Related papers: Quantum Dynamics on the three-dimensional q-deform…
We propose quantum-mechanical systems in which the number of spatial dimensions is promoted to a dynamical quantum variable, making the effective dimension state-dependent. Interestingly, systems of this form can exhibit enhanced symmetries…
Using differential and integral calculi on the quantum plane which are invariant with respect to quantum inhomogeneous Euclidean group E(2)q , we construct path integral representation for the quantum mechanical evolution operator kernel of…
The talk is devoted to the "extended phase space" approach to Quantum Geometrodynamics. The premises that have led to the formulation of this approach are briefly reviewed, namely, non-trivial topology of the Universe which implies the…
We investigate the classical limit of a type of semiclassical evolution, the pertinent system representing the interaction between matter and a given field. On using as a quantifier of the ensuing dynamics Tsallis q-entropy, we encounter…
In recent years, growing attention has been devoted to the possibility that theories with deformed symmetries, associated with certain models of non-commutative spacetime, may encode a fundamental form of decoherence. This effect should be…
Geometric effects make evolution time vary for different evolution curves that connect the same two quantum states. Thus, it is important to be able to control along which path a quantum state evolve to achieve maximal speed in quantum…
Several years ago the so-called quantum geometrodynamics in extended phase space was proposed. The main role in this version of quantum geometrodynamics is given to a wave function that carries information about geometry of the Universe as…
We briefly describe the construction of a consistent $q$-deformation of the quantum mechanical isotropic harmonic oscillator on ordinary $\rn^N$ space.
We consider the $q$-deformed Schr\"odinger equation of the harmonic oscillator on the $N$-dimensional quantum Euclidian space. The creation and annihilation operator are found, which systematically produce all energy levels and…
We provide a systematic procedure to relate a three dimensional q-deformed oscillator algebra to the corresponding algebra satisfied by canonical variables describing noncommutative spaces. The large number of possible free parameters in…
The real- and imaginary-time evolution of quantum states are powerful tools in physics, chemistry, and beyond, to investigate quantum dynamics, prepare ground states or calculate thermodynamic observables. On near-term devices, variational…
We study a quantum theory with complex time parameter and non-Hermitian Hamiltonian structure. In this theory, the real part of the complex time is equal to `usual' physical time, whereas the imaginary one is proportional to inverse…
A new approach to quantum walks is presented. Considering a quantum system undergoing some unitary discrete-time evolution in a directed graph G, we think of the vertices of G as sites that are occupied by the quantum system, whose internal…
We consider a quantum Otto cycle with a $q$-deformed quantum oscillator working substance and classical thermal baths. We investigate the influence of the quantum statistical deformation parameter $q$ on the work and efficiency of the…
The operator and the functional formulations of the dynamics of constrained systems are explored for determining unambiguously the quantum Hamiltonian of a nonrelativistic particle in a curved space.
We briefly describe our application of a version of noncommutative differential geometry to the 3-dim quantum space covariant under the quantum group of rotations $SO_q(3)$ and sketch how this might be used to determine the correct physical…
We advocate that the dual picture of spacetime noncommutativity , i.e. the existence of a curved momentum space, could be a way out to solve some of the open conceptual problems in the field, such as the basis dependence of observables. In…
We consider deformations of quantum mechanical operators by using the novel construction of warped convolutions. The deformation enables us to obtain several quantum mechanical effects where electromagnetic and gravitomagnetic fields play a…
We present a nonperturbative, first-principles numerical approach for time-dependent problems in the framework of quantum field theory. In this approach the time evolution of quantum field systems is treated in real time and at the…
The article is dedicated to q-deformed versions of spinor calculus. As a kind of review, the most relevant properties of the two-dimensional quantum plane are summarized. Additionally, the relationship between the quantum plane and…