Single Cooper pair tunneling induced by non-classical microwaves

A mesoscopic Josephson junction interacting with a mode of non-classical microwaves with frequency $\omega$ is considered. Squeezing of the electromagnetic field drastically affects the dynamics of Cooper tunneling. In particular, Bloch steps can be observed even when the microwaves are in the squeezed vacuum state with {\em zero} average amplitude of the field $\langle E(t) \rangle = 0$. The interval between these steps is double in size in comparison to the conventional Bloch steps.Comment: 8 pages, 2 figures are available upon request to: [email protected]

Correlation properties of interfering electrons in a mesoscopic ring under nonclassical microwave radiation

Original paper can be found at: http://eproceedings.worldscinet.com/ Copyright World Scientific Publishing Co. DOI: 10.1142/9789812704474_0009Interfering electrons in a mesoscopic ring are irradiated with both classical and nonclassical microwaves. The average intensity of the charges is calculated as a function of time and it is found that it depends on the nature of the irradiating electromagnetic field. For various quantum states of the microwaves, the electron autocorrelation function is calculated and it shows that the quantum noise of the external field affects the interference of the charges. Two-mode entangled microwaves are also considered and the results for electron average intensity and autocorrelation are compared with those of the corresponding separable state. In both cases, the results depend on whether the ratio of the two frequencies is rational or irrational.Peer reviewe

Symmetries of the finite Heisenberg group for composite systems

Symmetries of the finite Heisenberg group represent an important tool for the study of deeper structure of finite-dimensional quantum mechanics. As is well known, these symmetries are properly expressed in terms of certain normalizer. This paper extends previous investigations to composite quantum systems consisting of two subsystems - qudits - with arbitrary dimensions n and m. In this paper we present detailed descriptions - in the group of inner automorphisms of GL(nm,C) - of the normalizer of the Abelian subgroup generated by tensor products of generalized Pauli matrices of orders n and m. The symmetry group is then given by the quotient group of the normalizer.Comment: Submitted to J. Phys. A: Math. Theo

Production of a chaotic squeezed state from a ``pion liquid" and overbunching of identical pion correlations

It is shown that a one to one correspondence between quantum fields in two different "phases" as might be realized for pions produced from a "hadron liquid" leads to squeezed states. The single and double inclusive cross sections for at chaotic superposition of such states are calculated. The correlation of identical pions is overbunched in comparison with canonical Bose-Einstein correlations.Comment: Latex File, 6 page

Essays on financial stability

Defence date: 31 May 2017Examining Board: Prof. Elena Carletti, EUI & Bocconi University (Supervisor); Prof. David K. Levine, EUI; Prof. Bruno Maria Parigi, University of Padua; Prof. Hans Degryse, University of LeuvenThis thesis consists of two essays concerning how banking regulations may promote financial stability. The first chapter investigates the competition-concentration-stability nexus from a novel perspective, by considering how concentration and, inter alia competition, affect the likelihood of an individual bank failing, and the likelihood of the bank failure spreading contagiously to the rest of the banking system. Competition is shown to reduce individual bank and systemic stability by reducing banks' profit buffers to absorb liquidity shocks. The impact of concentration on stability is more nuanced however, as increased concentration increases banks' profit buffers but also increases the concentration risk in the interbank market, widening the channel of contagion by which a liquidity shock can spread throughout the network. The second chapter concerns optimal ex-ante prudential regulation and ex-post resolution policy of globally systemically important banks. It characterises the conditions under which weakly capitalised, limitedly liable banks have incentives to 'gamble for resurrection' by investing in risky asset portfolios, in the knowledge that the downside risk is shifted onto the deposit insurance fund. In this context it is shown that a bank resolution by `bailing in' unsecured debt holders can restore the incentive for banks to act prudently, and that the bail-in should occur above the point of insolvency to ensure the bank has sufficient skin in the game. The interplay of three ex-ante prudential regulatory instruments is analysed: the minimum capital and total loss absorbing capacity requirements and the minimum capital buffer. The minimum capital and TLAC requirements are set to ensure that the bank has sufficient skin in the game to invest prudently and tradeoff the ex-post costs of bailing in unsecured debt holders, the cost of bailing out depositors and the cost of equity issuance, and minimum equity buffer is set to ensure an appropriate trigger for resolution.--1. Competition, concentration and contagion; --2. Debt, equity and moral hazard: the optimal structure of banks' loss absorbing capacit

