545 research outputs found
Nose-Hoover dynamics for coherent states
The popular method of Nose and Hoover to create canonically distributed
positions and momenta in classical molecular dynamics simulations is
generalized to a genuine quantum system of infinite dimensionality. We show
that for the quantum harmonic oscillator, the equations of motion in terms of
coherent states can easily be modified in an analogous manner to mimic the
coupling of the system to a thermal bath and create a quantum canonical
ensemble. Possible applications to more complex systems, especially interacting
Fermion systems, are proposed.Comment: 13 pages, 3 figure
Nose-Hoover sampling of quantum entangled distribution functions
While thermostated time evolutions stand on firm grounds and are widely used
in classical molecular dynamics (MD) simulations, similar methods for quantum
MD schemes are still lacking. In the special case of a quantum particle in a
harmonic potential, it has been shown that the framework of coherent states
permits to set up equations of motion for an isothermal quantum dynamics. In
the present article, these results are generalized to indistinguishable quantum
particles. We investigate the consequences of the (anti-)symmetry of the
many-particle wavefunction which leads to quantum entangled distribution
functions. The resulting isothermal equations of motion for bosons and fermions
contain new terms which cause Bose-attraction and Pauli-blocking. Questions of
ergodicity are discussed for different coupling schemes.Comment: 15 pages, 4 figures, submitted to PHYSICA A. More information at
http://www.physik.uni-osnabrueck.de/makrosysteme
Minimum energy states of the plasma pinch in standard and Hall magnetohydrodynamics
Axisymmetric relaxed states of a cylindrical plasma column are found
analytically in both standard and Hall magnetohydrodynamics (MHD) by complete
minimization of energy with constraints imposed by invariants inherent in
corresponding models. It is shown that the relaxed state in Hall MHD is the
force-free magnetic field with uniform axial flow and/or rigid azimuthal
rotation. The relaxed states in standard MHD are more complex due to the
coupling between velocity and magnetic field. Application of these states for
reversed-field pinches (RFP) is discussed
Thermodynamics of the one-dimensional frustrated Heisenberg ferromagnet with arbitrary spin
The thermodynamic quantities (spin-spin correlation functions <{\bf S}_0{\bf
S}_n>, correlation length {\xi}, spin susceptibility {\chi}, and specific heat
C_V) of the frustrated one-dimensional J1-J2 Heisenberg ferromagnet with
arbitrary spin quantum number S below the quantum critical point, i.e. for J2<
|J1|/4, are calculated using a rotation-invariant Green-function formalism and
full diagonalization as well as a finite-temperature Lanczos technique for
finite chains of up to N=18 sites. The low-temperature behavior of the
susceptibility {\chi} and the correlation length {\xi} is well described by
\chi = (2/3)S^4 (|J1|-4J2) T^{-2} + A S^{5/2} (|J1|-4J2)^{1/2} T^{-3/2} and \xi
= S^2 (|J1|-4J2) T^{-1} + B S^{1/2} (|J1|-4J2)^{1/2} T^{-1/2} with A \approx
1.1 ... 1.2 and B \approx 0.84 ... 0.89. The vanishing of the factors in front
of the temperature at J2=|J1|/4 indicates a change of the critical behavior of
{\chi} and {\xi} at T \to 0. The specific heat may exhibit an additional
frustration-induced low-temperature maximum when approaching the quantum
critical point. This maximum appears for S=1/2 and S=1, but was not found for
S>1.Comment: 8 pages, 7 figure
Quantum rotational band model for the Heisenberg molecular magnet Mo72Fe30
We derive the low temperature properties of the molecular magnet Mo72Fe30,
where 30 Fe(3+) paramagnetic ions occupy the sites of an icosidodecahedron and
interact via isotropic nearest-neighbour antiferromagnetic Heisenberg exchange.
The key idea of our model (J.S. & M.L.) is that the low-lying excitations form
a sequence of rotational bands, i.e., for each such band the excitation
energies depend quadratically on the total spin quantum number. For
temperatures below 50 mK we predict that the magnetisation is described by a
staircase with 75 equidistant steps as the magnetic field is increased up to a
critical value and saturated for higher fields. For higher temperatures thermal
broadening effects wash out the staircase and yield a linear ramp below the
critical field, and this has been confirmed by our measurements (R.M.). We
demonstrate that the lowest two rotational bands are separated by an energy gap
of 0.7 meV, and this could be tested by EPR and inelastic neutron scattering
measurements. We also predict the occurrence of resonances at temperatures
below 0.1 K in the proton NMR spin-lattice relaxation rate associated with
level crossings. As rotational bands characterize the spectra of many magnetic
molecules our method opens a new road towards a description of their
low-temperature behaviour which is not otherwise accessible.Comment: 7 pages, 6 figures, accepted for Europhysics Letter
Structure and dynamics of the coronal magnetic field
The last few years have seen a marked increase in the sophistication of models of the solar corona. This has been brought about by a confluence of three key elements. First, the collection of high-resolution observations of the Sun, both in space and time, has grown tremendously. The SOHO (Solar Heliospheric Observatory) mission is providing additional correlated high-resolution magnetic, white-light and spectroscopic observations. Second, the power and availability of supercomputers has made two- and three-dimensional modeling routine. Third, the sophistication of the models themselves, both in their geometrical realism and in the detailed physics that has been included, has improved significantly. The support from our current Space Physics Theory grant has allowed us to exploit this confluence of capabilities. We have carried out direct comparisons between observations and models of the solar corona. The agreement between simulated coronal structure and observations has verified that the models are mature enough for detailed analysis, as we will describe. The development of this capability is especially timely, since observations obtained from three space missions that are underway (Ulysses, WIND and SOHO) offer an opportunity for significant advances in our understanding of the corona and heliosphere. Through this interplay of observations and theory we can improve our understanding of the Sun. Our achievements thus far include progress modeling the large-scale structure of the solar corona, three-dimensional models of active region fields, development of emerging flux and current, formation and evolution of coronal loops, and coronal heating by current filaments
Spin dynamics of quantum and classical Heisenberg dimers
Analytical solutions for the time-dependent autocorrelation function of the
classical and quantum mechanical spin dimer with arbitrary spin are presented
and compared. For large spin quantum numbers or high temperature the classical
and the quantum dimer become more and more similar, yet with the major
difference that the quantum autocorrelation function is periodic in time
whereas the classical is not.Comment: 10 pages, 4 postscript figures, uses 'epsfig.sty'. Submitted to
Physica A. More information available at
http://www.physik.uni-osnabrueck.de/makrosysteme
Exact magnetic properties for classical delta-chains with ferromagnetic and antiferromagnetic interactions in applied magnetic field
We study the thermodynamics of the delta-chain with competing ferro- and antiferromagnetic interactions in an external magnetic field which generalizes the field-free case studied previously. This model plays an important role for the recently synthesized compound Fe10Gd10, which is nearly quantum critical, as well as for the new kagome fluoride Cs2LiTi3F12. The classical version of the model is solved exactly and explicit analytical results for the low-temperature thermodynamics are obtained. The s-spin quantum model is studied using exact diagonalization and finite-temperature Lanczos techniques. Particular attention is focused on the magnetization and the susceptibility. The magnetization of the classical model in the ferromagnetic part of the phase diagram defines the universal scaling function which is valid for the quantum model. The dependence of the susceptibility on the spin quantum number s at the critical point between the ferro- and ferrimagnetic phases is studied and the relation to Fe10Gd10 is discussed
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