Two-orbital Hubbard model vs spin S=1S=1 Heisenberg model: studies on clusters

We perform exact numeric calculations for the two-orbital Hubbard model on the four-site cluster. In the limit of large on-site coupling the model becomes equivalent to the spin $S=1$ Heisenberg model. By comparing energy spectra of these two models, we quantified the range of interaction parameters for which the Heisenberg model satisfactorily reproduces the two-orbital Hubbard model. Then we examined how the spectrum evolves when we are outside of this region, focusing especially on checking of how it is modified when various ways of interatomic hoppings of electrons between different orbitals are taken into account. We finally show how these modifications affect the dependence of specific heat on temperature.Comment: 8 pages, 7 figures, 2 table

Auditory cortex modelled as a dynamical network of oscillators: Understanding event-related fields and their adaptation

Adaptation, the reduction of neuronal responses by repetitive stimulation, is a ubiquitous feature of auditory cortex (AC). It is not clear what causes adaptation, but short-term synaptic depression (STSD) is a potential candidate for the underlying mechanism. We examined this hypothesis via a computational model based on AC anatomy, which includes serially connected core, belt, and parabelt areas. The model replicates the event-related field (ERF) of the magnetoencephalogram as well as ERF adaptation. The model dynamics are described by excitatory and inhibitory state variables of cell populations, with the excitatory connections modulated by STSD. We analysed the system dynamics by linearizing the firing rates and solving the STSD equation using time-scale separation. This allows for characterization of AC dynamics as a superposition of damped harmonic oscillators, so-called normal modes. We show that repetition suppression of the N1m is due to a mixture of causes, with stimulus repetition modifying both the amplitudes and the frequencies of the normal modes. In this view, adaptation results from a complete reorganization of AC dynamics rather than a reduction of activity in discrete sources. Further, both the network structure and the balance between excitation and inhibition contribute significantly to the rate with which AC recovers from adaptation. This lifetime of adaptation is longer in the belt and parabelt than in the core area, despite the time constants of STSD being spatially constant. Finally, we critically evaluate the use of a single exponential function to describe recovery from adaptation

Adaptive Resolution Simulation of Liquid Water

We present a multiscale simulation of liquid water where a spatially adaptive molecular resolution procedure allows for changing on-the-fly from a coarse-grained to an all-atom representation. We show that this approach leads to the correct description of all essential thermodynamic and structural properties of liquid water.Comment: 4 pages, 3 figures; changed figure