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A complete framework for exciting and detecting thermally-induced, stabilized sine-Gordon breathers in ac-driven long Josephson junctions is developed. The formation of long-time stable breathers locked to the ac source occurs for a sufficiently high temperature. The latter emerges as a powerful control parameter, allowing for the remarkably stable localized modes to appear. Nonmonotonic behaviors of both the breather generation probability and the energy spatial correlations versus the thermal noise strength are found. The junction's resistive switching characteristics provides a clear experimental signature of the breather., 5 pages, 4 figures; Supp Mat: 4 pages, 2 figures

Single parameter estimation is known to benefit from extreme sensitivity to parameter changes in quantum critical systems. However, the simultaneous estimation of multiple parameters is generally limited due to the incompatibility arising from the quantum nature of the underlying system. A key question is whether quantum criticality may also play a positive role in reducing the incompatibility in the simultaneous estimation of multiple parameters. We argue that this is generally the case and verify this prediction in paradigmatic quantum many-body systems close to first and second order phase transitions. The antiferromagnetic and ferromagnetic 1-D Ising chain with both transverse and longitudinal fields are analysed across different regimes and close to criticality., Comment: 12 pages, 6 figures

The dynamics of sine-Gordon breathers is studied in the presence of dissipative and stochastic perturbations. Taking a stationary breather with a random phase value as the initial state, the performed simulations demonstrate that a spatially-homogeneous noisy source can make the oscillatory excitation more stable, i.e., it enables the latter to last significantly longer than it would in a noise-free scenario. Both the frequency domain and the localization of energy are examined to document the effectiveness of the noise-enhanced stability phenomenon, which emerges as a nonmonotonic behavior of an average characteristic time for the breather as a function of the noise intensity. The influence of the mode's starting frequency on the results and their robustness against an additional thermal background are also addressed., 24 pages, 8 figures

The generation of travelling sine-Gordon breathers is achieved through the nonlinear supratransmission effect in a magnetically driven long Josephson junction, in the presence of losses, a current bias, and a thermal noise source. We demonstrate how to exclusively induce breather modes by means of controlled magnetic pulses. A nonmonotonic behavior of the breather-only generation probability is observed as a function of the noise intensity. An experimental protocol providing evidence of the Josephson breather's existence is proposed., 5 pages, 4 figures

We propose a stochastic model of a voltage controlled bipolar memristive system, which includes the properties of widely used dynamic SPICE models and takes into account the fluctuations inherent in memristors. The proposed model is described by rather simple equations of Brownian diffusion, does not require significant computational resources for numerical modeling, and allows obtaining the exact analytical solutions in some cases. The noise-induced transient bimodality phenomenon, arising under resistive switching, was revealed and investigated theoretically and experimentally in a memristive system, by finding a quite good qualitatively agreement between theory and experiment. Based on the proposed model, the mathematical apparatus of Markov processes for the first passage time of the boundaries can be used to analyse the temporal characteristics of resistive switching.

We identify a class of dressed atom-photon states formingat the same energy of the atom at any coupling strength. As a hallmark, their photonic component is an eigenstate of the bare photonic bath with a vacancy in place of the atom. The picture accommodates waveguide-QED phenomena where atoms behave as perfect mirrors, connecting in particular dressed bound states (BS) in the continuum or BIC with geometrically-confined photonic modes. When applied to photonic lattices, the framework provides a general criterion to predict dressed BS in lattices with topological properties by putting them in one-to-one correspondence with photonic BS. New classes of dressed BS are thus predicted in the photonic Creutz-ladder and Haldane models. In the latter case, states with non-zero local photon flux occur, where an atom is dressed by a photon orbiting around it., Comment: 6+17 pages, 4 figures

