamiltonian, and with the aid of irreducible tensor theory, the theory of relativistic corrections to the non-relativistic energies of many-electron atoms has been generalized to the case in which Racah wave functions are the linear combinations of multi-Slater wave functions, analytic formulism for calculating the relativistic corrections, which include mass correction, one-and two-body Darwin correction and spin-spin contact interaction, has been derived, all the angular interactions and spin sums involved in the problem have been worked out explicitly by using irreducible theory. The theory is applied to the ground state of carbon-like atoms.%以Breit-Pauli哈密顿的球张量形式为基础,借助不可约张量理论,将多电子原子能量的相对论修正理论拓展到了原子的拉卡波函数为多个Slater基函数的线性组合的情形,导出了此情形下多电子原子能量相对论修正(包括相对论质量修正项、单体和双体迭尔文修正项、自旋-自旋接触相互作用项)的解析表达式,完成了所有角向积分和自旋求和计算.利用所建立的理论,对类碳体系基态能量的相对论修正进行了具体计算.
Breakdown of the Bardeen-Cooper-Schrieffer ground state at a quantum phase transtion.
Energy Technology Data Exchange (ETDEWEB)
Jaramillo, R.; Feng, Y.; Lang, J. C.; Islam, Z.; Srajer, G.; Littlewood, P. B.; Mc Whan, D. B.; Rosenbaum, T. F.; Univ. of Chicago; Univ. of Cambridge; Massachusetts Innst. of Tech.
2009-05-21
Advances in solid-state and atomic physics are exposing the hidden relationships between conventional and exotic states of quantum matter. Prominent examples include the discovery of exotic superconductivity proximate to conventional spin and charge order, and the crossover from long-range phase order to preformed pairs achieved in gases of cold fermions and inferred for copper oxide superconductors. The unifying theme is that incompatible ground states can be connected by quantum phase transitions. Quantum fluctuations about the transition are manifestations of the competition between qualitatively distinct organizing principles, such as a long-wavelength density wave and a short-coherence-length condensate. They may even give rise to 'protected' phases, like fluctuation-mediated superconductivity that survives only in the vicinity of an antiferromagnetic quantum critical point. However, few model systems that demonstrate continuous quantum phase transitions have been identified, and the complex nature of many systems of interest hinders efforts to more fully understand correlations and fluctuations near a zero-temperature instability. Here we report the suppression of magnetism by hydrostatic pressure in elemental chromium, a simple cubic metal that demonstrates a subtle form of itinerant antiferromagnetism formally equivalent to the Bardeen-Cooper-Schrieffer (BCS) state in conventional superconductors. By directly measuring the associated charge order in a diamond anvil cell at low temperatures, we find a phase transition at pressures of 10 GPa driven by fluctuations that destroy the BCS-like state but preserve the strong magnetic interaction between itinerant electrons and holes. Chromium is unique among stoichiometric magnetic metals studied so far in that the quantum phase transition is continuous, allowing experimental access to the quantum singularity and a direct probe of the competition between conventional and exotic order in a theoretically
Ground-state and excited-state structures of tungsten-benzylidyne complexes
Energy Technology Data Exchange (ETDEWEB)
Lovaasen, B. M.; Lockard, J. V.; Cohen, B. W.; Yang, S.; Zhang, X.; Simpson, C. K.; Chen, L. X.; Hopkins, M. D. (Chemical Sciences and Engineering Division); ( XSD); (The Univ. of Chicago)
2012-01-01
The molecular structure of the tungsten-benzylidyne complex trans-W({triple_bond}CPh)(dppe){sub 2}Cl (1; dppe = 1,2-bis(diphenylphosphino)ethane) in the singlet (d{sub xy}){sup 2} ground state and luminescent triplet (d{sub xy}){sup 1}({pi}*(WCPh)){sup 1} excited state (1*) has been studied using X-ray transient absorption spectroscopy, X-ray crystallography, and density functional theory (DFT) calculations. Molecular-orbital considerations suggest that the W-C and W-P bond lengths should increase in the excited state because of the reduction of the formal W-C bond order and decrease in W {yields} P {pi}-backbonding, respectively, between 1 and 1*. This latter conclusion is supported by comparisons among the W-P bond lengths obtained from the X-ray crystal structures of 1, (d{sub xy}){sup 1}-configured 1{sup +}, and (d{sub xy}){sup 2} [W(CPh)(dppe){sub 2}(NCMe)]{sup +} (2{sup +}). X-ray transient absorption spectroscopic measurements of the excited-state structure of 1* reveal that the W-C bond length is the same (within experimental error) as that determined by X-ray crystallography for the ground state 1, while the average W-P/W-Cl distance increases by 0.04 {angstrom} in the excited state. The small excited-state elongation of the W-C bond relative to the M-E distortions found for M({triple_bond}E)L{sub n} (E = O, N) compounds with analogous (d{sub xy}){sup 1}({pi}*(ME)){sup 1} excited states is due to the {pi} conjugation within the WCPh unit, which lessens the local W-C {pi}-antibonding character of the {pi}*(WCPh) lowest unoccupied molecular orbital (LUMO). These conclusions are supported by DFT calculations on 1 and 1*. The similar core bond distances of 1, 1{sup +}, and 1* indicates that the inner-sphere reorganization energy associated with ground- and excited-state electron-transfer reactions is small.
Zou, Haiyuan; Zhao, Erhai; Liu, W. Vincent
2017-08-01
Motivated by the experimental realization of quantum spin models of polar molecule KRb in optical lattices, we analyze the spin 1 /2 dipolar Heisenberg model with competing anisotropic, long-range exchange interactions. We show that, by tilting the orientation of dipoles using an external electric field, the dipolar spin system on square lattice comes close to a maximally frustrated region similar, but not identical, to that of the J1-J2 model. This provides a simple yet powerful route to potentially realize a quantum spin liquid without the need for a triangular or kagome lattice. The ground state phase diagrams obtained from Schwinger-boson and spin-wave theories consistently show a spin disordered region between the Néel, stripe, and spiral phase. The existence of a finite quantum paramagnetic region is further confirmed by an unbiased variational ansatz based on tensor network states and a tensor renormalization group.
Hirose, Yuhei; Miura, Shoma; Yasuda, Chitoshi; Fukumoto, Yoshiyuki
2017-08-01
Quantum Monte Carlo (QMC) simulations are performed to study ground-state properties of a mixed spin-1 and spin-1/2 Lieb-lattice Heisenberg antiferromagnet, in order to get further insight beyond the modified spin-wave (MSW) study reported in [https://doi.org/10.7566/JPSJ.86.014002" xlink:type="simple">J. Phys. Soc. Jpn. 86, 014002 (2017)]. It is confirmed that the MSW results are in good agreement with the QMC results. In particular, the scaling relation found in the MSW study, which argues that sublattice spin reductions are inversely proportional to the sublattice sizes, is observed in our QMC simulation. We present a rigorous proof for spontaneous sublattice magnetizations induced by an infinitesimal uniform magnetic field. The calculation process in the MSW theory is reexamined to clarify the mathematical structure behind the scaling relation for sublattice long-range orders.
