Floquet Theory of Classical Relaxation in Time-Dependent Field
The anomalous transport of particles in the presence of a time-dependent field is considered in the framework of a comb model. This turbulent-like dynamics consists of inhomogeneous time-dependent advection along the <i>x</i>-backbone and Brownian motion along the <i>y</i>-si...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/13/2832 |
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| author | Alexander Iomin |
| author_facet | Alexander Iomin |
| author_sort | Alexander Iomin |
| collection | DOAJ |
| description | The anomalous transport of particles in the presence of a time-dependent field is considered in the framework of a comb model. This turbulent-like dynamics consists of inhomogeneous time-dependent advection along the <i>x</i>-backbone and Brownian motion along the <i>y</i>-side branches. This geometrically constrained transport leads to anomalous diffusion along the backbone, which is described by a fractional diffusion equation with time-dependent coefficients. The time periodic process leads to localization of the transport and a particular form of relaxation. The analytical approach is considered in the framework of the Floquet theory, which is developed for the fractional diffusion equation with periodic in time coefficients. This physical situation is considered in detail and analytical expressions for both the probability density function and the mean squared displacement are obtained. The new analytical approach is developed in the framework of the fractional Floquet theory that makes it possible to investigate a new class of anomalous diffusion in the presence of time periodic fields. |
| first_indexed | 2024-03-11T01:34:50Z |
| format | Article |
| id | doaj.art-0b8f97384c6a41a8a4a9909307cb701d |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T01:34:50Z |
| publishDate | 2023-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-0b8f97384c6a41a8a4a9909307cb701d2023-11-18T17:01:58ZengMDPI AGMathematics2227-73902023-06-011113283210.3390/math11132832Floquet Theory of Classical Relaxation in Time-Dependent FieldAlexander Iomin0Department of Physics, Technion-Israel Institute of Technology, Haifa 32000, IsraelThe anomalous transport of particles in the presence of a time-dependent field is considered in the framework of a comb model. This turbulent-like dynamics consists of inhomogeneous time-dependent advection along the <i>x</i>-backbone and Brownian motion along the <i>y</i>-side branches. This geometrically constrained transport leads to anomalous diffusion along the backbone, which is described by a fractional diffusion equation with time-dependent coefficients. The time periodic process leads to localization of the transport and a particular form of relaxation. The analytical approach is considered in the framework of the Floquet theory, which is developed for the fractional diffusion equation with periodic in time coefficients. This physical situation is considered in detail and analytical expressions for both the probability density function and the mean squared displacement are obtained. The new analytical approach is developed in the framework of the fractional Floquet theory that makes it possible to investigate a new class of anomalous diffusion in the presence of time periodic fields.https://www.mdpi.com/2227-7390/11/13/2832fractional diffusion equationFloquet theoryfractional Schrödinger equationMittag-Leffler functiondilatation operatorGreen function |
| spellingShingle | Alexander Iomin Floquet Theory of Classical Relaxation in Time-Dependent Field Mathematics fractional diffusion equation Floquet theory fractional Schrödinger equation Mittag-Leffler function dilatation operator Green function |
| title | Floquet Theory of Classical Relaxation in Time-Dependent Field |
| title_full | Floquet Theory of Classical Relaxation in Time-Dependent Field |
| title_fullStr | Floquet Theory of Classical Relaxation in Time-Dependent Field |
| title_full_unstemmed | Floquet Theory of Classical Relaxation in Time-Dependent Field |
| title_short | Floquet Theory of Classical Relaxation in Time-Dependent Field |
| title_sort | floquet theory of classical relaxation in time dependent field |
| topic | fractional diffusion equation Floquet theory fractional Schrödinger equation Mittag-Leffler function dilatation operator Green function |
| url | https://www.mdpi.com/2227-7390/11/13/2832 |
| work_keys_str_mv | AT alexanderiomin floquettheoryofclassicalrelaxationintimedependentfield |