I discuss the problem of many polymers that compete in the same random potential but are forced to avoid each other. By means of replica trick, this model is mapped into the usual Lieb-Liniger model of quantum particles but with a generalized statistics. I will introduce the nested Bethe-Ansatz method which allows for an exact solution of this quantum system. The result agrees with a previous derivation based on Macdonald process. In this way, we arrive to a general Fredholm determinant formula which can be used to study general clusters of avoiding polymers. We apply this formalism to the study of the non-crossing probability P for two polymers. We compute exactly the leading large time behavior of all its moments. From this, we extract the tail of the probability distribution of the non-crossing probability. The exact formula is compared to numerical simulations, with excellent agreement.

Andrea De Luca (CNRS)Tue, Feb 9

I discuss the problem of many polymers that compete in the same random potential but are forced to avoid each other. By means of replica trick, this model is mapped into the usual Lieb-Liniger model of quantum particles but with a generalized statistics. I will introduce the nested Bethe-Ansatz method which allows for an exact solution of this quantum system. The result agrees with a previous derivation based on Macdonald process. In this way, we arrive to a general Fredholm determinant formula which can be used to study general clusters of avoiding polymers. We apply this formalism to the study of the non-crossing probability P for two polymers. We compute exactly the leading large time behavior of all its moments. From this, we extract the tail of the probability distribution of the non-crossing probability. The exact formula is compared to numerical simulations, with excellent agreement.