Hamiltonian interacting boson

Kirson, M. W., and Leviatan, A. (1985), Resolution of Any Interacting-Boson-Model Hamiltonian into Intrinsic and Collective Parts, Phys. Rev. Lett. 55, 2846. 

The G-reduced Hamiltonians are necessary and sufficient for at least three important classes of Hamiltonians (i) all one-particle Hamiltonians, (ii) bosons or fermions with harmonic interactions [24], and (iii) all Hamiltonians with... 

One of the most interesting aspects of the Interacting Boson Model concerns its connections with the underlying fermion space. The understanding of the mechanism through which bosonlike features arise from effective nuclear hamiltonians provides, in fact, a way to relate collective spectra to the fermion motion. 

As we show later, the energy of the state of any system of N indistinguishable fermions or bosons can be expressed in terms of the Hamiltonian and D (12,1 2 ) if its Hamiltonian involves at most two-particle interactions. Thus it should be possible to find the ground-state energy by variation of the 2-matrix, which depends on four particles. Contrast this with current methods involving direct use of the wavefunction that involves N particles. A principal obstruction for this procedure is the A-representability conditions, which ensure that the proposed RDM could be obtained from a system of N identical fermions or bosons. 

The weak interaction contribution to the Lamb shift is generated by the Z-boson exchange in Fig. 6.7, which may be described by the effective local low-energy Hamiltonian... 

The weak interaction contribution to hyperfine splitting is due to Z-boson exchange between the electron and muon in Fig. 6.7. Due to the large mass of the Z-boson this exchange is effectively described by the local four-fermion interaction Hamiltonian... 

In this contribution, we have presented a new mapping procedure from fermion onto boson spaces. This procedure has been tested for a fermion quadrupole-quadrupole interaction in the case of nucleons moving in a single j-orbit. The energy spectrum generated by this interaction within the S-D subspace has been found to compare rather well with the spectrum of an SU(3) 0(6) IBM hamiltonian whose parameters have been obtained with this procedure. 

As for the case of a bosonic bath, the Hamiltonian describing the molecular junction is separated into the relevant system Hs(t), describing the wire, the field-matter interaction Hp(t) and reservoirs Hr modeling the leads... 

To describe superconductors it is argued Refs. [1-9] that a system of electrons with energies a such that eF -hcoD spherical shell in k-space in 3D) may be divided into two coexisting dynamically interacting subsystems a) fermions (pairable but unpaired) and b) boson CPs made up of two bound fermions. Here eF is the Fermi energy of the ideal Fermi gas (IFG) and hmD the Debye energy. The Hamiltonian describing the binary BF mixture with BF interactions is [1,4]... 

The model Hamiltonian [Eq. (3)] defined on a continuum has some exact solutions [35]. These have culminated in what is now known as the bosonization technique, in which the interacting fermion fields can be expressed in terms of boson field operators. This method is reviewed in Refs. 15, 16, and 31. 

Let us now switch our attention to the quantum statistical effects and entanglement production for the case of perfect symmetry between the modes (7i = 72 = 7> Ai = A2 = A). In order to obtain general expressions for the variances, we first write them in terms of the boson operators corresponding to the Hamiltonian (lb). We perform the transformations at —> at exp (i (I>j), which restore the previous phase structure of the intracavity interaction and find, quite generally, the variances at some arbitrary quadrature phase angles 0i, 02 as... 

We consider individual bosonic reservoirs / ,.. .., Fj with finite thermal energy ksT characterized by mode operators Ajk, Ajk, etc. Environmentally induced spin flips can be described by the interaction Hamiltonian... 

For reasons that will become clear in Section V, the operators and D in (2.95) have basically the same physical meaning as the coordinate and momentum operators. The final result of this replacement is that one can write the second-quantized form of the spherical invariant Hamiltonian operator in terms of U(4) coupled boson operators (up to two-body interactions and with the compact notation h j = b =pI-3> k = 2, 3,... 

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