Related papers: Detecting level crossings without looking at the s…
The spectrum of eigenenergies of a quantum integrable system whose hamiltonian depends on a single parameter shows degeneracies (crossings) when the parameter varies. We derive a semiclassical expression for the density of crossings in the…
Reciprocal and nonreciprocal effects in dielectric and magnetic materials provide crucial information about the microscopic properties of electrons. However, experimentally distinguishing the two has proven to be challenging, especially…
We show how the Eulcidean algorithm for polynomials can be used to find the intersection points, with multiplicities, of two plane algebraic curves.
We calculate numerically the exact energy spectrum of the six dimensional problem of two interacting Bosons in a three-well optical lattice. The particles interact via a full Born-Oppenheimer potential which can be adapted to model the…
Scattering resonances are an essential tool for controlling interactions of ultracold atoms and molecules. However, conventional Feshbach scattering resonances, which have been extensively studied in various platforms, are not expected to…
Modern quantum chemistry can make quantitative predictions on an immense array of chemical systems. However, the interpretation of those predictions is often complicated by the complex wave function expansions used. Here we show that an…
Collisional resonances are an important tool which has been used to modify interactions in ultracold gases, for realizing novel Hamiltonians in quantum simulations, for creating molecules from atomic gases and for controlling chemical…
The atomic Bose gas is studied across a Feshbach resonance, mapping out its phase diagram, and computing its thermodynamics and excitation spectra. It is shown that such a degenerate gas admits two distinct atomic and molecular superfluid…
We discuss the non-Abelian artificial magnetic monopoles associated with $n$-level energy crossing in quantum systems. We found that hidden symmetries reveal themselves as observables such as spin, charge, and other physical degrees of…
We characterize all possible relative positions between a hyperboloid of one sheet and a sphere through the roots of a characteristic polynomial associated to these quadrics. The classification is also suitable for a hyperboloid and a…
We discover that tautological intersection numbers on $\bar{\mathcal{M}}_{g, n}$, the moduli space of stable genus $g$ curves with $n$ marked points, are evaluations of Ehrhart polynomials of partial polytopal complexes. In order to prove…
Scanning tunneling microscopy (STM) can be used to detect inelastic spin transitions in magnetic nano-structures comprising only a handful of atoms. Here we demonstrate that STM can uniquely identify the electrostatic spin crossover effect,…
Electrons coupled to local lattice deformations end up in selftrapped localized molecular states involving their binding into bipolarons when the coupling is stronger than a certain critical value. Below that value they exist as essentially…
Many nonlinear quantum phenomena of intense laser-atom physics can be intuitively explained with the concept of trajectory. In this paper, Bohmian mechanics (BM) is introduced to study a multiphoton process of atoms interacting with the…
An effective yet simple means disclosed herewith has allowed us to gain the atomistic, local, and quantitative information of bonds and electrons at sites surrounding undercoordinated atoms, complementing the scanning tunneling…
We study the exact solution for two atomic particles in an optical lattice interacting via a Feshbach resonance. The analysis includes the influence of all higher bands, as well as the proper renormalization of molecular energy in the…
Overlapping Feshbach resonances are commonly observed in experiments with ultracold atoms and can influence the molecule production process. We derive an effective approach to describe magnetoassociation in an external trap in the presence…
We analyze the sharpness of crossing ("isosbestic") points of a family of curves which are observed in many quantities described by a function f(x,p), where x is a variable (e.g., the frequency) and p a parameter (e.g., the temperature). We…
An exceptional point is a special point in parameter space at which two (or more) eigenvalues and eigenvectors coincide. The discovery of exceptional points within mechanical and optical systems has uncovered peculiar effects in their…
Equivalence between algebraic equations of motion may be detected by using a $p$-adic method, methods using factorization and linear algebra, or by systematic computer search of suitable Tschirnhausen transformations. Here, we show standard…