LPTMC Seminars

Superconducting dome and incipient modulate phase in SrTiO3

SrTiO₃ is a “quantum paraelectric” in which dipolar fluctuations grow upon cooling, yet long-range ferroelectric order never develops. In this seminar, I will discuss the evolution of these dipolar fluctuations, as measured by inelastic neutron scattering, as the system is tuned toward superconducting and ferroelectric phases.

First, I will show that the superconducting dome of SrTiO₃ is driven by the competition between the increase in the density of states and the inevitable collapse of the quantum paraelectric phase under electron doping. Second, I will demonstrate that these dipolar fluctuations couple to a transverse acoustic mode (elastic constant c₄₄), with this coupling being most pronounced at small q-vectors. I will further show that SrTiO₃ lies near a modulated phase, as evidenced by significant softening of its transverse acoustic branch.

Both the amplitude of the coupling and the modulation vector are strongly influenced by the enhancement of the ferroelectric and antiferrodistortive (AFD) phase transitions. These findings suggest that SrTiO₃ is not only an incipient ferroelectric but also an incipient modulated material, with the modulated phase cooperating, rather than competing, with ferroelectricity and the AFD transition.

If time permits, I will also present the electric-field dependence of the thermal conductivity—another probe of acoustic phonons—in SrTiO₃. This will provide further evidence of TO–TA hybridization in SrTiO₃.

Rare events and single big jump effects in stochastic processes

Rare events in stochastic processes are typically described within large deviation theory (LDT), where atypical fluctuations arise from the accumulation of many small contributions. In systems with sub-exponential statistics, however, rare events can instead be dominated by a single large fluctuation, as prescribed by the big jump principle (BJP). In this talk, I will discuss this alternative mechanism and its interplay with standard large deviation behavior across different classes of stochastic processes. I will first focus on power-law dynamics, such as Lévy processes, where single big jump effects control extreme value statistics and first-passage properties, including the behavior of the fastest trajectories in multi-particle settings, in particular their mean exit time from a bounded domain. I will then turn to processes with stretched-exponential statistics, with particular emphasis on the Ornstein–Uhlenbeck process. Using a renewal representation, one can identify a crossover between a regime of typical fluctuations described by LDT and a rare-event regime governed by the BJP, providing a physical interpretation of previously observed anomalous solutions in terms of single big jump effects. Finally, I will briefly discuss a perturbative approach that allows one to access intermediate regimes of moderate deviations, interpolating between these two limits.