Effect of thermal ground state correlations on the statistical properties of the Lipkin model
Energy Technology Data Exchange (ETDEWEB)
Vdovin, A.I.; Storozhenko, A.N. [Joint Inst. for Nuclear Research, Dubna (Russian Federation). Lab. of Theoretical Physics
1999-07-01
The renormalized random phase approximation for hot finite Fermi systems is evaluated with the use of the thermofield dynamics formalism. This approximation treats vibrations of a hot finite Fermi system as harmonic ones but takes into account the Pauli principle in a more proper way than the usual thermal RPA, thus incorporating a new type of correlations in a thermal ground state. To demonstrate advantages of the approximation and to analyze a range of its validity, it is applied to the exactly solvable Lipkin model. A comparison is made with the exact grand canonical ensemble calculations, results of the thermal Hartree-Fock approximation and the thermal random phase approximation. The intrinsic energy of the system, the heat capacity, the average value of the quasispin operator z-projection and the particle number variance are calculated as functions of temperature. On the whole, the thermal renormalized RPA appears to be a better approximation than the other two. Its advantage is especially evident in the vicinity of the phase transition point. It is found that within TRRPA the phase transition occurs at lower temperature than in THFA and TRPA. (orig.) 28 refs.
Random-field Ising model on isometric lattices: Ground states and non-Porod scattering
Bupathy, Arunkumar; Banerjee, Varsha; Puri, Sanjay
2016-01-01
We use a computationally efficient graph cut method to obtain ground state morphologies of the random-field Ising model (RFIM) on (i) simple cubic (SC), (ii) body-centered cubic (BCC), and (iii) face-centered cubic (FCC) lattices. We determine the critical disorder strength Δc at zero temperature with high accuracy. For the SC lattice, our estimate (Δc=2.278 ±0.002 ) is consistent with earlier reports. For the BCC and FCC lattices, Δc=3.316 ±0.002 and 5.160 ±0.002 , respectively, which are the most accurate estimates in the literature to date. The small-r behavior of the correlation function exhibits a cusp regime characterized by a cusp exponent α signifying fractal interfaces. In the paramagnetic phase, α =0.5 ±0.01 for all three lattices. In the ferromagnetic phase, the cusp exponent shows small variations due to the lattice structure. Consequently, the interfacial energy Ei(L ) for an interface of size L is significantly different for the three lattices. This has important implications for nonequilibrium properties.
Three-body problem in 3D space: ground state, (quasi)-exact-solvability
Turbiner, Alexander V; Escobar-Ruiz, Adrian M
2016-01-01
We study aspects of the quantum and classical dynamics of a $3$-body system in 3D space with interaction depending only on mutual distances. The study is restricted to solutions in the space of relative motion which are functions of mutual distances only. It is shown that the ground state (and some other states) in the quantum case and the planar trajectories in the classical case are of this type. The quantum (and classical) system for which these states are eigenstates is found and its Hamiltonian is constructed. It corresponds to a three-dimensional quantum particle moving in a curved space with special metric. The kinetic energy of the system has a hidden $sl(4,R)$ Lie (Poisson) algebra structure, alternatively, the hidden algebra $h^{(3)}$ typical for the $H_3$ Calogero model. We find an exactly solvable three-body generalized harmonic oscillator-type potential as well as a quasi-exactly-solvable three-body sextic polynomial type potential.
Ground state correlations in Deep Inelastic Scattering and the Drell-Yan process
Linnyk, O; Mosel, U
2004-01-01
Non-perturbative corrections to the LO cross section formulae for DIS and the Drell-Yan process were calculated. The interaction of partons was taken into account via dressing the incoming quark lines with spectral functions. We found the effect of ground state correlation in DIS to be large in the region of small Bjorken x and low momentum transfer Q. For a quark width of the order of 200 MeV, the deviation from parton model cross section reaches as much as 50% for Q^2=10 GeV^2. On the other hand, for the values of Q well above the resonance region, the effect of ISI turned out to be small in DIS, but still substantial for the triple differential Drell-Yan cross section. Our calculations show that the shape of the high mass Drell-Yan pair transverse momentum distribution is fully determined by quark off-shellness. From comparison to the resent data on the Drell-Yan cross section from NuSea collaboration, we obtained for the quark width in the nucleon the value about 200 MeV.
Wave Function Structure in Two-Body Random Matrix Ensembles
Kaplan, L; Kaplan, Lev; Papenbrock, Thomas
2000-01-01
We study the structure of eigenstates in two-body interaction random matrix ensembles and find significant deviations from random matrix theory expectations. The deviations are most prominent in the tails of the spectral density and indicate localization of the eigenstates in Fock space. Using ideas related to scar theory we derive an analytical formula that relates fluctuations in wave function intensities to fluctuations of the two-body interaction matrix elements. Numerical results for many-body fermion systems agree well with the theoretical predictions.
OPERA Collaboration have observed phase speed of neutrino wave function
Li, Shi-Yuan
2011-01-01
First we call the attention that velocity defined by ratio between some intervals of space and time respectively is sometimes ambiguous, in the framework of quantum theory. Velocity in general is not possible to be well defined as some generator of certain space-time symmetry operation. Then by analyzing the OPERA experiment we show that the OPERA Collaboration may have measured the phase speed of the neutrino wave function. Employing a very (maybe too) simple model which is just a reproduction from Brillouin's classical book, we demonstrate the phase velocity and group velocity. These are just a qualitative illustration rather than aiming to quantitively explain the OPERA data.
Baryon Wave Functions in Covariant Relativistic Quark Models
Dillig, M
2002-01-01
We derive covariant baryon wave functions for arbitrary Lorentz boosts. Modeling baryons as quark-diquark systems, we reduce their manifestly covariant Bethe-Salpeter equation to a covariant 3-dimensional form by projecting on the relative quark-diquark energy. Guided by a phenomenological multigluon exchange representation of a covariant confining kernel, we derive for practical applications explicit solutions for harmonic confinement and for the MIT Bag Model. We briefly comment on the interplay of boosts and center-of-mass corrections in relativistic quark models.
New Forms of Deuteron Equations and Wave Function Representations
Fachruddin, I; Glöckle, W; Elster, Ch.
2001-01-01
A recently developed helicity basis for nucleon-nucleon (NN) scattering is applied to th e deuteron bound state. Here the total spin of the deuteron is treated in such a helicity representation. For the bound state, two sets of two coupled eigenvalue equations are developed, where the amplitudes depend on two and one variable, respectively. Numerical illustrations based on the realistic Bonn-B NN potential are given. In addition, an `operator form' of the deuteron wave function is presented, and several momentum dependent spin densities are derived and shown, in which the angular dependence is given analytically.
Cosmic Wave Functions with the Brans-Dicke Theory
Institute of Scientific and Technical Information of China (English)
ZHU Zong-Hong
2000-01-01
Using the standard Wentzel-Kramers-Brillouin method, the Wheeler-De Witt equation for the Brans-Dicke theory is solved under three kinds of boundary conditions (proposed by Hattie-Hawking, Vilenkin and Linde, respectively). It is found that, although the gravitational and cosmological"constants" are dynamical and timedependent in the classical models, they will acquire constant values when the universe comes from the quantum creation, and that in particular, the amplitude of the resulting wave function under Linde or Vilenkin boundary conditions reaches its maximum if the cosmological constant is the minimum.
On the Convergence to Ergodic Behaviour of Quantum Wave Functions
Jacquod, P; Jacquod, Ph.
1996-01-01
We study the decrease of fluctuations of diagonal matrix elements of observables and of Husimi densities of quantum mechanical wave functions around their mean value upon approaching the semi-classical regime ($\\hbar strongly chaotic regime. We show that the fluctuations are Gaussian distributed, with a width $\\sigma^2$ decreasing as the square root of Planck's constant. This is consistent with Random Matrix Theory (RMT) predictions, and previous studies on these fluctuations. We further study the width of the probability distribution of $\\hbar$-dependent fluctuations and compare it to the Gaussian Orthogonal Ensemble (GOE) of RMT.
