31 citations · 104 across the 18 of their papers we have counts for
19 papers
Lee-Huang-Yang Energy for Dilute Bose Gases: an Upper Bound for General Potentials
Giulia Basti, Morris Brooks, Serena Cenatiempo +2
We establish an upper bound for the ground state energy density of a dilute Bose gas, interacting through a general short-range, repulsive potential. To reach this goal, we extend…
The Lee-Huang-Yang energy for a dilute gas of hard spheres: an upper bound
Giulia Basti, Morris Brooks, Serena Cenatiempo +2
We consider a quantum gas consisting of hard spheres with radius , obeying bosonic statistics and moving in the box with periodic boundary conditions…
Third order corrections to the ground state energy of a Bose gas in the Gross-Pitaevskii regime
Cristina Caraci, Alessandro Olgiati, Diane Saint Aubin +1
For a translation invariant system of bosons in the Gross-Pitaevskii regime, we establish a precise bound for the ground state energy . While the leading, order , contr…
Convergence of states for polaron models in the classical limit
Marco Falconi, Alessandro Olgiati, Nicolas Rougerie
We consider the quasi-classical limit of Nelson-type regularized polaron models describing a particle interacting with a quantized bosonic field. We break translation-invariance by…
Upper bound for the ground state energy of a dilute Bose gas of hard spheres
Giulia Basti, Serena Cenatiempo, Alessandro Giuliani +3
We consider a gas of bosons interacting through a hard-sphere potential with radius in the thermodynamic limit. We derive a simple upper bound for the ground state energ…
Trial states for Bose gases: singular scalings and non-integrable potentials
Alessandro Olgiati
We review two results in which trial states for bosonic Hamiltonians were discussed. The problem of finding a trial state for a system with a hard-core potential in the Gross-Pitae…
Ground state energy of a Bose gas in the Gross-Pitaevskii regime
Giulia Basti, Serena Cenatiempo, Alessandro Olgiati +2
We review some rigorous estimates for the ground state energy of dilute Bose gases. We start with Dyson's upper bound, which provides the correct leading order asymptotics for hard…
A second order upper bound for the ground state energy of a hard-sphere gas in the Gross-Pitaevskii regime
Giulia Basti, Serena Cenatiempo, Alessandro Olgiati +2
We prove an upper bound for the ground state energy of a Bose gas consisting of hard spheres with radius , moving in the three-dimensional unit torus . Our e…
Reduced fluctuations for bosons in a double well
Alessandro Olgiati
We review two recent results on the ground state properties of bosonic systems trapped by a double well external potential. In the limit of large population and large separation be…
Bosons in a double well: two-mode approximation and fluctuations
Alessandro Olgiati, Nicolas Rougerie, Dominique Spehner
We study the ground state for many interacting bosons in a double-well potential, in a joint limit where the particle number and the distance between the potential wells both go to…
The Hartree functional in a double well
Alessandro Olgiati, Nicolas Rougerie
We consider a non-linear Hartree energy for bosonic particles in a symmetric double-well potential. In the limit where the wells are fare apart and the potential barrier is high, w…
Stability of the Laughlin phase against long-range interactions
Alessandro Olgiati, Nicolas Rougerie
A natural, "perturbative", problem in the modelization of the fractional quantum Hall effect is to minimize a classical energy functional within a variational set based on Laughlin…
On some rigorous aspects of fragmented condensation
Daniele Dimonte, Marco Falconi, Alessandro Olgiati
In this paper we discuss some aspects of fragmented condensation from a mathematical perspective. We first propose a simple way of characterizing finite fragmentation. Then, inspir…
Ground state energy of mixture of Bose gases
Alessandro Michelangeli, Phan Thành Nam, Alessandro Olgiati
We consider the asymptotic behavior of a system of multi-component trapped bosons, when the total particle number becomes large. In the dilute regime, when the interaction pote…
Effective non-linear spinor dynamics in a spin-1 Bose-Einstein condensate
Alessandro Michelangeli, Alessandro Olgiati
We derive from first principles the experimentally observed effective dynamics of a spinor Bose gas initially prepared as a Bose-Einstein condensate and then left free to expand ba…
Remarks on the derivation of Gross-Pitaevskii equation with magnetic Laplacian
Alessandro Olgiati
The effective dynamics for a Bose-Einstein condensate in the regime of high dilution and subject to an external magnetic field is governed by a magnetic Gross-Pitaevskii equation.…
Gross-Pitaevskii non-linear dynamics for pseudo-spinor condensates
Alessandro Michelangeli, Alessandro Olgiati
We derive the equations for the non-linear effective dynamics of a so called pseudo-spinor Bose-Einstein condensate, which emerges from the linear many-body Schrödinger equation at…
Effective non-linear dynamics of binary condensates and open problems
Alessandro Olgiati
We report on a recent result concerning the effective dynamics for a mixture of Bose-Einstein condensates, a class of systems much studied in physics and receiving a large amount o…
Mean-field quantum dynamics for a mixture of Bose-Einstein condensates
Alessandro Michelangeli, Alessandro Olgiati
We study the effective time evolution of a large quantum system consisting of a mixture of different species of identical bosons in interaction. If the system is initially prepared…