Boundary conditions and the entropy bound

Physical Review D

Volumn 63, Issue 4, 2001, Pages

  Solodukhin, Sergey N ^a  

^a UTRECHT UNIVERSITY   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; ENERGY; ENTROPY; MATHEMATICAL ANALYSIS; MOLECULAR DYNAMICS; MOLECULAR INTERACTION;

EID: 0035080067     PISSN: 05562821     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevD.63.044002     Document Type: Article

References (19)

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16. For arbitrary degeneracy gt>\ we find that max(S(E)/E) = ln(gi + l)/ojj.
17. In general, there is one bound state if the following conditions are satisfied: -/i0/j,5=0, /J0+/ii==0, and //0+/i,/-/)0/i,5=l; two bound states if/!0+/ii>0 and -/!0/i,<0, and no bound states in any other case.
18. It is particularly easy to see for a special case h0+hl = 0. The bound state then is \2b=-h0hl and the roots of Eq. (7) are an=Trn, n = 1,2,... . Including both the bound state and the states with a2>0 it is straightforward to evaluate the sum -l/\j+2"=1l/a=l//i0/!i +j. It exactly coincides with what we get by expanding the logarithm of Eq. (9) by powers of z2. The contribution of the bound state is evident. I thank J.S. Dowker for this example.
19. One should also subtract the contributions of all other bound states appearing for / = 0,... ,/0- 1.