290
8 Manifestations of Chaos in Quantum Scattering Processes
those systems (Weaver 1989; Sridhar and Kudrolli 1994; Ellegaard et al. 1995, 1996;
Chinnery and Humphrey 1996, 1997). However, acoustic cavities do not have the
direct correspondence to quantum dynamics that microwave cavities can have.
We have not attempted to discuss the problem of scattering in open quantum
systems from the point of view of semiclassical theory. Numerical studies of the
correspondence between classical and quantum scattering processes in waveguides
with a ripple cavity can be found in (Luna-Acosta et al. 2002) and (MendezBermundez et al. 2002). In Chap. 9, we will develop theoretical tools necessary to
study the semiclassical regime.
References
Akguc G, Reichl LE (2001) Phys Rev E 64:56221
Akguc G, Reichl LE (2003) Phys Rev E 67:46202
Alhassid Y (1997) Rev Mod Phys 69:731
Baranger HU, Stone AD (1989) Phys. Rev. B 40:8169
Barr AD, Estrella FJ, Reichl LE (2020) Phys Rev A 101:022706
Barr AM, Reichl LE (2010) Phys Rev A 81:022707
Beenakker CWJ (2000) Rev Mod Phys 72:895
Bloch C (1957) Nucl Phys 4:503
Bohm D (1950) Quantum theory. Prentice-Hall, Englewood Cliffs, p. 260
Brody TA, Flores J, French JB, Mello PA, Pandey A, Wong SSM (1981) Rev Mod Phys. 53:385
Brouwer PW (1995) Phys Rev B 51:16878
Buttiker M (1988) IBM J Res Dev 32:306
Camarda HS, Georgopulos PD (1983) Phys Rev Lett 50:492
Chang AM, Baranger HU, Pfeiffer LN, West KW (1994) Phys Rev Lett 73:2111
Chinnery PA, Humphrey VF (1996) Phys Rev E 53:272
Chinnery PA, Humphrey VF (1997) J Acoust Soc Am 101:250
Dicke RH (1953) Phys Rev 89:472
Dyson FJ (1962a) J Math Phys 3:140
Dyson FJ (1962b) J Math Phys 3:166
Dyson FJ (1962c) J Math Phys 3:1191
Ellegaard C, Guhr T, Lindemann K, Lorensen HQ, Nygard J, Oxborrow M (1995) Phys Rev Lett
75:1546
Ellegaard C, Guhr T, Lindemann K, Nygard J, Oxborrow M (1996) Phys Rev Lett 77:4918
Feshbach H (1962) Ann Phys 19:287
Fyodorov YV, Sommers H-J (1997) J Math Phys 38:1918
Garg JB, Rainwater J, Petersen JS, Havens WW (1964) Phys Rev B 134:B985
Guhr T, Muller-Groeling A, Weidenmuller H (1998) Phys Rep 299:189
Haake F (2001) Quantum signatures of chaos, 2nd edn. Springer, Berlin
Hacken G, Werbin R, Rainwater J (1978) Phys Rev C 17:43
Haller E, Koppel H, Cederbaum LS (1983) Chem Phys Lett 101:215
Haq RU, Pandey A, Bohigas O (1982) Phys Rev Lett 48:1086
Hua LK (1963) Harmonic analysis of functions of several complex variables in the classical
domains. American Mathematical Society, Providence
Jalaber, RA, Baranger HU, Stone AD (1990) Phys Rev Lett 65:2442
Jensen RV (1991) Chaos 1:101
Jung C, Seligman TH (1997) Phys Rep 285:77
Kapur PL, Peierls R (1938) Proc R Soc Lond A 166:227
8 Manifestations of Chaos in Quantum Scattering Processes
those systems (Weaver 1989; Sridhar and Kudrolli 1994; Ellegaard et al. 1995, 1996;
Chinnery and Humphrey 1996, 1997). However, acoustic cavities do not have the
direct correspondence to quantum dynamics that microwave cavities can have.
We have not attempted to discuss the problem of scattering in open quantum
systems from the point of view of semiclassical theory. Numerical studies of the
correspondence between classical and quantum scattering processes in waveguides
with a ripple cavity can be found in (Luna-Acosta et al. 2002) and (MendezBermundez et al. 2002). In Chap. 9, we will develop theoretical tools necessary to
study the semiclassical regime.
References
Akguc G, Reichl LE (2001) Phys Rev E 64:56221
Akguc G, Reichl LE (2003) Phys Rev E 67:46202
Alhassid Y (1997) Rev Mod Phys 69:731
Baranger HU, Stone AD (1989) Phys. Rev. B 40:8169
Barr AD, Estrella FJ, Reichl LE (2020) Phys Rev A 101:022706
Barr AM, Reichl LE (2010) Phys Rev A 81:022707
Beenakker CWJ (2000) Rev Mod Phys 72:895
Bloch C (1957) Nucl Phys 4:503
Bohm D (1950) Quantum theory. Prentice-Hall, Englewood Cliffs, p. 260
Brody TA, Flores J, French JB, Mello PA, Pandey A, Wong SSM (1981) Rev Mod Phys. 53:385
Brouwer PW (1995) Phys Rev B 51:16878
Buttiker M (1988) IBM J Res Dev 32:306
Camarda HS, Georgopulos PD (1983) Phys Rev Lett 50:492
Chang AM, Baranger HU, Pfeiffer LN, West KW (1994) Phys Rev Lett 73:2111
Chinnery PA, Humphrey VF (1996) Phys Rev E 53:272
Chinnery PA, Humphrey VF (1997) J Acoust Soc Am 101:250
Dicke RH (1953) Phys Rev 89:472
Dyson FJ (1962a) J Math Phys 3:140
Dyson FJ (1962b) J Math Phys 3:166
Dyson FJ (1962c) J Math Phys 3:1191
Ellegaard C, Guhr T, Lindemann K, Lorensen HQ, Nygard J, Oxborrow M (1995) Phys Rev Lett
75:1546
Ellegaard C, Guhr T, Lindemann K, Nygard J, Oxborrow M (1996) Phys Rev Lett 77:4918
Feshbach H (1962) Ann Phys 19:287
Fyodorov YV, Sommers H-J (1997) J Math Phys 38:1918
Garg JB, Rainwater J, Petersen JS, Havens WW (1964) Phys Rev B 134:B985
Guhr T, Muller-Groeling A, Weidenmuller H (1998) Phys Rep 299:189
Haake F (2001) Quantum signatures of chaos, 2nd edn. Springer, Berlin
Hacken G, Werbin R, Rainwater J (1978) Phys Rev C 17:43
Haller E, Koppel H, Cederbaum LS (1983) Chem Phys Lett 101:215
Haq RU, Pandey A, Bohigas O (1982) Phys Rev Lett 48:1086
Hua LK (1963) Harmonic analysis of functions of several complex variables in the classical
domains. American Mathematical Society, Providence
Jalaber, RA, Baranger HU, Stone AD (1990) Phys Rev Lett 65:2442
Jensen RV (1991) Chaos 1:101
Jung C, Seligman TH (1997) Phys Rep 285:77
Kapur PL, Peierls R (1938) Proc R Soc Lond A 166:227