Abstract
We apply a previous analysis of the dependence of the dynamic time-convolution equations and their solution on the degree λ of the initial strength of the polaron cloud to the usual zero-bias spin-boson model and standard second order (i.e. Born) approximation (in tunneling, i.e. the standard dilute blip approximation at λ=1). At temperatureT=0 and for the usual Ohmic type spin-boson coupling, the asymptotic-time-symmetry-breaking phenomenon as a function of the coupling strentghg can be analyzed, in the above Born approximation, in the wholeg-λ plane. A hardly interpretable conclusion is found that the symmetry breaking in the above approximation appears just at discrete lines in the plane. This implies instability of the phenomenon in the second-order theory with respect to arbitrarily small perturbations of the initial state and complies with exact proofs of absence of the partial symmetry-breaking phenomenon in analogous symmetric models.
Similar content being viewed by others
References
Čápek V.: Physica A203 (1994) 495.
Chakravarty S.: Phys. Rev. Lett.49 (1982) 681.
Bray A.J. and Moore M.A.: Phys. Rev. Lett.49 (1982) 1545.
Legget A.J., Chakravarty S., Dorsey A.T., Fisher M.P.A., Garg A., and Zwerger W.: Rev. Mod. Phys.59 (1987) 1.
Nakajima S.: Progr. Theor. Phys.20 (1958) 948.
Zwanzig R.W.:In Lectures in Theoretical Physics, Vol. III (Lectures delivered at the Summer Institute for Theoretical Physics, University of Colorado, Boulder 1960.) (Editors W.E. Brittin, B.W. Downs and J. Downs.) Interscience, New York, 1961, p. 106.
Zwanzig R.: Physica30 (1964) 1109.
Aslangul C., Pottier N., and Saint-James D.: J. Phys. (France)47 (1986) 1657.
Chakravarty S. and Leggett A.J.: Phys. Rev. Lett.52 (1984) 5.
Čápek V.: J. Phys. (France)50 (1989) 775.
Gradshtein I.S. and Ryzhik I.M.: Tables of integrals, sums, series and products (in Russian). GIFML, Moscow 1963.
Dekker H.: Phys. Rev. A35 (1987) 1436.
Vitali D., Bonci L., Mannella R., and Grigolini P.: Phys. Rev. A45 (1992) 2285.
Čápek V.: Czech. J. Phys.40 (1990) 857.
Čápek V. and Chvosta P.: Phys. Rev. A43 (1991) 2819.
Čápek V.:in Dynamical Processes in Condensed Molecular Systems, Proc. Emil Warburg Symp., April 22–24, 1990, Bayreuth (Germany). (Eds. A. Blumen, J. Klafter, and D. Haarer.) World Scientific, Singapore, 1990, p. 400.
Swenson R. J.: Physica29 (1963) 1174.
Balescu R.: Physica38 (1968) 98.
Čápek V.: Czech. J. Phys. B36 (1986) 1182.
Čápek V.: Czech. J. Phys.45 (1995) 785.
Weiss U.: Quantum Dissipative Systems. Series in Modern Condensed Matter Physics, Vol.2. World Scientific, Singapore, 1993.
Tsuzuki T.: Solid State Commun.69 (1989) 7.
Vitali D.: Ph.D. Thesis. Scuola Normale Superiore, Pisa, 1993 (defended 1994).
Amann A.: Ann. Phys.208 (1991) 414.
Author information
Authors and Affiliations
Additional information
The author has pleasure in acknowledging fruitful discussions with Dr. P. Chvosta and Prof. M. Wagner. Supports of grants 292/1994 from the Grant agency of Charles University and 202/93/2428 from the Czech Grant Agency are also gratefully acknowledged.
Rights and permissions
About this article
Cite this article
Čápek, V. Instability of the asymptotic-time-symmetry-breaking in the second order in quantum tunneling. Czech J Phys 46, 1001–1009 (1996). https://doi.org/10.1007/BF01690032
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01690032