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The method of geometrical quantization of symplectic manifolds is applied to constructing infinite dimensional irreducible unitary representations of the algebra of functions on the compact quantum group $SU_q(2)$. A formulation of the…
This study examines the simulation of quantum algorithms on a classical computer. The program code implemented on a classical computer will be a straight connection between the mathematical formulation of quantum mechanics and computational…
To reconstruct a mixed or pure quantum state of a spin s is possible through coherent states: its density matrix is fixed by the probabilities to measure the value s along 4s(s+1) appropriately chosen directions in space. Thus, after…
Symmetric quantum states are fascinating objects. They correspond to multipartite systems that remain invariant under particle permutations. This symmetry is reflected in their compact mathematical characterisation but also in their unique…
Representative wave functions, which encode the topological properties of the spin polarized fractional quantum Hall states in the lowest Landau level, can be expressed in terms of correlation functions in conformal field theories. Until…
The quantum-to-classical correspondence (QCC) in spin models is a puzzling phenomenon where the static susceptibility of a quantum system agrees with its classical-system counterpart, at a different corresponding temperature, within the…
We introduce a phase-space representation for qubits and spin models. The technique uses an SU(n) coherent state basis, and can equally be used for either static or dynamical simulations. We review previously known definitions and operator…
In recent years there has been an increasing interest on the theoretical and experimental investigation of space-time dual quantum circuits. They exhibit unique properties and have applications to diverse fields. Periodic space-time dual…
Quantum mechanical phase factors can be related to dynamical effects or to the geometrical properties of a trajectory in a given space - either parameter space or Hilbert space. Here, we experimentally investigate a quantum mechanical phase…
We relate a large class of classical spin models, including the inhomogeneous Ising, Potts, and clock models of q-state spins on arbitrary graphs, to problems in quantum physics. More precisely, we show how to express partition functions as…
We study some quantum systems described by noncanonical commutation relations formally expressed as [q,p]=ihbar(I + chi H), where H is the associated (harmonic oscillator-like) Hamiltonian of the system, and chi is a Hermitian (constant)…
We consider the quantum-classical correspondence from a classical perspective by discussing the potential for chaotic systems to support behaviors normally associated with quantum mechanical systems. Our main analytical tool is a chaotic…
We compare the quantum and classical properties of the (Quantum) Isoperiodic Stable Structures -- (Q)ISSs -- which organize the parameter space of a paradigmatic dissipative ratchet model, i.e. the dissipative modified kicked rotator. We…
We introduce the notion of noncommutative complex spheres with partial commutation relations for the coordinates. We compute the corresponding quantum symmetry groups of these spheres, and this yields new quantum unitary groups with partial…
The relationship between classical and quantum three one-mode systems interacting in a non-linear way is described. We investigate the integrability of these systems by using the reduction procedure. The reduced coherent states for the…
Lie algebroids provide a natural medium to discuss classical systems, however, quantum systems have not been considered. In aim of this paper is to attempt to rectify this situation. Lie algebroids are reviewed and their use in classical…
In order to get the classical analogue of quantum interaction picture in classical symplectic geometric description, the space of solutions of free equations of motion is suggested to replace the phase space in $T^{*}Q$ description or the…
The use of geometric methods has proved useful in the hamiltonian description of classical constrained systems. In this note we provide the first steps toward the description of the geometry of quantum constrained systems. We make use of…
We study the quantum-classical correspondence of an experimentally accessible system of interacting bosons in a tilted triple-well potential. With the semiclassical analysis, we get a better understanding of the different phases of the…
The topic of quantum reference frames (QRFs) has attracted a great deal of attention in the recent literature. Potentially, the correct description of such frames is important for both the technological applications of quantum mechanics and…