Unperturbed Ground State Research Articles

Quantum dynamics of an electron moving in coupled quartic and coupled double-well oscillators under intense laser fields

The phenomenon of quantum chaos is investigated by employing the model of an electron moving in coupled nonlinear two-dimensional oscillators, namely, coupled quartic and coupled double-well oscillators, under intense laser fields. The unperturbed ground-state wavefunctions of the oscillators, obtained by solving the time-dependent Schrödinger equation (TDSE) in imaginary time, are evolved in real time by numerically solving the TDSE. Various signatures like autocorrelation function, distance function, quantum “phase space” volume, “phase space” trajectories and overlap integral (similar to quantum fidelity or Loschmidt echo) have been studied to diagnose quantum chaos in terms of sensitivity towards an initial state characterized by a mixture of quantum states (wavepacket), brought about by small changes in the Hamiltonian, rather than towards a “pure” quantum state (i.e., a single eigenstate). Other quantum dynamical aspects such as time-dependent probability density distributions as well as power spectra and high harmonic generation (HHG) spectra at different laser intensities have also been examined. In case of the coupled double-well oscillator, suppression of quantum chaos has been observed.

Perturbation theory for isotropic velocity-dependent potentials: Bound-states case

Starting from the time-independent Schrodinger equation we develop formulae for the changes in the bound-state energies in the presence of an isotropic, velocity-dependent perturbing potential. The corresponding changes in the wave functions are also obtained. Unlike the case of the standard perturbation theory, determination of the changes in the energy and the wave function of a state only requires knowledge of the unperturbed ground-state wave function in addition to the perturbing potential. Evaluations of the energy changes and the corresponding wave functions are given for two examples in the s-wave case.

Casimir's spheres near the Coulomb limit: energy density, pressures and radiative effects

We study the quantum mechanics of an infinitesimally thin spherical fluid shell of radius R, having continuous charge and mass densities e/a2 and m/a2 per unit area, with a R, and subject to a Debye-type cut-off on surface-parallel wave numbers. Attention is confined to the regime ? ? 4?e2R/mc2a2 1, where nonretarded (NR) Coulomb forces dominate, and the coupling to the quantized Maxwell field is only a weak perturbation. The unperturbed ground-state energy BNR is of order (e2/ma7)1/2R2. Half of BNR is kinetic energy, localized on the shell; the other half is Coulomb energy, with a density u appreciable only within distances of order a from the shell. The pressure P = 3BNR/8?R3 follows directly from the principle of virtual work: more detailed analysis shows that P/3 comes from Coulomb forces, and 2P/3 from the zero-point motion of the fluid. It seems likely that u and P behave in much the same way also for large ?. The purely Coulombic system has stable discrete-frequency excitations (plasmons); to leading order the perturbation displaces the frequencies and allows a plasmon to decay into a photon. The displacements and decay rates tally with what one infers from the exact classical multipole phase shifts, and from the already-known energy for arbitrary values of ?.

Theoreticalstudy of the static screening in insulators: ab initio andmodel dielectric functions

We study the screening properties of the three cubic crystalsSi, SrTiO3, and MgO, considered as prototypes of materialswith various degrees of ionic and covalent bonding. First, wecarry out a numerical calculation of the density induced by ashort-range time-independent perturbation, in the framework ofthe density functional theory. The short- and medium-rangefeatures of screening are discussed and differences from andsimilarities with the homogeneous electron gas are stressed.Secondly, we address the question of how local fields can bemimicked by simplified models of the microscopic staticdielectric function in which the screening lengths are functionsof the unperturbed ground-state local density. While short-rangecharacteristics are fairly well reproduced, we show that theoscillatory behaviour of the induced density in direct spacecannot be accounted for by such models. Thirdly, we use the spectraldecomposition of the one-electron static polarization responsefunction and propose a simple way to take into account thecontribution of the high-energy conduction band states withoutcalculating them explicitly. This method lightens thenumerical burden of the polarization calculation considerably and maythus open the way to the computation of static responsefunctions of large systems.

