Inequivalent Leggett-Garg inequalities

It remains an open question how realist view of macroscopic world emerges from quantum formalism. For testing the macrorealism in quantum domain, an interesting approach was put forward by Leggett and Garg in $1985$, by formulating a suitable inequality valid for any macrorealistic theory. Recently, by following the Wigner idea of local realist inequality, a probabilistic version of standard Leggett-Garg inequalities have also been proposed. While the Wigner form of local realist inequalities are equivalent to the two-party, two-measurements and two outcomes CHSH inequalities, in this paper we provide a generic proof to demonstrate that the Wigner form of Leggett-Garg inequalities are not only inequivalent to the standard ones but also stronger than the later. This is demonstrated by quantifying the amount of disturbance caused by a prior measurement to the subsequent measurements. In this connection, the relation between LGIs and another formulation of macrorealism known as no-signaling in time is examined.Comment: Close to the published version. arXiv admin note: text overlap with arXiv:1705.0993

Drastic improvement of surface structure and current-carrying ability in YBa2Cu3O7 films by introducing multilayered structure

Much smoother surfaces and significantly improved superconducting properties of relatively thick YBa2Cu3O7 (YBCO) films have been achieved by introducing a multilayered structure with alternating main YBCO and additional NdBCO layers. The surface of thick (1 microm) multilayers has almost no holes compared to YBCO films. Critical current density (Jc) have been drastically increased up to a factor > 3 in 1 microm multilayered structures compared to YBCO films over entire temperature and applied magnetic filed range. Moreover, Jc values measured in thick multilayers are even larger than in much thinner YBCO films. The Jc and surface improvement have been analysed and attributed to growth conditions and corresponding structural peculiarities.Comment: Accepted to Appl. Phys. Lett. 88, June (2006), in press 4 pages, 3 figure

Blowup of smooth solutions for relativistic Euler equations

We study the singularity formation of smooth solutions of the relativistic Euler equations in $(3+1)$-dimensional spacetime for both finite initial energy and infinite initial energy. For the finite initial energy case, we prove that any smooth solution, with compactly supported non-trivial initial data, blows up in finite time. For the case of infinite initial energy, we first prove the existence, uniqueness and stability of a smooth solution if the initial data is in the subluminal region away from the vacuum. By further assuming the initial data is a smooth compactly supported perturbation around a non-vacuum constant background, we prove the property of finite propagation speed of such a perturbation. The smooth solution is shown to blow up in finite time provided that the radial component of the initial "generalized" momentum is sufficiently large.Comment: 30 page

Cat state, sub-Planck structure and weak measurement

Heisenberg-limited and weak measurements are the two intriguing notions, used in recent times for enhancing the sensitivity of measurements in quantum metrology. Using a quantum cat state, endowed with sub-Planck structure, we connect these two novel concepts. It is demonstrated that these two phenomena manifest in complementary regimes, depending upon the degree of overlap between the mesoscopic states constituting the cat state under consideration. In particular, we find that when sub-Planck structure manifests, the imaginary weak value is obscured and vice-versa.Comment: 7 pages, 7 figure