Research Topics

  • Chaos and quantum mechanics ("Quantum Chaos").
  • Stochastic versus Coherent dynamics.
  • Dissipative dynamics, Brownian motion, Sinai spreading, Relaxation.
  • Dynamics of condensed particles, Bose-Hubbard (BH) model.
  • Theory of superfluidity in low dimensional BH circuits.
  • Theory of driven mesoscopic (nano) systems.
  • Adiabatic and non-adiabatic transport.
  • Pumping and stirring of particles in closed geometries.
  • Beyond linear response: energy absorption; mesoscopic conductance.
  • Theory of dissipation and quantum irreversibility.
  • Random Matrix Theory (RMT) modelling of semiclassical systems.
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Our recent studies concern the dynamics of particles in ring-shaped geometries. In particular we consider circuits: (a) with classical particles that perform stochastic motion; (b) with quantum Bose particles whose dynamics is coherent.

(a) It is possible to induce non-equilibrium steady state current, which requires e.g. a radiation source. We have studied the non-monotonic dependence of the current on the intensity of the driving, and its statistical properties. We also have addressed questions that concern the relaxation of such current, and how it depends on percolation and localization properties of the model. (b) Superfluidity is the possibility to have a current that does not decay even in the absence of an external driving source. Our study provides a theory for the meta-stability of such flow-states. A central observation is that the analysis should take into account the chaos that prevails in the classical limit of the model. It is the first time that the theory of "chaos" meets the theory of super-fluidity.
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Non-equilibrium steady state of stochastic circuits
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Dynamics of condensed particles in a few site system



Recent research activity:
Our recent studies consider minimal quantum models (a) with classical particles that perform random walk in disordered environment; (b) with quantum Bose particles whose dynamics is coherent. Four PhD students were involved in those projects during the last 3 years. In the first category we can bring as an example our study of relaxation of currents in one dimensional rings, taking into account percolation and localization properties of the model [SciReports 2016], where we fuse together themes that came from the works of Sinai-Derrida and Hatano-Nelson. Lately we have extended the study to active networks with topological stochastic disorder [PRE 2018]. In the second category we highlight our quantum-chaos theory for superfludity of one-dimensional bosonic gas in a ring lattice [SciReports 2015, PRB 2017], for which we also addressed the feasibility of SQUID operation [NJP 2016] and Insulator-Superfluid resonances [Editor's Suggestion PRA 2017]. Recently we have made a paradigm shift, introducing the concept of adiabatic passage through chaos [PRL 2018], with application to non-linear STIRAP. On the one hand we are interested in stability issues, e.g. our recent work shows how Monodromy and Chaos combine to explain the stability of a condensates in optical lattices [PRA 2019]; while on the other hand we have interest in thermalization [NJP 2015], introducing a semiclassical theory for many-body dynamical localization in extremely small systems [PRE 2018]. A full list of publications (by subject) is appended below.

Past research activity (1):
A major theme in our studies during 2006-2015 was a "resistor network" theory for the energy absorption of weakly chaotic systems. The theory was mainly applied to discuss the heating of cold atoms in vibrating traps; and to the conductance of closed mesoscopic rings. This work was a natural extension for the 1998-2002 quest for anomalies in the quantum response of driven mesoscopic systems.

Past research activity (2):
The scope of the 2003-2006 publications was to place quantum pumping in open systems and quantum stirring in closed systems under the umbrella of linear response theory. Later works (2008, 2013) have illuminated the physical picture using a heuristic "splitting ratio" approach, and provided results for the counting statistics.

Past research activity (3):
The main themes of the 1997-2004 studies were related to models of quantum dissipation, addressing the effect of noisy disorder, the induced dephasing, and the destruction of localization. This was a natural extension my PhD thesis (1987-1993) regarding the quantum kicked rotor in the presence of noise and dissipation.





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