Coherent states operators

Spin-Hamiltonians that are linear in the spin operators, HSpm propagate spin-coherent states exactly,... 

As opposed to (50), here the term with the spin operator is of effective order one. The Weyl quantisations of (50) and (51) propagate initial coherent states... 

The expectation value of H in the coherent state (7.17) can be evaluated explicitly for any Hamiltonian. However, an even simpler construction of Hd (valid to leading order in N) can be done (Cooper and Levine, 1989) by introducing intensive boson operators (Gilmore, 1981). In view of its simplicity, we report here this construction. If one divides the individual creation and annihilation operators by the square root of the total number of bosons, the relevant commutation relations become... 

Any algebraic operator, written in terms of the boson operators a, n of Chapter 2 can be converted into a classical operator, written in terms of the variables (or p, q). We describe here again the derivation of van Roosmalen 1982. One introduces a group coherent state... 

As in the previous case of a single U(4), we introduce projective coherent states, constructed with condensate boson operators (Leviatan and Kirson, 1988 Shao, Walet, and Amado, 1992, 1993)... 

We will determine a coherent-state/holomorphic path integral representation for the parallel-transport operator, deriving an appropriate transition amplitude [a path integral counterpart of the l.h.s. in Eq. (14)]. 

The phase factor is unimportant here because we shall generally take the expectation value of any operator in the coherent state. 

B. A. Hess The reason that macroscopic motions display coherence is that they are in most cases at the classical limit of quantum dynamics. In this case, a suitable occupation of quantum states ensures that quantum mechanical expectation values equal the classical value of an observable. In particular, the classical state of an electromagnetic field (the coherent state) is one in which the expectation value of the operator of the electromagnetic field equals the classical field strengths. 

The Coherent State as the Result of the Action of the Translation Operator on the Ground State of the Number Operator... 

Coherent States as Minimizing the Heisenberg Uncertainty Relation Statistical Equilibrium Density Operator of a Coherent State... 

Appendix N shows that within quantum representation /// and according to Eq. (N12), when the fast mode is in its first excited state, the ground state of the slow mode is a coherent state, that is, an eigenstate of the lowering operator ... 

Appendix N also shows that the expansion of a coherent state on the eigenstates of the number occupation operator is given by Eq. (Nil), so that Eq. (56) leads to... 

This operator is that of a coherent state at any temperature T (see Appendix N). Now, for the special situation of zero temperature, this density operator reduces to... 

Note that this dynamics is classical-like, as the coherent state properties density operator. 

Note that, as above, this classical-like dynamics is not without relation to the quasiclassical coherent state properties of the density operator involved in this average. 

Later, it will appear that in the presence of indirect relaxation, Eqs. (91) and (94) Eqs. (92), (95), and Eqs. (93) and (96) respectively, transform into damped forms. Then, at any temperature the density operators in both quantum representations // and /// appear to be those of coherent states at any temperature (see Appendix N) ... 

Recall that the coherent states are by definition the eigenkets of the lowering operator ... 

We see that this density operator is that of a coherent state at temperature T which, according to a theorem given in the Louisell book [54], reduces at zero temperature to... 

It is shown in Appendix N that the action of the translation operator on the ground state (0) ) of the Hamiltonian of the quantum harmonic oscillator gives a coherent state a ) ... 

On the other hand, Louisell and Walker [22] studied the dynamics of a damped coherent-state density operator. At the initial time they considered the full density operator u] (0), as formed by the product of the density operator... 

By definition, a coherent state a) is the eigenvector of the non-Hermitean lowering operator a of the quantum harmonic oscillator. Thus, the basic equation and its conjugate are, respectively,... 

Now, we may insert in front of a coherent state, the closeness relation on the eigenstates of the number operator at a of the quantum harmonic oscillator (with [a, at] = 1), in the following way ... 

N.2 THE COHERENT STATE AS THE RESULT OF THE ACTION OF THE TRANSLATION OPERATOR ON THE GROUND STATE OF THE NUMBER OPERATOR... 

N.4 STATISTICAL EQUILIBRIUM DENSITY OPERATOR OF A COHERENT STATE... 

Thus, it appears by comparison of the canonical transformations (N.19) and (N.20), that the density operator of the coherent state a) (a may be viewed as the limit for zero temperature of the density operator pa,... 

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