7,198 research outputs found
Hooke's law correlation in two-electron systems
We study the properties of the Hooke's law correlation energy (\Ec),
defined as the correlation energy when two electrons interact {\em via} a
harmonic potential in a -dimensional space. More precisely, we investigate
the ground state properties of two model systems: the Moshinsky atom (in
which the electrons move in a quadratic potential) and the spherium model (in
which they move on the surface of a sphere). A comparison with their Coulombic
counterparts is made, which highlights the main differences of the \Ec in
both the weakly and strongly correlated limits. Moreover, we show that the
Schr\"odinger equation of the spherium model is exactly solvable for two values
of the dimension (), and that the exact wave function is
based on Mathieu functions.Comment: 7 pages, 5 figure
The Bravyi-Kitaev transformation for quantum computation of electronic structure
Quantum simulation is an important application of future quantum computers
with applications in quantum chemistry, condensed matter, and beyond. Quantum
simulation of fermionic systems presents a specific challenge. The
Jordan-Wigner transformation allows for representation of a fermionic operator
by O(n) qubit operations. Here we develop an alternative method of simulating
fermions with qubits, first proposed by Bravyi and Kitaev [S. B. Bravyi, A.Yu.
Kitaev, Annals of Physics 298, 210-226 (2002)], that reduces the simulation
cost to O(log n) qubit operations for one fermionic operation. We apply this
new Bravyi-Kitaev transformation to the task of simulating quantum chemical
Hamiltonians, and give a detailed example for the simplest possible case of
molecular hydrogen in a minimal basis. We show that the quantum circuit for
simulating a single Trotter time-step of the Bravyi-Kitaev derived Hamiltonian
for H2 requires fewer gate applications than the equivalent circuit derived
from the Jordan-Wigner transformation. Since the scaling of the Bravyi-Kitaev
method is asymptotically better than the Jordan-Wigner method, this result for
molecular hydrogen in a minimal basis demonstrates the superior efficiency of
the Bravyi-Kitaev method for all quantum computations of electronic structure
Exchange effects on electron scattering through a quantum dot embedded in a two-dimensional semiconductor structure
We have developed a theoretical method to study scattering processes of an
incident electron through an N-electron quantum dot (QD) embedded in a
two-dimensional (2D) semiconductor. The generalized Lippmann-Schwinger
equations including the electron-electron exchange interaction in this system
are solved for the continuum electron by using the method of continued
fractions (MCF) combined with 2D partial-wave expansion technique. The method
is applied to a one-electron QD case. Cross-sections are obtained for both the
singlet and triplet couplings between the incident electron and the QD electron
during the scattering. The total elastic cross-sections as well as the
spin-flip scattering cross-sections resulting from the exchange potential are
presented. Furthermore, inelastic scattering processes are also studied using a
multichannel formalism of the MCF.Comment: 11 pages, 4 figure
A comparison of the Bravyi-Kitaev and Jordan-Wigner transformations for the quantum simulation of quantum chemistry
The ability to perform classically intractable electronic structure
calculations is often cited as one of the principal applications of quantum
computing. A great deal of theoretical algorithmic development has been
performed in support of this goal. Most techniques require a scheme for mapping
electronic states and operations to states of and operations upon qubits. The
two most commonly used techniques for this are the Jordan-Wigner transformation
and the Bravyi-Kitaev transformation. However, comparisons of these schemes
have previously been limited to individual small molecules. In this paper we
discuss resource implications for the use of the Bravyi-Kitaev mapping scheme,
specifically with regard to the number of quantum gates required for
simulation. We consider both small systems which may be simulatable on
near-future quantum devices, and systems sufficiently large for classical
simulation to be intractable. We use 86 molecular systems to demonstrate that
the use of the Bravyi-Kitaev transformation is typically at least approximately
as efficient as the canonical Jordan-Wigner transformation, and results in
substantially reduced gate count estimates when performing limited circuit
optimisations.Comment: 46 pages, 11 figure
Quantized Nambu-Poisson Manifolds and n-Lie Algebras
We investigate the geometric interpretation of quantized Nambu-Poisson
structures in terms of noncommutative geometries. We describe an extension of
the usual axioms of quantization in which classical Nambu-Poisson structures
are translated to n-Lie algebras at quantum level. We demonstrate that this
generalized procedure matches an extension of Berezin-Toeplitz quantization
yielding quantized spheres, hyperboloids, and superspheres. The extended
Berezin quantization of spheres is closely related to a deformation
quantization of n-Lie algebras, as well as the approach based on harmonic
analysis. We find an interpretation of Nambu-Heisenberg n-Lie algebras in terms
of foliations of R^n by fuzzy spheres, fuzzy hyperboloids, and noncommutative
hyperplanes. Some applications to the quantum geometry of branes in M-theory
are also briefly discussed.Comment: 43 pages, minor corrections, presentation improved, references adde
Mechanics of the Ski-Snow Contact
Two outstanding questions of the ski-snow friction are considered: the deformation mode of the snow and the real contact area. The deformation of hard, well sintered snow in a short time impact has been measured with a special linear friction tester. Four types of deformations have been identified: brittle fracture of bonds, plastic deformation of ice at the contact spots, elastic and delayed elastic deformation of the snow matrix. The latter is the dominant deformation in the ski-snow contact. Based on the measured loading curves the mechanical energy dissipation of snow deformation in skiing on hard snow has been determined and found negligible compared to the thermal energy dissipation. A mechanical model consisting of ice spheres supported by rheological elements (a non-linear spring in series with a Kelvin element) is proposed to model the deformation of snow in the ski-snow contact. The model can describe the delayed elastic behaviour of snow. Coupled with the complete topographical description of the snow surface obtained from X-ray micro computer tomography measurements, the model predicts the number and area of contact spots between ski and snow. An average contact spot size of 110μm, and a relative real contact area of 0.4% has been foun
Ground-state densities and pair correlation functions in parabolic quantum dots
We present an extensive comparative study of ground-state densities and pair
distribution functions for electrons confined in two-dimensional parabolic
quantum dots over a broad range of coupling strength and electron number. We
first use spin-density-functional theory to determine spin densities that are
compared with Diffusion Monte Carlo (DMC) data. This accurate knowledge of
one-body properties is then used to construct and test a local approximation
for the electron-pair correlations. We find very satisfactory agreement between
this local scheme and the available DMC data, and provide a detailed picture of
two-body correlations in a coupling-strength regime preceding the formation of
Wigner-like electron ordering.Comment: 18 pages, 12 figures, submitte
Model ab initio study of charge carrier solvation and large polaron formation on conjugated carbon chains
Using long C_{N}H_{2} conjugated carbon chains with the polyynic structure as
prototypical examples of one-dimensional (1D) semiconductors, we discuss
self-localization of excess charge carriers into 1D large polarons in the
presence of the interaction with a surrounding polar solvent. The solvation
mechanism of self-trapping is different from the polaron formation due to
coupling with bond-length modulations of the underlying atomic lattice
well-known in conjugated polymers. Model ab initio computations employing the
hybrid B3LYP density functional in conjunction with the polarizable continuum
model are carried out demonstrating the formation of both electron- and
hole-polarons. Polarons can emerge entirely due to solvation but even larger
degrees of charge localization occur when accompanied by atomic displacements
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