Loris Ferrari
University of Bologna, Italy
Title: Pseudobosons and quasiphonons: The hidden side of bogoliubov collective excitations
Biography
Biography: Loris Ferrari
Abstract
In a gas of N interacting bosons, Bogoliubov’s first step is dropping all the interaction terms between free bosons with moment ,which leads to the truncated Hamiltonian Hc. Bogoliubov’s second step (Bogoliubov Canonic Approximation) is approssimating Hc with a bi-linear canonic form HBCA in the creation/annihilation operators, which can be diagonalized by the well known Bogoliubov transformations. All this leads to the current notion of quasiphonons, i.e. collective bosonic excitation, with wave-like character (at low k), each carrying a finite moment Here we show what happens when Hc is diagonalized exactly. The resulting eigenstates depend on two discrete indices where numerates the quasiphonons carrying a moment , responsible for transport or dissipation processes. S, in turn, numerates a ladder of vacua , with increasing equispaced energies, formed by boson pairs with opposite moment. Passing from one vacuum to another , results from creation/annihilation of new momentless collective excitations, reminiscent of bosonic cooper pairs, that we call pseudo-bosons. Exact quasiphonons originate from one of the vacua by creating an asymmetry in the number of opposite moment bosons. The well known Bogoliubov quasiphonons (QPs) are shown to coincide with the exact eigenstates , i.e. with the QPs created from the lowest-level vacuum (S=0). All this is discussed, in view of existing or future experimental observations of what we call the hidden side of Bogoliubov collective excitations (CEs), i.e. the
pseudobosons.