90 research outputs found
Decay process accelerated by tunneling in its very early stage
We examine a fast decay process that arises in the transition period between
the Gaussian and exponential decay processes in quantum decay systems. It is
usually expected that the decay is decelerated by a confinement potential
barrier. However, we find a case where the decay in the transition period is
accelerated by tunneling through a confinement potential barrier. We show that
the acceleration gives rise to an appreciable effect on the time evolution of
the nonescape probability of the decay system.Comment: 4 pages, 6 figures; accepted for publication in Phys. Rev.
Hylleraas-Configuration Interaction calculations on the 1 ^1S ground state of helium atom
Hylleraas-Configuration Interaction (Hy-CI) calculations on the ground S
state of helium atom are presented using s-, p-, d-, and f-Slater orbitals of
both real and complex form. Techniques of construction of adapted
configurations, optimization of the orbital exponents and structure of the wave
function expansion are explored. A new method to evaluate the two-electron
kinetic energy integrals occurring in the Hy-CI method has been tested here and
compared with other methods. The non-relativistic Hy-CI values are
approximately 10 picohartree accurate, about 2.2 x 10 cm. The
Hy-CI calculations are compared with Configuration Interaction (CI) and
Hylleraas (Hy) calculations employing the same orbital basis set, same computer
code and same computer machines. The computational required times are reported.Comment: 33 pages, 9 tables, 38 references and 0 figure
The transformation of irreducible tensor operators under spherical functions
The irreducible tensor operators and their tensor products employing Racah
algebra are studied. Transformation procedure of the coordinate system
operators act on are introduced. The rotation matrices and their
parametrization by the spherical coordinates of vector in the fixed and rotated
coordinate systems are determined. A new way of calculation of the irreducible
coupled tensor product matrix elements is suggested. As an example, the
proposed technique is applied for the matrix element construction for two
electrons in a field of a fixed nucleus.Comment: To appear in Int. J. Theor. Phy
A Plaquette Basis for the Study of Heisenberg Ladders
We employ a plaquette basis-generated by coupling the four spins in a
lattice to a well-defined total angular momentum-for the study of
Heisenberg ladders with antiferromagnetic coupling. Matrix elements of the
Hamiltonian in this basis are evaluated using standard techniques in
angular-momentum (Racah) algebra. We show by exact diagonalization of small
( and ) systems that in excess of 90% of the ground-state
probability is contained in a very small number of basis states. These few
basis states can be used to define a severely truncated basis which we use to
approximate low-lying exact eigenstates. We show how, in this low-energy basis,
the isotropic spin-1/2 Heisenberg ladder can be mapped onto an anisotropic
spin-1 ladder for which the coupling along the rungs is much stronger than the
coupling between the rungs. The mapping thereby generates two distinct energy
scales which greatly facilitates understanding the dynamics of the original
spin-1/2 ladder. Moreover, we use these insights to define an effective
low-energy Hamiltonian in accordance to the newly developed COntractor
REnormalization group (CORE) method. We show how a simple range-2 CORE
approximation to the effective Hamiltonian to be used with our truncated basis
reproduces the low-energy spectrum of the exact theory at the \alt
1% level.Comment: 12 pages with two postscript figure
Recurrence and differential relations for spherical spinors
We present a comprehensive table of recurrence and differential relations
obeyed by spin one-half spherical spinors (spinor spherical harmonics)
used in relativistic atomic, molecular, and
solid state physics, as well as in relativistic quantum chemistry. First, we
list finite expansions in the spherical spinor basis of the expressions
and
{}, where , , and
are either of the following vectors or vector operators:
(the radial unit vector), ,
(the spherical, or cyclic, versors),
(the Pauli matrix vector),
(the dimensionless
orbital angular momentum operator; is the unit matrix),
(the dimensionless
total angular momentum operator). Then, we list finite expansions in the
spherical spinor basis of the expressions
and
, where at least one of the objects
, , is the nabla operator
, while the remaining ones are chosen from the set
, , , ,
, .Comment: LaTeX, 12 page
A model for single electron decays from a strongly isolated quantum dot
Recent measurements of electron escape from a non-equilibrium charged quantum
dot are interpreted within a 2D separable model. The confining potential is
derived from 3D self-consistent Poisson-Thomas-Fermi calculations. It is found
that the sequence of decay lifetimes provides a sensitive test of the confining
potential and its dependence on electron occupation.Comment: 9 pages, 10 figure
Symmetry of the Atomic Electron Density in Hartree, Hartree-Fock, and Density Functional Theory
The density of an atom in a state of well-defined angular momentum has a
specific finite spherical harmonic content, without and with interactions.
