Publisher’s Note: Complex Chemical Potential: Signature of Decay in a Bose-Einstein Condensate [Phys. Rev. Lett.94, 190402 (2005)]

Discovery of exceptional points in the Bose-Einstein condensation of gases with attractive1/rinteraction

“…A complex chemical potential as a signature of a decaying condensate has already been discussed in Ref. [40].…”

“…The physical interpretation might be that at large negative scattering lengths the contact potential is so attractive that the atoms of the condensate form molecules or clusters as discussed, e.g., in Refs. [7,40,41]. The decreasing number of atoms means the decay of the condensate.…”

Independent pair approximation for attractive bose condensates

“…Comparing this with the many-body treatment, the density equation differs from (16) only in the coefficient of (−μ) 3/2 , which is √ 2/(3π 2 ) in the former calculation [8]. Accordingly, the lowest order decay rate obtained from (18), Γ = (h/m)16 √ 2π 3/2 a( ) 5/2 ρ 3/2 a , is 17% smaller than its many-body counterpart.…”

“…In previous work [8] a variational many-body calculation shows that the μ < 0 solution yields a two-piece energy per particle with a negative slope for all values of the density. Since the pressure acquires the same sign as de/dρ, we identify this solution as the collapsing ground state of the system.…”

Phase transition in a system of 1D harmonic oscillators obeying Polychronakos statistics with a complex parameter

“…The parameter of statistics is considered a complex number [8]. Complex-valued physical quantities can occur effectively in some physical systems: complex energy is connected to a dissipative process [9]; complex chemical potential is also used, e.g., in quantum chromodynamics [10] or physics of semiconductors [11]; complex external potential is applied to describe the interaction between the light field and atoms moving in crystals [12,13] and also can be used to study -symmetry breaking [14].…”