Hermitian effective Hamiltonian formalisms

Note that in contrast to a general similarity transformation (e.g., as found in the usual coupled-cluster theory) the canonical transformation produces a Hermitian effective Hamiltonian, which is computationally very convenient. When U is expressed in exponential form, the effective Hamiltonian can be constructed termwise via the formally infinite Baker-Campbell-Hausdorff (BCH) expansion,... 

The simple projection relation between the right model eigenfunctions of Hg and their true counterparts is an appealing aspect of Bloch s formalism. However, the non-Hermiticity of the resulting effective Hamiltonian represents a strong drawback, as discussed in Section VII. This has led many, beginning with des Cloizeaux [7], to derive Hermitian effective Hamiltonians, des Cloizeaux s method transforms the lag)ol not the... 

Both VU and SU MR CC methods employ the effective Hamiltonian formalism the relevant cluster amplimdes are obtained by solving Bloch equations and the (in principle exact) energies result as eigenvalues of a non-Hermitian effective Hamiltonian that is defined on a finite-dimensional model space Mq. An essential feature characterizing this formalism is the so-called intermediate or Bloch normalization of the projected target space wave functions I f, ) with respect to the corresponding model space configurations 1, ), namely = 8 (for details, see, e.g. Refs. [172,174]). 

The first volume contained nine state-of-the-art chapters on fundamental aspects, on formalism, and on a variety of applications. The various discussions employ both stationary and time-dependent frameworks, with Hermitian and non-Hermitian Hamiltonian constructions. A variety of formal and computational results address themes from quantum and statistical mechanics to the detailed analysis of time evolution of material or photon wave packets, from the difficult problem of combining advanced many-electron methods with properties of field-free and field-induced resonances to the dynamics of molecular processes and coherence effects in strong electromagnetic fields and strong laser pulses, from portrayals of novel phase space approaches of quantum reactive scattering to aspects of recent developments related to quantum information processing. 

Recently the same problem has been reanalyzed by Dicus et al. [86], and indeed they confirmed that the survival probability deviates from exponential at long times. This model and its variants have been applied to study the effect of a distant detector (by adding an absorptive potential) [87], anomalous decay from a flat initial state [44], resonant state expansions [3], initial state reconstruction (ISR) [58], or the relevance of the non-Hermitian Hamiltonian concept (associated with a projector formalism for internal and external regions of space) in potential scattering [88]. In Ref. [88] the model was extended to a chain of delta functions to study overlapping resonances. 

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