Fractional Hardy–Lieb–Thirring and Related Inequalities for Interacting Systems

TY - JOUR

T1 - Fractional Hardy–Lieb–Thirring and Related Inequalities for Interacting Systems

AU - Lundholm, Douglas

AU - Nam, Phan Thành

AU - Portmann, Fabian Daniel

PY - 2016/3/1

Y1 - 2016/3/1

N2 - We prove analogues of the Lieb–Thirring and Hardy–Lieb–Thirring inequalities for many-body quantum systems with fractional kinetic operators and homogeneous interaction potentials, where no anti-symmetry on the wave functions is assumed. These many-body inequalities imply interesting one-body interpolation inequalities, and we show that the corresponding one- and many-body inequalities are actually equivalent in certain cases.

AB - We prove analogues of the Lieb–Thirring and Hardy–Lieb–Thirring inequalities for many-body quantum systems with fractional kinetic operators and homogeneous interaction potentials, where no anti-symmetry on the wave functions is assumed. These many-body inequalities imply interesting one-body interpolation inequalities, and we show that the corresponding one- and many-body inequalities are actually equivalent in certain cases.

U2 - 10.1007/s00205-015-0923-5

DO - 10.1007/s00205-015-0923-5

M3 - Journal article

SN - 0003-9527

VL - 219

SP - 1343

EP - 1382

JO - Archive for Rational Mechanics and Analysis

JF - Archive for Rational Mechanics and Analysis

IS - 3

ER -