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We establish a fluctuation-correlation theorem by relating the quantum fluctuations in the generator of the parameter change to the time integral of the quantum correlation function between the projection operator and force operator of the ``fast system. By taking a cue from linear response theory we relate the quantum fluctuation in the generator to the generalised susceptibility. Relation between the open-path geometric phase, diagonal elements of the quantum metric tensor and the force-force correlation function is provided and the classical limit of the fluctuation-correlation theorem is also discussed.
Correlation function and mutual information are two powerful tools to characterize the correlations in a quantum state of a composite system, widely used in many-body physics and in quantum information science, respectively. We find that these two to
In terms of quantum probability statistics the Bell inequality (BI) and its violation are extended to spin-$s$ entangled Schr{o}dinger cat-state (called the Bell cat-state) with both parallel and antiparallel spin-polarizations. The BI is never ever
In a ring of s-wave superconducting material the magnetic flux is quantized in units of $Phi_0 = frac{h}{2e}$. It is well known from the theory of Josephson junctions that if the ring is interrupted with a piece of d-wave material, then the flux is q
New relations among the mixture direct correlation function integrals (or fluctuation integrals) in terms of concentration variables are developed. These relations indicate that, for example, for a binary mixture only one of the three direct correlat
The influence of the phase fluctuation of the pump laser on the phase-correlation between the signal and idler modes of the output fields from as non-degenerate optical parametric oscillator operating above oscillation threshold was experimentally in