Stochastic Resonance. The shape of the confining part of a bistable potential U(x) can strongly influence the occurrence of stochastic resonance, i.e., the appearance of a peak versus temperature T in some quantifier of the response of the system to a time-periodic force. In the case of a bistable potential with a general confining part U(x) ~ | x |^q (for large values of |x |), it is found that the SR peak sharpens with increasing q for super-harmonic (q > 2) potentials, while it can broaden or be suppressed for sub-harmonic (q < 2) potentials, being replaced by a increasing monotonic response of the system as a function of T.
- E. Heinsalu, M. Patriarca and F. Marchesoni, Stochastic resonance in confining potentials. On the role of confinement. Eur. J. Phys. B, in press.

Anomalous Diffusion. "Anomalous" diffusion is actually an ubiquitus phenomenon in condensed matter, biological, and complex systems, characterizable e.g. throguh the non-linear time dependence of the mean square displacement. For some analytical and numerical studies of anomalous diffusion of a particle in an external field see:
- E. Heinsalu, M. Patriarca, I. Goychuk, and P. Hänggi, Use and abuse of a fractional Fokker- Planck dynamics for time-dependent driving, Phys. Rev. Lett. 99 (2007) 120602
- E. Heinsalu, M. Patriarca, I. Goychuk, and P. Hänggi, Fractional diffusion in periodic potentials, J. Phys.: Condensed Matter 19 (2007) 065114
- E. Heinsalu, M. Patriarca, I. Goychuk, G. Schmid, and P. Hänggi, Fractional Fokker-Planck dynamics: Numerical algorithm and simulations, Phys. Rev. E 73 (2006) 020101
- I. Goychuk, E. Heinsalu, M. Patriarca, G. Schmid, and P. Hänggi, Current and universal scaling in anomalous transport, Phys. Rev. E 73 (2006) 020101.

Quantum dissipation. The Feynman-Vernon model of linear dissipative systems, first applied to the study of quantum Brownian motion by Caldeira and Leggett, is questioned by the appearance of infinite quantities. Such divergencies also appear in the classical version of the model, which suggests a natural way to fix them. In fact, they can be traced back to the form of the uncorrelated Lagrangian and the corresponding uncorrelated initial conditions of the total system (central particle) + (environment oscillators) used in the original formulation.
The work was started with my PhD Thesis:
- Sistemi quantistici in ambienti dissipativi (Quantum systems in dissipative environments), University of Perugia, 1993.
The infinities appearing in the Feynman-Vernon model are considered in detail in:
- M. Patriarca, Statistical correlations in the oscillator model of quantum Brownian motion, Il Nuovo Cimento B 111 (1996) 61.
A generalization of the oscillator model to space- and time-modulated thermal environments:
- F. Illuminati, M. Patriarca, and P. Sodano, Classical and quantum dissipation in nonhomogeneous environments, Physica A 211 (1994) 449.
Another generalization to environments moving with a given velocity:
- M. Patriarca, Feynman-Vernon model for a moving thermal environment, Physica E 29 (2005) 243.

Kinetic exchange models. Kinetic exchange models are very simple statistical models, independently introduced in different disciplines, such as sociology, econophysics, and the kinetic theory of gases, which can describe a generalized (e.g. energy, wealth) flow in a complex system composed of N units.
- Marco Patriarca, Els Heinsalu, Anirban Chakraborti, The ABCD's of statistical many-agent economy models, presented at MARF2 - II Conference on Management of Risk Factors in economically relevant human activities, 2006 August 31 - September 2, Rome, Italy.
- Marco Patriarca, Els Heinsalu, Anirban Chakraborti, and Guido Germano, Relaxation in Statistical Many-agent Economy Models, Eur. Phys. J. B 57 (2007) 219.
- M. Patriarca, A. Chakraborti, K. Kaski, and G. Germano, Kinetic theory models for the distribution of wealth: power law from overlap of exponentials, in: Econophysics of Wealth Distributions - Econophys-Kolkata I, A. Chatterjee, S.Yarlagadda, and B. K. Chakrabarti Editors, Springer 2005.
- M. Patriarca, A. Chakraborti, and K. Kaski, A statistical model with a standard gamma distribution, Phys. Rev. E 70, (2004) 016104.
- M. Patriarca, A. Chakraborti, and Kimmo Kaski, Gibb's versus non-Gibb's distributions in money dynamics, Physica A 340 (2004) 334.

Language competition. Statistical mechanics of languages is a new and rapidly growing field. Among the various applications, geographical spreading and competition of two languages can be described under some conditions through population dynamics models.
- M. Patriarca and E. Heinsalu, Influence of geography on language competition, Physica A (2008), doi:10.1016/j.physa.2008.09.034
- M. Patriarca and T. Leppänen, Modelling language competition, Physica A 338 (2004) 296.