Dressed states forming when quantum emitters or atoms couple to a photonic bath underpin a number of phenomena and applications, in particular dispersive effective interactions occurring within photonic bandgaps. Here, we present a compact formulation of the resolvent-based theory for calculating atom-photon dressed states built on the idea that the atom behaves as an effective impurity. This establishes an explicit connection with the standard impurity problem in condensed matter. Moreover, it allows us to formulate and settle in a model-independent context a number of properties previously known only for specific models or not entirely formalized. The framework is next extended to the case of more than one emitter, which is used to derive a general expression of dissipationless effective Hamiltonians explicitly featuring the overlap of single-emitter dressed bound states., Comment: 11 pages, 3 figures

The stochastic resonance phenomenon has been studied experimentally and theoretically for a state-of-art metal-oxide memristive device based on yttria-stabilized zirconium dioxide and tantalum pentoxide, which exhibits bipolar filamentary resistive switching of anionic type. The effect of white Gaussian noise superimposed on the sub-threshold sinusoidal driving signal is analyzed through the time series statistics of the resistive switching parameters, the spectral response to a periodic perturbation and the signal-to-noise ratio at the output of the nonlinear system. The stabilized resistive switching and the increased memristance response are revealed in the observed regularities at an optimal noise intensity corresponding to the stochastic resonance phenomenon and interpreted using a stochastic memristor model taking into account an external noise source added to the control voltage. The obtained results clearly show that noise and fluctuations can play a constructive role in nonlinear memristive systems far from equilibrium.

Giant atoms are a new paradigm of quantum optics going beyond the usual local coupling. Building on this, a new type of decoherence-free (DF) many-body Hamiltonians was shown in a broadband waveguide. Here, these are incorporated in a general framework (not relying on master equations) and contrasted to dispersive DF Hamiltonians with normal atoms: the two schemes are shown to correspond to qualitatively different ways to match the same general condition for suppressing decoherence. Next, we map the giant atoms dynamics into a cascaded collision model (CM), providing an intuitive interpretation of the connection between non-trivial DF Hamiltonians and coupling points topology. The braided configuration is shown to implement a scheme where a shuttling system subject to periodic phase kicks mediates a DF coupling between the atoms. From the viewpoint of CMs theory, this shows a collision model where ancillas effectively implement a dissipationless, maximally-entangling two-qubit gate on the system., Comment: 15 pages, 9 figures

The effective description of the weak interaction between an emitter and a bosonic field as a sequence of two-body collisions provides a simple intuitive picture compared to traditional quantum optics methods as well as an effective calculation tool of the joint emitter-field dynamics. Here, this collisional approach is extended to many emitters (atoms or resonators), each generally interacting with the field at many coupling points ("giant" emitter). In the regime of negligible delays, the unitary describing each collision in particular features a contribution of a chiral origin resulting in an effective Hamiltonian. The picture is applied to derive a Lindblad master equation (ME) of a set of giant atoms coupled to a (generally chiral) waveguide field in an arbitrary white-noise Gaussian state, which condenses into a single equation and extends a variety of quantum optics and waveguide-QED MEs. The effective Hamiltonian and jump operators corresponding to a selected photodetection scheme are also worked out., 21 pages, 7 figures

We report on the results of the experimental investigations of the local resistive switching (RS) in the contact of a conductive atomic force microscope (CAFM) probe to a nanometer-thick yttria stabilized zirconia (YSZ) film on a conductive substrate under a Gaussian noise voltage applied between the probe and the substrate. The virtual memristor was found to switch randomly between the low resistance state and the high resistance state as a random telegraph signal (RTS). The potential profile of the virtual memristor calculated from its response to the Gaussian white noise shows two local minima, which is peculiar of a bistable nonlinear system.

