Ultrathin Picoscale White Light Interferometer

White light interferometry is a well established technique with diverse precision applications, however, the conventional interferometers such as Michelson, Mach-Zehnder or Linnik are large in size, demand tedious alignment for obtaining white light fringes, require noise-isolation to achieve sub-nanometric stability and importantly, exhibit unbalanced dispersion causing uncertainty in absolute zero delay reference. Here, we demonstrate an ultrathin white light interferometer enabling picometer resolution by exploiting the wavefront division of a broadband incoherent light beam after transmission through a pair of micrometer thin identical glass plates. Spatial overlap between the two diffracted split wavefronts readily produce high-contrast and stable white light fringes, with unambiguous reference to absolute zero path-delay position. The colored fringes evolve when one of the ultrathin plates is rotated to tune the interferometer with picometric precision over tens of µm range. Our theoretical analysis validates formation of fringes and highlights self-calibration of the interferometer for picoscale measurements. We demonstrate measurement of coherence lengths of several broadband incoherent sources as small as a few micrometer with picoscale precision. Furthermore, we propose a versatile double-pass configuration using the ultrathin interferometer enabling a sample cavity for additional applications in probing dynamical properties of matter.

An operator-theoretical study on the BCS-Bogoliubov model of superconductivity near absolute zero temperature

In the preceding papers the present author gave another proof of the existence and uniqueness of the solution to the BCS-Bogoliubov gap equation for superconductivity from the viewpoint of operator theory, and showed that the solution is partially differentiable with respect to the temperature twice. Thanks to these results, we can indeed partially differentiate the solution and the thermodynamic potential with respect to the temperature twice so as to obtain the entropy and the specific heat at constant volume of a superconductor. In this paper we show the behavior near absolute zero temperature of the thus-obtained entropy, the specific heat, the solution and the critical magnetic field from the viewpoint of operator theory since we did not study it in the preceding papers. Here, the potential in the BCS-Bogoliubov gap equation is an arbitrary, positive continuous function and need not be a constant.

Computational Assessment of Novel Predicted Compounds in Ni-Re Alloy System

Ab initio high-throughput efforts are continuously identifying new intermetallic compounds in a wide range of alloy systems that were previously thought to be well-characterized. While such predictions are likely valid near absolute zero, they carry the risk that such phases become unstable at the higher temperature relevant to typical synthesis conditions. We illustrate how this possibility can be rapidly tested by integrating Calphad modeling into the high-throughput loop. As an example, we investigate the Ni-Re system, in which D019 and D1a phases were predicted as possible intermetallic compounds. We confirm that these phases are indeed stable at practical synthesis temperatures and explain how they could have been overlooked in prior assessments.

Energy of a free Brownian particle coupled to thermal vacuum

Experimentalists have come to temperatures very close to absolute zero at which physics that was once ordinary becomes extraordinary. In such a regime quantum effects and fluctuations start to play a dominant role. In this context we study the simplest open quantum system, namely, a free quantum Brownian particle coupled to thermal vacuum, i.e. thermostat in the limiting case of absolute zero temperature. We analyze the average energy $$E=E(c)$$ E = E ( c ) of the particle from a weak to strong interaction strength c between the particle and thermal vacuum. The impact of various dissipation mechanisms is considered. In the weak coupling regime the energy tends to zero as $$E(c) \sim c\, \ln {(1/c)}$$ E ( c ) ∼ c ln ( 1 / c ) while in the strong coupling regime it diverges to infinity as $$E(c) \sim \sqrt{c}$$ E ( c ) ∼ c . We demonstrate it for selected examples of the dissipation mechanisms defined by the memory kernel $$\gamma (t)$$ γ ( t ) of the Generalized Langevin Equation. We reveal how at a fixed value of c the energy E(c) depends on the dissipation model: one has to compare values of the derivative $$\gamma '(t)$$ γ ′ ( t ) of the dissipation function $$\gamma (t)$$ γ ( t ) at time $$t=0$$ t = 0 or at the memory time $$t=\tau _c$$ t = τ c which characterizes the degree of non-Markovianity of the Brownian particle dynamics. The impact of low temperature is also presented.

An Operator-theoretical Study on the BCS-Bogoliubov Model of Superconductivity Near Absolute Zero Temperature

In the BCS-Bogoliubov model of superconductivity, no one gave a proof of the statement that the solution to the BCS-Bogoliubov gap equation is differentiable with respect to the temperature. But, without such a proof, one differentiates the solution and the thermodynamic potential with respect to the temperature twice, and one obtains the entropy and the specific heat at constant volume of a superconductor. In the preceding papers, the present author showed that the solution is indeed differentiable with respect to the temperature twice. Thanks to these results, we in this paper differentiate the thermodynamic potential with respect to the temperature twice so as to obtain the entropy and the specific heat at constant volume from the viewpoint of operator theory. Here, the potential in the BCS-Bogoliubov gap equation is a function and need not be a constant. We then show the behavior near absolute zero temperature of the entropy, the specific heat, the solution and the critical magnetic field. Mathematics Subject Classification 2020. 45G10, 47H10, 47N50, 82D55.

Engines and Refrigerators

The laws of energy conservation and entropy increase put limits on the efficiency of any heat engine and any refrigeration device working over a given temperature range. The limits are independent of the details of how these machines operate, so this chapter first explains them by considering only energy and entropy flows. The detailed mechanisms are still interesting, however, so the chapter ends with descriptions of a variety of engine and refrigeration mechanisms, including methods of reaching temperatures near absolute zero.