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Materials science forum

Polymer Conformational Transitions: A Quantum Decoherence Theory Approach

Dejan I. Raković, M. Dugić, M.B. Plavšić

Published May 1, 2004• 11 citations
Publisher
DOI
10.4028/www.scientific.net/msf.453-454.521

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Quantum Theory of Polymers

J. M. André, J. Delhalle, Janos J. Ladik

Springer eBooks•Jan 1, 1978•71 citations

The Polymer Conformational Stability and Transitions: A Quantum Decoherence Theory Approach

Aleksandar M. Spasic, Jyh-Ping Hsu

I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 II. The Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218 A. The Born-Oppenheimer Adiabatic Approximation . . . . . . . . . . . . . . . . . . . . . 218 B. The Molecules Conformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 C. Levinthal’s Paradox: A Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 D. Levinthal’s Paradox: Revisited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 III. New Approach: The Clue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 IV. The Fundamentals of the Decoherence Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 A. Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 B. Open Quantum Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 C. The Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 D. The Environment-Induced Decoherence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 E. The Physical Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 V. New Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 A. The Conformation Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 B. Nonstationary State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 C. The Relaxation Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 D. The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 VI. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230 VII. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231 In this chapter, we describe the problem of polymer conformational stability and transitions in the framework of the so-called quantum decoherence theory. We propose a rather qualitative scenario yet bearing generality in the context of the quantum decoherence theory, enabling us to reproduce both, existence and stability of the polymers conformations, and the short time scales for the quantum-mechanical processes resulting effectively in the conformational transitions. The proposed model is qualitative yet providing us with the possibility to overcome the main obstacle in resolving the problem of (semi-)classically unreasonably long time necessary for the change of conformation of the polymers in a solution.

CRC Press eBooks•Oct 14, 2005•6 citations

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In the context of the macroscopic quantum phenomena of the second kind, we hereby seek for a solution-in-principle of the long standing problem of the polymer folding, which was considered by Levinthal as (semi)classically intractable. To illuminate it, we applied quantum-chemical and quantum decoherence approaches to conformational transitions. Our analyses imply the existence of novel macroscopic quantum biomolecular phenomena, with biomolecular chain folding in an open environment considered as a subtle interplay between energy and conformation eigenstates of this biomolecule, governed by quantum-chemical and quantum decoherence laws. On the other hand, within an open biological cell, a system of all identical (noninteracting and dynamically noncoupled) biomolecular proteins might be considered as corresponding spatial quantum ensemble of these identical biomolecular processors, providing spatially distributed quantum solution to a single corresponding biomolecular chain folding, whose density of conformational states might be represented as Hopfield-like quantum-holographic associative neural network too (providing an equivalent global quantum-informational alternative to standard molecular-biology local biochemical approach in biomolecules and cells and higher hierarchical levels of organism, as well).

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The inverse square potential arises in a variety of different quantum phenomena, yet notoriously it must be handled with care: it suffers from pathologies rooted in the mathematical foundations of quantum mechanics. We show that its recently studied conformality breaking corresponds to an infinitely smooth winding-unwinding topological transition for the classical statistical mechanics of a one-dimensional system: this describes the tangling or untangling of floppy polymers under a biasing torque. When the ratio between torque and temperature exceeds a critical value the polymer undergoes tangled oscillations, with an extensive winding number. At lower torque or higher temperature the winding number per unit length is zero. Approaching criticality, the correlation length of the order parameter-the extensive winding number-follows a Kosterlitz-Thouless-type law. The model is described by the Wilson line of a (0+1) U(1) gauge theory, and applies to the tangling or untangling of floppy polymers and to the winding or diffusing kinetics in diffusion-convection reactions.

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Jean Marie André, Jean‐Luc Brédas, J. Delhalle +3 more

Lecture notes in physics•Jan 1, 1980•79 citations
I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 II. The Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218 A. The Born-Oppenheimer Adiabatic Approximation . . . . . . . . . . . . . . . . . . . . . 218 B. The Molecules Conformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 C. Levinthal’s Paradox: A Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 D. Levinthal’s Paradox: Revisited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 III. New Approach: The Clue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 IV. The Fundamentals of the Decoherence Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 A. Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 B. Open Quantum Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 C. The Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 D. The Environment-Induced Decoherence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 E. The Physical Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 V. New Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 A. The Conformation Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 B. Nonstationary State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 C. The Relaxation Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 D. The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 VI. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230 VII. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231 In this chapter, we describe the problem of polymer conformational stability and transitions in the framework of the so-called quantum decoherence theory. We propose a rather qualitative scenario yet bearing generality in the context of the quantum decoherence theory, enabling us to reproduce both, existence and stability of the polymers conformations, and the short time scales for the quantum-mechanical processes resulting effectively in the conformational transitions. The proposed model is qualitative yet providing us with the possibility to overcome the main obstacle in resolving the problem of (semi-)classically unreasonably long time necessary for the change of conformation of the polymers in a solution.
In the context of the macroscopic quantum phenomena of the second kind, we hereby seek for a solution-in-principle of the long standing problem of the polymer folding, which was considered by Levinthal as (semi)classically intractable. To illuminate it, we applied quantum-chemical and quantum decoherence approaches to conformational transitions. Our analyses imply the existence of novel macroscopic quantum biomolecular phenomena, with biomolecular chain folding in an open environment considered as a subtle interplay between energy and conformation eigenstates of this biomolecule, governed by quantum-chemical and quantum decoherence laws. On the other hand, within an open biological cell, a system of all identical (noninteracting and dynamically noncoupled) biomolecular proteins might be considered as corresponding spatial quantum ensemble of these identical biomolecular processors, providing spatially distributed quantum solution to a single corresponding biomolecular chain folding, whose density of conformational states might be represented as Hopfield-like quantum-holographic associative neural network too (providing an equivalent global quantum-informational alternative to standard molecular-biology local biochemical approach in biomolecules and cells and higher hierarchical levels of organism, as well).
The inverse square potential arises in a variety of different quantum phenomena, yet notoriously it must be handled with care: it suffers from pathologies rooted in the mathematical foundations of quantum mechanics. We show that its recently studied conformality breaking corresponds to an infinitely smooth winding-unwinding topological transition for the classical statistical mechanics of a one-dimensional system: this describes the tangling or untangling of floppy polymers under a biasing torque. When the ratio between torque and temperature exceeds a critical value the polymer undergoes tangled oscillations, with an extensive winding number. At lower torque or higher temperature the winding number per unit length is zero. Approaching criticality, the correlation length of the order parameter-the extensive winding number-follows a Kosterlitz-Thouless-type law. The model is described by the Wilson line of a (0+1) U(1) gauge theory, and applies to the tangling or untangling of floppy polymers and to the winding or diffusing kinetics in diffusion-convection reactions.