Electromagnetism and multiple-valued loop-dependent wave functionals
Leal, Lorenzo
2009-01-01
We quantize the Maxwell theory in the presence of a electric charge in a "dual" Loop Representation, i.e. a geometric representation of magnetic Faraday's lines. It is found that the theory can be seen as a theory without sources, except by the fact that the wave functional becomes multivalued. This can be seen as the dual counterpart of what occurs in Maxwell theory with a magnetic pole, when it is quantized in the ordinary Loop Representation. The multivaluedness can be seen as a result of the multiply-connectedness of the configuration space of the quantum theory.
Black hole mass function from gravitational wave measurements
Kovetz, Ely D.; Cholis, Ilias; Breysse, Patrick C.; Kamionkowski, Marc
2017-05-01
We examine how future gravitational-wave measurements from merging black holes (BHs) can be used to infer the shape of the black-hole mass function, with important implications for the study of star formation and evolution and the properties of binary BHs. We model the mass function as a power law, inherited from the stellar initial mass function, and introduce lower and upper mass cutoff parametrizations in order to probe the minimum and maximum BH masses allowed by stellar evolution, respectively. We initially focus on the heavier BH in each binary, to minimize model dependence. Taking into account the experimental noise, the mass measurement errors and the uncertainty in the redshift dependence of the merger rate, we show that the mass function parameters, as well as the total rate of merger events, can be measured to years of advanced LIGO observations at its design sensitivity. This can be used to address important open questions such as the upper limit on the stellar mass which allows for BH formation and to confirm or refute the currently observed mass gap between neutron stars and BHs. In order to glean information on the progenitors of the merging BH binaries, we then advocate the study of the two-dimensional mass distribution to constrain parameters that describe the two-body system, such as the mass ratio between the two BHs, in addition to the merger rate and mass function parameters. We argue that several years of data collection can efficiently probe models of binary formation, and show, as an example, that the hypothesis that some gravitational-wave events may involve primordial black holes can be tested. Finally, we point out that in order to maximize the constraining power of the data, it may be worthwhile to lower the signal-to-noise threshold imposed on each candidate event and amass a larger statistical ensemble of BH mergers.
Breuer, H P; Petruccione, F; Breuer, Heinz-Peter; Kappler, Bernd; Petruccione, Francesco
1997-01-01
Within the framework of probability distributions on projective Hilbert space a scheme for the calculation of multitime correlation functions is developed. The starting point is the Markovian stochastic wave function description of an open quantum system coupled to an environment consisting of an ensemble of harmonic oscillators in arbitrary pure or mixed states. It is shown that matrix elements of reduced Heisenberg picture operators and general time-ordered correlation functions can be expressed by time-symmetric expectation values of extended operators in a doubled Hilbert space. This representation allows the construction of a stochastic process in the doubled Hilbert space which enables the determination of arbitrary matrix elements and correlation functions. The numerical efficiency of the resulting stochastic simulation algorithm is investigated and compared with an alternative Monte Carlo wave function method proposed first by Dalibard et al. [Phys. Rev. Lett. {\\bf 68}, 580 (1992)]. By means of a stan...
Georgescu, Ionuţ; Jitomirskaya, Svetlana; Mandelshtam, Vladimir A
2013-11-28
Given a quantum many-body system, the Self-Consistent Phonons (SCP) method provides an optimal harmonic approximation by minimizing the free energy. In particular, the SCP estimate for the vibrational ground state (zero temperature) appears to be surprisingly accurate. We explore the possibility of going beyond the SCP approximation by considering the system Hamiltonian evaluated in the harmonic eigenbasis of the SCP Hamiltonian. It appears that the SCP ground state is already uncoupled to all singly- and doubly-excited basis functions. So, in order to improve the SCP result at least triply-excited states must be included, which then reduces the error in the ground state estimate substantially. For a multidimensional system two numerical challenges arise, namely, evaluation of the potential energy matrix elements in the harmonic basis, and handling and diagonalizing the resulting Hamiltonian matrix, whose size grows rapidly with the dimensionality of the system. Using the example of water hexamer we demonstrate that such calculation is feasible, i.e., constructing and diagonalizing the Hamiltonian matrix in a triply-excited SCP basis, without any additional assumptions or approximations. Our results indicate particularly that the ground state energy differences between different isomers (e.g., cage and prism) of water hexamer are already quite accurate within the SCP approximation.
Ground-state Properties of Inhomogeneous Graphene Sheets
Polini, Marco
2009-03-01
When inter-valley scattering is weak and gauge fields due to e.g. ripples are neglected, doped and gated graphene sheets can be described using an envelope-function Hamiltonian with a new sublattice pseudospin degree-of freedom, an ultrarelativistic massless-Dirac free-fermion term, a pseudospin scalar disorder potential, and a non-relativistic instantaneous Coulombic interaction term. There is considerable evidence from experiment that this simplified description of a honeycomb lattice of Carbon atoms is usually a valid starting point for theories of those observables that depend solely on the electronic properties of π-electrons near the graphene Dirac point [1]. Although the use of this model simplifies the physics considerably it still leaves us with a many-body problem without translational invariance, which we do not know how to solve. In this talk we present a Kohn-Sham-Dirac density-functional-theory (DFT) scheme for graphene sheets that treats slowly-varying inhomogeneous scalar external potentials and electron-electron interactions on an equal footing [2]. The theory is able to account for the unusual property that the exchange-correlation contribution to chemical potential increases with carrier density in graphene [3,4]. Consequences of this property, and advantages and disadvantages of using the DFT approach to describe it, are discussed. The approach is illustrated by solving the Kohn-Sham-Dirac equations self-consistently for a model random potential describing charged point-like impurities located close to the graphene plane. The influence of electron-electron interactions on these non-linear screening calculations is discussed at length, in the light of recent experiments [5,6] reporting evidence for the presence of electron-hole puddles in nearly-neutral graphene sheets. [4pt] [1] A.K. Geim and K.S. Novoselov, Nature Mater. 6, 183 (2007); A.K. Geim and A.H. MacDonald, Phys. Today 60, 35 (2007); A.H. Castro Neto, F. Guinea, N.M.R. Peres, K
Two-nucleon Hulthen-type interactions for few higher partial waves
Indian Academy of Sciences (India)
U Laha; J Bhoi
2015-04-01
By exploiting supersymmetry and factorization method, higher partial wave nucleon–nucleon potentials (ℓ = 1,2,3) for a few selected triplet and singlet states are generated from the ground-state interaction and wave function. The nuclear Hulthen potential and the corresponding wave function with the parameters of Arnold and Mackellar which fit the deuteron binding energy are used as the starting point of our calculation. The scattering phase shifts are computed for the constructed potentials using phase function method to examine the merit of our approach to the problem.
Cieplicka-Oryńczak, N.; Szpak, B.; Leoni, S.; Fornal, B.; Bazzacco, D.; Blanc, A.; Bocchi, G.; Bottoni, S.; de France, G.; Jentschel, M.; Köster, U.; Mutti, P.; Simpson, G.; Soldner, T.; Ur, C.; Urban, W.
