相关论文: Coherent states for arbitrary Lie group
We give an apriori description of a set of irreducible representations of a Weyl group which parametrize the nilpotent orbits in the Lie algebra of a connected reductive group in arbitrary characteristic. We also answer a question of Serre…
The coherent states are viewed as a powerful tool in differential geometry. It is shown that some objects in differential geometry can be expressed using quantities which appear in the construction of the coherent states. The following…
The article explores a new formalism for describing motion in quantum mechanics. The construction is based on generalized coherent states with evolving fiducial vector. Weyl-Heisenberg coherent states are utilised to split quantum systems…
This review is intended for readers who want to have a quick understanding on the theoretical underpinnings of coherent states and squeezed states which are conventionally generated from the prototype harmonic oscillator but not always…
We illustrate the emergence of classical analogue of coherent state and its generalisation in a purely classical field theoretical setting. Our algebraic approach makes use of the Poisson bracket and symmetries of the underlying field…
We classify connected Lie groups which are locally isomorphic to generalized Heisenberg groups. For a given generalized Heisenberg group $N$, there is a one-to-one correspondence between the set of isomorphism classes of connected Lie…
We discuss the notion of coherent states from three different perspectives: the seminal approach of Schroedinger, the experimental take of quantum optics, and the theoretical developments in quantum gravity. This comparative study tries to…
A generalized version of the coupled coherent states method for coherent states of arbitrary Lie groups is developed. In contrast to the original formulation, which is restricted to frozen-Gaussian basis sets, the extended method is…
We demonstrate how large classes of discrete and continuous statistical distributions can be incorporated into coherent states, using the concept of a reproducing kernel Hilbert space. Each family of coherent states is shown to contain, in…
We consider relativistic coherent states for a spin-0 charged particle that satisfy the next additional requirements: (i) the expected values of the standard coordinate and momentum operators are uniquely related to the real and imaginary…
Hardy's type uncertainty principle on connected nilpotent Lie groups for the Fourier transform is proved. An analogue of Hardy's theorem for Gabor transform has been established for connected and simply connected nilpotent Lie groups.…
The first two parts of this article surveys results related to the heat-kernel coherent states for a compact Lie group K. I begin by reviewing the definition of the coherent states, their resolution of the identity, and the associated…
Quantum dynamics of integrable systems is discussed. Localized wave packets generalizing the conventional coherent states of minimal uncertainty are constructed. The wave packet moves along a certain trajectory and does not change its shape…
Classes of coherent states are presented by replacing the labeling parameter $z$ of Klauder-Perelomov type coherent states by confluent hypergeometric functions with specific parameters. Temporally stable coherent states for the isotonic…
We find that a bipartite quantum state is entangled if and only if it is quantum coherent with respect to complete bases of states in the corresponding system that are distinguishable under local quantum operations and classical…
New quantal states which interpolate between the coherent states of the Heisenberg_Weyl and SU(1,1) algebras are introduced. The interpolating states are obtained as the coherent states of a closed and symmetric algebra which interpolates…
We discuss a general strategy to construct coherence measures. One can build an important class of coherence measures which cover the relative entropy measure for pure states, the $l_1$-norm measure for pure states and the $\alpha$-entropy…
Schr\" odinger-Robertson uncertainty relation is minimized for the quadrature components of Weyl generators of the algebra $su(N)$. This is done by determining explicit Fock-Bargamann representation of the $su(N)$ coherent states and the…
Robertson intelligent states which minimize the Schr\" odinger-Robertson uncertainty relation are constructed as eigenstates of a linear combination of Weyl generators of the $su(3)$ algebra. The construction is based on the analytic…
The purpose of this paper is to introduce several basic theorems of coherent states and generalized coherent states based on Lie algebras su(2) and su(1,1), and to give some applications of them to quantum information theory for graduate…