Abstract Despite the successes of machine learning methods in physical sciences, prediction Hamiltonian, and thus electronic properties, is still unsatisfactory. Based on graph neural network (NN) architecture, we present an extendable NN model to determine Hamiltonian from ab initio data, with only local atomic structures as inputs. The rotational equivariance achieved by our complete coordina...

We study the quantum field theory of light-matter interactions for quantum degenerate atomic gases at low light intensity. We argue that the contact interactions between atoms emerging in the dipole gauge may be ignored. Specifically, they are canceled by concurrent infinite level shifts of the atoms. Our development yields the classic Lorentz-Lorenz local-field shift of the atomic resonance. 0...

We consider a simple model of lossless interaction between a two-level single atom and a standing-wave single-mode laser field which creates a one-dimensional optical lattice. Internal dynamics of the atom is governed by the laser field which is treated to be classical with a large number of photons. Center-of-mass classical atomic motion is governed by the optical potential and the internal at...

An interaction-free evolution (IFE) of a quantum system is an evolution which is not influenced by a certain part of the Hamiltonian which is addressed as the interaction term [1]. In other words, the dynamics generated by the ‘unperturbed’ Hamiltonian H0 is essentially the same as the evolution generated by the total Hamiltonian which is the sum of H0 and the interaction term HI: H = H0 + HI. ...

  The traveling salesman problem is a well-known and important combinatorial optimization problem. The goal of this problem is to find the shortest Hamiltonian path that visits each city in a given list exactly once and then returns to the starting city. In this paper, for the first time, the shortest Hamiltonian path is achieved for 1071 Iranian cities. For solving this large-scale problem, tw...

In the last years, the theory of numerical methods for system of non-stiff and stiff ordinary differential equations has reached a certain maturity. So, there are many excellent codes which are based on Runge–Kutta methods, linear multistep methods, Obreshkov methods, hybrid methods or general linear methods. Although these methods have good accuracy and desirable stability properties such as A...

‎let $r$ be a commutative ring with non-zero identity. ‎we describe all $c_3$‎- ‎and $c_4$-free intersection graph of non-trivial ideals of $r$ as well as $c_n$-free intersection graph when $r$ is a reduced ring. ‎also, ‎we shall describe all complete, ‎regular and $n$-claw-free intersection graphs. ‎finally, ‎we shall prove that almost all artin rings $r$ have hamiltonian intersection graphs. ...

Approximate Bayesian computation (ABC) is a powerful and elegant framework for performing inference in simulation-based models. However, due to the difficulty in scaling likelihood estimates, ABC remains useful for relatively low-dimensional problems. We introduce Hamiltonian ABC (HABC), a set of likelihood-free algorithms that apply recent advances in scaling Bayesian learning using Hamiltonia...