Microscopical theory of non-linear thermodifusion-phoresis taking into account quantum corrections, critical fluctuations, and anomalous transport

Aim. Development of a microscopic theory of nonlinear thermodiffusophoresis that combines quantum corrections, critical fluctuations, and anomalous transport regimes for systems with strong temperature gradients.

Methodology. Methods of nonequilibrium statistical mechanics (nonequilibrium statistical operator), renormalization group analysis for critical phenomena, and fractional calculus for describing anomalous transport are used.

Results. Within the framework of the developed theory, generalized transport equations are derived, including a non-local memory kernel K (r, t; T), which explicitly depends on the temperature. Anomalous behavior of the thermodiffusion coefficient near the critical point is established, described by the scaling 𝐷_T~|𝑇 – 𝑇_c𝑇|^-𝛾 with an effective exponent 𝛾 = 1,24 + 0,17 where the addition of 0,17 is due to hydrodynamic interactions. Regimes of anomalous transport with fractional exponents are discovered and classified, where the root-mean-square displacement of particles follows the law ⟨∆𝑟²⟩~𝑡^α with the exponent α that smoothly varies from 0,7 (subdiffusion) to 1.5 (superdiffusion) depending on the magnitude of the temperature gradient. For nanoscale systems at low temperatures, we have obtained explicit expressions for quantum corrections to the system's Hamiltonian that account for tunneling effects and the nonlocality of the temperature field.

Research implications include creating a fundamental basis for the design of microfluidic devices, nanoparticle control in biomedicine, and the development of new materials with thermally controlled properties.

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