Related papers: Coherent states for arbitrary Lie group
Let $G$ be a nilpotent Lie group and let $\pi$ be a coherent state representation of $G$. The interplay between the cyclicity of the restriction $\pi|_{\Gamma}$ to a lattice $\Gamma \leq G$ and the completeness of subsystems of coherent…
In this paper, we construct the coherent states for a system of an electron moving on plane in uniform external magnetic and electric fields. These coherent states are built in the context of both discrete and continuous spectra and satisfy…
Conventional Bell and Stirling numbers arise naturally in the normal ordering of simple monomials in boson operators. By extending this process we obtain generalizations of these combinatorial numbers, defined as coherent state matrix…
The uncertainty principle of SE(2) allows to construct a coherent states transform that is strictly related to the Bargmann transform for the second Heisenberg group H2. The corresponding target space is characterized constructively and…
We construct coherent states using sequences of combinatorial numbers such as various binomial and trinomial numbers, and Bell and Catalan numbers. We show that these states satisfy the condition of the resolution of unity in a natural way.…
Coherent state theory is shown to reproduce three categories of representations of the spectrum generating algebra for an algebraic model: (i) classical realizations which are the starting point for geometric quantization; (ii) induced…
We discuss several methods to produce superpositions of optical coherent states (also known as "cat states"). Cat states have remarkable properties that could allow them to be powerful tools for quantum information processing and metrology.…
In this note a combinatorial formula related to the symmetric group is generalized to an arbitrary finite Weyl group.
As part of a wider study of coherent states in (loop) quantum gravity, we introduce a modification to the standard construction, based on the recently introduced (non-commutative) flux representation. The resulting quantum states have some…
In this paper, the generalized coherent state for quantum systems with degenerate spectra is introduced. Then, the nonclassicality features and number-phase entropic uncertainty relation of two particular degenerate quantum systems are…
We define coherent states carrying SU(2) charges by exploiting Schwinger boson representation of SU(2) Lie algebra. These coherent states satisfy continuity property and provide resolution of identity on $S^{3}$. We further generalize these…
We introduce magnetic coherent states for a particle in a variable magnetic field. They provide a pure state quantization of the phase space R^{2N} endowed with a magnetic symplectic form.
A $q$-deformed Weyl-Heisenberg algebra is used to define a deformed displacement operator giving rise to a naturally normalized nonlinear coherent states type. Robust maximally entangled deformed coherent states are studied and the effect…
Based on the definition of coherent states for continuous spectra and analogous to photon added coherent states for discrete spectra, we introduce the excited coherent states for continuous spectra. It is shown that, the main axioms of…
Lie systems form a class of systems of first-order ordinary differential equations whose general solutions can be described in terms of certain finite families of particular solutions and a set of constants, by means of a particular type of…
Perelomov coherent states for equally spaced, infinite homogeneous waveguide arrays with Euclidean E(2) symmetry are defined, and a new resolution of the identity is obtained. The key point to construct this novel resolution of the identity…
Generalized coherent states arise from reference states by the action of locally compact transformation groups and thereby form manifolds on which there is an invariant measure. It is shown that this implies the existence of canonically…
In this paper, we study the role of coherent states in the realm of quantum cosmology, both in a second-quantized single universe and in a third-quantized quantum multiverse. In particular, most emphasis will be paid to the quantum…
Based on the {\it nonlinear coherent states} method, a general and simple algebraic formalism for the construction of \textit{`$f$-deformed intelligent states'} has been introduced. The structure has the potentiality to apply to systems…
The affine coherent states quantization is a promising integral quantization of Hamiltonian systems when the phase space includes at least one conjugate pair of variables which takes values from a half-plane. Such a situation is common for…