3,485 research outputs found
Enigmas
No full textArising from the 2020 Darwin College Lectures, this book presents eight essays from prominent public intellectuals on the theme of Enigmas. Each author examines this theme through the lens of their own particular area of expertise, together constituting an illuminating and diverse interdisciplinary volume. Enigmas features contributions by professor of physics Sean M. Carroll, author Jo Marchant, writer and broadcaster Adam Rutherford, professor of earth sciences Tamsin A. Mather, professor of the history of the book Erik Kwakkel, reader in cultural history Tiffany Watt Smith, mathematician and public speaker James Grime, assistant professor of positive AI J. Derek Lomas, and explorer Albert Y.- M. Lin. This volume will appeal to anyone fascinated by puzzles and mysteries, solved and unsolved
Lower bound on entanglement in subspaces defined by Young diagrams
No full textEigenvalues of 1-particle reduced density matrices of N-fermion states are upper bounded by 1/N, resulting in a lower bound on entanglement entropy. We generalize these bounds to all other subspaces defined by Young diagrams in the Schur-Weyl decomposition of circle times C-N(d). Published under license by AIP Publishing
Generalized Pauli constraints in large systems: the Pauli principle dominates
No full textLately, there has been a renewed interest in fermionic 1-body reduced density
matrices and their restrictions beyond the Pauli principle. These restrictions
are usually quantified using the polytope of allowed, ordered eigenvalues of
such matrices. Here, we prove this polytope's volume rapidly approaches the
volume predicted by the Pauli principle as the dimension of the 1-body space
grows, and that additional corrections, caused by generalized Pauli
constraints, are of much lower order unless the number of fermions is small.
Indeed, we argue the generalized constraints are most restrictive in
(effective) few-fermion settings with low Hilbert space dimension.Comment: Published version; 37 pages, 5 figure
Ground State Energy of Dilute Bose Gases in 1D
No full textWe study the ground state energy of a gas of 1D bosons with density ρ, interacting through a general, repulsive 2-body potential with scattering length a, in the dilute limit ρ|a|≪1. The first terms in the expansion of the thermodynamic energy density are (π2ρ3/3)(1+2ρa), where the leading order is the 1D free Fermi gas. This result covers the Tonks–Girardeau limit of the Lieb–Liniger model as a special case, but given the possibility that a>0, it also applies to potentials that differ significantly from a delta function. We include extensions to spinless fermions and 1D anyonic symmetries, and discuss an application to confined 3D gases.</p
The Bogoliubov free energy functional II:The dilute limit
No full textWe analyse the canonical Bogoliubov free energy functional at low temperatures in the dilute limit. We prove existence of a first order phase transition and, in the limit , we determine the critical temperature to be to leading order. Here, is the critical temperature of the free Bose gas, is the density of the gas, is the scattering length of the pair-interaction potential , and its first order approximation. We also prove asymptotic expansions for the free energy. In particular, we recover the Lee-Huang-Yang formula in the limit
The Bogoliubov Free Energy Functional I: Existence of Minimizers and Phase Diagram
No full textThe Bogoliubov free energy functional is analysed. The functional serves as a model of a translation invariant Bose gas at positive temperature. We prove the existence of minimizers in the case of repulsive interactions given by a sufficiently regular two-body potential. Furthermore, we prove existence of a phase transition in this model and provide its phase diagram
Ground state energy of a dilute two-dimensional Bose gas from the Bogoliubov free energy functional
No full textWe extend the analysis of the Bogoliubov free energy functional to two dimensions at very low temperatures. For sufficiently weak interactions, we prove two term asymptotics for the ground state energy.</p
A Flea on Schrodinger's Cat
No full textContains fulltext :
111305.pdf (Author’s version preprint ) (Open Access
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