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

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.