Internal Seminar: Hikami unit and Wickens unit

Mathematical and Theoretical Physics Unit (Shinobu Hikami)

Speaker : Hirohiko Shimada

Title : Conformal symmetry in fractal dimensions: bootstrapping the 3D Ising model as an example

Abstract : Physicists are creatures who tend to "have a habit of taking the simplest example of any phenomenon and calling it 'physics,' leaving the more complicated examples to the concern of other fields". This attitude is often further justified by the universality: a phenomenon that common stable structures emerge as consequences of genuinely nonlinear interactions. In the study of phase transitions, important properties (symmetries, space-time dimensions) of the system manifest themselves in the universal critical exponents, while these values are independent of the microscopic details (lattice structures, atomic compositions, etc.). As far as the universality concerns, thus, considering a good simplified model of the real complicated materials is not an approximation but a quantitatively accurate strategy. However, computing the exponents beyond the perturbation theory has for long remained an important theoretical challenge even in the simplest model of a magnet, namely, the celebrated 3D Ising model.

We study the critical exponents including those in the long-standing problem of the 3D Ising universality class by the conformal symmetry (local scale invariance), which is generally expected to hold at the critical point. The idea is to extend the 2D conformal field theory, what is called "the complex analysis in the quantum domain" by A. Polyakov, to higher dimensions. More concretely, we start from a consistency equation that follows from the partial wave expansions and the associativity (AB)C=A(BC) of the operator algebra. The power of this single equation can be compared with that of the Euler product formula of the Riemann zeta function, where the exact equation holds only if each factor ("partial wave") is chosen from the correct list of prime numbers ("spectrum of critical exponents"). We show a certain truncation, based on the fusion rule, of the above consistency equation may lead to sensible estimates of the critical exponents in diverse dimensions.

Neurobiology Research Unit (Jeff Wickens)

Speaker : Tomomi Shindou

Title : Dopamine-dependent synaptic plasticity in the striatum

Abstract : The striatum is the principal input nucleus of the basal ganglia, receiving glutamatergic afferents from the cerebral cortex. It has been suggested that activity-dependent synaptic plasticity in the striatum is a cellular mechanism for reinforcement learning and phasic dopamine (DA) release is associated with positive reinforcement. We tested that the hypothesis that phasic DA release in the striatum is a key determinant of the induction of corticostriatal synaptic plasticity. The electrophysiological and imaging studies using whole-cell patch clamp recordings showed the cell-type specific spike-timing dependent plasticity (STDP) in the striatum. In addition, recent findings indicated that phasically released DA by photolysis of caged DA caused spike-timing dependent long-term potentiation (t-LTP) under certain conditions. The results suggest the contribution of phasic DA on the induction of spike-timing dependent plasticity in the striatum and may support the concept of an eligibility trace, localized to synapses that were active prior to the actions that led to the reward.