Uhlmann curvature in dissipative phase transitions

We study the mean Uhlmann curvature in fermionic systems undergoing a dissipative driven phase transition. We consider a paradigmatic class of lattice fermion systems in non-equilibrium steady-state of an open system with local reservoirs, which are characterised by a Gaussian fermionic steady state. In the thermodynamical limit, in systems with translational invariance we show that a singular behaviour of the Uhlmann curvature represents a sufficient criterion for criticalities, in the sense of diverging correlation length, and it is not otherwise sensitive to the closure of the Liouvillian dissipative gap. In finite size systems, we show that the scaling behaviour of the mean Uhlmann curvature maps faithfully the phase diagram, and a relation to the dissipative gap is put forward. We argue that the mean Uhlmann phase can shade light upon the nature of non equilibrium steady state criticality in particular with regard to the role played by quantum vs classical fluctuations.Comment: 5 pages, 3 figures with appendix of 10 pages, 1 figur

The role of auxiliary states in state discrimination with linear optical evices

The role of auxiliary photons in the problem of identifying a state secretly chosen from a given set of L-photon states is analyzed. It is shown that auxiliary photons do not increase the ability to discriminate such states by means of a global measurement using only optical linear elements, conditional transformation and auxiliary photons.Comment: 5 pages. 1 figure. RevTex documen

Geometric phases and criticality in spin systems

A general formalism of the relation between geometric phases produced by circularly evolving interacting spin systems and their criticality behavior is presented. This opens up the way for the use of geometric phases as a tool to study regions of criticality without having to undergo a quantum phase transition. As a concrete example a spin-1/2 chain with XY interactions is presented and the corresponding geometric phases are analyzed. The generalization of these results to the case of an arbitrary spin system provides an explanation for the existence of such a relation.Comment: 12 pages, 4 figure

Quantum dissipative dynamics of a bistable system in the sub-Ohmic to super-Ohmic regime

We investigate the quantum dynamics of a multilevel bistable system coupled to a bosonic heat bath beyond the perturbative regime. We consider different spectral densities of the bath, in the transition from sub-Ohmic to super-Ohmic dissipation, and different cutoff frequencies. The study is carried out by using the real-time path integral approach of the Feynman-Vernon influence functional. We find that, in the crossover dynamical regime characterized by damped \emph{intrawell} oscillations and incoherent tunneling, the short time behavior and the time scales of the relaxation starting from a nonequilibrium initial condition depend nontrivially on the spectral properties of the heat bath.Comment: 16 pages, 7 figure

Effects of L\'evy noise on the dynamics of sine-Gordon solitons in long Josephson junctions

We numerically investigate the generation of solitons in current-biased long Josephson junctions in relation to the superconducting lifetime and the voltage drop across the device. The dynamics of the junction is modelled with a sine-Gordon equation driven by an oscillating field and subject to an external non-Gaussian noise. A wide range of $\alpha$-stable L\'evy distributions is considered as noise source, with varying stability index $\alpha$ and asymmetry parameter $\beta$. In junctions longer than a critical length, the mean switching time (MST) from superconductive to the resistive state assumes a values independent of the device length. Here, we demonstrate that such a value is directly related to the mean density of solitons which move into or from the washboard potential minimum corresponding to the initial superconductive state. Moreover, we observe: (i) a connection between the total mean soliton density and the mean potential difference across the junction; (ii) an inverse behavior of the mean voltage in comparison with the MST, with varying the junction length; (iii) evidences of non-monotonic behaviors, such as stochastic resonant activation and noise enhanced stability, of MST versus the driving frequency and noise intensity for different values of $\alpha$ and $\beta$; (iv) finally, these non-monotonic behaviors are found to be related to the mean density of solitons formed along the junction.Comment: 24 pages, 8 figures, submitted to J. Stat. Mech.: Theory Exp. arXiv admin note: text overlap with arXiv:1406.481

Trading activity and price impact in parallel markets: SETS vs. off-book market at the London Stock Exchange