Quantum mechanics and stochastic processes. Quantum mechanical processes resemble Brownian processes so much that it is possible to formally rewrite a quantum-mechanical process as a clssical stochastic process, e.g. as a classical Wiener or Langevin process. However, it turns out that this is only a formal analogy, since there appear the so-called negative or quasi-probabilities.
- M. Patriarca, Quantum mechanical vs stochastic processes in path integration, in: Path Integrals from peV to TeV: 50 years after Feynman's Paper, R. Casalbuoni, R. Giachetti, V. Tognetti, R. Vaia, and P. Verrucchi Editors, World Scientific, Singapore, 1999, p.589.

Measurement process. The quantum measurement process, interpreted as the outcome of the interaction between a quantum system and a classical macroscopic system composed by an infinite number of degrees of freedom, can be modeled (and exacly solved) through the oscillator model of quantum dissipative systems.
- C. Presilla, R. Onofrio, M. Patriarca, Classical and quantum measurements of position, J. Phys. A 30(21) (1997) 7385

ALINE (Atomic Laboratory for Interactive Numerical Experiments), aka boundary3D, is a graphical interactive program for molecular dynamics simulations of simple condensed matter systems. It has various visualization modes and the possibility to vary in real-time the main parameters of the system.
- M. Patriarca, A. Kuronen, M. Robles, and K. Kaski, Three dimensional interactive Molecular Dynamics program for the study of defect dynamics in crystals, Comp. Phys. Comm. 176 (2007) 38.

Numerical simulation of plane wave scattering. The numerical simulation of an incident plane wave, which is in principle infinitely extended, by only using a small numerical lattice, is of interest in various problems of scattering and transport. This is can be done through suitably modified boundary conditions, while maintaining the physical picture of an infinite plane wave entering the system.
- M. Patriarca, Boundary conditions for the Schrödinger equation in the simulation of quantum systems, Phys. Rev. E 50 (1994) 1616.

Macroion Overcharging. "Simple" electrostatic phenomena have a primary role in the dynamics of the complex biological systems and can produce non-intuitive results, such as Macro-ion overcharging, in which so many counter-ions condense around a macro-ion until they reverse the sign the dressed macro-ion.
- M. Patra, M. Patriarca, and M. Karttunen, Stability of charge inversion, Thomson problem, and application to electrophoresis, Phys. Rev. E 67 (2003) 031402.

Brownian dimers. The dynamics of Brownian dimers in a washboard potential can be used to model various physical systems. For instance, it can be used as a model of dissociated dislocations (Volterra model) in a fcc crystal; the two partials interact with each other and with the underlying periodic Peierls potential; mobility of the dislocation is highest for half-integer ratio between the equilibrium distance between partials and the lattice ratio:
- E. Heinsalu, M. Patriarca, and F. Marchesoni, Dimer diffusion in a washboard potential Phys. Rev. E 77, 021129 (2008).
If the model is used to describe a dimer diffusing on a crystal surface, various resonant-like effects are observed in the diffusion and mobility:
- M. Patriarca, P. Szelestey, and E. Heinsalu, Brownian Model of Dissociated Dislocations, Acta Physica Polonica B 36 (2005) 1745.

Misfit dislocations in hetero-structures. Study of the nucleation and dynamics of dislocations in lattice-mismatched hetero-structures, a complex phenomenon with a special interest due to its technological importance. Some videos on line in the The Home Page of ALINE
- M. Patriarca, A. Kuronen, and K. Kaski, Nucleation and dynamics of dislocations in mismatched heterostructures, in: 2001 MRS Fall Meeting Proceedings, Vol. 696 Symposium N 4.4, MRS - Materials Research Society
- A. Kuronen and M. Patriarca, Atomistic modeling of hetero-structures, in : Handbook of Theoretical and Computational Nanotechnology, Michael Rieth and Wolfram Schommers Editors, ASP, 2005.
- M. Patriarca, A. Kuronen, M. Robles, and K. Kaski, Three dimensional interactive Molecular Dynamics program for the study of defect dynamics in crystals, Comp. Phys. Comm. 176 (2007) 38.

Self-Organized Criticality in Dislocation Dynamics. The ubiquitus SOC - Self-Organized Criticality also characterizes the collective dynamics of interacting dislocations in metals and describes the peculiar noise spectrum observed at low frequencies.
- F. Marchesoni and M. Patriarca, Self-organized criticality in dislocation networks, Phys. Rev. Lett. 72 (1994) 4101.

Protonated rare gases. Based on the work for the Tesi di Laurea (Master Thesis) on protonated noble atoms. An analytical form of phenomenological potential is introduced to describe the interaction between a proton and a noble gas atom. Such potential can be inverted exactly from spectroscopic data and then used to predict different features of the systems; for instance, the scattering cross sections are consistently predicted.
- F. A. Gianturco and M. Patriarca, Accurate Ne-H⁺ and Ar-H⁺ interactions from spectroscopic and scattering states: a comparison of theory with experiments, Il Nuovo Cimento 11 D (1989) 1287.