Zero-temperature dielectric response of the charged Bose gas in a uniform magnetic field

The Non-relativistic Charged Bose Gas in a Magnetic Field II. Quantum Properties

“…It is interesting to note that in the limit of weak magnetic fields, i.e., | c Â| p < <1, HF [2] obtained four distinct dispersion relations corresponding to four sets of conditions. Their results do not depend upon z * , which contains the square of the characteristic length for a particle in a magnetic field ( cÂeB), but upon q …”

“…The z Ä limit corresponds to q z Ä 0 in Fourier space and if | c Â| p < <1, then we have the conditions for the second anisotropic case studied by HF [2]. HF claimed in this case that the screening potential could be represented by a 1D screening integral involving the field-free response function and thus obtained the potential…”

“…For example, in Fig. 16, which displays the tree diagram for c 11 (x), we draw branch lines to (0, 11), (2,9), (3,8), (4,7), and (5,6). Whenever a zero appears as the first number in a pair, the path stops, as evidenced by (0, 11) in the figure.…”

“…The principal aim of the first paper [1] was to develop formal results for the various response functions for the magnetised non-relativistic CBG, so that a study of the physical properties of this fundamental quantum mechanical system could follow. In that paper the pioneering study by Hore and Frankel [2] was developed further by using the more recent work of Witte et al [3], who had studied the relativistic version of the system by adopting the polarisation tensor approach in the random phase approximation (RPA). Through further simplification of this approach the formal results for the various response functions of the non-relativistic magnetised CBG were presented in a form more readily accessible to the classical plasma physicist.…”

“…The zero-temperature longitudinal dielectric response of the charged Bose gas in a uniform magnetic field has been studied extensively by Hore and Frankel [2], hereafter referred to as HF. By extending their own earlier work on the dielectric response of the field-free CBG [5], HF were able to study the system in a magnetic field at T=0 K after deriving the Fourier-transformed conductivity tensor, _(q, q$, |), via a second-quantised approach in the random phase approximation.…”