1,720,995 research outputs found
Bose-Einstein condensation: Analysis of problems and rigorous results
Full text linkThis work is an up-to-date and partially improved analysis of the basics of the mathe-
matical description of Bose-Einstein condensation in terms of first principles of Quantum
Mechanics.
The main aims are:
1) to provide a compact, yet coherent overview:
- of the basic mathematical tools used to formalise Bose-Einstein condensation,
- of the mathematical techniques for studying several features of this physical phenomenon,
- and of how such means emerge as the natural ones in connection with their physical interpretation;
2) to discuss and to place in the above perspective some new contributions and improvements:
- on equivalent characterizations of Bose-Einstein condensation,
- on the strength of the convergence for some currently available asymptotic results,
- and on the effects of interparticle correlations on the energy and the dynamics of the many-body condensate
Global well-posedness of the magnetic Hartree equation with non-Strichartz external fields
No full textWe study the magnetic Hartree equation with external fields to which magnetic Strichartz estimates are not necessarily applicable. We characterise the appropriate notion of energy space and in such a space we prove the global well-posedness of the associated initial value problem by means of energy methods only
Born approximation in the problem of the rigorous derivation of the Gross-Pitaevskii equation
No full textStrengthened convergence of marginals to the cubic nonlinear Schrödinger equation
No full textWe rewrite a recent derivation of the cubic non-linear Schrodinger equation by Adami, Golse, and Teta in the more natural form of the asymptotic factorisation of marginals at any fixed time and in the trace norm. This is the standard form in which the emergence of the non-linear effective dynamics of a large system of interacting bosons is proved in the literature
Lieb-Robinson bounds and growth of correlations in Bose mixtures
Full text linkFor a mixture of interacting Bose gases initially prepared in a regime of
condensation (uncorrelation), it is proved that in the course of the the time
evolution observables of disjoint sets of particles of each species have
correlation functions that remain asymptotically small in the total number of
particles and display a controlled growth in time. This is obtained by means of
ad hoc estimates of Lieb-Robinson type on the propagation of the interaction,
established here for the multi-component Bose mixture.Comment: 22 pages, To appear on Asymptotic Analysis (2022
Binding properties of the (2+1)-fermion system with zero-range interspecies interaction
No full textWe study analytically and numerically the binding properties, in particular the ground state, of the so-called (2+1)-fermion system, which is a three-dimensional system of two identical fermions interacting with a third particle of different species through a zero-range interaction. We model the system with a specific self-adjoint point interaction Hamiltonian recently constructed in the mathematical literature. First we characterize the internal symmetry of the bound states in the attractive case. Then we show that the system confines in a precise regime of masses and that its ground-state energy stays finite as the mass becomes close to the critical point of the collapse of the system. © 2013 American Physical Society
On point interactions realised as Ter-Martyrosyan-Skornyakov operators
No full textFor quantum systems of zero-range interaction we discuss the mathematical scheme within which modelling the two-body interaction by means of the physically relevant ultra-violet asymptotics known as the "Ter-Martirosyan-Skornyakov condition" gives rise to a self-adjoint realisation of the corresponding Hamiltonian. This is done within the self-adjoint extension scheme of Krein, Visik, and Birman. We show that the Ter-Martirosyan-Skornyakov asymptotics is a condition of self-adjointness only when is imposed in suitable functional spaces, and not just as a pointwise asymptotics, and we discuss the consequences of this fact on a model of two identical fermions and a third particle of different nature
Stability of the (2+2)-fermionic system with zero-range interaction
No full textWe introduce a 3D model, and we study its stability, consisting of two distinct pairs of identical fermions coupled with a two-body interaction between fermions of different species, whose effective range is essentially zero (a so called (2+2)-fermionic system with zero-range interaction). The interaction is modelled by implementing the celebrated (and ubiquitous in the literature of this field) Bethe-Peierls contact condition with given two-body scattering length within the Krein-Višik-Birman theory of extensions of semi-bounded symmetric operators, in order to make the Hamiltonian a well-defined (self-adjoint) physical observable. After deriving the expression for the associated energy quadratic form, we show analytically and numerically that the energy of the model is bounded below, thus describing a stable system. © 2016 IOP Publishing Ltd
Schrodinger operators on half-line with shrinking potentials at the origin
No full textWe discuss the general model of a Schrödinger quantum particle constrained on a straight half-line with given selfadjoint boundary condition at the origin and an interaction potential supported around the origin. We study the limit when the range of the potential scales to zero and its magnitude blows up. We show that in the limit the dynamics is generated by a self-adjoint negative Laplacian on the half-line, with a possible preservation or modification of the boundary condition at the origin, depending on the magnitude of the scaling and of the strength of the potential. © 2016 - IOS Press and the authors. All rights reserved
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