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Thermodynamics and transport properties of a dissipative particle in atight-binding model are studied through specific heat and optical conductivity.A weak coupling theory is constituted to study the crossover behavior betweenthe low-temperature region and the high-temperature region analytically. Wefound that coherent part around zero frequency in the optical conductivitydisappears for 0<s<2, where s is an exponent of a spectral function of theenvironment. Detailed calculation is performed for ohmic damping (s=1). In thiscase, the specific heat shows an unusual $T$-linear behavior at lowtemperatures, which indicates that the environment strongly influences theparticle motion, and changes the low-energy states of the dissipative particle.The optical conductivity \sigma(\omega) takes a non-Drude form even at zerotemperature, and the high-frequency side behaves as \omega^(2K-2), where K is adimensionless damping strength. The high frequency side of the opticalconductivity is independent of temperatures, while the low frequency sidedepends on the temperature, and behaves as T^(2K-2) at high temperatures. Wealso comment on the application of this model to the description of incoherentmotion in correlated electron systems.Comment: 30 pages, 11 figs, to be published on J. Phys. Soc. Jpn., improved  version by adding one new figure and removing some mistake

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