Zobrazeno 1 - 10
of 1 129
pro vyhledávání: '"NAM PHAN"'
Autor:
Duong, G. K., Nam, Phan Thành
We prove an analogue of the Lieb--Thirring inequality for many-body quantum systems with the kinetic operator $\sum_i (-\Delta_i)^s$ and the interaction potential of the form $\sum_i \delta_i^{-2s}$ where $\delta_i$ is the nearest-neighbor distance t
Externí odkaz:
http://arxiv.org/abs/2501.00866
Autor:
Dietze, Charlotte, Nam, Phan Thành
We give a new proof of the compactness of minimizing sequences of the Sobolev inequalities in the critical case. Our approach relies on a simplified version of the concentration-compactness principle, which does not require any refinement of the Sobo
Externí odkaz:
http://arxiv.org/abs/2412.08616
We study the ground state energy of a gas of spin $1/2$ fermions with repulsive short-range interactions. We derive an upper bound that agrees, at low density $\rho$, with the Huang-Yang conjecture. The latter captures the first three terms in an asy
Externí odkaz:
http://arxiv.org/abs/2409.17914
We prove a rigorous lower bound on the correlation energy of interacting fermions in the mean-field regime for a wide class of singular interactions, including the Coulomb potential. Combined with the upper bound obtained in \cite{ChrHaiNam-23b}, our
Externí odkaz:
http://arxiv.org/abs/2405.01386
We prove a Cwikel-Lieb-Rozenblum type inequality for the number of negative eigenvalues of the Hardy-Schr\"odinger operator $-\Delta - (d-2)^2/(4|x|^2) -W(x)$ on $L^2(\mathbb{R}^d)$. The bound is given in terms of a weighted $L^{d/2}-$norm of $W$ whi
Externí odkaz:
http://arxiv.org/abs/2312.16482
Autor:
Dietze, Charlotte, Nam, Phan Thành
Publikováno v:
Calc. Var. Partial Differential Equations 63 (2024), Art. 184
We derive a family of interpolation estimates which improve Hardy's inequality and cover the Sobolev critical exponent. We also determine all optimizers among radial functions in the endpoint case and discuss open questions on nonrestricted optimizer
Externí odkaz:
http://arxiv.org/abs/2312.11249
We consider a translation-invariant system of $N$ bosons in $\mathbb{T}^{3}$ that interact through a repulsive two-body potential with scattering length of order $N^{-1}$ in the limit $N\to \infty$. We derive second order expressions for the one- and
Externí odkaz:
http://arxiv.org/abs/2310.05448
Autor:
Lewin, Mathieu, Nam, Phan Thành
We consider the nonlinear Gross-Pitaevskii equation at positive density, that is, for a bounded solution not tending to 0 at infinity. We focus on infinite ground states, which are by definition minimizers of the energy under local perturbations. Whe
Externí odkaz:
http://arxiv.org/abs/2310.03495
Autor:
Nam, Phan Thành, Rademacher, Simone
We consider N bosons on the unit torus $\Lambda = [0,1]^3$ in the Gross-Pitaevski regime where the interaction potential scales as $N^2 V (N(x -y))$. We prove that the thermal equilibrium at low temperatures exhibits the Bose-Einstein condensation in
Externí odkaz:
http://arxiv.org/abs/2307.10622
We consider the dynamics of a 2D Bose gas with an interaction potential of the form $N^{2\beta-1}w(N^\beta\cdot)$ for $\beta\in (0,3/2)$. The interaction may be chosen to be negative and large, leading to the instability regime where the correspondin
Externí odkaz:
http://arxiv.org/abs/2307.00956