Molecules Coupled to their Environment

  • Anton Amann
Part of the NATO ASI Series book series (NSSB, volume 258)


Physical systems are never closed in a strict sense: Even a small coupling to another system (its “environment”) may change its behavior. An instructive example has been proposed in ([1]: p. 98). There the influence of a Sirian beetle (8.3 1016 m away) on a gas at normal conditions in a cube of 10 cm length is estimated. The beetle’s walk of just 1 cm changes the (classical mechanical) computation such that the position of an individual particle of the gas is changed by approx. 10 cm after 10−6 seconds. The cause seems almost negligible and nevertheless the effect is enormous. For quantum systems the situation is particularly intricate. Any two quantum systems — even entirely separated ones without any interacting force — are Einstein-Podolsky-Rosen correlated and pure states of the joint system do not necessarily restrict to pure states of the constituents (cf. [2–6]).


Hilbert Space Chiral Molecule Level Splitting Canonical Commutation Relation Superselection Rule 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Borel, E.: Introduction géométrique à quelques théories physiques, Paris. Gauthier-Villars (1914).Google Scholar
  2. [2]
    Schrödinger, E.: Discussion of probability relations between separated systems, Proc. Cambr. Phil. Soc. 31, 555–563 (1935).CrossRefGoogle Scholar
  3. [3]
    Schrödinger, E.: Die gegenwärtige Situation in der Quantenmechanik, Naturwissenschaften 23, 807–812, 823–828, 844–849 (1935).CrossRefGoogle Scholar
  4. [4]
    Schrödinger, E.: Probability relations between separated systems, Proc. Cambr. Phil. Soc. 32, 446–452(1936).CrossRefGoogle Scholar
  5. [5]
    Clauser, J. F. and A. Shimony: Bell’s theorem: experimental tests and implications, Rep. Prog. Phys. 41, 1881–1927 (1978).CrossRefGoogle Scholar
  6. [6]
    Aspect, A., G. Grangier and G. Roger: Experimental test of Bell’s inequalities using time-varying analyzers, Phys. Rev. Lett. 49, 1804–1807 (1982).CrossRefGoogle Scholar
  7. [7]
    Neumann, J. v.: Mathematische Grundlagen der Quantenmechanik, Berlin. Springer (1932).Google Scholar
  8. [8]
    Leggett, A. J., S. Chakravarty, A. T. Dorsey, M. P. A. Fisher, A. Garg and W. Zwerger: Dynamics of the dissipative two-state system, Rev. Mod. Phys. 59, 1–85 (1987).CrossRefGoogle Scholar
  9. [9]
    Einstein, A.: Elementare Überlegungen zur Interpretation der Quantenmechanik, In: Scientific Papers, presented to Max Born. Edinburgh. Oliver Boyd (1953)Google Scholar
  10. [10]
    Born, M.: Albert Einstein, Hedwig und Max Born, Briefwechsel 1916–1955, München. Nymphenburger Verlagshandlung (1969).Google Scholar
  11. [11]
    Amann, A., L. Cederbaum and W. Gans: Fractals, Quasicrystals, Chaos, Knots and Algebraic Quantum Mechanics, Dordrecht. Kluwer (1988).Google Scholar
  12. [12]
    Quack, M.: On the measurement of the parity violating energy difference between enantiomers, Chem. Phys. Lett. 132, 147–153 (1986).CrossRefGoogle Scholar
  13. [13]
    Quack, M.: Structure and dynamics of chiral molecules, Angew. Chem. Int. Ed. Engl. 28, 571–586 (1989).CrossRefGoogle Scholar
  14. [14]
    Amann, A.: Theories of molecular chirality: A short review, in this same volume.Google Scholar
  15. [15]
    Pfeifer, P.: Chiral Molecules–a Superselection Rule Induced by the Radiation Field, Zurich. Thesis ETH-Zürich No. 6551, ok Gotthard S+D AG (1980).Google Scholar
  16. [16]
    Amann, A.: Chirality as a classical observable in algebraic quantum mechanics, In: Fractals, Quasicrystals, Chaos, Knots and Algebraic Quantum Mechanics. Ed. by A. Amann, L. Cederbaum and W. Gans. Dordrecht. Kluwer (1988), Pp. 305–325.Google Scholar
  17. [17]
    Wightman, A. S. and N. Glance: Superselection rules in molecules, Nucl. Phys. B (Proc. Suppl.) 6, 202–206 (1989).CrossRefGoogle Scholar
  18. [18]
    Kukolich, S. G., J. H. S. Wang and D. E. Oates: Molecular beam maser measurements of relaxation cross sections in NH 3, Chem. Phys. Lett. 20, 519–524 (1973).CrossRefGoogle Scholar
  19. [19]
    Hund, F.: Zur Deutung der Molekelspektren III, Z. Phys. 43, 805–826 (1927).CrossRefGoogle Scholar
  20. [20]
    van Hemmen, J. L.: A note on the diagonalization of quadratic Boson and Fermion Hamil-tonians, Z. Phys. B 38, 271–277 (1980).CrossRefGoogle Scholar
