Energetics of quasi-one-dimensional Bose gases

Table 4.1 summarizes the techniques used to solve the 1D and 3D Hamiltonian, respectively. This table is meant to guide the reader through our result sections. Section 4.4.2 discusses our MC energies for two-particle systems, while Sec. 4.4.1 discusses the energetics for larger systems, calculated within various frameworks. Finally, Sec. 4.5 discusses the stability of quasi-one dimensional Bose gases.

Table 4.1: Guide that summarizes the techniques used to solve the 3D and 1D Hamiltonian, Eqs. 4.18 and 4.19, respectively. Column 2 specifies the atom-atom interactions of the many-body Hamiltonian, column 3 lists the techniques used to solve the corresponding many-body Schrödinger equation, and column 4 lists the sections that discuss the results obtained using this approach.

Hamiltonian	interaction	technique	Section
$\hat H_{3D}$	$V^{HS}$	DMC	4.4.2
$\hat H_{3D}$	$V^{SR}$	FN-MC	4.4.1, 4.4.2
$\hat H_{1D}$	$g_{1D}>0$	DMC	4.4.1, 4.4.2
$\hat H_{1D}$	$g_{1D}>0$	LDA, LL	4.4.2
$\hat H_{1D}$	$g_{1D}<0$	FN-MC	4.4.1, 4.4.2
$\hat H_{1D}$	$g_{1D}>0$	LDA, hard-rod	4.4.2
$\hat H_{1D}$	$g_{1D}<0$	VMC	4.5