Central Bank Money and Actual Performance

Central bank money refers to the liability of the balance sheets of central banks — namely, money created by a central bank to be used by fulfilling the four functions of money described earlier. Cash used to be the most important means of payment in the past. The amount of outstanding coins issued is much smaller than the amount of outstanding central bank notes in circulation due to the smaller units, so coins are used only for small purchases. Meanwhile, the development of the banking system and technological advances have given rise to interbank payments and settlement systems where commercial banks lend to each other. A central bank manages interbank payments and settlement systems through monitoring the movements of reserve deposit balances at the central bank. The amount of cash is issued based on the quantity demanded by the general public, which is associated with transaction demand (normally proxied with the nominal gross domestic product [GDP]) as well as the opportunity cost (normally a deposit rate paid by the commercial bank to the general public). Thus, a central bank supplies cash passively in response to changes in demand. A central bank provides commercial banks with cash by withdrawing the equivalent amount from their reserve deposit accounts; commercial banks then distribute the acquired cash to the general public on demand through windows of bank branches and/or ATMs. This is article is an excerpt taken from an original work of Dr. Sayuri Shirai which is published by Asian Development Bank Institute as a "Working Paper" (Series - No. 922 / February 2019). / The original work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 IGO License. Click here, to download the working paper. &nbsp

Photon and spin dependence of the resonance lines shape in the strong coupling regime

We study the quantum dynamics of a spin ensemble coupled to cavity photons. Recently, related experimental results have been reported, showing the existence of the strong coupling regime in such systems. We study the eigenenergy distribution of the multi-spin system (following the Tavis-Cummings model) which shows a peculiar structure as a function of the number of cavity photons and of spins. We study how this structure causes changes in the spectrum of the admittance in the linear response theory, and also the frequency dependence of the excited quantities in the stationary state under a probing field. In particular, we investigate how the structure of the higher excited energy levels changes the spectrum from a double-peak structure (the so-called vacuum field Rabi splitting) to a single peak structure. We also point out that the spin dynamics in the region of the double-peak structure corresponds to recent experiments using cavity ringing while in region of the single peak structure, it corresponds to the coherent Rabi oscillation in a driving electromagnetic filed. Using a standard Lindblad type mechanism, we study the effect of dissipations on the line width and separation in the computed spectra. In particular, we study the relaxation of the total spin in the general case of a spin ensemble in which the total spin of the system is not specified. The theoretical results are correlated with experimental evidence of the strong coupling regime, achieved with a spin 1/2 ensemble

Doping-induced quantum cross-over in Er2_2Ti2−x_{2-x}Snx_xO7_7

We present the results of the investigation of magnetic properties of the Er$_2$Ti$_{2-x}$Sn$_x$O$_7$ series. For small doping values the ordering temperature decreases linearly with $x$ while the moment configuration remains the same as in the $x = 0$ parent compound. Around $x = 1.7$ doping level we observe a change in the behavior, where the ordering temperature starts to increase and new magnetic Bragg peaks appear. For the first time we present evidence of a long-range order (LRO) in Er$_2$Sn$_2$O$_7$ ($x = 2.0$) below $T_N = 130$ mK. It is revealed that the moment configuration corresponds to a Palmer-Chalker type with a value of the magnetic moment significantly renormalized compared to $x = 0$. We discuss our results in the framework of a possible quantum phase transition occurring close to $x = 1.7$.Comment: accepted in PRB Rapi

Eigenfunctions decay for magnetic pseudodifferential operators

We prove rapid decay (even exponential decay under some stronger assumptions) of the eigenfunctions associated to discrete eigenvalues, for a class of self-adjoint operators in $L^2(\mathbb{R}^d)$ defined by ``magnetic'' pseudodifferential operators (studied in \cite{IMP1}). This class contains the relativistic Schr\"{o}dinger operator with magnetic field

Magnetocaloric Study of Spin Relaxation in `Frozen' Dipolar Spin Ice Dy2Ti2O7

The magnetocaloric effect of polycrystalline samples of pure and Y-doped dipolar spin ice Dy2Ti2O7 was investigated at temperatures from nominally 0.3 K to 6 K and in magnetic fields of up to 2 T. As well as being of intrinsic interest, it is proposed that the magnetocaloric effect may be used as an appropriate tool for the qualitative study of slow relaxation processes in the spin ice regime. In the high temperature regime the temperature change on adiabatic demagnetization was found to be consistent with previously published entropy versus temperature curves. At low temperatures (T < 0.4 K) cooling by adiabatic demagnetization was followed by an irreversible rise in temperature that persisted after the removal of the applied field. The relaxation time derived from this temperature rise was found to increase rapidly down to 0.3 K. The data near to 0.3 K indicated a transition into a metastable state with much slower relaxation, supporting recent neutron scattering results. In addition, magnetic dilution of 50 % concentration was found to significantly prolong the dynamical response in the milikelvin temperature range, in contrast with results reported for higher temperatures at which the spin correlations are suppressed. These observations are discussed in terms of defects and loop correlations in the spin ice state.Comment: 9 figures, submitted to Phys. Rev.