65 research outputs found
Spin dynamics of an ultra-small nanoscale molecular magnet
We present mathematical transformations which allow us to calculate the spin dynamics of an ultra-small nanoscale molecular magnet consisting of a dimer system of classical (high) Heisenberg spins. We derive exact analytic expressions (in integral form) for the time-dependent spin autocorrelation function and several other quantities. The properties of the time-dependent spin autocorrelation function in terms of various coupling parameters and temperature are discussed in detail
Exact time correlation functions for N classical Heisenberg spins in the `squashed' equivalent neighbor model
We present exact integral representations of the time-dependent spin-spin
correlation functions for the classical Heisenberg N-spin `squashed' equivalent
neighbor model, in which one spin is coupled via the Heisenberg exchange
interaction with strength to the other N-1 spins, each of which is
coupled via the Heisenberg exchange coupling with strength to the
remaining N-2 spins. At low temperature T we find that the N spins oscillate in
four modes, one of which is a central peak for a semi-infinite range of the
values of the exchange coupling ratio. For the N=4 case of four spins on a
squashed tetrahedron, detailed numerical evaluations of these results are
presented. As , we calculate exactly the long-time asymptotic
behavior of the correlation functions for arbitrary N, and compare our results
with those obtained for three spins on an isosceles triangle.Comment: 9 pages, 8 figures, submitted to Phys. Rev.
Collective excitations in quantum Hall liquid crystals: Single-mode approximation calculations
A variety of recent experiments probing the low-temperature transport
properties of quantum Hall systems have suggested an interpretation in terms of
liquid crystalline mesophases dubbed {\em quantum Hall liquid crystals}. The
single mode approximation (SMA) has been a useful tool for the determination of
the excitation spectra of various systems such as phonons in He and in the
fractional quantum Hall effect. In this paper we calculate (via the SMA) the
spectrum of collective excitations in a quantum Hall liquid crystal by
considering {\em nematic}, {\em tetratic}, and {\em hexatic} generalizations of
Laughlin's trial wave function having two-, four- and six-fold broken
rotational symmetry, respectively. In the limit of zero wavevector \qq the
dispersion of these modes is singular, with a gap that is dependent on the
direction along which \qq=0 is approached for {\em nematic} and {\em
tetratic} liquid crystalline states, but remains regular in the {\em hexatic}
state, as permitted by the fourth order wavevector dependence of the
(projected) oscillator strength and static structure factor.Comment: 6 pages, 5 eps figures include
Covalency effects on the magnetism of EuRh2P2
In experiments, the ternary Eu pnictide EuRh2P2 shows an unusual coexistence
of a non-integral Eu valence of about 2.2 and a rather high Neel temperature of
50 K. In this paper, we present a model which explains the non-integral Eu
valence via covalent bonding of the Eu 4f-orbitals to P2 molecular orbitals. In
contrast to intermediate valence models where the hybridization with
delocalized conduction band electrons is known to suppress magnetic ordering
temperatures to at most a few Kelvin, covalent hybridization to the localized
P2 orbitals avoids this suppression. Using perturbation theory we calculate the
valence, the high temperature susceptibility, the Eu single-ion anisotropy and
the superexchange couplings of nearest and next-nearest neighbouring Eu ions.
The model predicts a tetragonal anisotropy of the Curie constants. We suggest
an experimental investigation of this anisotropy using single crystals. From
experimental values of the valence and the two Curie constants, the three free
parameters of our model can be determined.Comment: 9 pages, 5 figures, submitted to J. Phys.: Condens. Matte
A Fundamental Theorem on the Structure of Symplectic Integrators
I show that the basic structure of symplectic integrators is governed by a
theorem which states {\it precisely}, how symplectic integrators with positive
coefficients cannot be corrected beyond second order. All previous known
results can now be derived quantitatively from this theorem. The theorem
provided sharp bounds on second-order error coefficients explicitly in terms of
factorization coefficients. By saturating these bounds, one can derive
fourth-order algorithms analytically with arbitrary numbers of operators.Comment: 4 pages, no figure
Short time evolved wave functions for solving quantum many-body problems
The exact ground state of a strongly interacting quantum many-body system can
be obtained by evolving a trial state with finite overlap with the ground state
to infinite imaginary time. In this work, we use a newly discovered fourth
order positive factorization scheme which requires knowing both the potential
and its gradients. We show that the resultaing fourth order wave function
alone, without further iterations, gives an excellent description of strongly
interacting quantum systems such as liquid 4He, comparable to the best
variational results in the literature.Comment: 5 pages, 3 figures, 1 tabl
Three strongly correlated charged bosons in a one-dimensional harmonic trap: natural orbital occupancies
We study a one-dimensional system composed of three charged bosons confined
in an external harmonic potential. More precisely, we investigate the
ground-state correlation properties of the system, paying particular attention
to the strong-interaction limit. We explain for the first time the nature of
the degeneracies appearing in this limit in the spectrum of the reduced density
matrix. An explicit representation of the asymptotic natural orbitals and their
occupancies is given in terms of some integral equations.Comment: 6 pages, 4 figures, To appear in European Physical Journal
Structural relationships and theoretical study of the free energies of electron transfer, electrochemical properties, and electron transfer kinetic of cephalosporin antibiotics derivatives with fullerenes in nanostructure of [R]·C n (R = cefadroxil, cefepime, cephalexin, cefotaxime, cefoperazone and ceftriaxone) supramolecular complexes
Short-time-evolved wave functions for solving quantum many-body problems
The exact ground state of a strongly interacting quantum many-body system can be obtained by evolving a trial state with finite overlap with the ground state to infinite imaginary time. In many cases, since the convergence is exponential, the system converges essentially to the exact ground state in a relatively short time. Thus a short-time evolved wave function can be an excellent approximation to the exact ground state. Such a short-time-evolved wave function can be obtained by factorizing, or splitting, the evolution operator to high order. However, for the imaginary time Schrödinger equation, which contains an irreversible diffusion kernel, all coefficients, or time steps, must be positive. (Negative time steps would require evolving the diffusion process backward in time, which is impossible.) Heretofore, only second-order factorization schemes can have all positive coefficients, but without further iterations, these cannot be used to evolve the system long enough to be close to the exact ground state. In this work, we use a newly discovered fourth-order positive factorization scheme which requires knowing both the potential and its gradient. We show that the resulting fourth-order wave function alone, without further iterations, gives an excellent description of strongly interacting quantum systems such as liquid 4He, comparable to the best variational results in the literature. This suggests that such a fourth-order wave function can be used to study the ground state of diverse quantum many-body systems, including Bose-Einstein condensates and Fermi systems. © 2003 The American Physical Society
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