The Frobenius formalism in Galois quantum systems

Quantum systems in which the position and momentum take values in the ring ${\cal Z}_d$ and which are described with $d$-dimensional Hilbert space, are considered. When $d$ is the power of a prime, the position and momentum take values in the Galois field $GF(p^ \ell)$, the position-momentum phase space is a finite geometry and the corresponding `Galois quantum systems' have stronger properties. The study of these systems uses ideas from the subject of field extension in the context of quantum mechanics. The Frobenius automorphism in Galois fields leads to Frobenius subspaces and Frobenius transformations in Galois quantum systems. Links between the Frobenius formalism and Riemann surfaces, are discussed

Coherent spaces, Boolean rings and quantum gates

YesCoherent spaces spanned by a nite number of coherent states, are introduced. Their coherence properties are studied, using the Dirac contour representation. It is shown that the corresponding projectors resolve the identity, and that they transform into projectors of the same type, under displacement transformations, and also under time evolution. The set of these spaces, with the logical OR and AND operations is a distributive lattice, and with the logical XOR and AND operations is a Boolean ring (Stone's formalism). Applications of this Boolean ring into classical CNOT gates with n-ary variables, and also quantum CNOT gates with coherent states, are discussed

Comonotonicity and Choquet integrals of Hermitian operators and their applications.

yesIn a quantum system with d-dimensional Hilbert space, the Q-function of a Hermitian positive semide nite operator , is de ned in terms of the d2 coherent states in this system. The Choquet integral CQ( ) of the Q-function of , is introduced using a ranking of the values of the Q-function, and M obius transforms which remove the overlaps between coherent states. It is a gure of merit of the quantum properties of Hermitian operators, and it provides upper and lower bounds to various physical quantities in terms of the Q-function. Comonotonicity is an important concept in the formalism, which is used to formalize the vague concept of physically similar operators. Comonotonic operators are shown to be bounded, with respect to an order based on Choquet integrals. Applications of the formalism to the study of the ground state of a physical system, are discussed. Bounds for partition functions, are also derived

Ultra-quantum coherent states in a single finite quantum system

A set of $n$ coherent states is introduced in a quantum system with $d$-dimensional Hilbert space $H(d)$. It is shown that they resolve the identity, and also have a discrete isotropy property. A finite cyclic group acts on the set of these coherent states, and partitions it into orbits. A $n$-tuple representation of arbitrary states in $H(d)$, analogous to the Bargmann representation, is defined. There are two other important properties of these coherent states which make them `ultra-quantum'. The first property is related to the Grothendieck formalism which studies the `edge' of the Hilbert space and quantum formalisms. Roughly speaking the Grothendieck theorem considers a `classical' quadratic form ${\mathfrak C}$ that uses complex numbers in the unit disc, and a `quantum' quadratic form ${\mathfrak Q}$ that uses vectors in the unit ball of the Hilbert space. It shows that if ${\mathfrak C}\le 1$, the corresponding ${\mathfrak Q}$ might take values greater than $1$, up to the complex Grothendieck constant $k_G$. ${\mathfrak Q}$ related to these coherent states is shown to take values in the `Grothendieck region' $(1,k_G)$, which is classically forbidden in the sense that ${\mathfrak C}$ does not take values in it. The second property complements this, showing that these coherent states violate logical Bell-like inequalities (which for a single quantum system are quantum versions of the Frechet probabilistic inequalities). In this sense also, our coherent states are deep into the quantum region