Related papers: A quantum homogeneous space of nilpotent matrices
Deformations of the canonical commutation relations lead to non-Hermitian momentum and position operators and therefore almost inevitably to non-Hermitian Hamiltonians. We demonstrate that such type of deformed quantum mechanical systems…
In some special zones of the high-dimensional coordinate space of few-body systems with identical particles, the operation of an element (or a product of elements) of the symmetry groups of the Hamiltonian on a quantum state might be…
By the universal integrability objects we mean certain monodromy-type and transfer-type operators, where the representation in the auxiliary space is properly fixed, while the representation in the quantum space is not. This notion is…
We construct start-products on the co-adjoint orbit of Lie group $\Aff({\bf C})$ of affine transformations of the complex straight line and apply them to obtain the irreducible unitary representations of this group. These results show…
We explore the extension of quantum cosmology outside the homogeneous approximation, using the formalism of loop quantum gravity. We introduce a model where some of the inhomogeneous degrees of freedom are present, providing a tool for…
A discrete quantum spin system is presented in which several modern methods of canonical quantum gravity can be tested with promising results. In particular, features of interacting dynamics are analyzed with an emphasis on homogeneous…
The random matrix ensembles are applied to the quantum statistical two-dimensional systems of electrons. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The…
We study the noncommutative geometrical structures of quantum entangled states. We show that the space of a pure entangled state is a noncommutative space. In particular we show that by rewritten the conifold or the Segre variety we can get…
We study the action of space-time symmetries on quantum fields in the presence of small departures from locality determined by dynamical gravity. It is shown that, under such relaxation of locality, the symmetries of the theory cannot be…
We study quantization of a class of inhomogeneous Lie bialgebras which are crossproducts in dual sectors with Abelian invariant parts. This class forms a category stable under dualization and the double operations. The quantization turns…
The three-dimensional quantum Euclidean space is an example of a non-commutative space that is obtained from Euclidean space by $q$-deformation. Simultaneously, angular momentum is deformed to $so_q(3)$, it acts on the $q$-Euclidean space…
We study some basic quantum confinement effects through investigation a deformed harmonic oscillator algebra. We show that spatial confinement effects on a quantum harmonic oscillator can be represented by a deformation function within the…
Unambiguous unitary maps and unambiguous unitary quantum channels are introduced and some of their properties are derived. These properties ensure certain simple form for the measurements involved in realizing an unambiguous unitary quantum…
Most of the potential physical effects of loop quantum gravity have been derived in effective models that modify the constraints of canonical general relativity in specific forms. Emergent modified gravity evaluates important conditions…
Quantum families of maps between quantum spaces are defined and studied. We prove that quantum semigroup (and sometimes quantum group) structures arise naturally on such objects out of more fundamental properties. As particular cases we…
We obtain a new inequality for arbitrary Hermitian matrices. We describe particular linear maps called the matrix portrait of arbitrary NxN matrices. The maps are obtained as analogs of partial tracing of density matrices of multipartite…
Canonical methods allow the derivation of effective gravitational actions from the behavior of space-time deformations reflecting general covariance. With quantum effects, the deformations and correspondingly the effective actions change,…
Into this note we collect topics related to homogeneous vector bundles, elliptic adjoint orbits and so forth.
A pure quantum state of $n$ parties associated with the Hilbert space $\CC^{d_1}\otimes \CC^{d_2}\otimes\cdots\otimes \CC^{d_n}$ is called $k$-uniform if all the reductions to $k$-parties are maximally mixed. The $n$ partite system is…
Starting from noncommutative generalization of Minkowski space we consider quantum deformed relativistic symmetries which lead to the modification of kinematics of special relativity. The noncommutative field theory framework described by…