Quantum invariants of links and 3-valent graphs in 3-manifolds
Quantum isometries and group dual subgroups
We study the discrete groups whose duals embed into a given compact quantum group, . In the matrix case the embedding condition is equivalent to having a quotient map , where is a certain family of groups associated to . We develop here a number of techniques for computing , partly inspired from Bichon’s classification of group dual subgroups . These results are motivated by Goswami’s notion of quantum isometry group, because a compact connected Riemannian manifold cannot have non-abelian...
Quantum isometry group for spectral triples with real structure.
Quantum Itô algebra and quantum martingale
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...
Quantum logics representable as kernels of measures
Quantum logics with classically determined states
Quantum mechanics and coherent states on the anti-de Sitter spacetime and their Poincaré contraction
Quantum mechanics and nonabelian theta functions for the gauge group SU(2)
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...
Quantum mechanics in strong time dependent external fields
Quantum moment equations for a two-band Hamiltonian
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.
Quantum nonlinear Schrödinger equation. I. Intertwining operators
Quantum potential and symmetries in extended phase space.
Quantum probability, renormalization and infinite-dimensional *-Lie algebras.
Quantum random walk revisited
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.
Quantum relativistic Toda chain.
Quantum scattering by external metrics and Yang-Mills potentials
Quantum scattering near the lowest Landau threshold for a Schrödinger operator with a constant magnetic field
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...
Quantum spaces: notes and comments on a lecture by S. L. Woronowicz
Quantum spacetime
Quantum spacetime: a disambiguation.