Intruder states in8Be

Low-lying intruder $T=0$ states in ${}^{8}\mathrm{Be}$ have been posited and challenged. To address this issue, we performed ab initio shell model calculations in model spaces consisting of up to $10\ensuremath{\Elzxh}\ensuremath{\Omega}$ excitations above the unperturbed ground state with the basis state dimensions reaching $1.87\ifmmode\times\else\texttimes\fi{}{10}^{8}.$ To gain predictive power we derive and use effective interactions from realistic nucleon-nucleon $(\mathrm{NN})$ potentials in a way that guarantees convergence to the exact solution with increasing model space. Our $0\ensuremath{\Elzxh}\ensuremath{\Omega}$ dominated states show good stability when the model space size increases. At the same time, we observe a rapid drop in excitation energy of the $2\ensuremath{\Elzxh}\ensuremath{\Omega}$ dominated $T=0$ states. In the $10\ensuremath{\Elzxh}\ensuremath{\Omega}$ space the intruder ${0}^{+}0$ state falls below 18 MeV of excitation and, also, below the lowest ${0}^{+}1$ state. Our extrapolations suggest that this state may stabilize around 12 MeV. We hypothesize that these states might be the broad resonance intruder states needed in R-matrix analysis of $\ensuremath{\alpha}\ensuremath{-}\ensuremath{\alpha}$ elastic scattering. In addition, we present our predictions for the $A=8$ binding energies with the CD-Bonn $\mathrm{NN}$ potential.

Antiferromagnetism of the two-dimensional Hubbardmodel at half-filling: the analytic ground state for weak coupling

We introduce a local formalism to deal with the Hubbard modelon an N×N square lattice (for even N) in terms ofeigenstates of number operators, having well defined point symmetry.For U→0, the low-lying shells of the kinetic energyare filled in the ground state. At half-filling, using the 2N-2one-body states of the partially occupied shell \U0001d4aehf, webuild a set of degenerate unperturbed groundstates with Sz = 0 which are then resolved by the Hubbardinteraction Ŵ = U∑rn̂r↑n̂r↓. We study the many-body eigenstates in\U0001d4aehf of the kinetic energy with vanishing eigenvalue ofthe Hubbard repulsion (W = 0 states). In the Sz = 0 sector, thisis an N-times-degenerate multiplet. From the singlet componentone obtains the ground state of the Hubbard model for U = 0+,which is unique, in agreement with a theorem of Lieb. The wavefunction demonstrates an antiferromagnetic order, a lattice steptranslation being equivalent to a spin flip. We show that the totalmomentum vanishes, while the point symmetry is s or d for even orodd N/2, respectively.

Non trivial overlap distributions at zero temperature

We explore the consequences of Replica Symmetry Breaking at zero temperature. We introduce a repulsive coupling between a system and its unperturbed ground state. In the Replica Symmetry Breaking scenario a finite coupling induces a non trivial overlap probability distribution among the unperturbed ground state and the one in presence of the coupling. We find a closed formula for this probability for arbitrary ultrametric trees, in terms of the parameters defining the tree. The same probability is computed in numerical simulations of a simple model with many ground states, but no ultrametricity: polymers in random media in 1+1 dimension. This gives us an idea of what violation of our formula can be expected in cases when ultrametricity does not hold.

Simulation of the zero-temperature behavior of a three-dimensional elastic medium

