TY - JOUR
T1 - Monotonicity of quantum ground state energies
T2 - Bosonic atoms and stars
AU - Kiessling, Michael K.H.
N1 - Funding Information:
Acknowledgements This paper was written with support from the NSF under grant DMS-0807705. Any opinions expressed in this paper are entirely those of the author and not those of the NSF. I thank Elliott H. Lieb for drawing my attention to the work of Post and collaborators, and Detlev Buchholz, Jerry Percus, Walter Thirring, and two anonymous referees for their helpful comments.
PY - 2009/12
Y1 - 2009/12
N2 - The N-dependence of the non-relativistic bosonic ground state energy is studied for quantum N-body systems with either Coulomb or Newton interactions. The Coulomb systems are "bosonic atoms," with their nucleus fixed, and it is shown that grows monotonically in N > 1, where. The Newton systems are "bosonic stars," and it is shown that when the Bosons are centrally attracted to a fixed gravitational "grain" of mass M > 0, and N >2, then grows monotonically in N, where PN(N) = N (N - 1)(N-2); in the translation-invariant problem (M = 0), it is shown that when N > 1 then grows monotonically in N, with from the Coulomb problem. Some applications of the new monotonicity results are discussed.
AB - The N-dependence of the non-relativistic bosonic ground state energy is studied for quantum N-body systems with either Coulomb or Newton interactions. The Coulomb systems are "bosonic atoms," with their nucleus fixed, and it is shown that grows monotonically in N > 1, where. The Newton systems are "bosonic stars," and it is shown that when the Bosons are centrally attracted to a fixed gravitational "grain" of mass M > 0, and N >2, then grows monotonically in N, where PN(N) = N (N - 1)(N-2); in the translation-invariant problem (M = 0), it is shown that when N > 1 then grows monotonically in N, with from the Coulomb problem. Some applications of the new monotonicity results are discussed.
KW - Bosonic atoms
KW - Bosonic stars
KW - Ground state energies
KW - N body problems
KW - Non-relativistic quantum mechanics
KW - Rigorous results
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U2 - 10.1007/s10955-009-9843-9
DO - 10.1007/s10955-009-9843-9
M3 - Article
AN - SCOPUS:74449091433
SN - 0022-4715
VL - 137
SP - 1063
EP - 1078
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
IS - 5
ER -