Recent interest in square-cell configurations in chemistry+" prompted the present report. The name used for these configurations in discrete mathematics is square animals." A square-cell configuration is made up of square s which are simplyor multiply-connected.š It starts with asingle square and grows by adding squares, one at a time, in such amanner that the new square has at least one side i...

We study the survival probability for long times in an open spherical billiard, extending previous work on the circular billiard. We provide details of calculations regarding two billiard configurations, specifically a sphere with a circular hole and a sphere with a square hole. The constant terms of the long-time survival probability expansions have been derived analytically. Terms that vanish...

The ultrasonic transmission through plates perforated with 2 × 2 or 3 × 3 square array of subwavelength holes per unit cell are studied by numerical simulations. Calculations are obtained by means of a theoretical model under the rigid-solid assumption. It is demonstrated that when the inter-hole distance within the unit cell is reduced, new transmission dips appear resulting from Wood anomalie...

We show that a basic difference between the electron- and hole-doped cuprates is their proximity to two different quantum critical points in a 2D free fermion system on a square lattice and that the spin dynamics observed recently for the first time in the electron-doped Nd2-xCexCuO4, very different from that in the hole-doped cuprates, can be understood as a consequence of this effect.

Square-root topological phases have been discussed mainly for systems with chiral symmetry. In this paper, we analyze the topology of squared Hamiltonian preserving time-reversal and particle-hole Our analysis elucidates that two-dimensional class CII host helical edge states due to nontrivial in contrast absence ordinary phases. The emergence modes is demonstrated by analyzing a toy model. We ...

The ground state energy dispersion curve of a single mobile hole in the two-dimensional t-J model is studied numerically by means of the Green function Monte Carlo method on square lattices of various sizes up to 16 16. Transient estimation results show evidence of a gap of the order of 0:2 t, in the physical region of the model, between the energy value at k = (=2; =2), which corresponds to th...

A well known result of Fraenkel and Simpson states that the number of distinct squares in a word of length n is bounded by 2n since at each position there are at most two distinct squares whose last occurrence start. In this paper, we investigate the problem of counting distinct squares in partial words, or sequences over a finite alphabet that may have some “do not know” symbols or “holes” (a ...

We theoretically investigate the Fermi-edge singularity in a spin-incoherent Luttinger liquid. Both cases of finite and infinite core hole mass are explored, as well as the effect of a static external magnetic field of arbitrary strength. For a finite mass core hole the absorption edge behaves as (omega-omega th)alpha/square root of absolute value (ln(omega-omega th)) for frequencies omega just...