Two-dimensional non commutative Swanson model and its bicoherent states

We introduce an extended version of the Swanson model, defined on a two-dimensional non commutative space, which can be diagonalized exactly by making use of pseudo-bosonic operators. Its eigenvalues are explicitly computed and the biorthogonal sets of eigenstates of the Hamiltonian and of its adjoint are explicitly constructed. We also show that it is possible to construct two displacement-like operators from which a family of bi-coherent states can be obtained. These states are shown to be eigenstates of the deformed lowering operators, and their projector allows to produce a suitable resolution of the identity in a dense subspace of \Lc^2(\Bbb R^2)

Visual assessment of multi-photon interference

Classical machine learning algorithms can provide insights on high-dimensional processes that are hardly accessible with conventional approaches. As a notable example, t-distributed Stochastic Neighbor Embedding (t-SNE) represents the state of the art for visualization of data sets of large dimensionality. An interesting question is then if this algorithm can provide useful information also in quantum experiments with very large Hilbert spaces. Leveraging these considerations, in this work we apply t-SNE to probe the spatial distribution of n-photon events in m-dimensional Hilbert spaces, showing that its findings can be beneficial for validating genuine quantum interference in boson sampling experiments. In particular, we find that nonlinear dimensionality reduction is capable to capture distinctive features in the spatial distribution of data related to multi-photon states with different evolutions. We envisage that this approach will inspire further theoretical investigations, for instance for a reliable assessment of quantum computational advantage

Contemporaneous Threshold Autoregressive Models: Estimation, Testing and Forecasting

This paper proposes a contemporaneous smooth transition threshold autoregressive model (C-STAR) as a modification of the smooth transition threshold autoregressive model surveyed in Teräsvirta (1998), in which the regime weights depend on the ex ante probability that a latent regime-specific variable will exceed a threshold value. We argue that the contemporaneous model is well-suited to rational expectations applications (and pricing exercises), in that it does not require the initial regimes to be predetermined. We investigate the properties of the model and evaluate its finitesample maximum likelihood performance. We also propose a method to determine the number of regimes based on a modified Hansen (1992) procedure. Furthermore, we construct multiple-step ahead forecasts and evaluate the forecasting performance of the model. Finally, an empirical application of the short term interest rate yield is presented and discussed.Smooth Transition Threshold Autoregressive, Forecasting, Nonlinear Models

Contemporaneous threshold autoregressive models: estimation, testing and forecasting

This paper proposes a contemporaneous smooth transition threshold autoregressive model (C-STAR) as a modification of the smooth transition threshold autoregressive model surveyed in Teräsvirta (1998), in which the regime weights depend on the ex ante probability that a latent regime-specific variable will exceed a threshold value. We argue that the contemporaneous model is well-suited to rational expectations applications (and pricing exercises), in that it does not require the initial regimes to be predetermined. We investigate the properties of the model and evaluate its finite-sample maximum likelihood performance. We also propose a method to determine the number of regimes based on a modified Hansen (1992) procedure. Furthermore, we construct multiple-step ahead forecasts and evaluate the forecasting performance of the model. Finally, an empirical application of the short term interest rate yield is presented and discussed. ; Earlier title: Contemporaneous threshold autoregressive models: estimation, forecasting and rational expectations applicationsRational expectations (Economic theory) ; Forecasting

Measurement-induced quantum operations on multiphoton states

We investigate how multiphoton quantum states obtained through optical parametric amplification can be manipulated by performing a measurement on a small portion of the output light field. We study in detail how the macroqubit features are modified by varying the amount of extracted information and the strategy adopted at the final measurement stage. At last the obtained results are employed to investigate the possibility of performing a microscopic-macroscopic non-locality test free from auxiliary assumptions.Comment: 13 pages, 13 figure

Entanglement criteria for microscopic-macroscopic systems

We discuss the conclusions that can be drawn on a recent experimental micro-macro entanglement test [F. De Martini, F. Sciarrino, and C. Vitelli, Phys. Rev. Lett. 100, 253601 (2008). The system under investigation is generated through optical parametric amplification of one photon belonging to an entangled pair. The adopted entanglement criterion makes it possible to infer the presence of entanglement before losses, that occur on the macrostate, under a specific assumption. In particular, an a priori knowledge of the system that generates the micro-macro pair is necessary to exclude a class of separable states that can reproduce the obtained experimental results. Finally, we discuss the feasibility of a micro-macro "genuine" entanglement test on the analyzed system by considering different strategies, which show that in principle a fraction epsilon, proportional to the number of photons that survive the lossy process, of the original entanglement persists in any losses regime.Comment: 11 pages, 10 figure

Brutality or frequency? An empirical investigation of the effects of terrorism on economic growth in India

© Presses de Sciences Po (P.F.N.S.P.). Tous droits réservés pour tous pays. In this paper we investigate the effects of terrorism on economic growth in India. Using a Markov switching model, we find evidence that terror has a significant and negative impact on Indian economic growth. Our empirical results also show that the magnitude of these effects is larger in periods of high growth. Finally, we compare the magnitude of the effects of the brutality and the frequency of terror attacks, and conclude that the effect of the frequency is slightly higher than the effect of the brutality

Non-Hermitian Hamiltonian for a Modulated Jaynes-Cummings Model with PT Symmetry

We consider a two-level system such as a two-level atom, interacting with a cavity field mode in the rotating wave approximation, when the atomic transition frequency or the field mode frequency is periodically driven in time. We show that in both cases, for an appropriate choice of the modulation parameters, the state amplitudes in a generic $n${-}excitation subspace obey the same equations of motion that can be obtained from a \emph{static} non-Hermitian Jaynes-Cummings Hamiltonian with ${\mathcal PT}$ symmetry, that is with an imaginary coupling constant. This gives further support to recent results showing the possible physical interest of ${\mathcal PT}$ symmetric non-Hermitian Hamiltonians. We also generalize the well-known diagonalization of the Jaynes-Cummings Hamiltonian to the non-Hermitian case in terms of pseudo-bosons and pseudo-fermions, and discuss relevant mathematical and physical aspects.Comment: 9 page