Approximate single-particle schemes, such as the Hartree, Hartree-Fock, and
Local Density Approximations, generally violate this feature. We analyze, by
means of perturbation theory, the degree of this violation and show that it is
small. The correct symmetry of the density can be assured by a
constrained-search formulation without significantly altering the calculated
energies. We compare our procedure to the (different) common practice of
spherically averaging the self-consistent potential. Kohn-Sham density
functional theory with the exact exchange-correlation potential has the correct
finite spherical harmonic content in its density; but the corresponding exact
single particle potential and wavefunctions contain an infinite number of
spherical harmonics.Comment: 11 pages, 6 figures. Expanded discussion of spherical harmonic
expansion of Hartree density. Some typos corrected, references adde
Correcting 100 years of misunderstanding: electric fields in superconductors, hole superconductivity, and the Meissner effect
From the outset of superconductivity research it was assumed that no
electrostatic fields could exist inside superconductors, and this assumption
was incorporated into conventional London electrodynamics. Yet the London
brothers themselves initially (in 1935) had proposed an electrodynamic theory
of superconductors that allowed for static electric fields in their interior,
which they unfortunately discarded a year later. I argue that the Meissner
effect in superconductors necessitates the existence of an electrostatic field
in their interior, originating in the expulsion of negative charge from the
interior to the surface when a metal becomes superconducting. The theory of
hole superconductivity predicts this physics, and associated with it a
macroscopic spin current in the ground state of superconductors ("Spin Meissner
effect"), qualitatively different from what is predicted by conventional
BCS-London theory. A new London-like electrodynamic description of
superconductors is proposed to describe this physics. Within this theory
superconductivity is driven by lowering of quantum kinetic energy, the fact
that the Coulomb repulsion strongly depends on the character of the charge
carriers, namely whether electron- or hole-like, and the spin-orbit
interaction. The electron-phonon interaction does not play a significant role,
yet the existence of an isotope effect in many superconductors is easily
understood. In the strong coupling regime the theory appears to favor local
charge inhomogeneity. The theory is proposed to apply to all superconducting
materials, from the elements to the high cuprates and pnictides, is
highly falsifiable, and explains a wide variety of experimental observations.Comment: Proceedings of the conference "Quantum phenomena in complex matter
2011 - Stripes 2011", Rome, 10 July -16 July 2011, to be published in J.
Supercond. Nov. Mag
Infrared activity of hydrogen molecules trapped in Si
The rovibrational-translational states of a hydrogen molecule moving in a cage site in Si, when subjected to an electrical field arising from its surroundings, are investigated. The wave functions are expressed in terms of basis functions consisting of the eigenfunctions of the molecule confined to move in the cavity and rovibrational states of the free molecule. The energy levels, intensities of infrared and Raman transitions, effects of uniaxial stress, and a neighboring oxygen defect are found and compared with existing experimental data
Model study on the photoassociation of a pair of trapped atoms into an ultralong-range molecule
Using the method of quantum-defect theory, we calculate the ultralong-range
molecular vibrational states near the dissociation threshold of a diatomic
molecular potential which asymptotically varies as . The properties of
these states are of considerable interest as they can be formed by
photoassociation (PA) of two ground state atoms. The Franck-Condon overlap
integrals between the harmonically trapped atom-pair states and the
ultralong-range molecular vibrational states are estimated and compared with
their values for a pair of untrapped free atoms in the low-energy scattering
state. We find that the binding between a pair of ground-state atoms by a
harmonic trap has significant effect on the Franck-Condon integrals and thus
can be used to influence PA. Trap-induced binding between two ground-state
atoms may facilitate coherent PA dynamics between the two atoms and the
photoassociated diatomic molecule.Comment: 11 pages, 4 figures, to appear in Phys. Rev. A (September, 2003
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