Non-equilibrium Wigner function and application to model of catalyzed polymerization
The quantum Wigner function and non-equilibrium equation for a microscopic particle in one spatial dimension (1) subject to a potential and a heat bath at thermal equilibrium are considered by non-trivially extending a previous analysis. The non-equilibrium equation yields a general hierarchy for su...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/102718 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/102718 |
| Access Level: | acceso abierto |
| Palabra clave: | 53 Non-equilibrium Wigner function and hierarchy for moments Short thermal wavelength and long-time regimes Approximate Smoluchovski equation Catalyzed polymerization Física (Física) 2212 Física Teórica |
| Sumario: | The quantum Wigner function and non-equilibrium equation for a microscopic particle in one spatial dimension (1) subject to a potential and a heat bath at thermal equilibrium are considered by non-trivially extending a previous analysis. The non-equilibrium equation yields a general hierarchy for suitable non-equilibrium moments. A new non-trivial solution of the hierarchy combining the continued fractions and infinite series thereof is obtained and analyzed. In a short thermal wavelength regime (keeping quantum features adequate for chemical reactions), the hierarchy is approximated by a three-term one. For long times, in turn, the three-term hierarchy is replaced by a Smoluchovski equation. By extending that 1 analysis, a new model of the growth (polymerization) of a molecular chain (template or ) by binding an individual unit (an atom) and activation by a catalyst is developed in three spatial dimensions (3). The atom, , and catalyst move randomly as solutions in a fluid at rest in thermal equilibrium. Classical statistical mechanics describe the and catalyst approximately. Atoms and bindings are treated quantum-mechanically. A mixed non-equilibrium quantum–classical Wigner–Liouville function and dynamical equations for the atom and for the and catalyst, respectively, are employed. By integrating over the degrees of freedom of and with the catalyst assumed to be near equilibrium, an approximate Smoluchowski equation is obtained for the unit. The mean first passage time (MFPT) for the atom to become bound to the , facilitated by the catalyst, is considered. The resulting MFPT is consistent with the Arrhenius formula for rate constants in chemical reactions. |
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