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Abstract:

An interacting spin system is investigated within the scenario of the Feynman path integral representation of quantum mechanics. Short-time propagator algorithms and a discrete time formalism are used in combination with a basis set involving Grassmann variables coherent states to get a many-body analytic propagator. The generating function thus obtained leads, after an adequate tracing over Grassmann variables in the imaginary time domain, to the partition function. A spin 1/2 Hamiltonian involving the whole set of interactions is considered. Fermion operators satisfying the standard anticommutation relations are constructed from the raising and lowering spin operators via the Jordan-Wigner transformation. The partition function obtained is more general than the partition function of the traditional Ising model involving only first-neighbor interactions. Computations were performed assuming that the coupling as a function of the distance can be reasonably well represented by an Airy function.

Registro:

Documento: Artículo
Título:Grassmann coherent states representation of the path integral: Evaluation of the generating function for spin systems
Autor:Anicich, P.G.O.; Grinberg, H.
Filiación:Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellón 1, Ciudad Universitaria, 1428 Buenos Aires, Argentina
WESTERN GECO S. A., Seismic Data Processing Center, Argentina
Palabras clave:Generating function; Grassmann algebra; Ising model; Path integral; Spin system; Algebra; Algorithms; Functions; Integral equations; Magnetization; Mathematical transformations; Time domain analysis; Generating functions; Grassmann coherent states representation; Ising model; Jordan-Wigner transformations; Path integral; Spin systems; Quantum theory
Año:2002
Volumen:90
Número:6
Página de inicio:1562
Página de fin:1576
DOI: http://dx.doi.org/10.1002/qua.10342
Título revista:International Journal of Quantum Chemistry
Título revista abreviado:Int J Quantum Chem
ISSN:00207608
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00207608_v90_n6_p1562_Anicich

Referencias:

  • Shulman, L.S., (1981) Techniques and Applications of Path Integration, , Wiley: New York
  • Swanson, M., (1992) Path Integrals and Quantum Processes, , Academic Press: San Diego, CA
  • Khandekar, D.C., Lawande, S.V., Bhagwat, K.V., (1993) Path-Integral Methods and Their Applications, , World Scientific: Singapore
  • Kashiwa, T., Ohnuki, Y., Suzuki, M., (1997) Path Integral Methods, , Clarendon Press: Oxford, UK
  • Ramírez, R., López-Ciudad, T., (2001) J Chem Phys, 115, pp. 103-114
  • Blinov, N.V., Roy, P.N., Voth, G.A., (2001) J Chem Phys, 115, pp. 4484-4495
  • Campolieti, G., Brumer, P., (1994) Phys Rev A, 50, pp. 997-1018
  • Kay, K.G., (1994) J Chem Phys, 100, pp. 4377-4392
  • Kay, K.G., (1994) J Chem Phys, 100, pp. 4432-4445
  • Grossmann, F., Xavier, A.L., Jr., (1998) Phys Lett A, 243, pp. 243-248
  • Marañón, J., Grinberg, H., (1984) J Chem Phys, 81, pp. 4537-4539
  • Mielke, S.L., Truhlar, D.G., (2001) J Chem Phys, 115, pp. 652-662
  • Bochicchio, R.C., Grinberg, H., (1990) Phys Rev A, 41, pp. 5814-5819
  • Klauder, J.R., (1960) Ann Phys NY, 11, pp. 123-168
  • Klauder, J.R., (1979) Phys Rev D, 19, pp. 2349-2356
  • Kuratsuji, H., Suzuki, T., (1980) J Math Phys, 21, pp. 472-476
  • Chudnovsky, E.M., Gunther, L., (1988) Phys Rev Lett, 60, pp. 661-664
  • Loss, D., Vincenzo, D.P., Grinstein, G., (1992) Phys Rev Lett, 69, pp. 3232-3235
  • Von Delft, J., Henley, C.L., (1992) Phys Rev Lett, 69, pp. 3236-3239
  • Wernsdorfer, W., Sessoli, R., (1999) Science, 284, pp. 133-135
  • Klauder, J.R., Skagerstam, B.S., (1985) Coherent States, Applications in Physics and Mathematical Physics, , World Scientific Singapore
  • Glauber, R.J., (1963) Phys Rev Lett, 10, pp. 84-86
  • Deumens, E., Diz, A., Longo, R., Öhrn, Y., (1994) Rev Mod Phys, 66, pp. 917-983
  • Morales, J.A., Deumens, E., Öhrn, Y., (2000) J Math Phys, 40, pp. 766-786
  • Mauritz Anderson, L., (2001) J Chem Phys, 115, pp. 1158-1165
  • Shibata, J., Takagi, S., (1999) Int J Mod Phys B, 13, pp. 107-140
  • Stone, M., Park, K.-S., (2000) J Math Phys, 41, pp. 8025-8049
  • Blaizot, J.P., Orland, H., (1981) Phys Rev C, 24, pp. 1740-1761
  • Suzuki, T., (1983) Nucl Phys A, 398, pp. 557-596
  • Fukui, T., (1993) J Math Phys, 34, pp. 4455-4468
  • Grinberg, H., Marañón, J., (1990) J Mol Struct THEOCHEM 1990, 210, pp. 39-44
  • Calamante, F., Bochicchio, R.C., Grinberg, H., (1994) Int J Quantum Chem, 49, pp. 789-804
  • Kuratsuji, H., Mizobouchi, Y., (1981) J Math Phys, 22, pp. 757-764
  • Samuel, S., (1980) J Math Phys, 21, pp. 2806-2814
  • Samuel, S., (1980) J Math Phys, 21, pp. 2815-2819
  • Samuel, S., (1980) J Math Phys, 21, pp. 2820-2833
  • Nojima, K., (1998) Int J Mod Phys B, 12, pp. 1995-2003
  • Fukutome, H., (1981) Progr Theor Phys, 65, pp. 809-827
  • Papadopoulos, G.J., (1978) Path Integrals and Their Applications in Quantum Statistical and Solid State Physics, pp. 85-162. , In: Papadopoulos, G. J.; Devreese, J. T., Eds.; Plenum: New York
  • Berezin, F.A., (1965) The Method of Second Quantization, , Academic Press: New York
  • Negele, J.W., Orland, H., (1998) Quantum Many-Particle Systems, , Perseus Books: Reading, MA
  • Lieb, E., Schultz, T., Mattis, D., (1961) Ann Phys, 16, pp. 407-466

Citas:

---------- APA ----------
Anicich, P.G.O. & Grinberg, H. (2002) . Grassmann coherent states representation of the path integral: Evaluation of the generating function for spin systems. International Journal of Quantum Chemistry, 90(6), 1562-1576.
http://dx.doi.org/10.1002/qua.10342
---------- CHICAGO ----------
Anicich, P.G.O., Grinberg, H. "Grassmann coherent states representation of the path integral: Evaluation of the generating function for spin systems" . International Journal of Quantum Chemistry 90, no. 6 (2002) : 1562-1576.
http://dx.doi.org/10.1002/qua.10342
---------- MLA ----------
Anicich, P.G.O., Grinberg, H. "Grassmann coherent states representation of the path integral: Evaluation of the generating function for spin systems" . International Journal of Quantum Chemistry, vol. 90, no. 6, 2002, pp. 1562-1576.
http://dx.doi.org/10.1002/qua.10342
---------- VANCOUVER ----------
Anicich, P.G.O., Grinberg, H. Grassmann coherent states representation of the path integral: Evaluation of the generating function for spin systems. Int J Quantum Chem. 2002;90(6):1562-1576.
http://dx.doi.org/10.1002/qua.10342