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Bogoliubov Spectrum of Interacting Bose Gases
We study the large-N limit of a system of N bosons interacting with a potential of intensity 1/N. When the ground state energy is to the first order given by Hartree's theory, we study the nextExpand
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Discrete Wirtinger-based inequality and its application
TLDR
We derive a discrete version of the Wirtinger-based integral inequality, which encompasses the discrete Jensen inequality. Expand
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Derivation of Hartree's theory for generic mean-field Bose systems
In this paper we provide a novel strategy to prove the validity of Hartree's theory for the ground state energy of bosonic quantum systems in the mean-field regime. For the well-known case of trappedExpand
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Derivation of nonlinear Gibbs measures from many-body quantum mechanics
We prove that nonlinear Gibbs measures can be obtained from the corresponding many-body, grand-canonical, quantum Gibbs states, in a mean-field limit where the temperature T diverges and theExpand
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Discrete inequalities based on multiple auxiliary functions and their applications to stability analysis of time-delay systems
TLDR
This paper presents new discrete inequalities for single summation and double summation for linear discrete systems with time-varying delay. Expand
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Ground states of large bosonic systems: The gross-pitaevskii limit revisited
We study the ground state of a dilute Bose gas in a scaling limit where the Gross-Pitaevskii functional emerges. This is a repulsive non-linear Schr\"odinger functional whose quartic term isExpand
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The mean-field approximation and the non-linear Schrödinger functional for trapped Bose gases
We study the ground state of a trapped Bose gas, starting from the full many-body Schrodinger Hamiltonian, and derive the nonlinear Schrodinger energy functional in the limit of large particleExpand
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REMARKS ON THE QUANTUM DE FINETTI THEOREM FOR BOSONIC SYSTEMS
The quantum de Finetti theorem asserts that the k-body density matrices of a N-body bosonic state approach a convex combination of Hartree states (pure tensor powers) when N is large and k fixed. InExpand
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An improved stability criterion for a class of neutral differential equations
TLDR
This work gives an improved criterion for asymptotical stability of a class of neutral differential equations. Expand
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Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations
We provide general conditions for which bosonic quadratic Hamiltonians on Fock spaces can be diagonalized by Bogoliubov transformations. Our results cover the case when quantum systems have infiniteExpand
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