Physics of projected wavefunctions

Miguel A. Cazalilla

It is argued that the recently observed Fermi liquids in strongly interacting ultracold Fermi gases are adiabatically connected to a projected Fermi gas. This conclusion is reached by constructing a set of Jastrow wavefunctions, following Tan's observations on the structure of the physical Hilbert space [Annals of Physics 323, 2952 (2008)]. The Jastrow projection merely implements the Bethe–Peierls condition on the BCS and Fermi gas wavefunctions. This procedure provides a simple picture of the emergence of Fermi polarons as composite fermions in the normal state of the highly polarized gas. It is also shown that the projected BCS wavefunction can be written as a condensate of pairs of composite fermions (or Fermi polarons). A Hamiltonian for the composite fermions is derived. Within a mean-field theory, it is shown that the ground state and excitations of this Hamiltonian are those of a non-interacting Fermi gas although they are described by Jastrow–Slater wavefunctions.

Martin Ringbauer, B. Duffus, Cyril Branciard +3 more

WUN, SYU JIA

This paper proposes a central thesis: The quantum-mechanical wavefunction ψ(x) is not a description of a particle itself, but a projection of higher-dimensional string amplitudes into 3+1 spacetime. Under this interpretation, quantum superposition, collapse, and nonlocality are no longer independent mysteries but distinct projection behaviors of the same higher-dimensional structure. We show that: Wavefunction superposition corresponds to the linear superposition of string amplitudes. Wavefunction collapse corresponds to selecting and stabilizing a point in the high-dimensional moduli space. Spatial spread of ψ(x) corresponds to the topological extensibility of strings in higher dimensions. Quantum nonlocality is the natural projection of high-dimensional connectedness. The measurement problem becomes: the selection of a projection boundary condition in higher-dimensional space. Because both quantum mechanics and string theory are built on amplitudes and moduli spaces, we unify them by proposing the String–ψ Correspondence: ψ(x)=P[Ψstring​(S)], where ψ(x) is the observed low-dimensional wavefunction and Ψ(S) is the full string-state wavefunction before projection. This unified framework offers new insights for quantum gravity, quantum information, cosmology, and particle physics.

Marlina Slamet, Xiao‐Yin Pan, Viraht Sahni