QUADRATURE-BASED, COARSE-GRAINED TREATMENT OF THE COORDINATE REPRESENTATION FREE PARTICLE REAL-TIME EVOLUTION OPERATOR

被引:19
作者
SHARAFEDDIN, OA
KOURI, DJ
NAYAR, N
HOFFMAN, DK
机构
[1] UNIV HOUSTON,DEPT PHYS,HOUSTON,TX 77204
[2] IOWA STATE UNIV SCI & TECHNOL,DEPT CHEM,AMES,IA 50011
[3] IOWA STATE UNIV SCI & TECHNOL,AMES LAB,AMES,IA 50011
关键词
D O I
10.1063/1.460879
中图分类号
O64 [物理化学(理论化学)、化学物理学];
学科分类号
070304 ; 081704 ;
摘要
In this paper we report a quadrature evaluation of the coordinate representation, short-time free particle propagator, <R \exp (- iH0-tau)\R'>. The result is the elimination of most of the highly oscillatory behavior in this quantity yielding in its stead a much smoother function, strongly peaked at R = R'. We view this as a numerical coarse graining of the propagator which leads to the intuitively reasonable result that for short times tau or large mass, the particle should not have a significant amplitude for R points that are far from R'. This leads to an interesting, and potentially useful, banded structure for <R\exp( - iH0-tau)\R'>. Calculations have been carried out both for zero and nonzero orbital angular momenta, for which we also give the exact analytic results, and the same behavior is found. The quadrature-coarse graining procedure still appears to retain the important quantum effects as demonstrated by subsequent use of the coarse-grained free propagator to calculate the scattering of an electron by a simple central potential. Results are in quantitative agreement with those obtained by alternative, numerically exact methods. The coarse-grained free propagator is, of course, independent of the potential, and we expect that it can provide a very useful tool for computing real-time dynamics for a variety of systems.
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页码:3224 / 3231
页数:8
相关论文
共 35 条
[1]   DYNAMICS OF A 2-LEVEL SYSTEM COUPLED TO A DISSIPATIVE BATH - COMPARISONS OF ANALYTICAL THEORIES WITH MONTE-CARLO SIMULATION [J].
BEHRMAN, EC ;
WOLYNES, PG .
JOURNAL OF CHEMICAL PHYSICS, 1985, 83 (11) :5863-5869
[2]   EXPLOITING THE ISOMORPHISM BETWEEN QUANTUM-THEORY AND CLASSICAL STATISTICAL-MECHANICS OF POLYATOMIC FLUIDS [J].
CHANDLER, D ;
WOLYNES, PG .
JOURNAL OF CHEMICAL PHYSICS, 1981, 74 (07) :4078-4095
[3]   MONTE-CARLO PATH INTEGRATION IN REAL-TIME VIA COMPLEX COORDINATES [J].
CHANG, J ;
MILLER, WH .
JOURNAL OF CHEMICAL PHYSICS, 1987, 87 (03) :1648-1652
[4]   MONTE-CARLO METHODS FOR REAL-TIME QUANTUM DYNAMICS OF DISSIPATIVE SYSTEMS [J].
CLINE, RE ;
WOLYNES, PG .
JOURNAL OF CHEMICAL PHYSICS, 1988, 88 (07) :4334-4350
[6]  
DEVRIES P, COMMUNICATION
[7]   SEMI-CLASSICAL MONTE-CARLO METHODS [J].
DOLL, JD ;
MYERS, LE .
JOURNAL OF CHEMICAL PHYSICS, 1979, 71 (07) :2880-2883
[8]   TOWARD A MONTE-CARLO THEORY OF QUANTUM DYNAMICS [J].
DOLL, JD ;
COALSON, RD ;
FREEMAN, DL .
JOURNAL OF CHEMICAL PHYSICS, 1987, 87 (03) :1641-1647
[9]   MONTE-CARLO FOURIER PATH INTEGRAL METHODS IN CHEMICAL-DYNAMICS [J].
DOLL, JD .
JOURNAL OF CHEMICAL PHYSICS, 1984, 81 (08) :3536-3541
[10]   RANDOMLY EXACT METHODS [J].
DOLL, JD ;
FREEMAN, DL .
SCIENCE, 1986, 234 (4782) :1356-1360