Кирилл Половников -- Гамильтониан самоподобных гауссовых полимерных состояний

Molecules consisting of sequentially connected beads without any additional interactions between the beads are known as ideal polymer chains in polymer physics. Long ideal chains can be renormalized such that the joint statistics of the beads coordinates is Gaussian and the fractal dimension equals to $df=2$, independently of the space dimension $D$. Inspired by experimental data on chromosome folding, in my talk I will pose the following question: how to introduce additional interactions between the beads of an ideal polymer such that the fractal dimension is different, say, $df=3$? I will propose the quadratic Hamiltonian with a tunable memory exponent that can generate Gaussian polymer conformations with an arbitrary fractal dimension between $df=2$ and $df=\inf$ for any $D$.
Based on the works: K.P., H. Brandao, S. Belan, M. Imakaev, L. Mirny. Physical Review X (2023); K.P., S. Nechaev, M. Tamm. Soft Matter (2018)