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Displaying 1461 –
1480 of
2286
In this paper, we study a representation of the quantum Itô algebra in Fock space and then by using a noncommutative Radon-Nikodym type theorem we study the density operators of output states as quantum martingales, where the output states are absolutely continuous with respect to an input (vacuum) state. Then by applying quantum martingale representation we prove that the density operators of regular, absolutely continuous output states belong to the commutant of the ⋆-algebra parameterizing the...
We propose a direction of study of nonabelian theta functions by establishing an analogy between the Weyl quantization of a one-dimensional particle and the metaplectic representation on the one hand, and the quantization of the moduli space of flat connections on a surface and the representation of the mapping class group on the space of nonabelian theta functions on the other. We exemplify this with the cases of classical theta functions and of the nonabelian theta functions for the gauge group...
The hydrodynamic moment equations for a quantum system described by a two-band Hamiltonian are derived. In the case of pure states, it is proved that the order-0 and order-1 moment equations yield a closed system which is the two band analogue of Madelung's fluid equations.
In the framework of the symmetric Fock space over L²(ℝ₊), the details of the approximation of the four fundamental quantum stochastic increments by the four appropriate spin-matrices are studied. Then this result is used to prove the strong convergence of a quantum random walk as a map from an initial algebra 𝓐 into 𝓐 ⊗ ℬ (Fock(L²(ℝ₊))) to a *-homomorphic quantum stochastic flow.
For fixed magnetic quantum number m results on spectral properties and scattering theory are given for the three-dimensional Schrödinger operator with a constant magnetic field and an axisymmetrical electric potential V. In various, mostly singular settings, asymptotic expansions for the resolvent of the Hamiltonian H m+Hom+V are deduced as the spectral parameter tends to the lowest Landau threshold. Furthermore, scattering theory for the pair (H m, H om) is established and asymptotic expansions...
For linear combinations of quantum product averages in an arbitrary bipartite state, we derive new quantum Bell-form and CHSH-form inequalities with the right-hand sides expressed in terms of a bipartite state. This allows us to specify bipartite state properties sufficient for the validity of a classical CHSH-form inequality and the perfect correlation form of the original Bell inequality for any bounded quantum observables. We also introduce a new general condition on a bipartite state and quantum...
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.
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2286