Classical mappings of the symplectic model and their application to the theory of large-amplitude collective motion

We study the algebra Sp(n,R) of the symplectic model, in particular for the cases n=1,2,3, in a new way. Starting from the Poisson-bracket realization we derive a set of partial differential equations for the generators as functions of classical canonical variables. We obtain a solution to these equations that represents the classical limit of a boson mapping of the algebra. The relationship to the collective dynamics is formulated as a theorem that associates the mapping with an exact solution of the time-dependent Hartree approximation. This solution determines a decoupled classical symplectic manifold, thus satisfying the criteria that define an exactly solvable model in the theory of large amplitude collective motion. The models thus obtained also provide a test of methods for constructing an approximately decoupled manifold in fully realistic cases. We show that an algorithm developed in one of our earlier works reproduces the main results of the theorem.Comment: 23 pages, LaTeX using REVTeX 3.

Stored energy in ultrafine-grained 316L stainless steel processed by high-pressure torsion

The energy stored in severely deformed ultrafine-grained (UFG) 316L stainless steel was investigated by differential scanning calorimetry (DSC). A sample was processed by high-pressure torsion (HPT) for N = 10 turns. In the DSC thermogram, two peaks were observed. The first peak was exothermic and related to the annihilation of vacancies and dislocations. During this recovery, the phase composition and the average grain size were practically unchanged. The energy stored in dislocations was calculated and compared with the heat released in the exothermic DSC peak. The difference was related to the annihilation of vacancy-like defects with a concentration of â¼5.2 Ã 10â4. The second DSC peak was endothermic which was caused by a reversion of αâ²-martensite into γ-austenite, however in this temperature range dislocation annihilation and a moderate grain growth also occurred. The specific energy of the reverse martensitic phase transformation was determined as about â11.7 J/g. Keywords: High-pressure torsion, Stored energy, Stainless steel, Phase transformation, Thermal stabilit