相关论文: The hyperbolic, the arithmetic and the quantum pha…
Phase-locking governs the phase noise in classical clocks through effects described in precise mathematical terms. We seek here a quantum counterpart of these effects by working in a finite Hilbert space. We use a coprimality condition to…
An operator-valued quantum phase space formula is constructed. The phase space formula of Quantum Mechanics provides a natural link between first and second quantization, thus contributing to the understanding of quantization problem. By…
We start to develop the quantization formalism in a hyperbolic Hilbert space. Generalizing Born's probability interpretation, we found that unitary transformations in such a Hilbert space represent a new class of transformations of…
An adapted representation of quantum mechanics sheds new light on the relationship between quantum states and classical states. In this approach the space of quantum states splits into a product of the state space of classical mechanics and…
A novel theory of hybrid quantum-classical systems is developed, utilizing the mathematical framework of constrained dynamical systems on the quantum-classical phase space. Both, the quantum and the classical descriptions of the respective…
To find the Hermitian phase operatorof a single-mode electromagnetic field in quantum mechanics, the Schroedinger representation is extended to a larger Hilbert space augmented by states with infinite excitation by nonstandard analysis. The…
A 4-dimensional Lorentzian static space-time is equivalent to 3-dimensional Euclidean gravity coupled to a massless Klein-field. By canonically quantizing the coupling model in the framework of loop quantum gravity, we obtain a quantum…
Phase operators are constructed using a Klauder-Berezin coherent state quantization in finite Hilbert subspaces of the Hilbert space of Fourier series. The study of infinite dimensional limits of mean values of some observables phase leads…
The entanglement properties of the phase transition in a two dimensional harmonic lattice, similar to the one observed in recent ion trap experiments, are discussed both, for finite number of particles and thermodynamical limit. We show…
The Adler equation is a well-known one-dimensional model describing phase locking and synchronization. Motivated by recent experiments using optomechanical oscillators, we extend the model to include overtone-synthesized sinusoidal coupling…
We explain that when quantising phase spaces with varying symplectic structures, the bundle of quantum Hilbert spaces over the parameter space has a natural unitary connection. We then focus on symplectic vector spaces and their fermionic…
We examine entanglement between number and polarization, or between number and relative phase, for pairs of coherent states and two-mode squeezed vacuum via linear entropy and covariance criteria. We consider the embedding of the two-mode…
In this paper, we describe some interesting properties of a non-Hermitian Jaynes-Cummings model. For this particular model, it is known that the Hilbert space can be described by infinitely-many two-dimensional invariant (closed) subspaces,…
Finite-dimensional Quantum Mechanics can be geometrically formulated as a proper classical-like Hamiltonian theory in a projective Hilbert space. The description of composite quantum systems within the geometric Hamiltonian framework is…
The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with…
We argue that the complex numbers are an irreducible object of quantum probability. This can be seen in the measurements of geometric phases that have no classical probabilistic analogue. Having complex phases as primitive ingredient…
In this paper we propose the idea that there is a corresponding relation between quantum states and points of the complex projective space, given that the number of dimensions of the Hilbert space is finite. We check this idea through…
Measures are introduced to quantify the degree of superposition in mixed states with respect to orthogonal decompositions of the Hilbert space of a quantum system. These superposition measures can be regarded as analogues to entanglement…
Several mathematical views of phase-locking are developed. The classical Huyghens approach is generalized to include all harmonic and subharmonic resonances and is found to be connected to 1/f noise and prime number theory. Two types of…
Recent work on state sum models of quantum gravity in 3 and 4 dimensions has led to interest in the `quantum tetrahedron'. Starting with a classical phase space whose points correspond to geometries of the tetrahedron in R^3, we use…