Thermodynamics and Optical Conductivity of a Dissipative Carrier in a Tight Binding Model

TL;DR

This paper investigates the thermodynamics and optical conductivity of a dissipative particle in a tight-binding model, revealing how environmental coupling affects low-energy states and transport properties across temperature regimes.

Contribution

It provides an analytical weak coupling theory for the crossover behavior and detailed calculations for ohmic damping, highlighting the environment's impact on low-temperature thermodynamics and optical responses.

Findings

Coherent optical conductivity component disappears for 0<s<2.

Specific heat exhibits T-linear behavior at low temperatures.

Optical conductivity shows non-Drude form with high-frequency power-law behavior.

Abstract

Thermodynamics and transport properties of a dissipative particle in a tight-binding model are studied through specific heat and optical conductivity. A weak coupling theory is constituted to study the crossover behavior between the low-temperature region and the high-temperature region analytically. We found that coherent part around zero frequency in the optical conductivity disappears for 0<s<2, where s is an exponent of a spectral function of the environment. Detailed calculation is performed for ohmic damping (s=1). In this case, the specific heat shows an unusual $T$-linear behavior at low temperatures, which indicates that the environment strongly influences the particle motion, and changes the low-energy states of the dissipative particle. The optical conductivity \sigma(\omega) takes a non-Drude form even at zero temperature, and the high-frequency side behaves as \omega^(2K-2), where K is a dimensionless damping strength. The high frequency side of the optical conductivity is independent of temperatures, while the low frequency side depends on the temperature, and behaves as T^(2K-2) at high temperatures. We also comment on the application of this model to the description of incoherent motion in correlated electron systems.