77,234 research outputs found
Stability of a fermionic particle system with point interactions
We prove that a system of fermions interacting with an additional
particle via point interactions is stable if the ratio of the mass of the
additional particle to the one of the fermions is larger than some critical
. The value of is independent of and turns out to be less than
. This fact has important implications for the stability of the unitary
Fermi gas. We also characterize the domain of the Hamiltonian of this model,
and establish the validity of the Tan relations for all wave functions in the
domain.Comment: LaTeX, 29 pages, 2 figures; typos corrected, explanations and
references added; to appear in Commun. Math. Phy
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Typhlops capitulatus
Number of Pages: 2Integrative BiologyGeological Science
Stability of the 2+2 fermionic system with point interactions
We give a lower bound on the ground state energy of a system of two fermions
of one species interacting with two fermions of another species via point
interactions. We show that there is a critical mass ratio m_c \approx 0.58 such
that the system is stable, i.e., the energy is bounded from below, for m \in
[m_c, m_c^{-1}]. So far it was not known whether this 2+2 system exhibits a
stable region at all or whether the formation of four-body bound states causes
an unbounded spectrum for all mass ratios, similar to the Thomas effect. Our
result gives further evidence for the stability of the more general N+M system.Comment: LaTeX, 12 pages; typos corrected, references and 2 figures added; to
appear in Math. Phys. Anal. Geo
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Typhlops schwartzi
Number of Pages: 2Integrative BiologyGeological Science
Triviality of a model of particles with point interactions in the thermodynamic limit
We consider a model of fermions interacting via point interactions, defined
via a certain weighted Dirichlet form. While for two particles the interaction
corresponds to infinite scattering length, the presence of further particles
effectively decreases the interaction strength. We show that the model becomes
trivial in the thermodynamic limit, in the sense that the free energy density
at any given particle density and temperature agrees with the corresponding
expression for non-interacting particles.Comment: LaTeX, 20 pages; final version, to appear in Lett. Math. Phy
Summing curious, slowly convergent, harmonic subseries
The harmonic series diverges. But if we delete from the harmonic series all terms whose denominators contain any string of digits such as "9", "42", or "314159", then the sum of the remaining terms converges. These series converge far too slowly to compute their sums directly. We describe an algorithm to compute these and related sums to high precision. For example, the sum of the series whose denominators contain no "314159" is approximately 2302582.33386. We explain why this sum is so close to 106 log 10 by developing asymptotic estimates for sums that omit strings of length n, as n approaches infinity. \ud
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The first author is supported by a Rhodes Scholarship
Colouring Isonemal Fabrics with more than two Colours by Thin Striping
Perfect colouring of isonemal fabrics by thin striping of warp and weft with
more than two colours is examined. Examples of thin striping in all possible
species with no redundancy and with redundant cells arranged as twills are
given. Colouring woven flat tori is discussed.Comment: 50 figure
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