1,720,967 research outputs found
A second order upper bound on the ground state energy of a Bose gas beyond the Gross-Pitaevskii regime
No full textWe consider a system of bosons in a unitary box in the grand-canonical
setting interacting through a potential with scattering length scaling as
This regimes interpolate between the
Gross-Pitaevskii regime () and the thermodynamic limit
(). In Forum Math. Sigma 9 (2021), e74, as an intermediate step to
prove an upper bound in agreement with the Lee-Huang-Yang formula in the
thermodynamic limit, it is obtained a second order upper bound on the ground
state energy for In this paper, thanks to a more careful analysis
of the error terms, we extend the above mentioned result to .Comment: Contribution to the Proceedings of ICMP 202
Low energy behavior in few-particle quantum systems: Efimov effect and zero-range interactions
Full text linkWe investigate the emergence of a universal behavior in certain few-particle quantum sys- tems at low-energy.
First we consider a system composed by two identical fermions of mass one and a dif- ferent particle of mass m in dimension three. Under the assumption that the two-particle Hamiltonians composed by one of the fermions and the third particle have a resonance at zero-energy, and for m less than a mass threshold m∗, we prove the occurrence of the Efimov effect, i. e., the existence of an infinite number of three-body bound states accumulating at zero. Then we study three-particle systems with zero-range interactions. In dimension one we give a rigorous definition of the Hamiltonian for three identical bosons and we prove that it is the limit of suitably rescaled regular Hamiltonians. In dimension three we write the expression of the quadratic form associated to the STM extension for a generic three-particle system. Then we focus on a system of three identical bosons proving stability outside the s-wave subspace. As a third example of universal behavior in few-particle system we con- sider a quantum Lorentz gas in dimension three: a particle moving through N obstacles whose positions are independently chosen according to a given common probability density. We assume that the particle interact with each obstacle via a Gross Pitaevskii potential. We prove the convergence, as N → ∞, to a Hamiltonian depending on the common distribution density of the obstacles and such that the only dependence on the interaction potential is through its scattering length
Efimov effect for a three-particle system with two identical fermions
Full text linkWe consider a three-particle quantum system in dimension three composed of two identical fermions of mass one and a different particle of mass m. The particles interact via two-body short range potentials. We assume that the Hamiltonians of all the two-particle subsystems do not have bound states with negative energy and, moreover, that the Hamiltonians of the two subsystems made of a fermion and the different particle have a zero-energy resonance. Under these conditions and for the number of negative eigenvalues of is finite and for $
On the quantum mechanical three-body problem with zero-range interactions
Full text linkIn this note we discuss the quantum mechanical three-body problem with pairwise zero-range interactions in dimension three.
We review the state of the art concerning the construction of the corresponding Hamiltonian as a self-adjoint operator in the bosonic and in the fermionic case. Exploiting a quadratic form method, we also prove self-adjointness and boundedness from below in the case of three identical bosons when the Hilbert space is suitably restricted, i.e., excluding the ``s-wave" subspace
Energy expansions for dilute Bose gases from local condensation results: a review of known results
No full textNon-relativistic interacting bosons at zero temperature, in two and three dimensions, are expected to exhibit a fascinating critical phase, famously known as condensate phase. Even though a proof of Bose-Einstein condensation in the thermodynamic limit is still beyond reach of the current available methods, in the past decades the mathematical physics community has gained an enhanced comprehension of other aspects of the macroscopic behavior of dilute Bose gases at zero temperature. In these notes we review part of these advances, by focusing on the strict relation among the occurrence of Bose-Einstein condensation on large – but finite – boxes, and the asymptotic expansion to the ground state energy of dilute Bose gases
The three-body problem in dimension one: From short-range to contact interactions
Full text linkWe consider a Hamiltonian describing three quantum particles in dimension one interacting through two-body short-range potentials. We prove that, as a suitable scale parameter in the potential terms goes to zero, such a Hamiltonian converges to one with zero-range (also called delta or point) interactions. The convergence is understood in the norm resolvent sense. The two-body rescaled potentials are of the form vσε(xσ)=ε-1vσ(ε-1xσ), where σ = 23, 12, 31 is an index that runs over all the possible pairings of the three particles, xσis the relative coordinate between two particles, and ε is the scale parameter. The limiting Hamiltonian is the one formally obtained by replacing the potentials vσ with ασδσ, where δσis the Dirac delta-distribution centered on the coincidence hyperplane xσ= 0 and ασ= Rvσdxσ. To prove the convergence of the resolvents, we make use of Faddeev's equations
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
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