Open quantum systems are at the center of many research fields in condensed matter physics. We will introduce the non Hermitian Hamiltonian approach to open quantum systems, showing that this approach, in its simplest form, can be viewed as an extension of the Fermi Golden Rule. This approach allows to take into account the effect of the opening beyond the perturbation limit, where novel collective effects can arise. As an example of quantum collective property we consider here single excitation Superradiance.
Among the many fascinating aspects of these properties, one important open question regards their robustness to the effects induced by the presence of an environment. This robustness might enable to exploit coherent quantum effects to build quantum devices for information technologies and basic energy science. Specifically, we analyze the interplay of Superradiance, induced by the coupling to a continuum of states, and disorder, induced by the coupling with another environment, in one dimensional nanostructures. We consider static disorder (position dependent), which leads to Anderson localization. Superradiance is shown to be robust with respect to disorder. Moreover the interplay of different environments is shown to lead to novel cooperative regimes, such as the "subradiant hybrid regime".

The transient dynamics of a noisy Josephson junction (JJ) is computationally explored, analyzing three different cases. First, the superconducting lifetime of a long JJ (LJJ) is investigated, analyzing its behavior as a function of the system and noise parameters. Specifically we study the dynamics of the parameter \(\phi\), i.e. the phase difference between the macroscopic wave functions in the two electrodes of the junction, whose dynamics is ruled by the perturbed sine-Gordon (SG) equation. We focus on the mean switching time (MST), calculated as a nonlinear relaxation time, from the superconducting metastable state to the resistive state. The dynamics of the phase difference \(\phi\) is studied in the presence of an external noise with different statistics, i.e. Gaussian, Cauchy-Lorentz and Lévy-Smirnov, implemented usin \(\alpha\)-stable (or Lévy) distributions. For proper values of the system parameters and different statistics of the noise source, the MST is characterized by non-monotonic trends. The study of the time evolution of \(\phi\) highlights the influence of noise induced solitons on the MST behavior. Moreover, in the presence of Lévy flights, another localized SG solutions, the breathers, can be detected. We also present a study on the exclusive breather generation in LJJ stimulated by an external driving signal. A breather is a bound pair of a soliton and an antisoliton oscillating with an internal frequency \(\omega\). Considerable amount of theoretical and computational studies, about breathers in LJJ, exists, despite of the absence of experimental works devoted to their detection. This study is devoted to establish an efficient experimental setting to generate a SG breather in a LJJ, exploiting a well-known phenomenon, the nonlinear supratransmission (NLS). In our model, one end of the junction is driven by a sinusoidal pulse of amplitude A and frequency \(\omega\) lower than the plasma frequency of the junction. In the 2D parameters space \((A, \omega)\), we observe a region where no NLS phenomena appear, that is no energy flow through the system is present. In other cases, in correspondence of specific \((A, \omega)\) values, we observe only breathers. Otherwise, different combinations of SG solutions propagate along the junction. The analysis is performed for different values of damping parameter, duration of the external driving and applied bias current. To check the robustness of the breathers generated, a Gaussian noise source is inserted into the perturbed SG model, and the percentage of surviving breathers is calculated. Finally, the phase dynamics in a short JJ, i.e. ballistic graphene-based JJ, is investigated. The phase dynamics is ruled by the Resistively and Capacitively Shunted Junction (RCSJ) model, here improved inserting a thermal noise contribute. The superconductor-graphene-superconductor system is characterized, as much as normal current biased JJs, by the presence of quantum metastable states. In this case, the mean first passage time (MFPT) from these metastable states is calculated in the presence of different sources of white or correlated Gaussian noise. MFPT data are obtained for different values of both noise intensity and frequency of the alternate current bias, observing noise induced phenomena.

In collaboration with: D. Valenti, B. Spagnolo, K. Fedorov, A. Ustinov

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In some many-body systems, certain ground state entanglement (Renyi) entropies increase even as the correlation length decreases. This entanglement non-monotonicity implies a stronger ``quantum nature" of the wave function and gives it a higher computational power, compared to classical manipulations. In this work we demonstrate that such a phenomenon, known as non-local convertibility, is due to the edge state (de)construction occurring in the system. To this end, we employ the example of the Ising chain, displaying an order-disorder quantum phase transitions. Employing both analytical and numerical methods, we compute entanglement entropies for various system's bipartitions (A|B) and consider ground states with and without Majorana edge states. We find that the thermal ground states, enjoying the Hamiltonian symmetries, show non-local convertibility if either A or B are smaller than, or of the order of, the correlation length. In contrast, the ordered (symmetry breaking) ground state is always locally convertible. The edge states behavior explains all these results and could disclose a paradigm to understand local convertibility in other quantum phases of matter. The connection we establish between convertibility and non-local, quantum correlations provides a clear criterion of which features a universal quantum simulator should possess to outperform a classical machine.

