Scientific session of the Division of General Physics and Astronomy and the Division of Nuclear Physics of the Academy of Sciences of the USSR

Abstract

We present a generalization of the quantum mechanical formalism to a class of propagators that is closely related to the generalized Lorentzian path integrals we proposed in an earlier publication [R. A. Treumann, Phys. Rev. E 57, 5150 (1998)] introducing a (real) control parameter k > 0. In this formulation the SchrÎdinger and Heisenberg formalisms assume a de¢nite form when introducing a new k-Hamilton operator that is a functional of the quantum Hamiltonian operator. For k 3 I the usual quantum mechanics is recovered. This approach though apparently successful for constant time su¡ers from violating the semi-group property of quantum operators. Currently we do not see how to cure this de¢ciency.We nevertheless present the idea to the public in the hope that a way may be found to handle this problem in the time domain. The formalism is formally applied to the harmonic oscillator. We de¢ne new creation and destruction operators, ¢nd their commutators, and calculate the eigenvalues of the new k-Hamilton operator. These eigenvalues turn out to become time-dependent, whatever this means. In addition the energy levels are not anymore equally spaced. It is believed that the theory may be of use in application to quantum chaos and quantum turbulence. Physica Scripta 66 # Physica Scripta 2002 418 Rudolf A. Treumann

The growth of atomically rough4He crystals

“…The observed dependence of the growth coefficient on temperature is in very good accord with data at lower temperatures, obtained by other groups from melting-crystallization waves [5] and sound transmission through the interface [6, 141. A comparison of these results for the different techniques is given in Fig.…”

“…It has been suggested already in the early work of Keshishev et al [5] that the growth in 4~e at low temperatures is dominated by phon6ns and rotons. In the region that we have investigated, T>0.9 K, the phonon contribution is negligible compared to the rotons.…”

“…This gives rise to a production of entropy and there-fore leads to a resistance to growth. In their original form these theories yield the experimentally observed temperature dependence of the kinetic growth coefficient -a contribution from rotons varying as e-7.8'T, from phonons as T-4 [5] -only for relatively low temperatures where the excitations propagate ballistically in the bulk phases. In the higher temperature (T20.6K) "hydrodynamic" regime, however, where all our measurements have been made, the growth coefficients predicted by the above mentioned theories strongly deviate from the experimental data.…”

“…for the low temperature data. The difference to the real roton gap (7.2 K) has been ascribed to a temperature dependence of the preexponential factor [5]. The phonon contribution to the growth resistance, which becomes important at low temperatures, has been subtracted here range of the growth coefficient accessible with He crystals.…”

Dynamics and morphology of superfluid bubbles inHe4quantum crystals

“…It has contributed greatly to the understanding of physics in crystal growth. To date three roughening transitions have been observed in hcp phase for c-facet, a-facet, and s-facet whose transition temperatures are T R1 = 1.3 K, T R2 = 0.9 K, and T R3 = 0.36 K, respectively [6][7][8][9].…”