Diverse processes rely on the viscous flow of polymer solutions through porous media. In many cases, the macroscopic flow resistance abruptly increases above a threshold flow rate in a porous
On scalar products and form factors by Separation of Variables: the antiperiodic XXZ model. (arXiv:2011.06109v1 [math-ph])
We consider the XXZ spin-1/2 Heisenberg chain with antiperiodic boundary conditions. The inhomogeneous version of this model can be solved by Separation of Variables (SoV). We compute in this framework
Space of initial conditions for the four-dimensional Fuji-Suzuki-Tsuda system. (arXiv:2011.06271v1 [nlin.SI])
A geometric study for an integrable 4-dimensional dynamical system so called the Fuji-Suzuki-Tsuda system is given. By the resolution of indeterminacy, the group of its B\”aklund transformations is lifted to
Isomonodromic tau functions on a torus as Fredholm determinants, and charged partitions. (arXiv:2011.06292v1 [math-ph])
We prove that the isomonodromic tau function on a torus with Fuchsian singularities and generic monodromies in $GL(N,\mathbb{C})$ can be written in terms of a Fredholm determinant of Cauchy-Plemelj operators.
Integrable Non-unitary Open Quantum Circuits. (arXiv:2011.06565v1 [cond-mat.stat-mech])
We explicitly construct an integrable interacting dissipative quantum circuit, via a trotterization of the Hubbard model with imaginary interaction strength. To prove integrability, we build an inhomogeneous transfer matrix, from
Quantum algorithm for nonlinear differential equations. (arXiv:2011.06571v1 [quant-ph])
Quantum computers are known to provide an exponential advantage over classical computers for the solution of linear differential equations in high-dimensional spaces. Here, we present a quantum algorithm for the
Aggression heuristics underlie animal dominance hierarchies and provide evidence of group-level social information. (arXiv:1810.07215v3 [q-bio.PE] UPDATED)
Members of a social species need to make appropriate decisions about who, how, and when to interact with others in their group. However, it has been difficult for researchers to
Multi-scale structural complexity of natural patterns. (arXiv:2003.04632v2 [nlin.PS] UPDATED)
Complexity of patterns is a key information for human brain to differ objects of about the same size and shape. Like other innate human senses, the complexity perception cannot be
Decay of two-dimensional quantum turbulence in binary Bose-Einstein condensates. (arXiv:2006.15239v2 [cond-mat.quant-gas] UPDATED)
We study two-dimensional quantum turbulence in miscible binary Bose-Einstein condensates in either a harmonic trap or a steep-wall trap through the numerical simulations of the Gross-Pitaevskii equations. The turbulence is
On symmetries of the non-stationary $P_{II}^{(n)}$ hierarchy and their applications. (arXiv:2010.10617v2 [nlin.SI] UPDATED)
In the current paper we study auto-B\”acklund transformations of the non-stationary second Painlev\’e hierarchy $\text{P}_\text{II}^{(n)}$ depending on $n$ parameters: a parameter $\alpha_n$ and times $t_1, \dots, t_{n-1}$. Using generators $s^{(n)}$
