Biomedical subjects

Maksym Kryvohuz

Publications and source records attributed to Maksym Kryvohuz.

3 recordsLinked to original sources

PubMed2006

Classical divergence of nonlinear response functions.

The time divergence of classical nonlinear response functions reveals the fundamental difficulty of dynamic perturbation based on classical mechanics. The nature of the divergence is established for systems in regular motions using asymptotic decomposition of Fourier integrals. The asymptotic analysis shows that the divergence cannot be removed by phase-space averaging such as the Boltzmann distribution function. The implications of this study are discussed in the context of the conceptual development of quantum-classical correspondence in dynamic response.

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PubMed2005

Quantum-classical correspondence in response theory.

The correspondence principle between the quantum commutator [A, B] and the classical Poisson brackets iota h{A, B} is examined in the context of response theory. The classical response function is obtained as the leading term of the expansion of the phase space representation of the response function in terms of Weyl-Wigner transformations and is shown to increase without bound at long times as a result of ignoring divergent higher-order contributions. Systematical inclusion of higher-order contributions improves the accuracy of the h expansion at finite times. Resummation of all the higher-order terms establishes the classical-quantum correspondence <--> alpha n e iota n omega t|Jv + nh/2. The time interval of the validity of the simple classical limit [A(t), B(0)] --> iota h{A(t), B(0)} is estimated for quasiperiodic dynamics and is shown to be inversely proportional to anharmonicity.

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PubMed2005

Nondivergent classical response functions from uncertainty principle: quasiperiodic systems.

Time-divergence in linear and nonlinear classical response functions can be removed by taking a phase-space average within the quantized uncertainty volume O(hn) 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 (Ju+Jv)/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.

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