2016-07-01
The multipolarity of the main transition leading to the ground state in 210Bi was investigated using the angular correlations of γ rays. The analyzed γ -coincidence data were obtained from the 209Bi(n ,γ )210Bi experiment performed at Institut Laue-Langevin Grenoble at the PF1B cold-neutron facility. The EXILL (EXOGAM at the ILL) multidetector array, consisting of 16 high-purity germanium detectors, was used to detect γ transitions. The mixing ratio of the 320-keV γ ray was defined by minimizing a multivariable χΣ2 function constructed from the coefficients of angular correlation functions for seven pairs of strong transitions in 210Bi. As a result, the almost pure M 1 multipolarity of the 320-keV γ ray was obtained, with an E 2 admixture of less than 0.6% only (95% confidence limit). Based on this multipolarity the neutron-capture cross section leading to the ground state in 210Bi, that decays in turn to radiotoxic 210Po, was determined to be within the limits 21.3(9) and 21.5(9) mb. This result is important for nuclear reactor applications.
Extracting Supersymmetry-Breaking Effects from Wave-Function Renormalization
Giudice, Gian Francesco
1998-01-01
We show that in theories in which supersymmetry breaking is communicated by renormalizable perturbative interactions, it is possible to extract the soft terms for the observable fields from wave-function renormalization. Therefore all the information about soft terms can be obtained from anomalous dimensions and beta functions, with no need to further compute any Feynman diagram. This method greatly simplifies calculations which are rather involved if performed in terms of component fields. For illustrative purposes we reproduce known results of theories with gauge-mediated supersymmetry breaking. We then use our method to obtain new results of phenomenological importance. We calculate the next-to-leading correction to the Higgs mass parameters, the two-loop soft terms induced by messenger-matter superpotential couplings, and the soft terms generated by messengers belonging to vector supermultiplets.
Quantum canonical tensor model and an exact wave function
Sasakura, Naoki
2013-01-01
Tensor models in various forms are being studied as models of quantum gravity. Among them the canonical tensor model has a canonical pair of rank-three tensors as dynamical variables, and is a pure constraint system with first-class constraints. The Poisson algebra of the first-class constraints has structure functions, and provides an algebraically consistent way of discretizing the Dirac first-class constraint algebra for general relativity. This paper successfully formulates the Wheeler-DeWitt scheme of quantization of the canonical tensor model; the ordering of operators in the constraints is determined without ambiguity by imposing Hermiticity and covariance on the constraints, and the commutation algebra of constraints takes essentially the same from as the classical Poisson algebra, i.e. is first-class. Thus one could consistently obtain, at least locally in the configuration space, wave functions of "universe" by solving the partial differential equations representing the constraints, i.e. the Wheeler...
Theoretical study of the fragmentation pathways of norbornane in its doubly ionized ground state.
Knippenberg, Stefan; Hajgató, Balazs; François, Jean-Pierre; Deleuze, Michael S
2007-10-25
The potential energy surface of norbornane in its dicationic singlet ground state has been investigated in detail using density functional theory along with the nonlocal hybrid and gradient-corrected Becke three-parameter Lee-Yang-Parr functional (B3LYP) and the cc-pVDZ basis set. For the sake of more quantitative insight into the chemical reactions induced by double ionization of norbornane, this study was supplemented by a calculation of basic thermodynamic state functions coupled to a focal point analysis of energy differences obtained using correlation treatments and basis sets of improving quality, enabling an extrapolation of these energy differences at the CCSD(T) level in the limit of an asymptotically complete (cc-pV infinity Z) basis set. Our results demonstrate the likelihood of an ultrafast intramolecular rearrangement of the saturated hydrocarbon cage after a sudden removal of two electrons into a kinetically metastable five-membered cyclic C5H8+-CH+-CH3 intermediate, prior to a Coulomb explosion into C5H7+=CH2 and CH3+ fragments, which might explain a tremendous rise of electron-impact (e, 2e) ionization cross sections at electron binding energies around the double-ionization threshold. The first step is straightforward and strongly exothermic (DeltaH298 = -114.0 kcal mol-1). The second step is also exothermic (DeltaH298 = -10.2 kcal mol-1) but requires an activation enthalpy (DeltaH298) of 39.7 kcal/mol. The various factors governing the structure of this intermediate, such as electrostatic interactions, inductive effects, cyclic strains, and methylenic hyperconjugation interactions, are discussed in detail.
Luo, Ding
2014-01-01
Polycyclic hydrocarbons (PHs) with a singlet biradical ground state have recently attracted extensive interest in physical organic chemistry and materials science. Replacing the carbon radical center in the open-shell PHs with a more electronegative nitrogen atom is expected to result in the more stable aminyl radical. In this work, two kinetically blocked stable/persistent derivatives (1 and 2) of indolo[2,3-b]carbazole, an isoelectronic structure of the known indeno[2,1-b]fluorene, were synthesized and showed different ground states. Based on variable-temperature NMR/ESR measurements and density functional theory calculations, it was found that the indolo[2,3-b]carbazole derivative 1 is a persistent singlet biradical in the ground state with a moderate biradical character (y0 = 0.269) and a small singlet-triplet energy gap (ΔES-T ≅ -1.78 kcal mol-1), while the more extended dibenzo-indolo[2,3-b]carbazole 2 exhibits a quinoidal closed-shell ground state. The difference can be explained by considering the number of aromatic sextet rings gained from the closed-shell to the open-shell biradical resonance form, that is to say, two for compound 1 and one for compound 2, which determines their different biradical characters. The optical and electronic properties of 2 and the corresponding aromatic precursors were investigated by one-photon absorption, transient absorption and two-photon absorption (TPA) spectroscopies and electrochemistry. Amphoteric redox behaviour, a short excited lifetime and a moderate TPA cross section were observed for 2, which can be correlated to its antiaromaticity and small biradical character. Compound 2 showed high reactivity to protic solvents due to its extremely low-lying LUMO energy level. Unusual oxidative dimerization was also observed for the unblocked dihydro-indolo[2,3-b]carbazole precursors 6 and 11. Our studies shed light on the rational design of persistent aminyl biradicals with tunable properties in the future. This journal
Van der Waals potential and vibrational energy levels of the ground state radon dimer
Sheng, Xiaowei; Qian, Shifeng; Hu, Fengfei
2017-08-01
In the present paper, the ground state van der Waals potential of the Radon dimer is described by the Tang-Toennies potential model, which requires five essential parameters. Among them, the two dispersion coefficients C6 and C8 are estimated from the well determined dispersion coefficients C6 and C8 of Xe2. C10 is estimated by using the approximation equation that C6C10 / C82 has an average value of 1.221 for all the rare gas dimers. With these estimated dispersion coefficients and the well determined well depth De and Re the Born-Mayer parameters A and b are derived. Then the vibrational energy levels of the ground state radon dimer are calculated. 40 vibrational energy levels are observed in the ground state of Rn2 dimer. The last vibrational energy level is bound by only 0.0012 cm-1.
Spin-Orbit Coupling Controlled J =3 /2 Electronic Ground State in 5 d3 Oxides
Taylor, A. E.; Calder, S.; Morrow, R.; Feng, H. L.; Upton, M. H.; Lumsden, M. D.; Yamaura, K.; Woodward, P. M.; Christianson, A. D.
2017-05-01
Entanglement of spin and orbital degrees of freedom drives the formation of novel quantum and topological physical states. Here we report resonant inelastic x-ray scattering measurements of the transition metal oxides Ca3 LiOsO6 and Ba2 YOsO6 , which reveals a dramatic spitting of the t2 g manifold. We invoke an intermediate coupling approach that incorporates both spin-orbit coupling and electron-electron interactions on an even footing and reveal that the ground state of 5 d3-based compounds, which has remained elusive in previously applied models, is a novel spin-orbit entangled J =3 /2 electronic ground state. This work reveals the hidden diversity of spin-orbit controlled ground states in 5 d systems and introduces a new arena in the search for spin-orbit controlled phases of matter.
