University of Heidelberg > Institute of Physical Chemistry > Theoretical Chemistry
Optimal lattice models
Lieb-Liniger model


  • Optimal time-dependent lattice models for nonequilibrium dynamics
    We have recently found a way to design optimal lattice models based entirely
    on the principle of least action. As an example we present the
    optimal Bose-Hubbard model. One of our results is that the commonly
    used parameters U and J are actually time-dependent and lattice
    site-dependent functions. Also the optimal coupling constants for
    stationary states can be found using our new concept. We have
    thereby provided a tool to end the long-lasting search for the
    optimal parameters of lattice models.

  • Exact quantum dynamics of a bosonic Josephson junction
    Few problems in the ultracold atoms literature have been studied
    as extensively as the bosonic Josephson Junction problem. The
    literature relies heavily on the use of either the Gross-Pitaevskii
    approximation or the Bose-Hubbard model. We have provided the
    first numerically exact results on this subject based on the
    time-dependent many-body Schrödinger equation. It
    turns out that the true physics is quite different from the
    predictions of either the Gross-Pitaevskii equation or the
    Bose-Hubbard model.

  • Correlation functions and coherence of trapped Bose-Einstein condensates
    In this work we investigate the ground state of the
    many-body Schrödinger equation of a BEC in
    a double well potential. We provide the correlation
    functions and show how the nature of the condensate
    changes depending on the barrier height from condensed
    to fragmented.

  • Bose-Einstein condensate on a ring
    Lieb and Liniger's model is a hallmark of mathematical physics.
    In this work we solved Lieb and Liniger's equations for finite
    numbers of particles and studied the approach to the thermodynamic
    limit with increasing particle numbers as well as the approach
    to Girardeau's gas of impenetrable bosons. The energies for
    repulsive and attractive interaction are listed on the above website.

  • Stochastic motion of a driven magnetic nanoparticle
    A magnetic nanoparticle in a magnetic field is generally
    subject to thermal fluctuations. These fluctuations can flip the
    orientation of the magnetization. The mean first passage times of
    such flips are computed.



[Uni Heidelberg] [Institute of Physical Chemistry] [Theoretical Chemistry]