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- Publications
- Influence
Derivation of the cubic non-linear Schrödinger equation from quantum dynamics of many-body systems
- L. Erdős, B. Schlein, H. Yau
- Mathematics, Physics
- 2 August 2005
We prove rigorously that the one-particle density matrix of three dimensional interacting Bose systems with a short-scale repulsive pair interaction converges to the solution of the cubic non-linear… Expand
Derivation of the Gross-Pitaevskii equation for the dynamics of Bose-Einstein condensate
- L. Erdős, B. Schlein, H. Yau
- Physics, Mathematics
- 2 October 2004
Consider a system of N bosons in three dimensions interacting via a repulsive short range pair potential N 2 V (N(xi − xj)), where x = (x1, . . ., xN) denotes the positions of the particles. Let HN… Expand
Derivation of the Gross-Pitaevskii hierarchy for the dynamics of Bose-Einstein condensate
- L. Erdős, B. Schlein, H. Yau
- Mathematics, Physics
- 2 October 2004
Consider a system of N bosons on the three-dimensional unit torus interacting via a pair potential N2V(N(xi − xj)) where x = (x1, …, xN) denotes the positions of the particles. Suppose that the… Expand
Rigorous derivation of the Gross-Pitaevskii equation with a large interaction potential
- L. Erdős, B. Schlein, H. Yau
- Mathematics, Physics
- 26 February 2008
Consider a system of N bosons in three dimensions interacting via a repulsive short range pair potential N 2 V (N(xi − xj)), where x = (x1, . . . , xN) denotes the positions of the particles. Let HN… Expand
Quantum Fluctuations and Rate of Convergence Towards Mean Field Dynamics
- I. Rodnianski, B. Schlein
- Mathematics, Physics
- 20 November 2007
The nonlinear Hartree equation describes the macroscopic dynamics of initially factorized N-boson states, in the limit of large N. In this paper we provide estimates on the rate of convergence of the… Expand
Semicircle law on short scales and delocalization of eigenvectors for Wigner random matrices
- L'aszl'o ErdHos, B. Schlein, H. Yau
- Physics, Mathematics
- 12 November 2007
We consider $N\times N$ Hermitian random matrices with i.i.d. entries. The matrix
is normalized so that the average spacing between consecutive eigenvalues is of order
$1/N$. We study the… Expand
Wegner estimate and level repulsion for Wigner random matrices
- L. Erdős, B. Schlein, H. Yau
- Mathematics, Physics
- 16 November 2008
We consider $N\times N$ Hermitian random matrices with independent identically distributed entries (Wigner matrices). The matrices are normalized so that the average spacing between consecutive… Expand
Universality of random matrices and local relaxation flow
- L. Erdős, B. Schlein, H. Yau
- Mathematics, Physics
- 31 July 2009
Consider the Dyson Brownian motion with parameter β, where β=1,2,4 corresponds to the eigenvalue flows for the eigenvalues of symmetric, hermitian and quaternion self-dual ensembles. For any β≥1, we… Expand
Gross-Pitaevskii Equation as the Mean Field Limit of Weakly Coupled Bosons
- A. Elgart, L. Erdős, B. Schlein, H. Yau
- Mathematics, Physics
- 14 October 2004
We consider the dynamics of N boson systems interacting through a pair potential N−1Va(xi−xj) where Va(x)=a−3V(x/a). We denote the solution to the N-particle Schrödinger equation by ΨN, t. Recall… Expand
Rigorous derivation of the Gross-Pitaevskii equation.
- L. Erdős, B. Schlein, H. Yau
- Physics, Medicine
- Physical review letters
- 10 December 2006
The time-dependent Gross-Pitaevskii equation describes the dynamics of initially trapped Bose-Einstein condensates. We present a rigorous proof of this fact starting from a many-body bosonic… Expand
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