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Spin Systems |
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The synthesis of molecular magnets has undergone rapid progress
in recent years. Each of the identical molecular units can contain as few as two
and up to several dozens of paramagnetic ions (``spins").
Although these materials appear as macroscopic samples,
i.e. crystals or powders, the intermolecular magnetic
interactions are utterly negligible as compared to the
intramolecular interactions. Therefore, measurements of their
magnetic properties reflect mainly ensemble properties of single
molecules.
We are interested in static and dynamical properties of magnetic molecules, our research focuses on:
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www.molmag.de (German Molecular Magnetism) |
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Mohammed Allalen - PhD Student @ UOS Klaus Bärwinkel - Professor, Senior Fellow @ UOS Mirko Brüger - Diploma Student @ UOS Matthias Exler - Graduate Student @ UOS Peter Hage - Diploma Student @ UOS Frank Hesmer - Diploma Student @ UOS Paul Kögerler - PostDoc, Fellow @ Ames Lab, Iowa Marshall Luban - Professor, Senior Fellow @ Ames Lab, Iowa Detlef Mentrup - PhD Student @ UOS, now Philips Research Robert Modler - Assistant Professor @ Ames Lab, Iowa Heinz-Jürgen Schmidt - Professor, Senior Fellow @ UOS Jürgen Schnack - Professor @ Bielefeld University Christian Schröder - Professor, Senior Fellow @ FH Bielefeld Stefan Torbrügge - Master Student @ UOS/UoG Athens |
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Thermostated Dynamics |
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Statistical properties of finite interacting systems are of
great interest. The aim is to describe the behaviour of systems
like atomic clusters, atomic vapours or atomic nuclei at finite
temperatures and to investigate properties like the specific
heat or phase transitions.
For realistic systems like atomic clusters or nuclei where the
Hamilton function or operator contains a (two-body)
interaction it is hard or impossible to evaluate the partition
function especially for the quantum description.
Equations of motion for the investigated system are often much easier; either they are exactly known and can be integrated at least numerically as it is the case with the classical Hamilton's equation or they can be approximated with standard methods like Time-dependent Hartree-Fock (TDHF) or quantum molecular dynamics methods as it is the case on the quantum side. The idea then is to extract the desired thermodynamic quantities from the time evolution of the system. If the system is ergodic, ensemble averages can be replaced by time averages. Our current research focuses on:
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Detlef Mentrup - PhD Student @ UOS, now Philips Research Hans Feldmeier - Professor, Senior Fellow @ GSI/TUD Jürgen Schnack - Professor @ Bielefeld University |
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Harmonic Oscillator - Fermions and Bosons in Traps |
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Ideal quantum gases are usually treated in the thermodynamic
limit, i.e. occupying an infinite volume but maintained at a
given density, since all applications which were important in
the past, like the electron gas, phonons or photons, deal with
huge particle numbers. Only the experimental attempts of the
last years to investigate finite Fermi and Bose systems and to
describe them in terms of thermodynamics called for new
theoretical effort.
Interesting finite Fermi systems are for instance nuclei, which
behave like a liquid drop and therefore can undergo a first
order liquid-gas-like phase transition.
On the low excitation site of the caloric curve the nuclear
systems can be very often well described as an ideal Fermi gas
in a common harmonic oscillator potential (shell model).
Small Bose systems became available through the development of
traps. Here the focus is on the Bose-Einstein condensation which
for instance could be found investigating dilute atomic vapours
(alkali atoms) in magnetic traps. Again the system
can be well described as an ideal quantum gas contained in an
external harmonic oscillator potential.
With the help of recursion formulae analytical and approximative results are obtained for small non-interacting Fermi and Bose systems. A closer inspection of the canonical partition function uncovers a surprising symmetry property which connects fermions and bosons contained in harmonic oscillator potentials of odd space dimensions. Simply speaking, it turns out that the properties of N fermions at temperature T are related to the properties of N bosons at the respective negative temperature -T. |
| Heinz-Jürgen Schmidt - Professor, Senior
Fellow @ UOS Jürgen Schnack - Research Associate @ UOS |
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Transport Theory |
| A quasi-particle theory for monatomic gases in equilibrium is formulated and evaluated to yield the exact virial contributions to the thermodynamic state functions in lowest order of the density. Van der Waals blocking has necessarily to be accounted for in occupation number statistics. The quasi-particle distribution function differs from the Wigner function by a bilinear functional thereof. The progress made so far is promising with respect to a corresponding version of kinetic theory. |
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Klaus Bärwinkel - Professor, Senior Fellow @ UOS Jürgen Schnack - Professor @ Bielefeld University |
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Fermionic Molecular Dynamics (FMD) |
| A new type of molecular dynamics is proposed to solve approximately the many-body problem of interacting identical fermions with spin 1/2 using variational principles. The interacting system is represented by an antisymmetrized many-body wave function consisting of single-particle states which are localized in phase space. The equations of motion for the parameters characterizing the many-body state (e.g. position, momentum, width and spin of the particles) are derived from a quantum variational principle. The model is designed to describe ground state properties of nuclii as well as heavy ion reactions. Therfore the ansatz is extended towards correlated many-body states, in order to include short-range correlations. Due to its non-linear equations of motion the model shows large fluctuations in the final stage as it is seen in fragmentation reactions. Not only heavy-ion reactions may be addressed, but also properties of excited nuclii like the nuclear liquid-gas phase transition. |
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FMD home
page,
local copy detailed description (PDF with hyperlinks) |
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Hans Feldmeier - Professor, Senior Fellow @ GSI/TUD Robert Roth - Junior Professor @ TUD Jürgen Schnack - Professor @ Bielefeld University Thomas Neff - PostDoc @ GSI/TUD |
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Unitary Correlation Operator Method (UCOM) |
| The short range repulsion between nucleons is treated by a unitary correlation operator which shifts the nucleons away from each other whenever their uncorrelated positions are within the replusive core. By formulating the correlation as a transformation of the relative distance between particle pairs, general analytic expressions for the correlated wave functions and correlated operators are given. The decomposition of correlated operators into irreducible n-body operators is discussed. The one- and two-body-irreducible parts are worked out explicitly and the contribution of three-body correlations is estimated to check convergence. Ground state energies of nuclei up to mass number A=48 are calculated with a spin-isospin-dependent potential and single Slater determinants as uncorrelated states. They show that the deduced energy- and mass-number-independent correlated two-body Hamiltonian reproduces all "exact" many-body calculations surprisingly well. |
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UCOM home page |
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Hans Feldmeier - Professor, Senior Fellow @ GSI/TUD Robert Roth - Junior Professor @ TUD Jürgen Schnack - Professor @ Bielefeld University Thomas Neff - PostDoc @ GSI/TUD |
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