Closer Look at Linear Response Theory via an Exactly Solvable Model of Classical Spins in a Rotating Magnetic Field

다국어 초록 (Multilingual Abstract)

Linear response theory is examined through an exactly solvable model of noninteracting classical spins in a rotating magnetic field. The nonequilibrium magnetizations obtained via linear response theory and exact calculation are compared to see explicitly how close their values are. We found that the nonequilibrium magnetization obtained via linear response theory had a value close to that of the exact calulation for very small fields and small angular frequencies far away from the resonance frequency. Furthermore, both magnetizations are again very close to each other for small fields, but very large angular frequencies far away from the resonance angular frequency. However, at or near the resonance angular frequency, the nonequilibrium magnetization obtained via linear response theory is markedly different from that of the exact calculation, irrespective of the magnitude of the magnetic field.

참고문헌 (Reference)

1 R. Kubo, 12 : 570-, 1957

2 M. S. Green, 22 : 398-, 1954

3 J.-P. Amiet, 24 : 1515-, 1991

4 N.-N.Huang, 13 : 302-, 2006

5 K.-H.Yang, 22 : 1814-, 1980

6 M. H.Lee, 61 : 428-, 1983

7 I. I.Rabi, 26 : 167-, 1954

8 C.Brouder, 40 : 9455-, 2007

9 A. V. Alekseev, 46 : 351-, 1992

10 F. T. Hioe,

11 H. C. Torrey, 76 : 1059-, 1949

12 F.BlochandI. I.Rabi, 17 : 237-, 1945

13 M. S. Green, 119 : 829-, 1960

14 R. L. Peterson, 39 : 69-, 1967

15 K. M. vanVliet, 19 : 1345-, 1978

16 K. M. vanVliet, 19 : 1345-, 1978

17 20 : 2573-, 1979

18 C. M. vanVliet, 53 : 49-, 1988

19 J. F. C. van Velsen, 41C : 135-, 1975

20 R. Kubo, 233 : 330-, 1986

21 M. O. Caceres, 291 : 317-, 2001

22 G.Bofeta, 13 : 806-, 2003

23 F.Bloch, 70 : 460-, 1946

24 R. K. Wangsnessand, 89 : 728-, 1953

25 J. Y. Sug, "The Quantum Transition Processes of the Electron-Piezoelectric-Phonon-Interacting Materials in the Circularly Polarized Oscilating Fields" 한국물리학회 53 (53): 519-526, 2008

26 H. S. Robertson, "Statistical Thermophνsics" PTR Pren­ticeHall 1993

27 R. Kubo, "Statisitical Phνsics II" Springer-Verlag 1985

28 C. P.Slichter, "Principles o1 Magnetic Resonance" Springer-Verlag 1978

29 Suhk Kun Oh, "Nonequilibrium Statistical Mechanics of Noninteracting Classical Spins in a Rotating Magnetic Field" 한국물리학회 52 (52): 1715-1725, 2008

30 G. F. Mazenko, "Nonequilibrium Statistical Mechanics" Wiley-VCH 2006

31 R. E. Burgess, "N.G.vanKampeninFluctuationPhenomenainNonlin­ear Sνstems" AcademicPress 5 : 279-, 1971

32 Hyung Koo Kim, "Method for Solving the Bloch Equation from the Connection with Time-Dependent Oscillator" 한국물리학회 48 (48): 119-124, 2006

33 K. F. Riley, "Mathemat­ical Methods 1or Phνsics and Engineering" CambridgeUniversity Press 2006

34 W. T. Grandy, "Foundations o1 Statistical Mechan­ics" 1988

35 이창진, "A Rigorous Calculation of the Linear Density Desponse Function in a 2D Electron Gas" 한국물리학회 53 (53): 3131-3139, 2008