Related papers: Quantum stochastic integrals as operators
In this work we discuss the notion of observable - both quantum and classical - from a new point of view. In classical mechanics, an observable is represented as a function (measurable, continuous or smooth), whereas in (von Neumann's…
It is well-known that if a symplectic integrator is applied to a Hamiltonian system, then the modified equation, whose solutions interpolate the numerical solutions, is again Hamiltonian. We investigate this property from the variational…
We obtain sufficient conditions for the efficient simulation of a continuous variable quantum algorithm or process on a classical computer. The resulting theorem is an extension of the Gottesman-Knill theorem to continuous variable quantum…
In this work we introduce a theory of stochastic integration with respect to general cylindrical semimartingales defined on a locally convex space $\Phi$. Our construction of the stochastic integral is based on the theory of tensor products…
Conserved operator quantities in quantum field theory can be defined via the Noether theorem in the Lagrangian formalism and as generators of some transformations. These definitions lead to generally different conserved operators which are…
We propose a categorical and algebraic study of quantale modules. The results and constructions presented are also applied to abstract algebraic logic and to image processing tasks.
In this paper, we define the multiplicative Hecke operators $\mathcal{T}(n)$ for any positive integer on the integral weight meromorphic modular forms for $\Gamma_{0}(N)$. We then show that they have properties similar to those of additive…
The Feynman integral is given a stochastic interpretation in the framework of Nelson's stochastic mechanics employing a time-symmetric variant of Nelson's kinematics recently developed by the author.
Integration by parts plays a crucial role in mathematical analysis, e.g., during the proof of necessary optimality conditions in the calculus of variations and optimal control. Motivated by this fact, we construct a new, right-weighted…
Resonant systems emerge as weakly nonlinear approximations to problems with highly resonant linearized perturbations. Examples include nonlinear Schroedinger equations in harmonic potentials and nonlinear dynamics in Anti-de Sitter…
We set up some weighted norm inequalities for fractional oscillatory integral operators. As applications, the corresponding results for commutators formed by $BMO(\mathbb{R}^{n})$ functions and the operators are established.
In the discussion about the quantumness of NMR computation a conclusion is done that computational states are separable and therefore can not be entangled. This conclusion is based on the assumption that the initial density matrix of an…
We improve previous estimates for matrices belonging to the quantum annulus or to the numerical annulus.
In this paper, we introduce two types of variational integrators, one originating from the discrete Hamilton's principle while the other from Galerkin variational approach. It turns out that these variational integrators are equivalent to…
The key concept discussed in these lectures is the relation between the Hamiltonians of a quantum integrable system and the Casimir elements in the underlying hidden symmetry algebra. (In typical applications the latter is either the…
Recently, Lloyd and Montangero have made a brief research proposal on universal quantum computation in integrable systems. The main idea is to encode qubits into quantum action variables and build up quantum gates by the method of resonant…
We construct bounded linear operators that map $H^1$ conforming Lagrange finite element spaces to $H^2$ conforming virtual element spaces in two and three dimensions. These operators are useful for the analysis of nonstandard finite element…
Variational integrators are derived for structure-preserving simulation of stochastic Hamiltonian systems with a certain type of multiplicative noise arising in geometric mechanics. The derivation is based on a stochastic discrete…
Collective operators that describe interaction of generic quantum system with discrete spectrum with a quantum field are investigated. These operators, considered as operators in the entangled Fock space (space generated by action of…
We argue that the complex numbers are an irreducible object of quantum probability. This can be seen in the measurements of geometric phases that have no classical probabilistic analogue. Having complex phases as primitive ingredient…