Related papers: The hyperbolic, the arithmetic and the quantum pha…
In the Hilbert space of a quantum particle the standard coherent-state resolution of unity is written in terms of a phase-space integration of the outer product $|z\rangle \langle z|$. Because no pair of coherent states is orthogonal, one…
An extension to computational mechanics complexity measure is proposed in order to tackle quantum states complexity quantification. The method is applicable to any $n-$partite state of qudits through some simple modifications. A Werner…
Symmetry is an important property of quantum mechanical systems which may dramatically influence their behavior in and out of equilibrium. In this paper, we study the effect of symmetry on tripartite entanglement properties of typical…
We consider the one-dimensional extended Hubbard model in the presence of an explicit dimerization $\delta$. For a sufficiently strong nearest neighbour repulsion we establish the existence of a quantum phase transition between a mixed…
A central feature of quantum metrology is the possibility of Heisenberg scaling, a quadratic improvement over the limits of classical statistics. This scaling, however, is notoriously fragile to noise. While for some noise types it can be…
In this doctoral thesis we have studied the quantum properties of several models which have been classified as statical and dynamical systems. The first part has been devoted to investigate the properties of the statical models including…
We develop the widest possible generalisation of the well-known connection between quantum mechanical Bargmann invariants and geometric phases. The key notion is that of null phase curves in quantum mechanical ray and Hilbert spaces.…
A formulation of quantum mechanics is introduced based on a $2D$-dimensional phase-space wave function $\text{\reflectbox{\text{p}}}\mkern-3mu\text{p}\left(q,p\right)$ which might be computed from the position-space wave function…
Smooth composite bundles provide the adequate geometric description of classical mechanics with time-dependent parameters. We show that the Berry's phase phenomenon is described in terms of connections on composite Hilbert space bundles.
Coherent states in a projected Hilbert space have many useful properties. When there are conserved quantities, a representation of the entire Hilbert space is not necessary. The same issue arises when conditional observations are made with…
Classical simulation of quantum systems plays an important role in the study of many-body phenomena and in the benchmarking and verification of quantum technologies. Exact simulation is often limited to small systems because the dimension…
We construct a class of generalized phase coherent states indexed by points of the unit circle and depending on three positive parameters "gamma","alpha" and "epsilon" by replacing the labelling coefficients of the canonical coherent states…
Complex numbers appear in the Hilbert space formulation of quantum mechanics, but not in the formulation in phase space. Quantum symmetries are described by complex, unitary or antiunitary operators defining ray representations in Hilbert…
Starting from the study of one-dimensional potentials in quantum mechanics having a small distance behavior described by a harmonic oscillator, we extend this way of analysis to models where such a behavior is not generally expected. In…
Taking several statistical examples, in particular one involving a choice of experiment, as points of departure, and making symmetry assumptions, the link towards quantum theory developed in Helland (2005a,b) is surveyed and clarified. The…
The paper develop the alternative formulation of quantum mechanics known as the phase space quantum mechanics or deformation quantization. It is shown that the quantization naturally arises as an appropriate deformation of the classical…
General conditions for the occurrence of mesoscopic phase fluctuations in condensed matter are considered. The description of different thermodynamic phases, which coexist as a mixture of mesoscopically separated regions, is based on the…
We propose an extended quantum theory, in which the number K of parameters necessary to characterize a quantum state behaves as fourth power of the number N of distinguishable states. As the simplex of classical N-point probability…
The classical thermostatics of equilibrium processes is shown to possess a quantum-mechanical dual theory with a finite-dimensional Hilbert space of quantum states. Specifically, the kernel of a certain Hamiltonian operator becomes the…
The relation between quantum phase transitions, entanglement, and geometric phases is investigated with a system of two qubits with XY type interaction. A seam of level crossings of the system is a circle in parameter space of the…