In this tutorial paper we present a comprehensive review of the escape dynamics from quantum metastable states in dissipative systems and related noise-induced effects. We analyze the role of dissipation and driving in the escape process from quantum metastable states with and without an external driving force, starting from a nonequilibrium initial condition. We use the Caldeira–Leggett model and a non-perturbative theoretical technique within the Feynman–Vernon influence functional approach in strong dissipation regime. In the absence of driving, we find that the escape time from the metastable region has a nonmonotonic behavior versus the system-bath coupling and the temperature, producing a stabilizing effect in the quantum metastable system. In the presence of an external driving, the escape time from the metastable region has a nonmonotonic behavior as a function of the frequency of the driving, the thermal-bath coupling and the temperature. The quantum noise enhanced stability phenomenon is observed in both systems investigated. Finally, we analyze the resonantly activated escape from a quantum metastable state in the spin-boson model. We find quantum stochastic resonant activation, that is the presence of a minimum in the escape time as a function of the driving frequency. Background and introductory material has been added in the first three sections of the paper to make this tutorial review reasonably self-contained and readable for graduate students and non-specialists from related areas.

In this article we derive a closed form expression for the incompatibility condition in multi-parameter quantum metrology when the reference states are Fermionic Gaussian states. Together with the quantum Fisher information, the knowledge of the compatibility condition provides a way of designing optimal measurement strategies for multi-parameter quantum estimation. Applications range from quantum metrology with thermal states to non-equilibrium steady states with Fermionic and spin systems.

We define the Uhlmann number as an extension of the Chern number, and we use this quantity to describe the topology of 2D translational invariant Fermionic systems at finite temperature. We consider two paradigmatic systems and we study the changes in their topology through the Uhlmann number. Through the linear response theory we linked two geometrical quantities of the system, the mean Uhlmann curvature and the Uhlmann number, to directly measurable physical quantities, i.e. the dynamical susceptibility and to the dynamical conductivity, respectively., 5 pages, 3 figures

We study finite temperature topological phase transitions 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 Fermionisation procedure to study the system as a two-band p-wave superconductor described by a BdG Hamiltonian. This allows 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 a gap in the phase of the system characterised by non-Abelian statistics, and makes the model to belong to a symmetry protected class, so that the Uhmann number can be analysed. 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 analysed considering the system to be in a Gibbs state at finite temperature. Then, we show that the mean Uhlmann curvature describes a cross-over effect of the phases at high temperature. We also find an interesting nonmonotonic behaviour of the Uhlmann number as a function of the temperature in the trivial phase, which is due to the partial filling of the conduction band around Dirac points., Comment: 11 pages, 8 figures

We consider the Haldane model, a 2D topological insulator whose phase is defined by the Chern number. We study its phases as temperature varies by means of the Uhlmann number, a finite temperature generalization of the Chern number. Because of the relation between the Uhlmann number and the dynamical transverse conductivity of the system, we evaluate also the conductivity of the model. This analysis does not show any sign of a phase transition induced by the temperature, nonetheless it gives a better understanding of the fate of the topological phase with the increase of the temperature, and it provides another example of the usefulness of the Uhlmann number as a novel tool to study topological properties at finite temperature., 12 pages, 5 figures

Resistive switching (RS) is studied in a memristor based on a ZrO2(Y)/Ta2O5 stack under a white Gaussian noise voltage signal. We have found that the memristor switches between the low resistance state and the high resistance state in a random telegraphic signal (RTS) mode. The effective potential profile of the memristor shows from two to three local minima and depends on the input noise parameters and the memristor operation. These observations indicate the multiplicative character of the noise on the dynamical behavior of the memristor, that is the noise perceived by the memristor depends on the state of the system and its electrical properties are influenced by the noise signal. The detected effects manifest the fundamental intrinsic properties of the memristor as a multistable nonlinear system.

