Charge fluctuations in nano-circuits with capacitor components are shown to give rise to a novel type of long-ranged interaction, which co-exist with the regular Casimir/van der Waals force. The developed theory distinguishes between thermal and quan
tum mechanical effects, and it is applied to capacitors involving graphene nanostructures. The charge fluctuations mechanism is captured via the capacitance of the system with geometrical and quantum mechanical components. The dependence on the distance separation, temperature, size, and response properties of the system shows that this type of force can have a comparable and even dominant effect to the Casimir interaction. Our results strongly indicate that fluctuations induced interactions due to various thermodynamic quantities can have important thermal and quantum mechanical contributions at the micro- and nanoscale.
Thermal effects contributing to the Casimir interaction between objects are usually small at room temperature and they are difficult to separate from quantum mechanical contributions at higher temperatures. We propose that the thermal Casimir force e
ffect can be observed for a graphene flake suspended in a fluid between substrates at the room temperature regime. The properly chosen materials for the substrates and fluid induce a Casimir repulsion. The balance with the other forces, such as gravity and buoyancy, results in a stable temperature dependent equilibrium separation. The suspended graphene is a promising system due to its potential for observing thermal Casimir effects at room temperature.
The Casimir force between graphene sheets is investigated with emphasis on the effect from spatial dispersion using a combination of factors, such as a nonzero chemical potential and an induced energy gap. We distinguish between two regimes for the i
nteraction - T=0 $K$ and $T eq 0$ $K$. It is found that the quantum mechanical interaction (T=0 $K$) retains its distance dependence regardless of the inclusion of dispersion. The spatial dispersion from the finite temperature Casimir force is found to contribute for the most part from $n=0$ Matsubara term. These effects become important as graphene is tailored to become a poor conductor by inducing a band gap.
The Casimir force between two infinitely thin parallel sheets in a setting of $N$ such sheets is found. The finite two-dimensional conductivities, which describe the dispersive and absorptive properties of each sheet, are taken into account, whereupo
n the theory is applied to interacting graphenes. By exploring similarities with in-plane optical spectra for graphite, the conductivity of graphene is modeled as a combination of Lorentz type oscillators. We find that the graphene transparency and the existence of a universal constant conductivity $e^2/(4hbar)$ result in graphene/graphene Casimir interaction at large separations to have the same distance dependence as the one for perfect conductors but with much smaller magnitude.
Recent studies of turbulence in superfluid Helium indicate that turbulence in quantum fluids obeys a Kolmogorov scaling law. Such a law was previously attributed to classical solutions of the Navier-Stokes equations of motion. It is suggested that tu
rbulence in all fluids is due to quantum fluid mechanical effects. Employing a field theoretical view of the fluid flow velocity, vorticity appears as quantum filamentary strings. This in turn leads directly to the Kolmogorov critical indices for the case of fully developed turbulence.
