相关论文: Coherent states for arbitrary Lie group
We generalise the notion of coherent states to arbitrary Lie algebras by making an analogy with the GNS construction in $C^*$-algebras. The method is illustrated with examples of semisimple and non-semisimple finite dimensional Lie algebras…
The original canonical coherent states could be defined in several ways. As applications for other sets of coherent states arose, the rules of definition were correspondingly changed. Among such rule changes were a change of group and…
We consider quantum systems, whose dynamical symmetry groups are semisimple Lie groups, which can be split or decay into two subsystems of the same symmetry. We prove that the only states of such a system that factorize upon splitting are…
Starting with the canonical coherent states, we demonstrate that all the so-called nonlinear coherent states, used in the physical literature, as well as large classes of other generalized coherent states, can be obtained by changes of…
A general algebraic procedure for constructing coherent states of a wide class of exactly solvable potentials e.g., Morse and P{\"o}schl-Teller, is given. The method, {\it a priori}, is potential independent and connects with earlier…
A general procedure for constructing coherent states, which are eigenstates of annihilation operators, related to quantum mechanical potential problems, is presented. These coherent states, by construction are not potential specific and…
The state spaces of generalised coherent states associated with special unitary groups are shown to form rational curves and surfaces in the space of pure states. These curves and surfaces are generated by the various Veronese embeddings of…
The problem of building coherent states from non-normalizable fiducial states is considered. We propose a way of constructing such coherent states by regularizing the divergence of the fiducial state norm. Then, we successfully apply the…
We provide a unified approach for finding the coherent states of various deformed algebras, including quadratic, Higgs and q-deformed algebras, which are relevant for many physical problems. For the non-compact cases, coherent states, which…
We concisely review the history, physics and significance of coherent states.
Properties of group coherent states can be derived "effectively" without knowing full wave functions. The procedure is detailed in this article as an example of general methods for effective constraints. The role of constraints in the…
We present a general unified approach for finding the coherent states of polynomially deformed algebras such as the quadratic and Higgs algebras, which are relevant for various multiphoton processes in quantum optics. We give a general…
Coherent states for a general Lie superalgebra are defined following the method originally proposed by Perelomov. Algebraic and geometrical properties of the systems of states thus obtained are examined, with particular attention to the…
Considering some important classes of generalized coherent states known in literature, we demonstrated that all of them can be created via conventional fashion, i.e. the "lowering operator eigen-state" and the "displacement operator"…
Coherent structures emerge from the dynamics of many kinds of dissipative, externally driven, nonlinear systems, and continue to provoke new questions that challenge our physical and mathematical understanding. In one specific sub-class of…
We propose the notion of faithful coherent states based on the fidelity-based coherence witness. The criterion for detecting faithful coherent states can be restricted to a subclass of fidelity-based criterion under unitary transformations…
Coherent states for general systems with discrete spectrum, such as the bound states of the hydrogen atom, are discussed. The states in question satisfy: (1) continuity of labeling, (2) resolution of unity, (3) temporal stability, and (4)…
A version of Paley-Wiener like theorem for connected, simply connected nilpotent Lie groups is proven.
Schwinger's algebra of selective measurements has a natural interpretation in terms of groupoids. This approach is pushed forward in this paper to show that the theory of coherent states has a natural setting in the framework of groupoids.…
The idea of construction of the nonlinear coherent states based on the hypergeometric- type operators associated to the Weyl-Heisenberg group [J:P hys:A 45(2012) 095304], are generalized to the similar states for the arbitrary Lie group…