Related papers: Quantales carrying ortholattice structure

Understanding the core content of quantum mechanics requires us to disentangle the hidden logical relationships between the postulates of this theory. Here we show that the mathematical structure of quantum measurements, the formula for…

The construction of nonlocal sets of quantum states has attracted much attention in recent years. We first introduce two Lemmas related to the triviality of orthogonality-preserving local measurements. Then we propose a general construction…

In this paper we show how the quantum mechanics of the inverted harmonic oscillator can be mapped to the quantum mechanics of a particle in a super-critical inverse square potential. We demonstrate this by relating both of these systems to…

Given a vector bundle $A\to M$ we study the geometry of the graded manifolds $T^*[k]A[1]$, including their canonical symplectic structures, compatible Q-structures and Lagrangian Q-submanifolds. We relate these graded objects to classical…

We introduce and investigate a weighted propositional configuration logic over commutative semirings. Our logic is intended to serve as a specification language for software architectures with quantitative features. We prove an efficient…

We obtain, for the first time, a modular many-valued semantics for combined logics, which is built directly from many-valued semantics for the logics being combined, by means of suitable universal operations over partial non-deterministic…

We study the quantization of many-body systems in two dimensions in rotating coordinate frames using a gauge invariant formulation of the dynamics. We consider reference frames defined by linear and quadratic gauge conditions. In both cases…

We analyze the properties of a quantum system composed of two coherently coupled quantum oscillators and show through simulations that it fulfills the two properties required for reservoir computing: non-linearity and fading memory. We…

A pluri-Lagrangian structure is an attribute of integrability for lattice equations and for hierarchies of differential equations. It combines the notion of multi-dimensional consistency (in the discrete case) or commutativity of the flows…

Recently, the search for topological states of matter has turned to non-Hermitian systems, which exhibit a rich variety of unique properties without Hermitian counterparts. Lattices modeled through non-Hermitian Hamiltonians appear in the…

Conventional understanding implies that the ground state of a nonmagnetic quantum mechanical system should be nodeless. While this notion also provides a valuable guidance in understanding the ordering of energy levels in semiconductor…

We illustrate some problems that are related to the existence of an underlying linear structure at the level of the property lattice associated with a physical system, for the particular case of two explicitly separated spin 1/2 objects…

A projective quantum logic in terms of relative states is developed, emphasizing the importance of information transfer between a system under study and its environment. The need for accounting for the historical evolution of system is…

We study real and integral structures in the space of solutions to the quantum differential equations. First we show that, under mild conditions, any real structure in orbifold quantum cohomology yields a pure and polarized tt^*-geometry…

Our main goal is to develop a representation for finite distributive nearlattices through certain ordered structures. This representation generalizes the well-known representation given by Birkhoff for finite distributive lattices through…

Faithful representations of regular $\ast$-rings and modular complemented lattices with involution within orthosymmetric sesquilinear spaces are studied within the framework of Universal Algebra. In particular, the correspondence between…

For general non-classical systems, we study the different classical representations that fulfill the specific context dependence imposed by the hidden measurement system formalism introduced in quant-ph/0008061. We show that the collection…

We consider a general weak perturbation of a non-interacting quantum lattice system with a non-degenerate gapped ground state. We prove that the presence of isolated eigenvalues in the spectrum of the decoupled model leads to the existence…

We prove that the 18-element non-lattice orthomodular poset depicted in the paper is the smallest one and unique up to isomorphism. Since not every Boolean poset is orthomodular, we consider the class of the so-called generalized…

The classical and the quantal problem of a particle interacting in one-dimension with an external time-dependent quadratic potential and a constant inverse square potential is studied from the Lie-algebraic point of view. The integrability…