The low-frequency noise in a nanometer-sized virtual memristor consisting of a contact of a conductive atomic force microscope (CAFM) probe to an yttria stabilized zirconia (YSZ) thin film deposited on a conductive substrate is investigated. YSZ is a promising material for the memristor application since it is featured by high oxygen ion mobility, and the oxygen vacancy concentration in YSZ can be controlled by varying the molar fraction of the stabilizing yttrium oxide. Due to the low diameter of the CAFM probe contact to the YSZ film (similar to 10nm), we are able to measure the electric current flowing through an individual filament both in the low resistive state (LRS) and in the high resistive state (HRS) of the memristor. Probability density functions (Pdfs) and spectra of the CAFM probe current in both LRS and HRS are measured. The noise in the HRS is found to be featured by nearly the same Pdf and spectrum as the inner noise of the experimental setup. In the LRS, a flicker noise 1/f(gamma) with gamma approximate to 1.3 is observed in the low-frequency band (up to 8kHz), which is attributed to the motion (drift/diffusion) of oxygen ions via oxygen vacancies in the filament. Activation energies of oxygen ion motion determined from the flicker noise spectra are distributed in the range of [0.52; 0.68] eV at 300K. Knowing these values is of key importance for understanding the mechanisms of the resistive switching in YSZ based memristors as well as for the numerical simulations of memristor devices.

In this article we provide a review of geometrical methods employed in the analysis of quantum phase transitions and non-equilibrium dissipative phase transitions. After a pedagogical introduction to geometric phases and geometric information in the characterisation of quantum phase transitions, we describe recent developments of geometrical approaches based on mixed-state generalisation of the Berry-phase, i.e. the Uhlmann geometric phase, for the investigation of non-equilibrium steady-state quantum phase transitions (NESS-QPTs ). Equilibrium phase transitions fall invariably into two markedly non-overlapping categories: classical phase transitions and quantum phase transitions, whereas in NESS-QPTs this distinction may fade off. The approach described in this review, among other things, can quantitatively assess the quantum character of such critical phenomena. This framework is applied to a paradigmatic class of lattice Fermion systems with local reservoirs, characterised by Gaussian non-equilibrium steady states. The relations between the behaviour of the geometric phase curvature, the divergence of the correlation length, the character of the criticality and the gap - either Hamiltonian or dissipative - are reviewed., Comment: 94 pages, 15 figures, 399 references, To appear in: Physics Reports (2019). arXiv admin note: text overlap with arXiv:1305.4527, arXiv:quant-ph/0701061 by other authors

We propose a stochastic model for a memristive system by generalizing known approaches and experimental results. We validate our theoretical model by experiments carried out on a memristive device based on multilayer structure. In the framework of the proposed model we obtain the exact analytic expressions for stationary and nonstationary solutions. We analyze the equilibrium and non-equilibrium steady-state distributions of the internal state variable of the memristive system and study the influence of fluctuations on the resistive switching, including the relaxation time to the steady-state. The relaxation time shows a nonmonotonic dependence, with a minimum, on the intensity of the fluctuations. This paves the way for using the intensity of fluctuations as a control parameter for switching dynamics in memristive devices.

We investigate how the combined effects of strong Ohmic dissipation and monochromatic driving affect the stability of a quantum system with a metastable state. We find that, by increasing the coupling with the environment, the escape time makes a transition from a regime in which it is substantially controlled by the driving, displaying resonant peaks and dips, to a regime of frequency-independent escape time with a peak followed by a steep falloff. The escape time from the metastable state has a nonmonotonic behavior as a function of the thermal-bath coupling, the temperature, and the frequency of the driving. The quantum noise-enhanced stability phenomenon is observed in the investigated system.

In this article we derive a closed form expression for the symmetric logarithmic derivative of Fermionic Gaussian states. This provides a direct way of computing the quantum Fisher Information for Fermionic Gaussian states. Applications ranges from quantum Metrology with thermal states and non-equilibrium steady states with Fermionic many-body systems., 15 pages. arXiv admin note: substantial text overlap with arXiv:1911.10196; text overlap with arXiv:1608.02634 by other authors