We have performed numerical simulation of a three-dimensional elastic medium, with scalar displacements, subject to quenched disorder. In the absence of topological defects this system is equivalent to a $(3+1)$-dimensional interface subject to a periodic pinning potential. We have applied an efficient combinatorial optimization algorithm to generate exact ground states for this interface representation. Our results indicate that this Bragg glass is characterized by power law divergences in the structure factor $S(k)\ensuremath{\sim}{\mathrm{Ak}}^{\ensuremath{-}3}.$ We have found numerically consistent values of the coefficient A for two lattice discretizations of the medium, supporting universality for A in the isotropic systems considered here. We also examine the response of the ground state to the change in boundary conditions that corresponds to introducing a single dislocation loop encircling the system. The rearrangement of the ground state caused by this change is equivalent to the domain wall of elastic deformations which span the dislocation loop. Our results indicate that these domain walls are highly convoluted, with a fractal dimension ${d}_{f}=2.60(5).$ We also discuss the implications of the domain wall energetics for the stability of the Bragg glass phase. Elastic excitations similar to these domain walls arise when the pinning potential is slightly perturbed. As in other disordered systems, perturbations of relative strength \ensuremath{\delta} introduce a new length scale ${L}^{*}\ensuremath{\sim}{\ensuremath{\delta}}^{\ensuremath{-}1/\ensuremath{\zeta}}$ beyond which the perturbed ground state becomes uncorrelated with the reference (unperturbed) ground state. We have performed a scaling analysis of the response of the ground state to the perturbations and obtain $\ensuremath{\zeta}=0.385(40).$ This value is consistent with the scaling relation $\ensuremath{\zeta}{=d}_{f}/2\ensuremath{-}\ensuremath{\theta},$ where \ensuremath{\theta} characterizes the scaling of the energy fluctuations of low energy excitations.

Four-nucleon shell-model calculations in a Faddeev-like approach

We use equations for Faddeev amplitudes to solve the shell-model problem for four nucleons in the model space that includes up to 14 hbar Omega harmonic-oscillator excitations above the unperturbed ground state. Two- and three-body effective interactions derived from the Reid93 and Argonne V8' nucleon-nucleon potentials are used in the calculations. Binding energies, excitations energies, point-nucleon radii and electromagnetic and strangeness charge form factors for 4He are studied. The structure of the Faddeev-like equations is discussed and a formula for matrix elements of the permutation operators in a harmonic-oscillator basis is given. The dependence on harmonic-oscillator excitations allowed in the model space and on the harmonic-oscillator frequency is investigated. It is demonstrated that the use of the three-body effective interactions improves the convergence of the results.

Chaos in the random field Ising model

The sensitivity of the random field Ising model to small random perturbations of the quenched disorder is studied via exact ground states obtained with a maximum-flow algorithm. In one and two space dimensions we find a mild form of chaos, meaning that the overlap of the old, unperturbed ground state and the new one is smaller than 1, but extensive. In three dimensions the rearrangements are marginal (concentrated in the well defined domain walls). Implications for finite temperature variations and experiments are discussed.

First-principles responses of solids to atomic displacements and homogeneous electric fields: Implementation of a conjugate-gradient algorithm

The changes in density, wave functions, and self-consistent potentials of solids, in response to small atomic displacements or infinitesimal homogeneous electric fields, are considered in the framework of the density-functional theory. A variational principle for second-order derivatives of the energy provides a basis for efficient algorithmic approaches to these linear responses, such as the state-by-state conjugate-gradient algorithm presented here in detail. The phase of incommensurate perturbations of periodic systems, that are, like phonons, characterized by some wave vector, can be factorized: the incommensurate problem is mapped on an equivalent one presenting the periodicity of the unperturbed ground state. The singularity of the potential change associated with an homogeneous field is treated by the long-wave method. The efficient implementation of these theoretical ideas using plane waves, separable pseudopotentials, and a nonlinear exchange-correlation core correction is described in detail, as well as other technical issues.

A new simple approach to the polarizability of atoms and ions using frontier orbitals from the Kohn-Sham density functional theory

We propose a simple approach for the calculation of dipole polarizability of atoms and positive ions using the Kohn-Sham version of spin-polarized density functional theory. The prescription is simple and utilises only the frontier orbitals obtained from a single Kohn-Sham calculation for the unperturbed ground state of the system. The calculated numerical results for a number of atoms and ions are shown to agree quite well with standard values of polarizability.