Exact many-electron ground states on the diamond Hubbard chain
Gulacsi, Zsolt; Kampf, Arno; Vollhardt, Dieter
2008-03-01
Exact ground states of interacting electrons on the diamond Hubbard chain in a magnetic field are constructed which exhibit a wide range of properties such as flat-band ferromagnetism, correlation induced metallic, half-metallic, or insulating behavior [1]. The properties of these ground states can be tuned by changing the magnetic flux, local potentials, or electron density.The results show that the studied simple one-dimensional structure displays remarkably complex physical properties. The virtue of tuning different ground states through external parameters points to new possibilities for the design of electronic devices which can switch between insulating or conducting and nonmagnetic or (fully or partially spin polarized) ferromagnetic states, open new routes for the design of spin-valve devices and gate induced ferromagnetism. [1] Z. Gulacsi, A. Kampf, D. Vollhardt, Phys. Rev. Lett. 99, 026404(2007).
Evidence for a gapped spin-liquid ground state in a kagome Heisenberg antiferromagnet.
Fu, Mingxuan; Imai, Takashi; Han, Tian-Heng; Lee, Young S
2015-11-06
The kagome Heisenberg antiferromagnet is a leading candidate in the search for a spin system with a quantum spin-liquid ground state. The nature of its ground state remains a matter of active debate. We conducted oxygen-17 single-crystal nuclear magnetic resonance (NMR) measurements of the spin-1/2 kagome lattice in herbertsmithite [ZnCu3(OH)6Cl2], which is known to exhibit a spinon continuum in the spin excitation spectrum. We demonstrated that the intrinsic local spin susceptibility χ(kagome), deduced from the oxygen-17 NMR frequency shift, asymptotes to zero below temperatures of 0.03J, where J ~ 200 kelvin is the copper-copper superexchange interaction. Combined with the magnetic field dependence of χ(kagome) that we observed at low temperatures, these results imply that the kagome Heisenberg antiferromagnet has a spin-liquid ground state with a finite gap.
Ground State Properties of the 1/2 Flux Harper Hamiltonian
Kennedy, Colin; Burton, William Cody; Chung, Woo Chang; Ketterle, Wolfgang
2015-05-01
The Harper Hamiltonian describes the motion of charged particles in an applied magnetic field - the spectrum of which exhibits the famed Hofstadter's butterfly. Recent advances in driven optical lattices have made great strides in simulating nontrivial Hamiltonians, such as the Harper model, in the time-averaged sense. We report on the realization of the ground state of bosons in the Harper Hamiltonian for 1/2 flux per plaquette utilizing a tilted two-dimensional lattice with laser assisted tunneling. We detail progress in studying various ground state properties of the 1/2 flux Harper Hamiltonian including ground state degeneracies, gauge-dependent observables, effects of micromotion, adiabatic loading schemes, and emergence and decay of coherence. Additionally, we describe prospects for flux rectification using a period-tripled superlattice and generalizations to three dimensions. MIT-Harvard Center for Ultracold Atoms, Research Laboratory of Electronics, Department of Physics, Massachusetts Institute of Technology.
Precision study of ground state capture in the 14N(p,gamma)15O reaction
Marta, M; Gyurky, Gy; Bemmerer, D; Broggini, C; Caciolli, A; Corvisiero, P; Costantini, H; Elekes, Z; Fülöp, Z; Gervino, G; Guglielmetti, A; Gustavino, C; Imbriani, G; Junker, M; Kunz, R; Lemut, A; Limata, B; Mazzocchi, C; Menegazzo, R; Prati, P; Roca, V; Rolfs, C; Romano, M; Alvarez, C Rossi; Somorjai, E; Straniero, O; Strieder, F; Terrasi, F; Trautvetter, H P; Vomiero, A
2008-01-01
The rate of the hydrogen-burning carbon-nitrogen-oxygen (CNO) cycle is controlled by the slowest process, 14N(p,gamma)15O, which proceeds by capture to the ground and several excited states in 15O. Previous extrapolations for the ground state contribution disagreed by a factor 2, corresponding to 15% uncertainty in the total astrophysical S-factor. At the Laboratory for Underground Nuclear Astrophysics (LUNA) 400 kV accelerator placed deep underground in the Gran Sasso facility in Italy, a new experiment on ground state capture has been carried out at 317.8, 334.4, and 353.3 keV center-of-mass energy. Systematic corrections have been reduced considerably with respect to previous studies by using a Clover detector and by adopting a relative analysis. The previous discrepancy has been resolved, and ground state capture no longer dominates the uncertainty of the total S-factor.
Ground State Transitions in Vertically Coupled Four-Layer Single Electron Quantum Dots
Institute of Scientific and Technical Information of China (English)
WANGAn-Mei; XIEWen-Fang
2005-01-01
We study a four-electron system in a vertically coupled four-layer quantum dot under a magnetic field by the exact diagonalization of the Hamiltonian matr/x. We find that discontinuous ground-state energy transitions are induced by an external magnetic field. We find that dot-dot distance and electron-electron interaction strongly affect the low-lying states of the coupled quantum dots. The inter-dot correlation leads to some sequences of possible disappearances of ground state transitions, which are present for uncoupled dots.
Ground state atomic oxygen in high-power impulse magnetron sputtering: a quantitative study
Britun, Nikolay; Belosludtsev, Alexandr; Silva, Tiago; Snyders, Rony
2017-02-01
The ground state density of oxygen atoms in reactive high-power impulse magnetron sputtering discharges has been studied quantitatively. Both time-resolved and space-resolved measurements were conducted. The measurements were performed using two-photon absorption laser-induced fluorescence (TALIF), and calibrated by optical emission actinometry with multiple Ar emission lines. The results clarify the dynamics of the O ground state atoms in the discharge afterglow significantly, including their propagation and fast decay after the plasma pulse, as well as the influence of gas pressure, O2 admixture, etc.
Preparing ground States of quantum many-body systems on a quantum computer.
Poulin, David; Wocjan, Pawel
2009-04-03
Preparing the ground state of a system of interacting classical particles is an NP-hard problem. Thus, there is in general no better algorithm to solve this problem than exhaustively going through all N configurations of the system to determine the one with lowest energy, requiring a running time proportional to N. A quantum computer, if it could be built, could solve this problem in time sqrt[N]. Here, we present a powerful extension of this result to the case of interacting quantum particles, demonstrating that a quantum computer can prepare the ground state of a quantum system as efficiently as it does for classical systems.
Ub-library of Atomic Masses and Nuclear Ground States Deformations (CENPL.AMD)
Institute of Scientific and Technical Information of China (English)
2001-01-01
The atomic mass is one of basic data of a nuclear. There are the atomic masses in all nuclear reaction model formulas and motion equations. For any reaction calculations atomic masses are basic data for getting binding energies or Q-values. In some applications, it is important also to have atomic masses even for exotic nuclei quite far from the valley of stability. In addition, nuclear ground state deformations and abundance values are also requisite in the nuclear data calculations. For this purpose, A data file on atomic masses and nuclear ground states deformations (AMD) were constructed, which
Expectation values of single-particle operators in the random phase approximation ground state
Kosov, Daniel S
2016-01-01
We developed a method for computing matrix elements of single-particle operators in the correlated random phase approximation ground state. Working with the explicit random phase approximation ground state wavefunction, we derived practically useful and simple expression for a molecular property in terms of random phase approximation amplitudes. The theory is illustrated by the calculation of molecular dipole moments. It is shown that Hartree-Fock based random phase approximation provides a systematic improvement of molecular dipole moment values in comparison to M{\\o}ller-Plesset second order perturbation theory and coupled cluster method for a considered set of molecules.
