Canonical coherent states

The last expression is the classical or canonical coherent state Iz). The Baker-Campbell-Hausdorff (BCH) formula, yields... 

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,... 

To proceed further, it is convenient to represent the grand canonical partition function for the redefined SB Hamiltonian (Eq. 12) in terms of a coherent-state functional integral [29] over Grassmann fermionic and complex hosonic fields as... 

In the transition from Stokes operators to canonical variables in Eqs. (15) the result (5) is a convenient tool for calculating variances. If for instance the input light state is the coherent vacuum state we have... 

The SRTS sequence consists of a preparatory pulse and an arbitrary long train of the phase-coherent RF pulses of the same flip angle applied with a constant short-repetition time. As was noted above, the "short time" in this case should be interpreted as the pulse spacing T within the sequence that meets the condition T T2 Hd. The state that is established in the spin system after the time, T2, is traditionally defined as the "steady-state free precession" (SSFP), ° and includes two other states (or sub-states) quasi-stationary, that exists at times T2effective relaxation time) and stationary, that is established after the time " 3Tie after the start of the sequence.The SSFP is a very particular state which requires a specific mechanism for its description. This mechanism was devised in articles on the basis of the effective field concept and canonical transformations. Later approaches on the basis of the average-Hamiltonian theory were developed. ... 

The objective of this work is to introduce some recent rigorous developments about the structure of the density matrices (DM), i.e., the state of the system as an ensemble of pure states of different number of fixed particles M commonly called grand-canonical ensemble (GC), the calculation of the energy under the hypothesis of its convexity for ground state isolated molecular systems and their extensions to systems under the influence of an environment interaction, i.e., a fragment or a reservoir [14]. In this way, we attempt to obtain a solution based on the interaction between the subsystems (S-R) inducing a coherent DM distribution which overcomes the inconsistencies mentioned above. Hence, the solution Ues within the formal structure of reactivity theory, and the second-type chanical descriptors (second derivatives) are obtained in the natural scenario of the GC [12, 13] and the chemical context in which the species exchanges or transfers electrons. 

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