148
8 Quantum Ratchets
Bibliography
1. Mitropolskii, Y.A., Petrina, D.Y.: On N. N. Bogolyubov’s works in classical and quantum
statistical mechanics.. Ukr. Math. J. 45, 171–214 (1993). https://doi.org/10.1007/BF01060975
2. Bogolyubov, N.N.: Elementary example for establishing statistical equilibrium in a system
coupled to a thermostat. On some statistical methods in mathematical physics, Publ. Acad. Sci.
Ukr. SSR, Kiev 1945, pp. 115–137 (in Russian)
3. Magalinski ˘ i, V.B.: Dynamical model in the theory of the Brownian motion. Sov. Phys. JETP 9,
1381 (1959), JETP 36, 1942 (1959)
4. Reimann, P.: Brownian motors: noisy transport far from equilibrium. Phys. Rep. 3
¯
61, 57–265,
(2002), 208–209
5. Banerjee, D., Bag, B.C., Banik, S.K., Ray, D.S.: Solution of quantum Langevin equation:
Approximations, theoretical and numerical aspects. J. Chem. Phys. 120(19), 8960 (2004)
6. Hänggi, P., Jung, P.: Colored noise in dynamical systems. Adv. Chem. Phys. 89, 239 (1995)
7. Machura, L., Kostur, M., Hänggi, P., Talkner, P., Luczka, J.: Consistent description of quantum
Brownian motors operating at strong friction. Phys. Rev. E. 70, 031107 (2004)
8. Luczka, J., Rudnicki, R., Hänggi. P.: The diffusion in the quantum Smoluchowski equation.
Phys. A 351, 60 (2005)
9. Reimann, P., Grifoni, M., Hänggi, P.: Quantum ratchets. Phys. Rev. Lett. 7
¯
9(1), 10–13 (1997)
10. Ankerhold, J., Pechukas, P., Grabert, H.: Strong friction limit in quantum mechanics: the
quantum smoluchowski equation. Phys. Rev. Lett. 87, 086802 (2001)
11. Machura, L., Luczka, J., Talkner, P., Hänggi, P.: Transport of forced quantum motors in the
strong friction limit. Acta Phys. Polonica Series B 38, 1855–1863 (2007)
12. Denisov, S., Kohler, S., Hänggi, P.: Underdamped quantum ratchets. Europhys. Lett. 85, 40003
(2009)
13. Denisov, S., Morales-Molina, L., Flach, S., Hänggi, P.: Periodically driven quantum ratchets:
symmetries and resonances. Phys. Rev. A 75, 063424 (2007)
14. Yevtushenko, O., Flach, S., Zolotaryuk, Y., Ovchinnikov, A.A.: Rectification of current in acdriven nonlinear systems and symmetry properties of the Boltzmann equation. Europhys. Lett.
54, 141 (2001)
8 Quantum Ratchets
Bibliography
1. Mitropolskii, Y.A., Petrina, D.Y.: On N. N. Bogolyubov’s works in classical and quantum
statistical mechanics.. Ukr. Math. J. 45, 171–214 (1993). https://doi.org/10.1007/BF01060975
2. Bogolyubov, N.N.: Elementary example for establishing statistical equilibrium in a system
coupled to a thermostat. On some statistical methods in mathematical physics, Publ. Acad. Sci.
Ukr. SSR, Kiev 1945, pp. 115–137 (in Russian)
3. Magalinski ˘ i, V.B.: Dynamical model in the theory of the Brownian motion. Sov. Phys. JETP 9,
1381 (1959), JETP 36, 1942 (1959)
4. Reimann, P.: Brownian motors: noisy transport far from equilibrium. Phys. Rep. 3
¯
61, 57–265,
(2002), 208–209
5. Banerjee, D., Bag, B.C., Banik, S.K., Ray, D.S.: Solution of quantum Langevin equation:
Approximations, theoretical and numerical aspects. J. Chem. Phys. 120(19), 8960 (2004)
6. Hänggi, P., Jung, P.: Colored noise in dynamical systems. Adv. Chem. Phys. 89, 239 (1995)
7. Machura, L., Kostur, M., Hänggi, P., Talkner, P., Luczka, J.: Consistent description of quantum
Brownian motors operating at strong friction. Phys. Rev. E. 70, 031107 (2004)
8. Luczka, J., Rudnicki, R., Hänggi. P.: The diffusion in the quantum Smoluchowski equation.
Phys. A 351, 60 (2005)
9. Reimann, P., Grifoni, M., Hänggi, P.: Quantum ratchets. Phys. Rev. Lett. 7
¯
9(1), 10–13 (1997)
10. Ankerhold, J., Pechukas, P., Grabert, H.: Strong friction limit in quantum mechanics: the
quantum smoluchowski equation. Phys. Rev. Lett. 87, 086802 (2001)
11. Machura, L., Luczka, J., Talkner, P., Hänggi, P.: Transport of forced quantum motors in the
strong friction limit. Acta Phys. Polonica Series B 38, 1855–1863 (2007)
12. Denisov, S., Kohler, S., Hänggi, P.: Underdamped quantum ratchets. Europhys. Lett. 85, 40003
(2009)
13. Denisov, S., Morales-Molina, L., Flach, S., Hänggi, P.: Periodically driven quantum ratchets:
symmetries and resonances. Phys. Rev. A 75, 063424 (2007)
14. Yevtushenko, O., Flach, S., Zolotaryuk, Y., Ovchinnikov, A.A.: Rectification of current in acdriven nonlinear systems and symmetry properties of the Boltzmann equation. Europhys. Lett.
54, 141 (2001)