Stability of the electroweak ground state in the Standard Model and its extensions
Directory of Open Access Journals (Sweden)
Luca Di Luzio
2016-02-01
Full Text Available We review the formalism by which the tunnelling probability of an unstable ground state can be computed in quantum field theory, with special reference to the Standard Model of electroweak interactions. We describe in some detail the approximations implicitly adopted in such calculation. Particular attention is devoted to the role of scale invariance, and to the different implications of scale-invariance violations due to quantum effects and possible new degrees of freedom. We show that new interactions characterized by a new energy scale, close to the Planck mass, do not invalidate the main conclusions about the stability of the Standard Model ground state derived in absence of such terms.
Boundedness and convergence of perturbed corrections for helium-like ions in ground states
Institute of Scientific and Technical Information of China (English)
Zhao Yun-Hui; Hai Wen-Hua; Zhao Cheng-Lin; Luo Xiao-Bing
2008-01-01
Applying the improved Rayleigh-Schr(o)dinger perturbation theory based on an integral equation to helium-like ions in ground states and treating electron correlations as perturbations,we obtain the second-order corrections to wavefunctions consisting of a few terms and the third-order corrections to energicity.It is demonstrated that the corrected wavefunctions are bounded and quadratically integrable,and the corresponding perturbation series is convergent.The results clear off the previous distrust for the convergence in the quantum perturbation theory and show a reciprocal development on the quantum perturbation problem of the ground state helium-like systems.
Singlet Ground State Magnetism: III Magnetic Excitons in Antiferromagnetic TbP
DEFF Research Database (Denmark)
Knorr, K.; Loidl, A.; Kjems, Jørgen
1981-01-01
The dispersion of the lowest magnetic excitations of the singlet ground state system TbP has been studied in the antiferromagnetic phase by inelastic neutron scattering. The magnetic exchange interaction and the magnetic and the rhombohedral molecular fields have been determined.......The dispersion of the lowest magnetic excitations of the singlet ground state system TbP has been studied in the antiferromagnetic phase by inelastic neutron scattering. The magnetic exchange interaction and the magnetic and the rhombohedral molecular fields have been determined....
Ground State Transitions in Vertically Coupled Four-Layer Single Electron Quantum Dots
Institute of Scientific and Technical Information of China (English)
WANG An-Mei; XIE Wen-Fang
2005-01-01
We study a four-electron system in a vertically coupled four-layer quantum dot under a magnetic field by the exact diagonalization of the Hamiltonian matrix. We find that discontinuous ground-state energy transitions are induced by an external magnetic field. We find that dot-dot distance and electron-electron interaction strongly affect the low-lying states of the coupled quantum dots. The inter-dot correlation leads to some sequences of possible disappearances of ground state transitions, which are present for uncoupled dots.
Ground State Properties of Superheavy Nuclei in Macroscopic-Microscopic Model
Institute of Scientific and Technical Information of China (English)
ZHI Qi-Jun; REN Zhong-Zhou; ZHANG Xiao-Ping; ZHENG Qiang
2008-01-01
The ground state properties of superheavy nuclei are systematically calculated by the macroscopic-microscopic (MM) model with the Nilsson potential The calculations well produced the ground state binding energies,a-decay energies,and half lives of superheavy nuclei.The calculated results are systematically compared with available experimental data.The calculated results are also compared with theoretical results from other MM models and from relativistic mean-field model.The calculations and comparisons show that the MM model is reliable in superheavy region and that the MM model results are not very sensitive to the choice of microscopic single-particle potential.
Exact spin-cluster ground states in a mixed diamond chain
Takano, Ken'Ichi; Suzuki, Hidenori; Hida, Kazuo
2009-09-01
The mixed diamond chain is a frustrated Heisenberg chain composed of successive diamond-shaped units with two kinds of spins of magnitudes S and S/2 ( S : integer). Ratio λ of two exchange parameters controls the strength of frustration. With varying λ , the Haldane state and several spin-cluster states appear as the ground state. A spin-cluster state is a tensor product of exact local eigenstates of cluster spins. We prove that a spin-cluster state is the ground state in a finite interval of λ . For S=1 , we numerically determine the total phase diagram consisting of five phases.
The Black Hole Mass Function from Gravitational Wave Measurements
Kovetz, Ely D; Breysse, Patrick C; Kamionkowski, Marc
2016-01-01
We examine how future gravitational-wave measurements from merging black holes (BHs) can be used to infer the shape of the black-hole mass function, with important implications for the study of star formation and evolution and the properties of binary BHs. We model the mass function as a power law, inherited from the stellar initial mass function, and introduce lower and upper mass cutoff parameterizations in order to probe the minimum and maximum BH masses allowed by stellar evolution, respectively. We initially focus on the heavier BH in each binary, to minimize model dependence. Taking into account the experimental noise, the mass measurement errors and the uncertainty in the redshift-dependence of the merger rate, we show that the mass function parameters, as well as the total rate of merger events, can be measured to <10% accuracy within a few years of advanced LIGO observations at its design sensitivity. This can be used to address important open questions such as the upper limit on the stellar mass ...
Precise wave-function engineering with magnetic resonance
Wigley, P. B.; Starkey, L. M.; Szigeti, S. S.; Jasperse, M.; Hope, J. J.; Turner, L. D.; Anderson, R. P.
2017-07-01
Controlling quantum fluids at their fundamental length scale will yield superlative quantum simulators, precision sensors, and spintronic devices. This scale is typically below the optical diffraction limit, precluding precise wave-function engineering using optical potentials alone. We present a protocol to rapidly control the phase and density of a quantum fluid down to the healing length scale using strong time-dependent coupling between internal states of the fluid in a magnetic field gradient. We demonstrate this protocol by simulating the creation of a single stationary soliton and double soliton states in a Bose-Einstein condensate with control over the individual soliton positions and trajectories, using experimentally feasible parameters. Such states are yet to be realized experimentally, and are a path towards engineering soliton gases and exotic topological excitations.
Human brain networks function in connectome-specific harmonic waves.
Atasoy, Selen; Donnelly, Isaac; Pearson, Joel
2016-01-21
A key characteristic of human brain activity is coherent, spatially distributed oscillations forming behaviour-dependent brain networks. However, a fundamental principle underlying these networks remains unknown. Here we report that functional networks of the human brain are predicted by harmonic patterns, ubiquitous throughout nature, steered by the anatomy of the human cerebral cortex, the human connectome. We introduce a new technique extending the Fourier basis to the human connectome. In this new frequency-specific representation of cortical activity, that we call 'connectome harmonics', oscillatory networks of the human brain at rest match harmonic wave patterns of certain frequencies. We demonstrate a neural mechanism behind the self-organization of connectome harmonics with a continuous neural field model of excitatory-inhibitory interactions on the connectome. Remarkably, the critical relation between the neural field patterns and the delicate excitation-inhibition balance fits the neurophysiological changes observed during the loss and recovery of consciousness.
