Van Hove Theorem Research Articles

Empirical relation between the energy of the topmost particle and the mean binding energy of nuclei

On the basis of experimental knowledge, it is shown that separation energy thresholds cannot be interpreted as experimental single-particle energies, and that the energy of the topmost particle in conventional nuclear single-particle potentials is smaller in absolute magnitude than the mean binding energy. Connections with Hugenholtz and Van Hove's theorem are briefly discussed.

Approach to a uniform theory of the liquid and solid phases of4He at absolute zero

Theoretical studies of liquid 4 He have led to recognition of a plausible general form for the exact ground-state wave function. Arguments are presented supporting the view that the same form is adequate to describe the solid. The notion of a local density is used to adapt the form to the description of the two-phase density range. Van Hove's theorem holds for the ground state.

Virtual symmetry

Virtual symmetry is the symmetry which an asymmetric or partially symmetric system acquires if it is possible to embed it, using symmetry operations, into a larger and more symmetrical system. Often the virtual symmetry of a system is so great, that its eigenvectors and eigenvalues can be determined on that basis alone. Such is the case for the small vibrations of a lumepd string or a square lattice, and in fact quite generally for any crystal lattice with a regular boundary. These systems often possess catastrophic degeneracies, not overtly related to their geometric symmetry group, but closely related to the singularities in their density of frequencies curve required by van Hove's theorem. The operators generating these degeneracies possess the unusual feature that they are symmetry operators only for the degenerate states and hence do not commute with the Hamiltonian. Nevertheless, not only do they supplement van Hove's theorem by yielding an accurate description of the density of frequencies, but their more casual use still gives quantitative information concerning relative densities and the number, types, and location of the singularities. In this paper we introduce the concept of virtual symmetry by an example, and give the subject a mathematical formulation, finally finding a new insight and some more details of the spectra of some well-known lattices. The origin of the ubiquituous eigenvalues λ = ±1 in the Hückel theory of alternant hydrocarbons is seen to be a sort of reverse virtual symmetry.

On a theorem concerning the single particle energy of a fermi gas with interactions

It is shown that the Hugenholtz and Van Hove theorem is a consequence of another theorem, which involves the existence of a hyperbolic partial differential equation, obeyed by the potential energy of a nucleon in an infinite sea of nuclear matter. The fundamental role played by this nuclear equation in describing the nucleus as a Fermi gas with interactions is discussed.