Geometric Phase and Modulo Relations for Probability Amplitudes as Functions on Complex Parameter Spaces

We investigate general differential relations connecting the respective behavior s of the phase and modulo of probability amplitudes of the form \amp{\psi_f}{\psi}, where $\ket{\psi_f}$ is a fixed state in Hilbert space and $\ket{\psi}$ is a section of a holomorphic line bundle over some complex parameter space. Amplitude functions on such bundles, while not strictly holomorphic, nevertheless satisfy generalized Cauchy-Riemann conditions involving the U(1) Berry-Simon connection on the parameter space. These conditions entail invertible relations between the gradients of the phase and modulo, therefore allowing for the reconstruction of the phase from the modulo (or vice-versa) and other conditions on the behavior of either polar component of the amplitude. As a special case, we consider amplitude functions valued on the space of pure states, the ray space ${\cal R} = {\mathbb C}P^n$, where transition probabilities have a geometric interpretation in terms of geodesic distances as measured with the Fubini-Study metric. In conjunction with the generalized Cauchy-Riemann conditions, this geodesic interpretation leads to additional relations, in particular a novel connection between the modulus of the amplitude and the phase gradient, somewhat reminiscent of the WKB formula. Finally, a connection with geometric phases is established.Comment: 11 pages, 1 figure, revtex

Monetary Convergence and Risk Premiums in the EU Candidate Countries

This study examines the link between various monetary policy regimes and the ability to manage inflation and exchange rate risk premiums in the EU candidate countries as they undergo monetary convergence to the eurozone. The underlying hypothesis is that a system of 'flexible inflation targeting' may be an optimal policy choice for managing these two categories of risk. A model of inflation and exchange rate risk premiums within the context of inflation targeting is proposed. Recent trends in these risk premiums in Hungary, the Czech Republic and Poland are tested by using the GARCH (1,1) methodology

The role of the ubiquitination-proteasome pathway in breast cancer: Applying drugs that affect the ubiquitin-proteasome pathway to the therapy of breast cancer

The ubiquitin-proteasome pathway is responsible for most eukaryotic intracellular protein degradation. This pathway has been validated as a target for antineoplastic therapy using both in vitro and preclinical models of human malignancies, and is influenced as part of the mechanism of action of certain chemotherapeutic agents. Drugs whose primary action involves modulation of ubiquitin-proteasome activity, most notably the proteasome inhibitor PS-341, are currently being evaluated in clinical trials, and have already been found to have significant antitumor efficacy. On the basis of the known mechanisms by which these agents work, and the available clinical data, they would seem to be well suited for the treatment of breast neoplasms. Such drugs, alone and especially in combination with current chemotherapeutics, may well represent important advances in the therapy of patients with breast cancer

How to determine a quantum state by measurements: The Pauli problem for a particle with arbitrary potential

The problem of reconstructing a pure quantum state ¿¿> from measurable quantities is considered for a particle moving in a one-dimensional potential V(x). Suppose that the position probability distribution ¿¿(x,t)¿2 has been measured at time t, and let it have M nodes. It is shown that after measuring the time evolved distribution at a short-time interval ¿t later, ¿¿(x,t+¿t)¿2, the set of wave functions compatible with these distributions is given by a smooth manifold M in Hilbert space. The manifold M is isomorphic to an M-dimensional torus, TM. Finally, M additional expectation values of appropriately chosen nonlocal operators fix the quantum state uniquely. The method used here is the analog of an approach that has been applied successfully to the corresponding problem for a spin system

Regulation of gap junction conductance by calcineurin through Cx43 phosphorylation: implications for action potential conduction

Cardiac arrhythmias are associated with raised intracellular [Ca2+] and slowed action potential conduction caused by reduced gap junction (GJ) electrical conductance (Gj). Ventricular GJs are composed of connexin proteins (Cx43), with Gj determined by Cx43 phosphorylation status. Connexin phosphorylation is an interplay between protein kinases and phosphatases but the precise pathways are unknown. We aimed to identify key Ca2+-dependent phosphorylation sites on Cx43 that regulate cardiac gap junction conductance and action potential conduction velocity. We investigated the role of the Ca2+-dependent phosphatase, calcineurin. Intracellular [Ca2+] was raised in guinea-pig myocardium by a low-Na solution or increased stimulation. Conduction velocity and Gj were measured in multicellular strips. Phosphorylation of Cx43 serine residues (S365 and S368) and of the intermediary regulator I1 at threonine35 was measured by Western blot. Measurements were made in the presence and absence of inhibitors to calcineurin, I1 or protein phosphatase-1 and phosphatase-2. Raised [Ca2 +]i decreased Gj, reduced Cx43 phosphorylation at S365 and increased it at S368; these changes were reversed by calcineurin inhibitors. Cx43-S368 phosphorylation was reversed by the protein kinase C inhibitor chelerythrine. Raised [Ca2+]i also decreased I1 phosphorylation, also prevented by calcineurin inhibitors, to increase activity of the Ca2+-independent phosphatase, PPI. The PP1 inhibitor, tautomycin, prevented Cx43-365 dephosphorylation, Cx43-S368 phosphorylation and Gj reduction in raised [Ca2+]i. PP2A had no role. Conduction velocity was reduced by raised [Ca2+]i and reversed by calcineurin inhibitors. Reduced action potential conduction and Gj in raised [Ca2+] are regulated by calcineurin-dependent Cx43-S365 phosphorylation, leading to Cx43-S368 dephosphorylation. The calcineurin action is indirect, via I1 dephosphorylation and subsequent activation of PP1.Centro de Investigaciones Cardiovasculare

Exchange Rate Risk and Convergence to the Euro

This paper proposes a new monetary policy framework for effectively navigating the path to adopting the euro. The proposed policy is based on relative inflation forecast targeting and incorporates an ancillary target of declining exchange rate risk, which is suggested as a key criterion for evaluating the currency stability. A model linking exchange rate volatility to differentials over the euro zone in both inflation (target variable) and interest rate (instrument variable) is proposed. The model is empirically tested for the Czech Republic, Poland and Hungary, the selected new Member States of the EU that use direct inflation targeting to guide their monetary policies. The empirical methodology is based on the TARCH(p,q,r)-M model