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This paper is concerned with the oscillations which appear in the smoothed density of eigenvalues... more This paper is concerned with the oscillations which appear in the smoothed density of eigenvalues when the smoothing width is relatively small. The existence of these oscillations is demonstrated by evaluating exactly the smoothed eigenvalue density for simple shapes of the volume-flat parallelepiped, sphere. A general theory of the density oscillations is then developed on the basis of the time-independent Green function formalism used in Part I of this work. An asymptotic evaluation of the various terms of the multiple reflection expansion is carried out by means of the principle of stationary phase, or by means of a contour integration method. A systematic investigation of the various resulting contributions shows that the dominant oscillations are associated with the closed classical trajectories, i.e., the closed polygons having their vertices on the boundary surface S and such that mirror reflections on S take place at each vertex. Various possible geometrical configurations of these closed paths are discusseddegenerate, accidentally degenerate, repeated paths. Several cases of cancellations between various contributions are indicated.
... Roger Balian CEA, Direction des Sciences de la Matière, Service de Physique Théorique de Sacl... more ... Roger Balian CEA, Direction des Sciences de la Matière, Service de Physique Théorique de Saclay F-91191 Gif-sur-Yvette, France and Ecole Polytechnique, F-91128 Palaiseau, France Translator: Dirk ter Haar PO Box 10, Petworth, West Sussex, GU28 0RY, England Title of ...
Physical Review B, 1975
The coefficient of 1n in the expansion of the critical temperature for a classical n-component sp... more The coefficient of 1n in the expansion of the critical temperature for a classical n-component spin system is shown to be an analytic function of the dimension d near d=4; this result holds both for the hypercubic-lattice model and for the continuous-space model.
Il Nuovo Cimento B Series 10, 1968
ABSTRACT
Nuclear Physics, 1963
ABSTRACT
Le Journal de Physique Colloques, 1984
The basic ideas of a recently developed geometric approach to dissipation in the evolution of man... more The basic ideas of a recently developed geometric approach to dissipation in the evolution of many-body systems are presented. The approach is applied to the microscopic description of dissipative nuclear dynamics.
Nuclear Physics, 1965
The real pseudo-orthogonal group of transformations in the space E, the direct sum of subspaces E... more The real pseudo-orthogonal group of transformations in the space E, the direct sum of subspaces Et (t 1 ... t,~) and E~(x 1 ... xn) , is considered. These transformations are cast into the canonical form ~,Seq/', where q/, qz" are orthogonal transformations which do not mix coordinates t~ with x3, and ~ is a special Lorentz transformation which operates separately in each (t~x~) plane. Some properties of the usual Lorentz group are thereby generalized. A similar decomposition is also obtained for the orthogonal group.
Journal de Physique I, 1996
Smart Structures and Materials 1994: Mathematics and Control in Smart Structures, 1994
ABSTRACT
Nuclear Physics, 1961
Abstract The perturbation expansions of the Gibbs potential and the propagators at finite tempera... more Abstract The perturbation expansions of the Gibbs potential and the propagators at finite temperature are put into a new form by means of an algebraic theorem on creation and annihilation operators. The new diagrams are made of subdiagrams having exactly the ...
International Journal of Modern Physics B, 2014
World Scientific Review Volume -9.75in x 6.5in
This paper is concerned with the oscillations which appear in the smoothed density of eigenvalues... more This paper is concerned with the oscillations which appear in the smoothed density of eigenvalues when the smoothing width is relatively small. The existence of these oscillations is demonstrated by evaluating exactly the smoothed eigenvalue density for simple shapes of the volume-flat parallelepiped, sphere. A general theory of the density oscillations is then developed on the basis of the time-independent Green function formalism used in Part I of this work. An asymptotic evaluation of the various terms of the multiple reflection expansion is carried out by means of the principle of stationary phase, or by means of a contour integration method. A systematic investigation of the various resulting contributions shows that the dominant oscillations are associated with the closed classical trajectories, i.e., the closed polygons having their vertices on the boundary surface S and such that mirror reflections on S take place at each vertex. Various possible geometrical configurations of these closed paths are discusseddegenerate, accidentally degenerate, repeated paths. Several cases of cancellations between various contributions are indicated.
... Roger Balian CEA, Direction des Sciences de la Matière, Service de Physique Théorique de Sacl... more ... Roger Balian CEA, Direction des Sciences de la Matière, Service de Physique Théorique de Saclay F-91191 Gif-sur-Yvette, France and Ecole Polytechnique, F-91128 Palaiseau, France Translator: Dirk ter Haar PO Box 10, Petworth, West Sussex, GU28 0RY, England Title of ...
Physical Review B, 1975
The coefficient of 1n in the expansion of the critical temperature for a classical n-component sp... more The coefficient of 1n in the expansion of the critical temperature for a classical n-component spin system is shown to be an analytic function of the dimension d near d=4; this result holds both for the hypercubic-lattice model and for the continuous-space model.
Il Nuovo Cimento B Series 10, 1968
ABSTRACT
Nuclear Physics, 1963
ABSTRACT
Le Journal de Physique Colloques, 1984
The basic ideas of a recently developed geometric approach to dissipation in the evolution of man... more The basic ideas of a recently developed geometric approach to dissipation in the evolution of many-body systems are presented. The approach is applied to the microscopic description of dissipative nuclear dynamics.
Nuclear Physics, 1965
The real pseudo-orthogonal group of transformations in the space E, the direct sum of subspaces E... more The real pseudo-orthogonal group of transformations in the space E, the direct sum of subspaces Et (t 1 ... t,~) and E~(x 1 ... xn) , is considered. These transformations are cast into the canonical form ~,Seq/', where q/, qz" are orthogonal transformations which do not mix coordinates t~ with x3, and ~ is a special Lorentz transformation which operates separately in each (t~x~) plane. Some properties of the usual Lorentz group are thereby generalized. A similar decomposition is also obtained for the orthogonal group.
Journal de Physique I, 1996
Smart Structures and Materials 1994: Mathematics and Control in Smart Structures, 1994
ABSTRACT
Nuclear Physics, 1961
Abstract The perturbation expansions of the Gibbs potential and the propagators at finite tempera... more Abstract The perturbation expansions of the Gibbs potential and the propagators at finite temperature are put into a new form by means of an algebraic theorem on creation and annihilation operators. The new diagrams are made of subdiagrams having exactly the ...
International Journal of Modern Physics B, 2014
World Scientific Review Volume -9.75in x 6.5in