Boson condensation

Finally, also in the laboratory the study of the interaction of cavities inside a uniform fermionic background is of importance (Bulgac and Wirzba., 2001). Examples are C6o buckyballs immersed in liquid mercury. The liquid metal itself serves only as free-moving shapeable neutral background which provides the Fermi gas environment by its conductance electrons, in which the buckyballs drill the voids. Another example would be buckyballs in liquid 3He as Fermi gas. Finally, in the future, boson condensate cavities immersed in dilute atomic Fermi condensates could serve as further system with which the effective interactions of cavities inside a Fermi gas can be studied in the lab. 

For this extended IBM, exact solutions are not possible, and we are forced to use a mean field approximation. The system is cranked to generate the high spin states. This HB approximation is simpler than the corresponding Hartree Fock lowest state all the bosons (of each type) are in a single boson condensate rather than in a set of occupied states as in the HF case. Finding the self consistent solution is a simple numerical problem and requires little computer time. The ground state is of the form ... 

Nonlinear dynamical effects on one-dimensional systems such as biomolecular chains, e.g., Davydov solitons, can also be analyzed in terms of boson condensation. " In the Frohlich wave case, the condensation... 

In conclusion from the above formalism we can deduce that the Davydov soliton is the macroscopic envelope of the localized boson condensation of the excitation quanta /) induced by the j8 transformation (3.19). The vanishing of the coefficient G of the nonlinear term of Eq. (3.29), via Eq. (3.13), implies the disappearance of the soliton, which then looks like a necessary consequence of the nonlinearities of the dynamics. 

E. Del Giudice, S. Doglia, M. Milani, and G. Vitiello, Spontaneous Synmietry Breakdown and Boson Condensation in Biology, Phys. Lett. A 95, 508-510 (1983) E. Del Giudice, S. Doglia, M. Milani, and G. Vitiello, A Quantum Field Theoretical Approach to the Collective Behaviour of Biological Systems, Nucl. Phys. B 251 [FS 13], 375-400 (1985). 

Putz, M. V. (2011a). Hidden side of chemical bond the bosonic condensate. In Advances in Chemistry Research. Volume 10, Taylor, J. C. (Ed.), NOVA Science Publishers, Inc., New York, Chapter 8, pp. 261-298. 

Equation (1.202) accounts for the bosonic condensation through the selfinteraction coupling ... 

Still, even for the hydrogen molecular system, the difference between the physical and chemical bonding behavior with respect to the bondonic-bosonic condensate emphasizes the specificity of natural law in the chemical realm, which is not necessarily viewed as a reducible physical counterpart. This affirms once more that chemical structure and bonding are special manifestations of nature at the level of atoms and molecules or as the surrealist poet Lucian Blaga writes an unveiled mystery more mysteries revealed . 

From the beginning, one needs some prerequisites regarding the Density Functional Theory and its analytical connections to the statistical mechanics of Bosonic condensation. The main point is that in Bosonic condensates the energies and potential of the system are functionals of the couple [4 (r),p(r)] in terms of the... 

Now, one may employ the exchange-correlation information to formulate the DFT-BEC equations, targeting the bosonic condensate density and the related density fimctional quantities [35, 44] ... 

Returning to the Thomas-Fermi approximation, the approximation is indeed in agreement with the thermodynamic limit for bosonic condensation and can also be used for chemical systems, for chemical bonds are present down to the limiting case of single-chemical-bond systems (as in the paradigmatic homopolar bindings of molecular hydrogen and helium, H2 and He2). 

Within this framework, for bonding electrons (with their mass mo), one has the generic bosonic condensation Hamiltonian, rooted in the nonlinear Schrodinger or Gross-Pitaevsky equation (67),... 

This formula represents the bonding-level reformulation for the inverse relationship between (i/ (r))pandg , as already noted from the above Thomas-Fermi approximation. However, for consistency, it is worth noting that the order parameter refers to the atomic gas bosonic property in the isolated condition, i.e., when it is treated only as a bosonic condensate alone this acquires chemical bonding relevance when combined with the bonding energy in gg. 

Remarkably, it is worth pointing out that the bosonic nature of chemical bonding primarily depends on the degree to which the atoms involved in bonding display bosonic condensation when considered as a single gas having a nonzero order parameter (i/ (r)) 0 because the BEC side of the chemical bonding imply terms such as [42, 44]... 

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