Saturation of deformation atN=60 in the Sr isotopes

From the halflife oft 1/2=3.91 (16) ns for the 21 + state in100Sr a deformation parameter ofβ=0.40(1) has been derived. Within the given uncertainties, this value is equal to the recently determinedβ-parameters for98Sr and99Sr, indicating that in the Sr isotopes saturation of deformation is reached immediately at its onset well before neutron midshell. This behaviour is reflected by the “twin” character of98Sr and100Sr with identical features of their unperturbed ground-state rotational bands. These observations are discussed in terms of strong two-nucleon interactions.

Criterion for a unique non-relativistic quark model

We have calculated the mean square charge radii of the neutron and proton, and compared them with the experimental values, to construct a unique non-relativistic quark potential model. It is shown for the first time that, contrary to general belief, it is possible to reproduce simultaneously the baryon mass spectrum and the electromagnetic sizes of neutron and proton using a single potential model. It was found necessary to add admixtures of excited states of the nucleon in the unperturbed ground state wavefunctions.

Theory of Many-Fermion System on Unitary-Transformation Method

A theory is formulated for solving a many-Fermion system in the framework of unitary-transformation method. A unitary transformation of a product form Πnexp S(n) with n-body operator S(n) is introduced. The operator exp S(n) is determined on the principle that the transformed Hamiltonian should not have interactions which induce n-particle-n-hole excitation. It is proved that the operator S(n) can be given in terms of eigenstates of n-body subsystem Hamiltonian and the true gound state can be given by Πn exp S(n)|φ0>, where |φ0> is the unperturbed free ground state.

LO‐Phonon Modes Bound to Neutral Impurities in Polar Semiconductors. I. General Theory

AbstractThe influence of the Fröhlich interaction between charge carriers bound at impurities and LO‐phonons in polar semiconductors is considered within second‐order perturbation theory taking into account the possibility of degenerate unperturbed electronic ground states. From the general theory presented here changes of the bare electronic excitation energies (bound polaron excitations), Jahn‐Teller like splittings of degenerate ground states and the formation of bound to neutral impurities phonons (dielectric modes) can be obtained. The application of the general theory to special cases and experimental results will be published in a forthcoming paper.

Some aspects of self-consistent propagator theories.

A general method for constructing bases for operator manifolds for any propagator, which satisfy ``vacuum annihilation conditions'' (VAC's) is developed. This approach is based on the observation that if the transformation of the unperturbed ground state to the correlated ground state is represented as a rotation in the Fock space, the corresponding rotation induced in the basis of the concerned operator space would generate a basis which satisfies VAC's on the correlated ground state. The associated requirements for the Hermiticity of superoperator Hamiltonian would also be met in this new basis. The proposed method is noniterative in that, once the form of the ground-state function is specified, the expansion of the operator manifold satisfying VAC's on the ground state does not require any iterative readjustment. The resultant propagators in this approach are fully linked. It is shown that this theory is equivalent to a propagator formalism in terms of hole- and particle-creation and/or annihilation operators with a modified effective Hamiltonian. The self-consistent electron and polarization propagators are considered as examples, and their underlying perturbative structures are analyzed. The role of density shift operators and higher-rank operators are discussed.

Microscopic formulation for a Josephson array

The theory for an array of Josephson coupled superconductors is formulated in terms of temperature-ordered Feynman diagrams. The individual grains have an unperturbed ground state with a fixed number of electrons rather than a fixed phase. The formulation is illustrated by calculating the free energy. With relevant approximations this justifies the frequently used planar rotator model and the Giovannini-Weiss form for the free energy.

Spontaneous emission from a single two-level atom and the radiative correction to the final state

By using a modified Robertson projection technique exact equations of motion for expectation values of atomic population inversion and dipole moment operators are derived. A radiative correction to the unperturbed ground state expectation value of the population inversion operator is obtained in the Born and Markov approximation if no long-time limit approximation is used.

Acceptor ground state problems in silicon

The effective mass potential that transforms ordinary acceptors into their associated X-acceptors is directly related to the presence of carbon neighbours. The physical mechanism which leads to carbon's effective potential is shown to be similar to that which leads to the chemical shift of unperturbed acceptor ground states.