Nondivergent classical response functions from uncertainty principle: Quasiperiodic systems

Journal Article · Sat Jan 08 04:00:00 EST 2005 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.1827212· OSTI ID:20662247

Kryvohuz, Maksym; Jianshu, Cao ^[1]

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1. Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)

Time-divergence in linear and nonlinear classical response functions can be removed by taking a phase-space average within the quantized uncertainty volume O(({Dirac_h}/2{pi}){sup n}) around the microcanonical energy surface. For a quasiperiodic system, the replacement of the microcanonical distribution density in the classical response function with the quantized uniform distribution density results in agreement of quantum and classical expressions through Heisenberg's correspondence principle: each matrix element <u|{alpha}(t)|v> corresponds to the (u-v)th Fourier component of {alpha}(t) evaluated along the classical trajectory with mean action (J{sub u}+J{sub v})/2. Numerical calculations for one- and two-dimensional systems show good agreement between quantum and classical results. The generalization to the case of N degrees of freedom is made. Thus, phase-space averaging within the quantized uncertainty volume provides a useful way to establish the classical-quantum correspondence for the linear and nonlinear response functions of a quasiperiodic system.

• OSTI ID: 20662247
• Journal Information: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 2 Vol. 122; ISSN JCPSA6; ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DEGREES OF FREEDOM
DENSITY
MATRIX ELEMENTS
NONLINEAR PROBLEMS
NUMERICAL ANALYSIS
PHASE SPACE
QUANTIZATION
RESPONSE FUNCTIONS
SURFACES
TWO-DIMENSIONAL CALCULATIONS
UNCERTAINTY PRINCIPLE