We consider the dissipative dynamics of a multi-state quantum system interacting with an environment modeled as a bosonic thermal bath. The system is a particle in a double well potential, characterized by a metastable state.
We calculate the time evolution of the populations in a spatially localized representation (discrete variable representation, DVR), starting form a non-equilibrium initial condition. Unlike the Born-Markov approximated master equation, the approach used, which is based on a real time path integral technique, is non-perturbative in the system-bath coupling and therefore is suited also for the strong coupling regime.
The resulting non-Markovian dynamics is given in terms of a set of coupled integro-differential equations (generalized master equation, GME) for the populations in the DVR. The kernels of the GME are derived in different approximation schemes, depending on the damping regime and bath temperature. Under appropriate conditions, a Markovian master equation can be derived from the GME.
Various physical systems, ranging from single-molecule magnets to superconducting devices with Josephson junctions, display dissipative tunneling and are effectively described by the model considered.

In collaboration with: Davide Valenti and Bernardo Spagnolo

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A possible experimental realization of a quantum analogue of Newton's cradle is proposed starting from a Bose-Einstein condensate of atoms with two internal states, say 0 and 1. They are trapped in a one-dimensional tube with a superimposed periodic potential. Inducing a strong repulsion (Tonks-Girardeau regime) the lattice wells can contain one atom only and the dynamics is ruled by the second-order process of the exchange between neighboring 0- and 1-atoms. Assuming an initial state made of 0-atoms, a 1-atom injected in the chain tunnels back and forth between its ends. The phenomenon of dispersion can rapidly deteriorate a perfect propagation, but with slight modifications of the setup it is possible to obtain a quasi-ideal quantum cradle.

We will review the statistical physics approach to the nonlinear interaction of electromagnetic modes in lasers. Within this approach, the mode-locking of lasers can be understood as a phase transition in the canonical ensemble, where the role of the temperature is played by the spontaneous emission. When applied to the random laser phenomenon, in which the randomness on the spatial position of the scatterers induces a frustration in the mode interaction, this approach contemplates a glassy phase with nonvanishing complexity for large enough disorder. In this context, we will present some novel results regarding the collective phases of vector spin models with four-body interactions, and their numerical analysis.

We consider a point process on the real line where the origin always belongs to the process and the spacings between two neighboring points are i.i.d. random variables with finite mean and infinite variance. For each realization, we study the continuous-time random walk starting at the origin and jumping between the points of the process with speed 1. This type of system is sometimes known as Levy-Lorentz gas, and we consider its quenched version. We prove a CLT and the convergence of the normally scaled moments to those of a Gaussian. As a corollary, we improve a bound of Barkai, Fleurov, Klafter (2000) on the annealed second moment (for nonequilibrium initial conditions).

Joint work with A. Bianchi, G. Cristadoro and M. Ligabò.

We study a one-dimensional random walk with memory. The behavior of the walker is modified with respect to the simple symmetric random walk only when he or she is at the maximum distance ever reached from his or her starting point (home). In this case, having the choice to move farther or to move closer, the walker decides with different probabilities. If the probability of a forward step is higher then the probability of a backward step, the walker is bold, otherwise he or she is timorous. We investigate the asymptotic properties of this bold-timorous random walk, showing that the scaling behavior varies continuously from subdiffusive (timorous) to superdiffusive (bold). The scaling exponents are fully determined with a new mathematical approach based on a decomposition of the dynamics in active journeys (the walker is at the maximum distance) and lazy journeys (the walker is not at the maximum distance).

We will discuss the first passage time from the negative semi axis of a one-dimensional random walker. The Sparre-Andersen theorem is a remarkable result in probability theory concerning the universality of the ubiquitous first-passage-time distribution in this setting. We modify the Sparre-Andersen proof to deal with spatio-temporal correlations then show that given these considerations, there are natural processes that display deviations from the standard universality. We then use this modification to discuss the first return time for a Levy walk.

The ecosystem of Italian Apennines is characterized by a complex trophic web including vegetation, two prey species, i.e. wild boar (Sus scrofa) and fallow deer (Dama dama), and a top predator, the wolf (Canis lupus).
Recent field investigations have shown that this trophic web is characterized by a very peculiar topology since wild boars are wolf's prey when young, but they, as adults, klepto-parasitize wolves (i.e. steal food, fallow deer carcasses, from them).
In this work we investigate the dynamics of this food web using a system of coupled ordinary differential equations and show that the presence of a certain degree of klepto-parasitism is able to stabilize its dynamics by eliminating the characteristic oscillations of both preys and predators in the absence of klepto-parasitism.
This system is different from previously studied web models, because we introduce new physiological elements in the equations (e.g., the reproduction of wild boar is a function of food they are able to gather) and behavioural elements represented by the level of dominance of wild boars on wolves. By this model we introduce in food web modelling elements of ecological realism which, in perspective, might be used for habitat conservation and management.

In collaboration with: Stefano Focardi, Giacomo Innocenti, Duccio Berzi

We investigate fracture in a monolayer graphene with a small concentration of vacancies by molecular dynamics simulations. We simulate monolayers of varying size encompassing more than three decades, and we systematically study the mechanical failure following simulated "constant engineering strain" conditions. We compute the fracture strength distribution as a function of system size and defect concentration and compare the results with extreme value statistics. We highlight similarities and differences between the size effects expected in the fracture of macroscopic disordered solids with those observed at the nanoscale.