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GATE is public domain software widely used for Monte Carlo simulation in emission tomography. Validations of GATE have primarily been performed on a whole-system basis, leaving the possibility that errors in one sub-system may be offset by errors in others. We assess the accuracy of the GATE PET coincidence generation sub-system in isolation, focusing on the options most closely modeling the majority of commercially available scanners. Independent coincidence generators were coded by teams at Toshiba Medical Research Unit (TMRU) and UC Davis. A model similar to the Siemens mCT scanner was created in GATE. Annihilation photons interacting with the detectors were recorded. Coincidences were generated using GATE, TMRU and UC Davis code and results compared to "ground truth" obtained from the history of the photon interactions. GATE was tested twice, once with every qualified single event opening a time window and initiating a coincidence check (the "multiple window method"), and once where a time window is opened and a coincidence check initiated only by the first single event to occur after the end of the prior time window (the "single window method"). True, scattered and random coincidences were compared. Noise equivalent count rates were also computed and compared. The TMRU and UC Davis coincidence generators agree well with ground truth. With GATE, reasonable accuracy can be obtained if the single window method option is chosen and random coincidences are estimated without use of the delayed coincidence option. However in this GATE version, other parameter combinations can result in significant errors.

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We present an exact diagonalization study of the low-energy singlet and triplet states for both the one-dimensional (1D) and 2D t-J models. A scan of the parameter ratio J/t shows that for most low-energy states in both 1D and 2D the excitation energy takes the form E(t,J)=a . t+b . J. In 1D this is the natural conse quence of the factorization of the low-energy wave functions, i.e., spin-charge separation. Examination of the low-energy eigenstates in 2D shows that most of these are collective modes, which for larger J correspond to a periodic modulation of the hole density. The modulation is well reproduced by treating holes as hard-core bosons with an attractive interaction.

We present an exact diagonalization study of the low-energy singlet and triplet states for both the one-dimensional (1D) and 2D t-J models. A scan of the parameter ratio J/t shows that for most low-energy states in both 1D and 2D the excitation energy takes the form E(t,J)=a . t+b . J. In 1D this is the natural conse quence of the factorization of the low-energy wave functions, i.e., spin-charge separation. Examination of the low-energy eigenstates in 2D shows that most of these are collective modes, which for larger J correspond to a periodic modulation of the hole density. The modulation is well reproduced by treating holes as hard-core bosons with an attractive interaction.