Free download скачать Information Complexity and Control in Quantum Physics: Proceedings of the 4th International Seminar on Mathematical Theory of Dynamical Systems and Microphysics Udine, September 4-13, 1985 by A. Blaquiere, S. Diner, G. Lochak
English | PDF | 1987 | 356 Pages | ISBN : 3211819924 | 27.4 MB
The  proceedings  have  been  divided into four  parts:

Part I deals with  Quantum  information theory,  Quantum  probability theo- ry  and  Quantum  symmetry.  The  papers  appear1ng  there, cover  some  fundamen- tal  general problematics in the  interpretation  and  use  of  quantum  theory. The  formulation of a  quantum  information theory  is  needed  for a proper use  of  quantum  optical devices for information transmission.  But  there are only a  few  presentation of  such  a theory in the  litterature.  A nice book  by  V.V.  Mitiugov  -Physical foundations of information theory,  was published in russian in  1976  but never  translated.  It  relies  heavily  on the  work  of  L.B.  Levitin,  who  has  given here  an  extended  summary  of the theory. This paper provides  at  the  same  time a kind of general conceptual framework  for the  whole  seminar.
F.  Fer discusses with precise criticisms the  interrelations  between the basic concepts of  statistical  physics  and  information theory, with the conclusion  that  there  is  no  logical proof  which  permits to  assert  that thermodynamical  entropy  is  to  be  assimilated to a lack of information. I.D. Ivanovic  shows  how  one  can  get the information allowing to determi- ne  the  state  of a  quantum  system through a sequence of measurements.
D.  Aerts  has  shown  previously  that  if  one  considers  that  the probabi- listic  character of  classical  statistical  mechanics  is  due  to a "lack of knowledge"  about the  state  of the system, the  probabilities  of  quantum mechanics  can  be  explained  as  due  to a lack of  knowledge  about the  measu- rement.  In  his paper  he  shows  why  a lack of  knowledge  about the  state  of a system gives  rise  to a  classical  (Kolmogorovian)  probability calculus, and  why  a lack of  knowledge  about the  measurements  give  rise  to a  non classical  (non  Kolmogorovian)  probability  model.
L.  Accardi  studies  from  a mathematical point of  view  the fine  structu- re of the  states  of a composite systems,  showing  in a sense the universa- lity  of the Einstein-Podolsky-Rosen  phenomenon.
The  paper of  G.  Lochak  illustrates  the kind of information  one  can extract  from  the  quantum  mechanical formalism using geometrical  -more  pre- cisely  symmetry- considerations.  He  shows  that  Dirac's equation admits not only  one  local  gauge  invariance, but  two,  and  only  two.  The  first  one  leads to the theory of the electron, the  second  one  can  be  shown  to lead to a magnetic  monopole.  The  neutrino  can  be  considered  as  a special case of this  monopole.
All  the papers of part I  stress  the  fact  that  quantum  mechanics  may  be considered  as  a mathematical  system  theory  which  is  specific  by  its  ori- ginal concept of  state  and  where  information, probability  and  symmetry play a central role.  In  fact  quantum  mechanics  contributes to the elabo- ration of a general theory  of  physical systems  and  one  can  only regret that  the general  system  theory  has  not  yet systematically included the quantum  point  of  view  in  its  general  framework.
One  can  only  remark  here  that  the definition  of  the concept of  state leads to a reflexion  on  the concept of  autonomy  and  as  such  on  the  con- cept of system.  One  is  faced with the  difficult  problem  of  the definitior of a closed  system  (and  the  opening  of  this  system).  The  privileged role played  by  hamiltonian  systems  comes  from  the  fact  that  they provide  an ideal  model  for the evolution of closed systems.  The  same  for self-adjoir operators  which  play a  dominant  role for closed  systems  and  reversible evolution.  As  a general mathematical  model,  quantum  mechanics  allows for different  kind  of mathematical representations.  Among  them  are the repre· sentations using stochastic processes
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