Noise-induced phenomena characterise the nonlinear relaxation of nonequilibrium physical systems towards equilibrium states. Often, this relaxation process proceeds through metastable states and the noise can give rise to resonant phenomena with an enhancement of lifetime of these states or some coherent state of the condensed matter system considered. In this paper three noise induced phenomena, namely the noise enhanced stability, the stochastic resonant activation and the noise-induced coherence of electron spin, are reviewed in the nonlinear relaxation dynamics of three different systems of condensed matter: (i) a long-overlap Josephson junction (JJ) subject to thermal fluctuations and non-Gaussian, Levy distributed, noise sources; (ii) a graphene-based Josephson junction subject to thermal fluctuations; (iii) electrons in a n-type GaAs crystal driven by a fluctuating electric field. In the first system, we focus on the switching events from the superconducting metastable state to the resistive state, by solving the perturbed stochastic sine-Gordon equation. Nonmonotonic behaviours of the mean switching time versus the noise intensity, frequency of the external driving, and length of the junction are obtained. Moreover, the influence of the noise induced solitons on the mean switching time behaviour is shown. In the second system, noise induced phenomena are observed, such as noise enhanced stability (NES) and stochastic resonant activation (SRA). In the third system, the spin polarised transport in GaAs is explored in two different scenarios, i.e. in the presence of Gaussian correlated fluctuations or symmetric dichotomous noise. Numerical results indicate an increase of the electron spin lifetime by rising the strength of the random fluctuating component. Furthermore, our findings for the electron spin depolarization time as a function of the noise correlation time point out (i) a non-monotonic behaviour with a maximum in the case of Gaussian correlated fluctuations, (ii) an increase up to a plateau in the case of dichotomous noise. The noise enhances the coherence of the spin relaxation process.

We investigate the superconducting lifetime of a long overdamped current-biased Josephson junction, in the presence of telegraph noise sources. The analysis is performed by randomly choosing the initial condition for the noise source. However, in order to investigate how the initial value of the dichotomous noise affects the phase dynamics, we extend our analysis using two different fixed initial values for the source of random fluctuations. In our study, the phase dynamics of the Josephson junction is analyzed as a function of the noise signal intensity, for different values of the parameters of the system and external driving currents. We find that the mean lifetime of the superconductive metastable state as a function of the noise intensity is characterized by nonmonotonic behavior, strongly related to the soliton dynamics during the switching towards the resistive state. The role of the correlation time of the noise source is also taken into account. Noise-enhanced stability is observed in the investigated system.

The stabilizing effect of quantum fluctuations on the escape process and the relaxation dynamics from a quantum metastable state are investigated. Specifically, the quantum dynamics of a multilevel bistable system coupled to a bosonic Ohmic thermal bath in strong dissipation regime is analyzed. The study is performed by a non-perturbative method based on the real-time path integral approach of the Feynman-Vernon influence functional. We consider a strongly asymmetric double well potential with and without a monochromatic external driving, and with an out-of-equilibrium initial condition. In the absence of driving we observe a nonmonotonic behavior of the escape time from the metastable region, as a function both of the system-bath coupling coefficient and the temperature. This indicates a stabilizing effect of the quantum fluctuations. In the presence of driving our findings indicate that, as the coupling coefficient γ increases, the escape time, initially controlled by the external driving, shows resonant peaks and dips, becoming frequency-independent for higher γ values. Moreover, the escape time from the metastable state displays a nonmonotonic behavior as a function of the temperature, the frequency of the driving, and the thermal-bath coupling, which indicates the presence of a quantum noise enhanced stability phenomenon. Finally, we investigate the role of different spectral densities, both in sub-Ohmic and super-Ohmic dissipation regime and for different cutoff frequencies, on the relaxation dynamics from the quantum metastable state. The results obtained indicate that, in the crossover dynamical regime characterized by damped intrawell oscillations and incoherent tunneling, the spectral properties of the thermal bath influence non-trivially the short time behavior and the time scales of the relaxation dynamics from the metastable state.

