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Fast forward evolution in heat equation:Tunable heat transport in adiabatic regime

J. Matrasulov, J. R. Yusupov, A. A. Saidov

Abstract

We consider the problem of fast forward evolution of the processes described in terms of the heat equation. The matter is considered on an adiabatically expanding time-dependent box. Attention is paid to acceleration of heat transfer processes. So called shortcuts to adiabaticity, implying fast forwarding of the adiabatic states are studied. Heat flux and temperature profiles are analyzed for standard and fast forwarded regimes.

Fast forward evolution in heat equation:Tunable heat transport in adiabatic regime

Abstract

We consider the problem of fast forward evolution of the processes described in terms of the heat equation. The matter is considered on an adiabatically expanding time-dependent box. Attention is paid to acceleration of heat transfer processes. So called shortcuts to adiabaticity, implying fast forwarding of the adiabatic states are studied. Heat flux and temperature profiles are analyzed for standard and fast forwarded regimes.
Paper Structure (4 sections, 41 equations, 3 figures)

This paper contains 4 sections, 41 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Fast forward of adiabatic dynamics described in terms of parabolic evolution equations
  3. Fast forwarding the heat equation based evolution
  4. Conclusions

Figures (3)

  • Figure 1: Temperature profiles of (a) standard and (b) fast forwarded systems. The value of the heat conductance is chosen as $\kappa=0.5$, and parameter $L_0=10$ for both plots, $\varepsilon=0.04$, $\bar{\alpha}=100$
  • Figure 2: Heat flux of of standard and (b) fast forwarded systems. The value of the heat conductance is chosen as $\kappa=0.5$, and parameter $L_0=10$ for both plots, $\varepsilon=0.04$, $\bar{\alpha}=100$
  • Figure 3: Heat flux of of standard (a) and fast forwarded (b) systems. The value of parameters are chosen as $\kappa=0.5$, $L_0=10$ and $\varepsilon=0.04$, $\bar{\alpha}=100$ for both plots.