Related papers: Remark on Quantum Nambu Bracket
It is shown that Nambu-Poisson and Nambu-Jacobi brackets can be defined inductively: a n-bracket, n>2, is Nambu-Poisson (resp. Nambu-Jacobi) if and only if fixing an argument we get a (n-1)-Nambu-Poisson (resp. Nambu-Jacobi) bracket. As a…
A binary expression in terms of operators is given which satisfies all the quantum counterparts of the algebraic properties of the classical antibracket. This quantum antibracket has therefore the same relation to the classical antibracket…
We give a sufficient condition for quantising integrable systems.
Linear quantum mechanics can be regarded as a particular example of a nonlinear Nambu-type theory. Some elements of this approach are presented.
We construct compact parametrix implementations of covariant derivations on the quantum annulus.
The investigation of quantum-classical correspondence may lead to gain a deeper understanding of the classical limit of quantum theory. We develop a quantum formalism on the basis of a linear-invariant theorem, which gives an exact…
The quantization of the Hamiltonian for a scalar field is performed in the framework of Quantum Reduced Loop Gravity. We outline how the regularization can be performed by using the analogous tools adopted in full Loop Quantum Gravity and…
The number of qubits used by a quantum algorithm will be a crucial computational resource for the foreseeable future. We show how to obtain the classical query complexity for continuous problems. We then establish a simple formula for a…
The Grassmann-odd Nambu bracket on the Grassmann algebra is proposed.
Phase Space is the framework best suited for quantizing superintegrable systems, naturally preserving the symmetry algebras of the respective hamiltonian invariants. The power and simplicity of the method is fully illustrated through new…
Phase space is a framework ideally suited for quantizing superintegrable systems through the use of deformation methods, as illustrated here by applications to de Sitter and chiral particles. Within this framework, Nambu brackets elegantly…
We consider the problem of defining quantum integrability in systems with finite number of energy levels starting from commuting matrices and construct new general classes of such matrix models with a given number of commuting partners. We…
Let U be the quantum group associated to a symmetrizable generalized Cartan matrix. We give a realization of U from the category of the representations of certain product valued quiver.
We study the problem of the practical realization of an abstract quantum circuit when executed on quantum hardware. By practical, we mean adapting the circuit to particulars of the physical environment which restricts/complicates the…
Quantum computing and quantum Monte Carlo (QMC) are respectively the state-of-the-art quantum and classical computing methods for understanding many-body quantum systems. Here, we propose a hybrid quantum-classical algorithm that integrates…
To any complex Hadamard matrix we associate a quantum permutation group. The correspondence is not one-to-one, but the quantum group encapsulates a number of subtle properties of the matrix. We investigate various aspects of the…
Nambu's construction of multi-linear brackets for super-integrable systems can be thought of as degenerate Poisson brackets with a maximal set of Casimirs in their kernel. By introducing privileged coordinates in phase space these…
We improve previous estimates for matrices belonging to the quantum annulus or to the numerical annulus.
Two possible realizations of the formal neuron are considered as quantum system. The first type complies with classical system. The second type vastly increases the possible problems.
In this paper we give an explicit solution to the rank constrained matrix approximation in Frobenius norm, which is a generalization of the classical approximation of an m by n matrix A by a matrix of rank k at most.