We empirically study the trading activity in the electronic on-book segment and in the dealership off-book segment of the London Stock Exchange, investigating separately the trading of active market members and of other market participants which are non-members. We find that (i) the volume distribution of off-book transactions has a significantly fatter tail than the one of on-book transactions, (ii) groups of members and non-members can be classified in categories according to their trading profile (iii) there is a strong anticorrelation between the daily inventory variation of a market member due to the on-book market transactions and inventory variation due to the off-book market transactions with non-members, and (iv) the autocorrelation of the sign of the orders of non-members in the off-book market is slowly decaying. We also analyze the on-book price impact function over time, both for positive and negative lags, of the electronic trades and of the off-book trades. The unconditional impact curves are very different for the electronic trades and the off-book trades. Moreover there is a small dependence of impact on the volume for the on-book electronic trades, while the shape and magnitude of impact function of off-book transactions strongly depend on volume.Comment: 16 pages, 9 figure

Anyons and transmutation of statistics via vacuum induced Berry phase

We show that bosonic fields may present anyonic behavior when interacting with a fermion in a Jaynes-Cummings-like model. The proposal is accomplished via the interaction of a two-level system with two quantized modes of a harmonic oscillator; under suitable conditions, the system acquires a fractional geometric phase. A crucial role is played by the entanglement of the system eigenstates, which provides a two-dimensional confinement in the effective evolution of the system, leading to the anyonic behavior. For a particular choice of parameters, we show that it is possible to transmute the statistics of the system continually from fermions to bosons. We also present an experimental proposal, in an ion-trap setup, in which fractional statistical features can be generated, controlled, and measured

Finite-temperature geometric properties of the Kitaev honeycomb model

We study finite-temperature topological properties of the Kitaev’s spin-honeycomb model in the vortex-free sector with the use of the recently introduced mean Uhlmann curvature. We employ an appropriate fermionization procedure to study the system as a two-band p-wave superconductor described by a Bogoliubov–de Gennes Hamiltonian. This allows us to study relevant quantities such as Berry and mean Uhlmann curvatures in a simple setting. More specifically, we consider the spin honeycomb in the presence of an external magnetic field breaking time-reversal symmetry. The introduction of such an external perturbation opens up a gap in the phase of the system characterized by non-Abelian statistics. The resulting model belongs to a symmetry-protected class, so that the Uhlmann number can be analyzed. We first consider the Berry curvature on a particular evolution line over the phase diagram. The mean Uhlmann curvature and the Uhlmann number are then analyzed by assuming a thermal state. The mean Uhlmann curvature describes a crossover effect as temperature rises. In the trivial phase, a nonmonotonic dependence of the Uhlmann number, as temperature increases, is reported and explained

A parsimonious model for generating arbitrage-free scenario trees

Simulation models of economic, financial and business risk factors are widely used to assess risks and support decision-making. Extensive literature on scenario generation methods aims at describing some underlying stochastic processes with the least number of scenarios to overcome the ‘curse of dimensionality’. There is, however, an important requirement that is usually overlooked when one departs from the application domain of security pricing: the no-arbitrage condition. We formulate a moment matching model to generate multi-factor scenario trees for stochastic optimization satisfying no-arbitrage restrictions with a minimal number of scenarios and without any distributional assumptions. The resulting global optimization problem is quite general. However, it is non-convex and can grow significantly with the number of risk factors, and we develop convex lower bounding techniques for its solution exploiting the special structure of the problem. Applications to some standard problems from the literature show that this is a robust approach for tree generation. We use it to price a European basket option in complete and incomplete markets

Geometric phase induced by a cyclically evolving squeezed vacuum reservoir

We propose a new way to generate an observable geometric phase by means of a completely incoherent phenomenon. We show how to imprint a geometric phase to a system by "adiabatically" manipulating the environment with which it interacts. As a specific scheme we analyse a multilevel atom interacting with a broad-band squeezed vacuum bosonic bath. As the squeezing parameters are smoothly changed in time along a closed loop, the ground state of the system acquires a geometric phase. We propose also a scheme to measure such geometric phase by means of a suitable polarization detection.Comment: 4 pages, 1 figur