Title: Volume Dependence of N-Body Bound States,
Abstract: We derive the finite-volume correction to the binding energy of an N-particle
quantum bound state in a cubic periodic volume. Our results are applicable to
bound states with arbitrary composition and total angular momentum, and in any
number of spatial dimensions. The only assumptions are that the interactions
have finite range. The finite-volume correction is a sum of contributions from
all possible breakup channels. In the case where the separation is into two
bound clusters, our result gives the leading volume dependence up to
exponentially small corrections. If the separation is into three or more
clusters, there is a power-law factor that is beyond the scope of this work,
however our result again determines the leading exponential dependence. We also
present two independent methods that use finite-volume data to determine
asymptotic normalization coefficients. The coefficients are useful to determine
low-energy capture reactions into weakly bound states relevant for nuclear
astrophysics. Using the techniques introduced here, one can even extract the
infinite-volume energy limit using data from a single-volume calculation. The
derived relations are tested using several exactly solvable systems and
numerical examples. We anticipate immediate applications to lattice
calculations of hadronic, nuclear, and cold atomic systems.