Quantum stochastic calculus for the uniform measure and Boolean convolution
Quantum stochastic calculus on full Fock space
We present a new version of integration of time-adapted processes with respect to creation, annihilation and conservation processes on the full Fock space. Among the new features, in the first place, there is a new formulation of adaptedness which is both simpler and more general than the known ones. The new adaptedness allows for processes which are not restricted to be elements of some norm closure of the ∗-algebra which is generated by the basic creation processes.
Quantum stochastic convolution cocycles -algebraic and C*-algebraic
We summarise recent results concerning quantum stochastic convolution cocycles in two contexts-purely algebraic and C*-algebraic. In each case the class of cocycles arising as the solution of a quantum stochastic differential equation is characterised and the form taken by the stochastic generator of a *-homomorphic cocycle is described. Throughout the paper a common viewpoint on the algebraic and C*-algebraic situations is emphasised; the final section treats the unifying example of convolution...
Quantum stochastic convolution cocycles I
Quantum stochastic differential equations driven by free noises and dilations of markovian semigroups
Quantum stochastic dynamics. I.
Quantum stochastic processes arising from the strong resolvent limits of the Schrödinger evolution in Fock space
By using F. A. Berezin's canonical transformation method [5], we derive a nonadapted quantum stochastic differential equation (QSDE) as an equation for the strong limit of the family of unitary groups satisfying the Schrödinger equation with singularly degenerating Hamiltonians in Fock space. Stochastic differentials of QSDE generate a nonadapted associative Ito multiplication table, and the coefficients of these differentials satisfy the formal unitarity conditions of the Hudson-Parthasarathy type...
Quantum stopping times and quasi-left continuity
Quantum structures in Galilei general relativity
Quantum super-integrable systems as exactly solvable models.
Quantum symmetries for exceptional modular invariants associated with conformal embeddings.
Quantum symmetries in noncommutative C*-systems
We introduce the notion of a completely quantum C*-system (A,G,α), i.e. a C*-algebra A with an action α of a compact quantum group G. Spectral properties of completely quantum systems are investigated. In particular, it is shown that G-finite elements form the dense *-subalgebra of A. Furthermore, properties of ergodic systems are studied. We prove that there exists a unique α-invariant state ω on A. Its properties are described by a family of modular operators acting on . It turns out that ω...
Quantum theory and consciousness: an overview with selected examples.
Quantum vacuum polarization at the Black-Hole horizon
Quantum-classical interactions and galois type extensions
An algebraic model for the relation between a certain classical particle system and the quantum environment is proposed. The quantum environment is described by the category of possible quantum states. The initial particle system is represented by an associative algebra in the category of states. The key new observation is that particle interactions with the quantum environment can be described in terms of Hopf-Galois theory. This opens up a possibility to use quantum groups in our model of particle...
Quantum-dot-based photon emission and media conversion for quantum information applications.
Quantum-graph vertex couplings: some old and new approximations
In 1986 P. Šeba in the classic paper considered one-dimensional pseudo-Hamiltonians containing the first derivative of the Dirac delta function. Although the paper contained some inaccuracy, it was one of the starting points in approximating one-dimension self-adjoint couplings. In the present paper we develop the above results to the case of quantum systems with complex geometry.
Quasi *-algebras valued quantized fields
Quasiclassical limit of KP hierarchy, -symmetries, and free fermions
Quasi-covariant repesentations of nuclear ...-algebras