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We consider electron transport in a model of a spinless superconductor described by a Kitaev type lattice Hamiltonian where the electron interactions are modelled through a superconducting pairing term. The superconductor is sandwiched…
In this paper, a high order implicit Method of Line Transpose (MOL$^T$ ) method based on a weighted essentially non-oscillatory (WENO) methodology is developed for one-dimensional linear transport equations and further applied to the…
We find an exact general solution to the three-dimensional (3D) Ising model via an exact self-consistency equation for nearest-neighbors' correlations. It is derived by means of an exact solution to the recurrence equations for partial…
This survey has been written in occasion of the School and Workshop about Optimal Transport on Quantum Structures at Erd\"os Center in September 2022. We discuss some recent results on noncommutative entropic optimal transport problems and…
Tensor network techniques, known for their low-rank approximation ability that breaks the curse of dimensionality, are emerging as a foundation of new mathematical methods for ultra-fast numerical solutions of high-dimensional Partial…
The recently proposed Wigner function for a particle in an infinite lattice [NJP 14, 103009 (2012)] is extended here to include an internal degree of freedom, as spin. The formalism is developed to account for dynamical processes, with or…
We consider the fully-coupled McKean-Vlasov equation with multi-time-scale potentials, and all the coefficients depend on the distributions of both the slow component and the fast motion. By studying the smoothness of the solution of the…
In this work we present a numerical method for the Optimal Mass Transportation problem. Optimal Mass Transportation (OT) is an active research field in mathematics.It has recently led to significant theoretical results as well as…
The Extended Wigner's Friend thought experiment, which involves a quantum system with an agent who draws conclusions based on the results of a measurement of a quantum state provided in two nonorthogonal versions by another agent, led its…
We consider coherent exciton transport modeled by continuous-time quantum walks (CTQWs) on long-range interacting cycles (LRICs), which are constructed by connecting all the two nodes of distance $m$ in the cycle graph. LRIC has a symmetric…
In this paper we reconsider the notion of an optimal effective Hamiltonian for the semiclassical propagation of the Wigner distribution in phase space. An explicit expression for the optimal effective Hamiltonian is obtained in the short…
We analyze travelling wave (TW) solutions for nonlinear systems consisting of an ODE coupled to a degenerate PDE with a diffusion coefficient that vanishes as the solution tends to zero and blows up as it approaches its maximum value.…
The quadratically regularized optimal transport problem has recently been considered in various applications where the coupling needs to be \emph{sparse}, i.e., the density of the coupling needs to be zero for a large subset of the product…
The role of noise in the transport properties of quantum excitations is a topic of great importance in many fields, from organic semiconductors for technological applications to light-harvesting complexes in photosynthesis. In this paper we…
We introduce a novel optimal transport framework for probabilistic circuits (PCs). While it has been shown recently that divergences between distributions represented as certain classes of PCs can be computed tractably, to the best of our…
We introduce and analyze a statistical estimator for Monge transport maps: solutions to the quadratic optimal transport problem in Euclidean space. For absolutely continuous source measures, this map is uniquely defined as the gradient of a…
A new method of approximation scheme with potential application to a general interacting quantum system is presented. The method is non-perturbative, self- consistent, systematically improvable and uniformly applicable for arbitrary…
A numerical method for the solution of the elliptic Monge-Ampere Partial Differential Equation, with boundary conditions corresponding to the Optimal Transportation (OT) problem is presented. A local representation of the OT boundary…
Quantum correlations can be used as a resource for quantum computing, eg for quantum state manipulation, and for quantum sensing, eg for creating non-classical states which allow to achieve the quantum advantage regime. This review collects…
The finite-size Tomonaga-Luttinger Hamiltonian with an arbitrary potential is mapped onto a non-interacting Fermi gas with renormalized potential. This is done by means of flow equations for Hamiltonians and is valid for small…