Related papers: How does Grover walk recognize the shape of crysta…
Spin-orbit beams, in which the orbital angular momentum degree of freedom is coupled to a two-level system such as polarization of light or spin in electrons and neutrons, have gained significant interest for their unique propagation…
We study an Eulerian walker on a square lattice, starting from an initially randomly oriented background using Monte Carlo simulations. We present evidence that, that, for large number of steps $N$, the asymptotic shape of the set of sites…
For surfaces of revolution $B$ in $\R^3$, we investigate the limit distribution of minimum energy point masses on $B$ that interact according to the logarithmic potential $\log (1/r)$, where $r$ is the Euclidean distance between points. We…
In this note we complete the calculation of the number of $GL(\mathbb R^n)$-orbits on $\Lambda^k(\mathbb R^n)^*$, by treating the cases $(n,k)= (7,4)$ and $(8,5)$ not covered in the literature. We also calculate the number of of…
Crystal lattices are known to be one of the generalizations of classical periodic lattices which can be embedded into some Euclidean spaces properly. As to make a wide range of multidimensional discrete distributions on Euclidean spaces…
We investigate the problem of determining the shape of a rotating celestial object - e.g., a comet or an asteroid - under its own gravitational field. More specifically, we consider an object symmetric with respect to one axis - such as a…
We introduce a microscopic model which unravels the physical mechanisms responsible for the observed phase diagram of the $R$VO$_3$ perovskites. It reveals a nontrivial interplay between superexchange, the orbital-lattice coupling due to…
The Grover walk, which is related to the Grover's search algorithm on a quantum computer, is one of the typical discrete time quantum walks. However, a localization of the two-dimensional Grover walk starting from a fixed point is striking…
We compare and contrast the kinematics of various classes of stars, both normal (with M-K spectral types) and peculiar. Numerous plots show the differences in spatial and velocity distributions as well as distributions in kinetic energy vs.…
The traditional way of estimating the gravitational field from observed motions of test objects is based on the virial relation between their kinetic and potential energy. We find a more efficient method. It is based on the natural…
We study the asymptotic behavior of the simple random walk on oriented versions of $\mathbb{Z}^2$. The considered lattices are not directed on the vertical axis but unidirectional on the horizontal one, with random orientations whose…
In this paper we develope a quantitative non-divergence theorem for translates of horospherical orbits, using the technique of Margulis' inequality as developed by Eskin-Margulis-Mozes and Eskin-Margulis. As we use the Margulis' inequality,…
We study the effect of cosmological expansion on orbits--galactic, planetary, or atomic--subject to an inverse-square force law. We obtain the laws of motion for gravitational or electrical interactions from general relativity--in…
We consider a discrete-time quantum walk, called the Grover walk, on a distance regular graph $X$. Given that $X$ has diameter $d$ and invertible adjacency matrix, we show that the square of the transition matrix of the Grover walk on $X$…
Orbits in galaxy bars are generally complex, but simple closed loop orbits play an important role in our conceptual understanding of bars. Such orbits are found in some well-studied potentials, provide a simple model of the bar in…
A choreographic time crystal is a dynamic lattice structure in which the points comprising the lattice move in a coordinated fashion. These structures were initially proposed for understanding the motion of synchronized satellite swarms.…
We perform a numerical study of the phase diagram of the model proposed in \cite{Shifman:2012vv}, which is a simple model containing non-Abelian vortices. As per the case of Abrikosov vortices, we map out a region of parameter space in…
This paper investigates the dynamics of a particle orbiting around a rotating homogeneous cube, and shows fruitful results that have implications for examining the dynamics of orbits around non-spherical celestial bodies. This study can be…
We calculate the diffusion coefficients of persistent random walks on cubic and hypercubic lattices, where the direction of a walker at a given step depends on the memory of one or two previous steps. These results are then applied to study…
Trying to enumerate all of the walks in a 2D lattice is a fun combinatorial problem and there are numerous applications, from polymers to sports. Computers provide a wonderful tool for analyzing these walks; we provide a Maple package for…