  21. [21]
    Cohen-Tannoudji, C., J. Dupont-Roc and G. Grynberg: Photons and Atoms, New York. John Wiley & Sons (1989).Google Scholar
  22. [22]
    Pfeifer, P.: Estimates of the A 2 -term in the interaction of matter with radiation, J. Phys. A 14, L129–L132 (1981).CrossRefGoogle Scholar
  23. [23]
    Craig, D. P. and T. Thirunamachandran: Molecular Quantum Electrodynamics. An Introduction to Radiation-Molecule Interactions, London. Academic Press (1984).Google Scholar
  24. [24]
    Reed, M. and B. Simon: Methods of Modern Mathematical Physics. Volume I: Functional Analysis, New York. Academic Press (1972).Google Scholar
  25. [25]
    Bratteli, O. and D. W. Robinson: Operator Algebras and Quantum Statistical Mechanics Vol 2, New York. Springer (1981).Google Scholar
  26. [26]
    Amann, A.: Observables in W*-algebraic quantum mechanics, Fortschr. Phys. 34, 167–215 (1986).Google Scholar
  27. [27]
    Amann, A. and U. Müller-Herold: Momentum operators for large systems, Helv. Phys. Acta 59, 1311–1320 (1986).Google Scholar
  28. [28]
    Kadison, R. V. and J. R. Ringrose: Fundamentals of the Theory of Operator Algebras. Volume II: Advanced Theory, New York. Academic Press (1986).Google Scholar
  29. [29]
    Guichardet, A.: Symmetric Hilbert Spaces and Related Topics. Lecture Notes in Mathematics Vol 261, Heidelberg. Springer (1970).Google Scholar
  30. [30]
    Amann, A.: Broken symmetries and the generation of classical observables in large systems, Helv. Phys. Acta 60, 384–393 (1987).Google Scholar
  31. [31]
    Nachtergaele, B.: Exakte resultaten voor het Spin-Boson model, Leuven. Thesis, Katholieke Universiteit Leuven (1987).Google Scholar
  32. [32]
    Fannes, M., B. Nachtergaele and A. Verbeure: Quantum tunneling in the spin-boson model, Europhys. Lett. 4, 963–965 (1987).CrossRefGoogle Scholar
  33. [33]
    Fannes, M., B. Nachtergaele and A. Verbeure: Tunneling in the equilibrium state of a spin-boson model, J. Phys. A 21, 1759–1768 (1988).CrossRefGoogle Scholar
  34. [34]
    Fannes, M., B. Nachtergaele and A. Verbeure: The equilibrium states of the spin-boson model, Commun. Math. Phys. 114, 537–548 (1988).CrossRefGoogle Scholar
  35. [35]
    Fannes, M.: Temperature states of spin-boson models, In: Quantum Probability and Applications IV. Lecture Notes in Mathematics Volume 1396. Ed. by L. Accardi and W. von Waldenfels. Berlin. Springer (1989)Google Scholar
  36. [36]
    Fannes, M. and A. Verbeure: On the time evolution automorphisms of the CCR-algebra for quantum mechanics, Commun. Math. Phys. 35, 257–264 (1974).CrossRefGoogle Scholar
  37. [37]
    Primas, H.: An introduction into algebraic quantum mechanics, in preparation. (1990).Google Scholar
  38. [38]
    Spohn, H.: Ground state(s) of the spin-boson Hamiltonian, Commun. Math. Phys. 123, 277–304 (1989).CrossRefGoogle Scholar
  39. [39]
    Spohn, H. and R. Dümcke: Quantum tunneling with dissipation and the Ising model over R, J. Stat. Phys. 41,389–423 (1985).CrossRefGoogle Scholar
  40. [40]
    Spohn, H.: Models of statistical mechanics in one dimension originating from quantum ground states, In: Statistical Mechanics and Field Theory: Mathematical Aspects. Ed. by T. C. Dorlas Hugenholtz, N.M. and Winnink, M. Berlin. Springer (1986).Google Scholar
  41. [41]
    Fannes, M. and B. Nachtergaele: Translating the spin-boson model into a classical system, J. Math. Phys. 29, 2288–2293 (1988).CrossRefGoogle Scholar
  42. [42]
    Bratteli, O. and D. W. Robinson: Operator Algebras and Quantum Statistical Mechanics Vol. 1, New York. Springer, 2nd revised edition (1987).Google Scholar
  43. [43]
    Amann, A.: Perturbation theory of boson dynamical systems, to appear in: J. Phys. A (1990).Google Scholar
  44. [44]
    Amann, A.: Perturbation theory of C*-systems without norm-continuity properties, preprint (1990).Google Scholar
  45. [45]
    Amann, A.: Ground states of the spin-boson model, preprint (1990).Google Scholar
  46. [46]
    Reed, M. and B. Simon: Methods of Modern Mathematical Physics. Volume IV: Analysis of Operators, New York. Academic Press (1978).Google Scholar

Copyright information

© Plenum Press, New York 1991

Authors and Affiliations

  • Anton Amann
    • 1
  1. 1.Laboratory of Physical ChemistryETH-ZentrumZürichGermany

Personalised recommendations