相关论文: Cubic Matrix, Nambu Mechanics and Beyond
Quantum computing, leveraging quantum phenomena like superposition and entanglement, is emerging as a transformative force in computing technology, promising unparalleled computational speed and efficiency crucial for engineering…
Coalgebras generalize various kinds of dynamical systems occuring in mathematics and computer science. Examples of systems that can be modeled as coalgebras include automata and Markov chains. We will present a coalgebraic representation of…
Quantum computation teaches us that quantum mechanics exhibits exponential complexity. We argue that the standard scientific paradigm of "predict and verify" cannot be applied to testing quantum mechanics in this limit of high complexity.…
Quantum mechanics increasingly penetrates modern technologies but, due to its non-deterministic nature seemingly contradicting our classical everyday world, our comprehension often stays elusive. Arguing along the correspondence principle,…
We present a new model of quantum gravity as a theory of random geometries given explicitly in terms of a multitrace matrix model. This is a generalization of the usual discretized random surfaces of 2D quantum gravity which works away from…
Two questions are suggested as having priority when trying to bring together Quantum Mechanics and General Relativity. Both questions have a scope which goes well beyond Physics, and in particular Quantum Mechanics and General Relativity.
A physical picture for Quantum Mechanics which permits to conciliate it with the usual common sense is proposed. The picture agrees with the canonical Copenhagen interpretation making more clear its statements.
We introduce a new structure, the critical multi-cubic lattice. Notably the critical multi-cubic lattice is the first true generalization of the cubic lattice to higher dimensional spaces. We then introduce the notion of a homomorphism in…
We describe a multi-scale resolution approach to analyzing problems in Quantum Mechanics using Daubechies wavelet basis. The expansion of the wavefunction of the quantum system in this basis allows a natural interpretation of each basis…
Quantum Computing is a new and exciting field at the intersection of mathematics, computer science and physics. It concerns a utilization of quantum mechanics to improve the efficiency of computation. Here we present a gentle introduction…
We consider the problem of gambling on a quantum experiment and enforce rational behaviour by a few rules. These rules yield, in the classical case, the Bayesian theory of probability via duality theorems. In our quantum setting, they yield…
This work has the purpose of applying the concept of Geometric Calculus (Clifford Algebras) to the Fibre Bundle description of Quantum Mechanics. Thus, it is intended to generalize that formulation to curved spacetimes [the base space of…
We relate classical and quantum Dirac and Nambu brackets. At the classical level, we use the relations between the two brackets to gain some insight into the Jacobi identity for Dirac brackets, among other things. At the quantum level, we…
Although the suspicion that quantum mechanics is emergent has been lingering for a long time, only now we begin to understand how a bridge between classical and quantum mechanics might be squared with Bell's inequalities and other…
Recent studies on quantum computing algorithms focus on excavating features of quantum computers which have potential for contributing to computational model enhancements. Among various approaches, quantum annealing methods effectively…
Quantum computers are considered as a part of the family of the reversible, lineary-extended, dynamical systems (Quanputers). For classical problems an operational reformulation is given. A universal algorithm for the solving of classical…
It is shown that a unified description of classical and `quantum mechanical' gravity in its linearized form is possible.
Familiar textbook quantum mechanics assumes a fixed background spacetime to define states on spacelike surfaces and their unitary evolution between them. Quantum theory has changed as our conceptions of space and time have evolved. But…
Canonical transformation in a three-dimensional phase space endowed with Nambu bracket is discussed in a general framework. Definition of the canonical transformations is constructed as based on canonoid transformations. It is shown that…
A generalization of classical gauge theory is presented, in the framework of a noncommutative-geometric formalism of quantum principal bundles over smooth manifolds. Quantum counterparts of classical gauge bundles, and classical gauge…