Response and correlation functions of nonlinear systems in equilibrium states

Area of Science:

• Condensed matter physics
• Statistical mechanics
• Nonlinear dynamics

Background:

• Studies on one-dimensional nonlinear lattices reveal interdependencies between correlation functions due to energy conservation.
• A recent proposal suggested a general relation between diverging heat conduction and super heat diffusion.
• Existing models often presume a coexistence of ballistic heat conduction and diffusion.

Purpose of the Study:

• To systematically study correlation functions in one-dimensional nonlinear lattices.
• To clarify the conditions under which a relation between heat conduction and diffusion holds.
• To investigate the role of temperature pressure in heat transport phenomena.

Main Methods:

• Analysis of serial correlation functions in one-dimensional nonlinear lattices.
• Investigation of autocorrelations of local energy density and local heat current.
• Theoretical examination of systems with and without temperature pressure.

Main Results:

• A general relation between diverging heat conduction and super heat diffusion is valid only in systems without temperature pressure.
• In systems with temperature pressure, a constant, nontrivial term appears in the heat transport.
• This term explains the coexistence of ballistic heat diffusion and slowly diverging heat conduction.

Conclusions:

• The existence of a general relation between diverging heat conduction and super heat diffusion is disproven.
• The long-term presumption of the coexistence of ballistic heat conduction and diffusion is challenged.
• Temperature pressure plays a crucial role in determining heat transport properties in nonlinear lattices.