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 figure

Nonlinear relaxation phenomena in three different systems of condensed matter are investigated. (i) First, the phase dynamics in Josephson junctions is analyzed. Specifically, a superconductor-graphene-superconductor (SGS) system exhibits quantum metastable states, and the average escape time from these metastable states in the presence of Gaussian and correlated fluctuations is calculated, accounting for variations in the the noise source intensity and the bias frequency. Moreover, the transient dynamics of a long-overlap Josephson junction (JJ) subject to thermal fluctuations and non-Gaussian noise sources is investigated. Noise induced phenomena are observed, such as the noise enhanced stability and the stochastic resonant activation. (ii) Second, the electron spin relaxation process in a n-type GaAs bulk driven by a fluctuating electric field is investigated. In particular, by using a Monte Carlo approach, we study the influence of a random telegraph noise on the spin polarized transport. Our findings show the possibility to raise the spin relaxation length by increasing the amplitude of the external fluctuations. Moreover, we find that, crucially, depending on the value of the external field strength, the electron spin depolarization length versus the noise correlation time increases up to a plateau. (iii) Finally, the stabilization of quantum metastable states by dissipation is presented. Normally, quantum fluctuations enhance the escape from metastable states in the presence of dissipation. We show that dissipation can enhance the stability of a quantum metastable system, consisting of a particle moving in a strongly asymmetric double well potential, interacting with a thermal bath. We find that the escape time from the metastable region has a nonmonotonic behavior versus the system- bath coupling and the temperature, producing a stabilizing effect.

In this article we derive a measure of quantumness in quantum multi-parameter estimation problems. We can show that the ratio between the mean Uhlmann Curvature and the Fisher Information provides a figure of merit which estimates the amount of incompatibility arising from the quantum nature of the underlying physical system. This ratio accounts for the discrepancy between the attainable precision in the simultaneous estimation of multiple parameters and the precision predicted by the Cram\'er-Rao bound. As a testbed for this concept, we consider a quantum many-body system in thermal equilibrium, and explore the quantum compatibility of the model across its phase diagram., Comment: 21 pages, 2 Figures. arXiv admin note: text overlap with arXiv:1911.10196

We analyse the Kitaev honeycomb model, by means of the Berry curvature with respect to Hamiltonian parameters. We concentrate on the ground-state vortex-free sector, which allows us to exploit an appropriate Fermionisation technique. The parameter space includes a time-reversal breaking term which provides an analytical headway to study the curvature in phases in which it would otherwise vanish. The curvature is then analysed in the limit in which the time-reversal-symmetry-breaking perturbation vanishes. This provides remarkable information about the topological phase transitions of the model. The Berry curvature in itself exhibits no singularities at criticality, nevertheless it distinguishes different phases by showing different behaviours. In particular, the analysis of the first derivative shows a critical behaviour around the transition point.

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:1406.4813

We study the dissipative quantum dynamics and the asymptotic behavior of a particle in a bistable potential interacting with a sub-Ohmic broadband environment. The reduced dynamics, in the intermediate to strong dissipation regime, is obtained beyond the two-level system approximation by using a real-time path integral approach. We find a crossover dynamic regime with damped intra-well oscillations and incoherent tunneling and a completely incoherent regime at strong damping. Moreover, a nonmonotonic behavior of the left/right well population difference is found as a function of the damping strength.

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 figures

We discuss the thermodynamic and finite size scaling properties of the geometric phase in the adiabatic Dicke model, describing the super-radiant phase transition for an $N$ qubit register coupled to a slow oscillator mode. We show that, in the thermodynamic limit, a non zero Berry phase is obtained only if a path in parameter space is followed that encircles the critical point. Furthermore, we investigate the precursors of this critical behavior for a system with finite size and obtain the leading order in the 1/N expansion of the Berry phase and its critical exponent.

We investigate quantum effects in geometric phases arising when a two-level system is interacting with a quantized electromagnetic field. When the system is adiabatically driven along a closed loop in the parameter space, signatures of the field quantization are observable in the geometric phase. We propose a feasible experiment to measure these effects in cavity QED and also analyse the semi-classical limit, recovering the usual Berry phase results.

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 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 assets, and scenarios 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 also use it to price a European basket option in complete and incomplete markets.