Generalized coherent states for arbitrary quantum systems

V. P. Karasev, V. I. Puzyrevskii

Kae Nemoto

Generalized coherent states are developed for SU ( n ) systems for arbitrary n . This is done by first iteratively determining explicit representations for the SU ( n ) coherent states and then determining parametric representations useful for applications. For SU ( n ), the set of coherent states is isomorphic to a coset space SU ( n )/ SU ( n -1), and thus shows the geometrical structure of the coset space. These results provide a convenient (2 n -1)-dimensional space for the description of arbitrary SU ( n ) systems. We further obtain the metric and measure on the coset space and show some properties of the SU ( n ) coherent states.

Barnana Roy, Pinaki Roy

A. H. El Kinani, Mohammed Daoud A

The so-called Gazeau–Klauder and Perelomov coherent states are introduced for an arbitrary quantum system. We give also the general framework to construct the generalized intelligent states which minimize the Robertson–Schrödinger uncertainty relation. As illustration, the Pöschl–Teller potentials of trigonometric type will be chosen. We show the advantage of the analytical representations of Gazeau–Klauder and Perelomov coherent states in obtaining the generalized intelligent states in analytical way.

A. M. Perelomov

John Schliemann

Coherent states provide a natural connection of quantum systems to their classical limit and are employed in various fields of physics. Here we derive general systematic expansions, with respect to quantum parameters, of expectation values of products of arbitrary operators within both oscillator coherent states and SU(2) coherent states. In particular, we generally prove that the energy fluctuations of an arbitrary Hamiltonian are in leading order entirely due to the time dependence of the classical variables. These results add to the list of well-known properties of coherent states and are applied here to the Lipkin-Meshkov-Glick model, the Dicke model, and to coherent intertwiners in spin networks as considered in loop quantum gravity.