Floquet theory for temporal correlations and spectra in time-periodic open quantum systems: Application to squeezed parametric oscillation beyond the rotating-wave approximation

Open quantum systems can display periodic dynamics at the classical level either due to external periodic modulations or to self-pulsing phenomena typically following a Hopf bifurcation. In both cases, the quantum fluctuations around classical solutions do not reach a quantum-statistical stationary state, which prevents adopting the simple and reliable methods used for stationary quantum systems. Here we put forward a general and efficient method to compute two-time correlations and corresponding spectral densities of time-periodic open quantum systems within the usual linearized (Gaussian) approximation for their dynamics. Using Floquet theory we show how the quantum Langevin equations for the fluctuations can be efficiently integrated by partitioning the time domain into one-period duration intervals, and relating the properties of each period to the first one. Spectral densities, like squeezing spectra, are computed similarly, now in a two-dimensional temporal domain that is treated as a chessboard with one-period x one-period cells. This technique avoids cumulative numerical errors as well as efficiently saves computational time. As an illustration of the method, we analyze the quantum fluctuations of a damped parametrically-driven oscillator (degenerate parametric oscillator) below threshold and far away from rotating-wave approximation conditions, which is a relevant scenario for modern low-frequency quantum oscillators. Our method reveals that the squeezing properties of such devices are quite robust against the amplitude of the modulation or the low quality of the oscillator, although optimal squeezing can appear for parameters that are far from the ones predicted within the rotating-wave approximation.Comment: Comments and constructive criticism are welcom

Oils and fats on food: is it possible to have a healthy diet?

Oils and fats are an important part of our diet as components of many food formulations. Thus, they are retailed for domestic or hostelry uses and broadly used by food industry for the elaboration of margarines, ice cream, canned food, pre-cooked dishes, bakery, confectionary, chocolates, etc. Chemically, the main component of oils and fats are triacylglycerols (TAGs), which account for up to 95% of their total weight. They consisted of a molecule of glycerol esterified with three fatty acids, usually the saturated, palmitic and stearic, the monounsatu�rated oleic, and the polyunsaturated, linoleic or linolenic, all with 18 carbons excepting the palmitic which has 16 carbons. Out of those most common fatty acids, we can found other fatty acids present only in certain oils such as saturated medium chained fatty acids like lauric and myristic, which contain 12 and 14 carbons respectively

Oils and fats on food: is it possible to have a healthy diet?

Oils and fats are an important part of our diet as components of many food formulations. Thus, they are retailed for domestic or hostelry uses and broadly used by food industry for the elaboration of margarines, ice cream, canned food, pre-cooked dishes, bakery, confectionary, chocolates, etc. Chemically, the main component of oils and fats are triacylglycerols (TAGs), which account for up to 95% of their total weight. They consisted of a molecule of glycerol esterified with three fatty acids, usually the saturated, palmitic and stearic, the monounsatu�rated oleic, and the polyunsaturated, linoleic or linolenic, all with 18 carbons excepting the palmitic which has 16 carbons. Out of those most common fatty acids, we can found other fatty acids present only in certain oils such as saturated medium chained fatty acids like lauric and myristic, which contain 12 and 14 carbons respectively

Bilinear maps on C∗^*-algebras that have product property at a compact element

We study bounded bilinear maps on a C$^*$-algebra $A$ having product property at $c\in A$. This leads us to the question of when a C$^*$-algebra is determined by products at $c.$ In the first part of our paper, we investigate this question for compact C$^*$-algebras, and in the second part, we deal with von Neumann algebras having non-trivial atomic part. Our results are applicable to descriptions of homomorphism-like and derivation-like maps at a fixed point on such algebras.Comment: The manuscript has been revised according to the referee's suggestions and comment