Norm of Bethe Wave Function as a Determinant
Korepin, Vladimir E
2009-01-01
This is a historical note. Bethe Ansatz solvable models are considered, for example XXZ Heisenberg anti-ferromagnet and Bose gas with delta interaction. Periodic boundary conditions lead to Bethe equation. The square of the norm of Bethe wave function is equal to a determinant of linearized system of Bethe equations (determinant of matrix of second derivatives of Yang action). The proof was first published in Communications in Mathematical Physics, vol 86, page 391 in l982. Also domain wall boundary conditions for 6 vertex model were discovered in the same paper [see Appendix D]. These play an important role for algebraic combinatorics: alternating sign matrices, domino tiling and plane partition. Many publications are devoted to six vertex model with domain wall boundary conditions.
From Bethe-Salpeter Wave functions to Generalised Parton Distributions
Mezrag, C.; Moutarde, H.; Rodríguez-Quintero, J.
2016-09-01
We review recent works on the modelling of generalised parton distributions within the Dyson-Schwinger formalism. We highlight how covariant computations, using the impulse approximation, allows one to fulfil most of the theoretical constraints of the GPDs. Specific attention is brought to chiral properties and especially the so-called soft pion theorem, and its link with the Axial-Vector Ward-Takahashi identity. The limitation of the impulse approximation are also explained. Beyond impulse approximation computations are reviewed in the forward case. Finally, we stress the advantages of the overlap of lightcone wave functions, and possible ways to construct covariant GPD models within this framework, in a two-body approximation.
From Bethe-Salpeter Wave Functions to Generalised Parton Distributions
Mezrag, C; Rodriguez-Quintero, J
2016-01-01
We review recent works on the modelling of Generalised Parton Distributions within the Dyson-Schwinger formalism. We highlight how covariant computations, using the impulse approximation, allows one to fulfil most of the theoretical constraints of the GPDs. Specific attention is brought to chiral properties and especially the so-called soft pion theorem, and its link with the Axial-Vector Ward-Takahashi identity. The limitation of the impulse approximation are also explained. Beyond impulse approximation computations are reviewed in the forward case. Finally, we stress the advantages of the overlap of lightcone wave functions, and possible ways to construct covariant GPD models within this framework, in a two-body approximation.
The wave function essays on the metaphysics of quantum mechanics
Albert, David Z
2013-01-01
This is a new volume of original essays on the metaphysics of quantum mechanics. The essays address questions such as: What fundamental metaphysics is best motivated by quantum mechanics? What is the ontological status of the wave function? Does quantum mechanics support the existence of any other fundamental entities, e.g. particles? What is the nature of the fundamental space (or space-time manifold) of quantum mechanics? What is the relationship between the fundamental ontology of quantum mechanics and ordinary, macroscopic objects like tables, chairs, and persons? This collection includes a comprehensive introduction with a history of quantum mechanics and the debate over its metaphysical interpretation focusing especially on the main realist alternatives.
Semiclassical-wave-function perspective on high-harmonic generation
Mauger, François; Abanador, Paul M.; Lopata, Kenneth; Schafer, Kenneth J.; Gaarde, Mette B.
2016-04-01
We introduce a semiclassical-wave-function (SCWF) model for strong-field physics and attosecond science. When applied to high-harmonic generation (HHG), this formalism allows one to show that the natural time-domain separation of the contribution of ionization, propagation, and recollisions to the HHG process leads to a frequency-domain factorization of the harmonic yield into these same contributions, for any choice of atomic or molecular potential. We first derive the factorization from the natural expression of the dipole signal in the temporal domain by using a reference system, as in the quantitative rescattering (QRS) formalism [J. Phys. B 43, 122001 (2010), 10.1088/0953-4075/43/12/122001]. Alternatively, we show how the trajectory component of the SCWF can be used to express the factorization, which also allows one to attribute individual contributions to the spectrum to the underlying trajectories.
The one loop gluon emission light cone wave function
Lappi, Tuomas
2016-01-01
Light cone perturbation theory has become an essential tool to calculate cross sections for various small-$x$ dilute-dense processes such as deep inelastic scattering and forward proton-proton and proton-nucleus collisions. Here we set out to do one loop calculations in an explicit helicity basis in the four dimensional helicity scheme. As a first process we calculate light cone wave function for one gluon emission to one-loop order in Hamiltonian perturbation theory on the light front. We regulate ultraviolet divergences with transverse dimensional regularization and soft divergences with using a cut-off on longitudinal momentum. We show that when all the renormalization constants are combined, the ultraviolet divergences can be absorbed into the standard QCD running coupling constant, and give an explicit expression for the remaining finite part.
Topological wave functions and the 4D-5D lift
Gao, Peng
2008-01-01
We revisit the holomorphic anomaly equations satisfied by the topological string amplitude from the perspective of the 4D-5D lift, in the context of ``magic'' N=2 supergravity theories. In particular, we interpret the Gopakumar-Vafa relation between 5D black hole degeneracies and the topological string amplitude as the result of a canonical transformation from 4D to 5D charges. Moreover we use the known Bekenstein-Hawking entropy of 5D black holes to constrain the asymptotic behavior of the topological wave function at finite topological coupling but large K\\"ahler classes. In the process, some subtleties in the relation between 5D black hole degeneracies and the topological string amplitude are uncovered, but not resolved. Finally we extend these considerations to the putative one-parameter generalization of the topological string amplitude, and identify the canonical transformation as a Weyl reflection inside the 3D duality group.
Dominant partition method. [based on a wave function formalism
Dixon, R. M.; Redish, E. F.
1979-01-01
By use of the L'Huillier, Redish, and Tandy (LRT) wave function formalism, a partially connected method, the dominant partition method (DPM) is developed for obtaining few body reductions of the many body problem in the LRT and Bencze, Redish, and Sloan (BRS) formalisms. The DPM maps the many body problem to a fewer body one by using the criterion that the truncated formalism must be such that consistency with the full Schroedinger equation is preserved. The DPM is based on a class of new forms for the irreducible cluster potential, which is introduced in the LRT formalism. Connectivity is maintained with respect to all partitions containing a given partition, which is referred to as the dominant partition. Degrees of freedom corresponding to the breakup of one or more of the clusters of the dominant partition are treated in a disconnected manner. This approach for simplifying the complicated BRS equations is appropriate for physical problems where a few body reaction mechanism prevails.
Multi-Determinant Wave-functions in Quantum Monte Carlo
Morales, M A; Clark, B K; Kim, J; Scuseria, G; 10.1021/ct3003404
2013-01-01
Quantum Monte Carlo (QMC) methods have received considerable attention over the last decades due to their great promise for providing a direct solution to the many-body Schrodinger equation in electronic systems. Thanks to their low scaling with number of particles, QMC methods present a compelling competitive alternative for the accurate study of large molecular systems and solid state calculations. In spite of such promise, the method has not permeated the quantum chemistry community broadly, mainly because of the fixed-node error, which can be large and whose control is difficult. In this Perspective, we present a systematic application of large scale multi-determinant expansions in QMC, and report on its impressive performance with first row dimers and the 55 molecules of the G1 test set. We demonstrate the potential of this strategy for systematically reducing the fixed-node error in the wave function and for achieving chemical accuracy in energy predictions. When compared to traditional quantum chemistr...
Ground State Reactions of nC60 with Free Chlorine in Water.
