- Email: [email protected]
15. Theory of the lambda transition
LIQUID HELIUM
S 137
Consideration of thin helium films on the basis of the equation (1) leads to the lowering of the A point temperature for the films. The specific heat of films behaves anomalously. The problem of the vortex line in He II is solved. In this calculation the expression F0 = Foo + o~ [~1~ + fl ]~214/2 was used. However, the other expressions for F0 also can be taken. The paper will be published in full extent in the Journal of Experimental and Theoretical Physics (USSR).
15. T h e o r y of t h e L a m b d a T r a n s i t i o n . S. G. BRUSH. Mathematical Institute, Oxford. F e y n m a n-proposed a partition function for liquid helium based on his path-integral formulation of q u a n t u m mechanics, using an 'effective-mass' approximation. K i k u c h i introduced a lattice model in order to evaluate this partition function, and obtained a second-order transition. The basic feature of the theory is the representation of the q u a n t u m effect by permutation-polygons in the partition function; nearly all of these polygons disappear above the transition temperature because the probability of a polygon of length L is o¢ e x p ( - - A T L ) . This model can be made more realistic by distinguishing between different kinds of polygons and by allowing vacant lattice sites. I t is thereby possible to obtain a negative slope for the Pline as well as a 'classical' liquid-gas transition. The only adjustable parameter is the effective mass for many-sided polygons. This lattice model can also be used to discuss the effect of foreign atoms on the transition.
16. S e m i c l a s s i c a l t h e o r y of H q u i d h e l i u m . EUGENE P. GROSS. Brandeis University, Waltham, Mass, U.S.A. The subject of discussion is the Hamiltonian for a system of bosons interacting by two body forces, as expressed in the formalism of second quantization. In this paper, we examine properties of the classical wave field governed by the Hamiltonian. For a general potential there is always an exact solution representing a uniform density. E x a c t solutions are exhibited, which represent disturbances of a definite velocity and of arbitrary amplitude. For small amplitudes the disturbances obey B o g o 1y u b o v 's dispersion relation. Corresponding exact solutions are found for disturbances when the system moves as a whole. For suitably attractive potentials we find a class of exact solutions, degenerate in energy, with spatially periodic density. These solutions have a lower energy than the uniform type. Small amplitude excitations are investigated for the periodic case. They are phonons for long wave lengths, b u t show a band character at shorter wave lengths. A theory of the motion of foreign atoms in the boson fluid is formulated.
17. H o w c a n t h e M u l t i p l i c i t y of t h e G r o u n d S t a t e W a v e F u n c t i o n of l i q u i d h e l i u m b e i n f e r r e d f r o m T h e r m o s t a t i c s *). LASZLO TISZA. D e p a r t m e n t of Physics and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts. I t was recently pointed out t h a t a sharpened version of the phase rule in conjunction with the observation of a ~-line singularity in liquid helium leads to the inference t h a t *) This work was supported in part by the U.S. Army and U.S. Air Force Office of Scientific Research.
S 137
Consideration of thin helium films on the basis of the equation (1) leads to the lowering of the A point temperature for the films. The specific heat of films behaves anomalously. The problem of the vortex line in He II is solved. In this calculation the expression F0 = Foo + o~ [~1~ + fl ]~214/2 was used. However, the other expressions for F0 also can be taken. The paper will be published in full extent in the Journal of Experimental and Theoretical Physics (USSR).
15. T h e o r y of t h e L a m b d a T r a n s i t i o n . S. G. BRUSH. Mathematical Institute, Oxford. F e y n m a n-proposed a partition function for liquid helium based on his path-integral formulation of q u a n t u m mechanics, using an 'effective-mass' approximation. K i k u c h i introduced a lattice model in order to evaluate this partition function, and obtained a second-order transition. The basic feature of the theory is the representation of the q u a n t u m effect by permutation-polygons in the partition function; nearly all of these polygons disappear above the transition temperature because the probability of a polygon of length L is o¢ e x p ( - - A T L ) . This model can be made more realistic by distinguishing between different kinds of polygons and by allowing vacant lattice sites. I t is thereby possible to obtain a negative slope for the Pline as well as a 'classical' liquid-gas transition. The only adjustable parameter is the effective mass for many-sided polygons. This lattice model can also be used to discuss the effect of foreign atoms on the transition.
16. S e m i c l a s s i c a l t h e o r y of H q u i d h e l i u m . EUGENE P. GROSS. Brandeis University, Waltham, Mass, U.S.A. The subject of discussion is the Hamiltonian for a system of bosons interacting by two body forces, as expressed in the formalism of second quantization. In this paper, we examine properties of the classical wave field governed by the Hamiltonian. For a general potential there is always an exact solution representing a uniform density. E x a c t solutions are exhibited, which represent disturbances of a definite velocity and of arbitrary amplitude. For small amplitudes the disturbances obey B o g o 1y u b o v 's dispersion relation. Corresponding exact solutions are found for disturbances when the system moves as a whole. For suitably attractive potentials we find a class of exact solutions, degenerate in energy, with spatially periodic density. These solutions have a lower energy than the uniform type. Small amplitude excitations are investigated for the periodic case. They are phonons for long wave lengths, b u t show a band character at shorter wave lengths. A theory of the motion of foreign atoms in the boson fluid is formulated.
17. H o w c a n t h e M u l t i p l i c i t y of t h e G r o u n d S t a t e W a v e F u n c t i o n of l i q u i d h e l i u m b e i n f e r r e d f r o m T h e r m o s t a t i c s *). LASZLO TISZA. D e p a r t m e n t of Physics and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts. I t was recently pointed out t h a t a sharpened version of the phase rule in conjunction with the observation of a ~-line singularity in liquid helium leads to the inference t h a t *) This work was supported in part by the U.S. Army and U.S. Air Force Office of Scientific Research.