Journal ArticleDOI
Relationship between Systems of Impenetrable Bosons and Fermions in One Dimension
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In this article, a rigorous one-one correspondence between one-dimensional systems of bosons and spinless fermions is established, subject only to the restriction that the interaction has an impenetrable core.Abstract:
A rigorous one‐one correspondence is established between one‐dimensional systems of bosons and of spinless fermions. This correspondence holds irrespective of the nature of the interparticle interactions, subject only to the restriction that the interaction have an impenetrable core. It is shown that the Bose and Fermi eigenfunctions are related by ψB=ψFA, where A(x1 … xn) is +1 or −1 according as the order pq … r, when the particle coordinates xj are arranged in the order xp<xq< … <xr, is an even or an odd permutation of 1 … n. The energy spectra of the two systems are identical, as are all configurational probability distributions, but the momentum distributions are quite different. The general theory is illustrated by application to the special case of impenetrable point particles; the one‐one correspondence between bosons with this particular interaction and completely noninteracting fermions leads to a rigorous solution of this many‐boson problem.read more
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Many-Body Physics with Ultracold Gases
TL;DR: In this article, a review of recent experimental and theoretical progress concerning many-body phenomena in dilute, ultracold gases is presented, focusing on effects beyond standard weakcoupling descriptions, such as the Mott-Hubbard transition in optical lattices, strongly interacting gases in one and two dimensions, or lowest-Landau-level physics in quasi-two-dimensional gases in fast rotation.
Journal ArticleDOI
Exact analysis of an interacting bose gas. i. the general solution and the ground state
Elliott H. Lieb,Werner Liniger +1 more
TL;DR: In this paper, the ground-state energy as a function of γ was derived for all γ, except γ = 0, and it was shown that Bogoliubov's perturbation theory is valid when γ is small.
Journal ArticleDOI
Theory of ultracold atomic Fermi gases
TL;DR: In this article, the physics of quantum degenerate atomic Fermi gases in uniform as well as in harmonically trapped configurations is reviewed from a theoretical perspective, focusing on the effect of interactions that bring the gas into a superfluid phase at low temperature.
Journal ArticleDOI
A quantum Newton's cradle
TL;DR: The preparation of out-of-equilibrium arrays of trapped one-dimensional Bose gases, each containing from 40 to 250 87Rb atoms, which do not noticeably equilibrate even after thousands of collisions are reported.
Journal ArticleDOI
Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems
TL;DR: In this paper, the authors review recent developments in the theoretical understanding and numerical implementation of variational renormalization group methods using matrix product states and projected entangled pair states, and present a survey of the literature.
References
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Journal ArticleDOI
Bose-Einstein Condensation and Liquid Helium
Oliver Penrose,Lars Onsager +1 more
TL;DR: In this paper, the authors generalized Bose-Einstein condensation to a system of interacting particles and showed that B.E. condensation is present whenever the largest eigenvalue of the one-particle reduced density matrix is an extensive rather than an intensive quantity.
Journal ArticleDOI
Determinants and matrices. By A. C. Aitken. Pp. vii, 135. 4s. 6d. 1939. University Mathematical Texts, 1. (Oliver and Boyd)
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Journal ArticleDOI
Theory of many-boson systems: pair theory
M. Girardeau,Richard L. Arnowitt +1 more
TL;DR: In this paper, a variational approach was proposed to treat the many-boson system with repulsive interactions by treating the ground state with respect to pairs of more than two particles.
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