Related papers: Composition of Two Potentials
We study the reachability problem of a quantum system modelled by a quantum automaton. The reachable sets are chosen to be boolean combinations of (closed) subspaces of the state space of the quantum system. Four different reachability…
We propose a simple scheme to construct composition-dependent interatomic potentials for multicomponent systems that when superposed onto the potentials for the pure elements can reproduce not only the heat of mixing of the solid solution…
For a set $S$ of quadratic polynomials over a finite field, let $C$ be the (infinite) set of arbitrary compositions of elements in $S$. In this paper we show that there are examples with arbitrarily large $S$ such that every polynomial in…
We consider the Novikov problem, namely, the problem of describing the level lines of quasiperiodic functions on the plane, for a special class of potentials that have important applications in the physics of two-dimensional systems.…
The program to construct minimum-uncertainty coherent states for general potentials works transparently with solvable analytic potentials. However, when an analytic potential is not completely solvable, like for a double-well or the linear…
For renormalizable models a method is presented to unambiguously compute the energy that is carried by localized field configurations (solitons). A variational approach for the total energy is utilized to search for soliton configurations.…
The composite system, formed by two $S=1$ particles, is considered. The field operators of constituents are transformed on the $(1,0)\oplus (0,1)$ representation of the Lorentz group. The problem of interaction of $S=1$ particle with the…
We provide an exact solution of the scattering problem for the potentials of the form $v(x,y)=\chi_a(x)[v_0(x)+ v_1(x)e^{i\alpha y}]$, where $\chi_a(x):=1$ for $x\in[0,a]$, $\chi_a(x):=0$ for $x\notin[0,a]$, $v_j(x)$ are real or…
A generalized definition of superpotential has proposed, which connects two one-dimensional potentials $V_{1}$ and $V_{2}$ with discrete energy spectra completely and where: 1) energy of factorization equals to arbitrary level of spectrum…
The correspondence between the integrability of classical mechanical systems and their quantum counterparts is not a 1-1, although some close correspondencies exist. If a classical mechanical system is integrable with invariants that are…
There are different meanings of the term "compositionality" within science: what one researcher would call compositional, is not at all compositional for another researcher. The most established conception is usually attributed to Frege,…
We provide a constructive algorithm to find the best separable approximation to an arbitrary density matrix of a composite quantum system of finite dimensions. The method leads to a condition of separability and to a measure of…
Contextuality is a particular quantum phenomenon that has no analogue in classical probability theory. Given two independent systems, a natural question is how to represent such a situation as a single test space. In other words, how…
The multiple scattering interferences due to the addition of several contiguous potential units are used to construct composite absorbing potentials that absorb at an arbitrary set of incident momenta or for a broad momentum interval.
We consider the Bohmian trajectories in a 2-d quantum harmonic oscillator with non commensurable frequencies whose wavefunction is of the form $\Psi=a\Psi_{m_1,n_1}(x,y)+b\Psi_{m_2,n_2}(x,y)+c\Psi_{m_3,n_3}(x,y)$. We first find the…
We describe some analogues of quantum potentials arising in fractional or deformed Schroedinger equations.
A solution is proposed for the problem of composition of ordinary generating functions. A new class of functions that provides a composition of ordinary generating functions is introduced; main theorems are presented; compositae are written…
The functional decomposition of polynomials has been a topic of great interest and importance in pure and computer algebra and their applications. The structure of compositions of (suitably normalized) polynomials f=g(h) over finite fields…
We establish that by parameterizing the configuration space of a one-dimensional quantum system by polynomial invariants of q-deformed Coxeter groups it is possible to construct exactly solvable models of Calogero type. We adopt the…
We define an equivalence relation on integer compositions and show that two ribbon Schur functions are identical if and only if their defining compositions are equivalent in this sense. This equivalence is completely determined by means of…