Spike-timing dependent plasticity is the process by which the strengths of connections between neurons are modified as a result of the precise timing of the action potentials fired by the neurons. We consider a model consisting of one integrate-and-fire neuron receiving excitatory inputs from a large number of Poisson neurons whose synapses are plastic. When correlations are introduced between the firing times of these input neurons, the distribution of synaptic strengths shows interesting, and apparently low-dimensional, dynamical behaviour. This behaviour is analysed in two different parameter regimes using equation-free techniques, which bypass the explicit derivation of the relevant low-dimensional dynamical system. We demonstrate both coarse projective integration (which speeds up the time integration of a dynamical system) and the use of recently-developed data-mining techniques to identify the appropriate low-dimensional description of the complex dynamical systems in our model.
This seminar shows that entangled state tunneling under bias can properly explain tunneling conductance line shapes of correlated systems such as cuprate and iron-based superconductors  as well as mesoscopic Kondo systems . In the former, the density of states (DOS) is an important quantity unlike the latter. We obtain the DOS in the fitting process of theoretical tunneling conductance to the experimental data. The obtained density of states is consistent with the spectral function given by angle-resolved photoemission spectroscopy (ARPES). It has been known that an inconsistency for the superconducting gap always exists in comparison between ARPES and scanning tunneling spectroscopy. Removing the inconsistency is a long standing task in condensed matter physics. I show that entangled state tunneling may resolve this problem. In addition, the origin of two side peaks appearing in tunneling conductance of all correlated systems is clarified. I will show that the appearance of two side peaks is a generic feature of non-equilibrium coherent tunneling in strongly correlated systems. We use the Green’s function technique in operator space (Liouvillian approach) instead of Hamiltonian approach because the latter has difficulties in determining basis vectors.
We explore the feasibility of realizing repulsive Casimir-Polder (CP) forces for a magnetic particle near a surface. Considering the toy model of an atom with an electric-dipole transition and an arbitrarily large magnetic spin, we analyze the interplay between the repulsive magnetic-dipole and the attractive electric-dipole contributions to the total CP force. Particularly noting that the magnetic CP interaction is relatively longer-ranged than the electric CP interaction due to the difference in their respective characteristic transition frequencies, we find a regime where the repulsive magnetic contribution to the total force can potentially exceed the attractive electric part in magnitude, thus making the overall force repulsive. We discuss some fundamental constraints and conditions necessary for achieving such a repulsion, identifying the magnetizability to polarizability ratio for the particle as a key figure of merit. We analyze ways to further enhance the magnitude of the repulsive magnetic CP force for an excited magnetic atom, such as, by preparing the atom in a "super-radiant" magnetic sub-level, and designing surface resonances close to the magnetic transition frequency. Our results could be instructive in identifying potential systems, mechanisms, and regimes where one could realize stable levitation via repulsive magnetic Casimir-Polder forces.