Related papers: Derivations and Spectral Triples on Quantum Domain…
We analyze constrained quantum systems where the dynamics do not preserve the constraints. This is done in particular for the restriction of a quantum particle in Euclidean n-space to a curved submanifold, and we propose a method of…
We consider hilbert spaces of holomorphic functions in Cartan domains (in particular in ball and polydisk) and operator of restriction of holomorphic function to a submanifold in Shilov boundary. We discuss conditions when this operator…
In this note we study the spectrum and the Waelbroeck spectrum of the derivative operator composed with isomorphic multiplication oper
Examples of noncommutative self-coverings are described, and spectral triples on the base space are extended to spectral triples on the inductive family of coverings, in such a way that the covering projections are locally isometric. Such…
The spectral action on the equivariant real spectral triple over \A(SU_q(2)) is computed explicitly. Properties of the differential calculus arising from the Dirac operator are studied and the results are compared to the commutative case of…
In this paper we begin a study of the space of unbounded self-adjoint Fredholm operators as a classifying space for K^{1}(X), with the goal of incorporating the information in the eigenspaces and eigenvalues of the operators. In particular,…
In quantum physics, the theoretical study of unbound many-body systems is typically quite complex -- owing to the combination of their large spatial extension and the so-called {\it curse of dimensionality}. Often, such systems are studied…
It has been recently conjectured that the spectral determinants of operators associated to mirror curves can be expressed in terms of a generalization of theta functions, called quantum theta functions. In this paper we study the symplectic…
Through the example of the quantum symplectic 4-sphere, we discuss how the notion of twisted spectral triple fits into the framework of quantum homogeneous spaces.
We study the phase space of periodically modulated gravitational cavity by means of quantum recurrence phenomena. We report that the quantum recurrences serve as a tool to connect phase space of the driven system with spectrum in quantum…
Differential calculi are obtained for quantum homogeneous spaces by extending Woronowicz' approach to the present context. Representation theoretical properties of the differential calculi are investigated. Connections on quantum…
We derive a set of invariants under local unitary transformations for arbitrary dimensional quantum systems. These invariants are given by hyperdeterminants and independent from the detailed pure state decompositions of a given quantum…
We give a description of complex geodesics and we study the structure of stationary discs in some non-convex domains for which complex geodesics are not unique.
We introduce compactness classes of Hilbert space operators by grouping together all operators for which the associated singular values decay at a certain speed and establish upper bounds for the norm of the resolvent of operators belonging…
Quantum computing is usually associated with discrete quantum states and physical quantities possessing discrete eigenvalue spectrum. However, quantum computing in general is any computation accomplished by the exploitation of quantum…
We study dynamical semigroups of positive, but not completely positive maps on finite-dimensional bipartite systems and analyze properties of their generators in relation to non-decomposability and bound-entanglement. An example of…
Generalizing the noncommutative harmonic oscillator construction, we propose a new extension of quantum field theory based on the concept of "noncommutative fields". Our description permits to break the usual particle-antiparticle…
In the framework of quantum group theory we obtain a noncommutative analog for the algebra of functions in a bounded symmetric domain, endowed with a whole symmetry. Also we provide a construction for its faithfull irreducible…
In this paper, we propose a new concept of derivative with respect to an arbitrary kernel-function. Several properties related to this new operator, like inversion rules, integration by parts, etc. are studied. In particular, we introduce…
We study different notions of quantum correlations in multipartite systems of distinguishable and indistinguishable particles. Based on the definition of quantum coherence for a single particle, we consider two possible extensions of this…