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Modified gravity theories can be used for the description of homogeneous and isotropic cosmological models through the corresponding field equations. These can be cast into systems of autonomous differential equations because of their sole…
Stabilizing thermodynamically unstable phases in many-body systems, such as suppressing pathological neuronal synchronization in Parkinson's disease or maintaining magnetic order across broad temperature ranges, remains a persistent…
Quantum groups lead to an algebraic structure that can be realized on quantum spaces. These are noncommutative spaces that inherit a well defined mathematical structure from the quantum group symmetry. In turn such quantum spaces can be…
A general prescription for the treatment of constrained quantum motion is outlined. We consider in particular constraints defined by algebraic submanifolds of the quantum state space. The resulting formalism is applied to obtain solutions…
Using the framework of Nambu's generalised mechanics, we obtain a new description of constrained Hamiltonian dynamics, involving the introduction of another degree of freedom in phase space, and the necessity of defining the action integral…
We describe how geometrical methods can be applied to a system with explicitly time-dependent second-class constraints so as to cast it in Hamiltonian form on its physical phase space. Examples of particular interest are systems which…
We construct a generalized controlled phased gate entangler for a multi-qubit state based on the geometrical structure of quantum systems. We also investigate relation between the generalized controlled phase construction of a quantum gate…
We give a geometric description of variational principles in mechanics, with special attention to constrained systems. For the general case of nonholonomic constraints, a unified variational approach is given, and the equations of motion of…
No mixed research of hybrid and fractional-order systems into a cohesive and multifaceted whole can be found in the literature. This paper focuses on such a synergistic approach of the theories of both branches, which is believed to give…
We study the role of driving in a two-level system evolving under the presence of a structured environment. We find that adding a periodical modulation to the two-level system can greatly enhance the survival of the geometric phase for many…
We described the $q$-deformed phase space. The $q$-deformed Hamilton eqations of motion are derived and discussed. Some simple models are considered.
The paper discusses the kinematics of manipulators builts of planar closed kinematic chains. A special kinematic scheme is extracted from the array of these mechanisms that looks the most promising for the creation of different types of…
We consider the simultaneous control of the relative phase and populations of two-level quantum systems by an external field. We apply a reverse engineering approach, which allows obtaining an analytical expression for the control field…
We address the deformation quantization of generally parametrized systems displaying a natural time variable. The purpose of this exercise is twofold: first, to illustrate through a pedagogical example the potential of quantum phase space…
An operator generalisation of the notion of geometric phase has been recently proposed purely based on physical grounds. Here we provide a mathematical foundation for its existence, while uncovering new geometrical structures in quantum…
A dynamical decoupling method is presented which is based on embedding a deterministic decoupling scheme into a stochastic one. This way it is possible to combine the advantages of both methods and to increase the suppression of undesired…
The framework of quantum invariants is an elegant generalization of adiabatic quantum control to control fields that do not need to change slowly. Due to the unavailability of invariants for systems with more than one spatial dimension, the…
We analyze the quantization of dynamical systems that do not involve any background notion of space and time. We give a set of conditions for the introduction of an intrinsic time in quantum mechanics. We show that these conditions are a…
Quantum Optimal Control (QOC) supports the advance of quantum technologies by tackling its problems at the pulse level: Numerical approaches iteratively work towards a given target by parametrising the applied time-dependent fields with a…
In this study, we address the challenge of controlling quantum systems under environmental influences using the theory of dynamical invariants. We employ a reverse engineering approach to develop control protocols designed to be robust…