Wu, Jiewei; Benoit, Denise; Lee, Seung Soo; Li, Wenlu; Fortner, John D
2016-01-19
Facile, photoenhanced transformations of water-stable C60 aggregates (nC60) to oxidized, soluble fullerene derivatives, have been described as key processes in understanding the ultimate environmental fate of fullerene based materials. In contrast, fewer studies have evaluated the aqueous reactivity of nC60 during ground-state conditions (i.e., dark conditions). Herein, this study identifies and characterizes the physicochemical transformations of C60 (as nC60 suspensions) in the presence of free chlorine, a globally used chemical oxidant, in the absence of light under environmentally relevant conditions. Results show that nC60 undergoes significant oxidation in the presence of free chlorine and the oxidation reaction rates increase with free chlorine concentration while being inversely related to solution pH. Product characterization by FTIR, XPS, Raman Spectroscopy, TEM, XRD, TOC, collectively demonstrates that oxidized C60 derivatives are readily formed in the presence of free chlorine with extensive covalent oxygen and even chlorine additions, and behave as soft (or loose) clusters in solution. Aggregation kinetics, as a function of pH and ionic strength/type, show a significant increase in product stabilities for all cases evaluated, even at pH values approaching 1. As expected with increased (surface) oxidation, classic Kow partitioning studies indicate that product clusters are relatively more hydrophilic than parent (reactant) nC60. Taken together, this work highlights the importance of understanding nanomaterial reactivity and the identification of corresponding stable daughter products, which are likely to differ significantly from parent material properties and behaviors.
Magnetostriction-driven ground-state stabilization in 2H perovskites
Porter, D. G.; Senn, M. S.; Khalyavin, D. D.; Cortese, A.; Waterfield-Price, N.; Radaelli, P. G.; Manuel, P.; zur-Loye, H.-C.; Mazzoli, C.; Bombardi, A.
2016-10-01
The magnetic ground state of Sr3A RuO6 , with A =(Li ,Na ) , is studied using neutron diffraction, resonant x-ray scattering, and laboratory characterization measurements of high-quality crystals. Combining these results allows us to observe the onset of long-range magnetic order and distinguish the symmetrically allowed magnetic models, identifying in-plane antiferromagnetic moments and a small ferromagnetic component along the c axis. While the existence of magnetic domains masks the particular in-plane direction of the moments, it has been possible to elucidate the ground state using symmetry considerations. We find that due to the lack of local anisotropy, antisymmetric exchange interactions control the magnetic order, first through structural distortions that couple to in-plane antiferromagnetic moments and second through a high-order magnetoelastic coupling that lifts the degeneracy of the in-plane moments. The symmetry considerations used to rationalize the magnetic ground state are very general and will apply to many systems in this family, such as Ca3A RuO6 , with A =(Li ,Na ) , and Ca3LiOsO6 whose magnetic ground states are still not completely understood.
DEFF Research Database (Denmark)
Reynisson, J.; Wilbrandt, R.; Brinck, V.
2002-01-01
of the long wavelength absorption band. A strong fluorescence is observed at 520 nm (tau(n) = 14.6 ns, phi(n) = 0.12 in deaerated acetonitrile). The fluorescence is quenched by 10 aromatic electron donors predominantly via a dynamic charge transfer mechanism, but ground state complexation is shown...
Fourier-transform spectroscopy of Sr2 and revised ground-state potential
Stein, A.; Knöckel, H.; Tiemann, E.
2008-10-01
Precise potentials for the ground-state XΣg+1 and the minimum region of the excited state 2Σu+1 of Sr2 are derived by high-resolution Fourier-transform spectroscopy of fluorescence progressions from single-frequency laser excitation of Sr2 produced in a heat pipe at 950°C . A change of the rotational assignment by four units compared to an earlier work [G. Gerber , J. Chem. Phys. 81, 1538 (1984)] is needed for a consistent description leading to a significant shift of the potentials toward longer interatomic distances. The huge amount of ground-state data derived for the three different isotopomers Sr288 , Sr86Sr88 , and Sr87Sr88 (almost 60% of all excisting bound rovibrational ground-state levels for the isotopomer Sr288 ) fixes this assignment beyond a doubt. The presented ground-state potential is derived from the observed transitions for the radial region from 4to11Å ( 9cm-1 below the asymptote) and is extended to the long-range region by the use of theoretical dispersion coefficients together with already available photoassociation data. New estimations of the scattering lengths for the complete set of isotopic combinations are derived by mass scaling with the derived potential. The data set for the excited state 2Σu+1 was sufficient to derive a potential energy curve around the minimum.
Theoretical Studies on Thermal Decomposition of Benzoyl Peroxide in Ground State
Institute of Scientific and Technical Information of China (English)
SUN Cheng-ke; YANG Si-ya; LIN Xue-fei; MA Si-yu; LI Zong-he
2003-01-01
Systematic studies of the thermal decomposition mechanism of benzoyl peroxide(BPO) in ground state, leading to various intermediates, products and the potential energy surface(PES) of possible dissociation reactions were made computationally. The structures of the transition states and the activation energies for all the paths causing the formation of the reaction products mentioned above were calculated by the AM1 semi-empirical method. This method is shown to to be one predict correctly the preferred pathway for the title reaction. It has been found that in ground state, the thermal decomposition of benzoyl peroxide has two kinds of paths. The first pathway PhC(O)O-OC(O)Ph→PhC(O)O*→Ph*+CO2 produces finally phenyl radicals and carbon dioxide. And the second pathway PhC(O)OO-C(O)Ph→PhC(O)OO*+PhC(O)*→PhC(O)*+O2→Ph*+CO+O2, via which the reaction takes place only in two steps, produces oxygen and PhC(O)* radicals, and the further thermal dissociation of PhC(O)* is quite difficult because of the high activation energy in ground state. The calculated activation energies and reaction enthalpies are in good agreement with the experimental values. The research results also show that also the thermal dissociation process of the two bonds or the three bonds for the benzoyl peroxide doesn′t take place in ground state.
Patterns of the ground states in the presence of random interactions : Nucleon systems
Zhao, YM; Arima, A; Shimizu, N; Ogawa, K; Yoshinaga, N; Scholten, O
2004-01-01
We present our results on properties of ground states for nucleonic systems in the presence of random two-body interactions. In particular, we calculate probability distributions for parity, seniority, spectroscopic (i.e., in the laboratory frame) quadrupole moments, and discuss a clustering in the
Seif, W M; Refaie, A I
2015-01-01
The ground-state spin and parity of a formed daughter in the radioactive Alpha-emitter is expected to influence the preformation probability of the Alpha and daughter clusters inside it. We investigate the Alpha and daughter preformation probability inside odd-A and doubly-odd radioactive nuclei when the daughter and parent are of different spin and/or parity. We consider only the ground-state to ground-state unfavored decays. This is to extract precise information about the effect of the difference in the ground states spin-parity of the involved nuclei far away any influences from the excitation energy if the decays are coming from isomeric states. The calculations are done for 161 Alpha-emitters, with Z=65-112 and N=84-173, in the framework of the extended cluster model, with WKB penetrability and assault frequency. We used a Hamiltonian energy density scheme based on Skyrme-SLy4 interaction to compute the interaction potential. The Alpha plus cluster preformation probability is extracted from the calculat...
A New Method for the Atomic Ground-State Energy in the Screened Coulomb Potential
Institute of Scientific and Technical Information of China (English)
YU Peng-Peng; GUO Hua
2001-01-01
The new method proposed recently by Friedberg,Lee and Zhao is applied to the derivation of the atomic ground-state energy with the inclusion of the screening effect.The present results are compared with those obtained in the pure Coulomb potential and by the variational approach.The overall good results are obtained with this new method.``