Giulio Giuseppe Giusteri

Cooperative robustness to static disorder: Superradiance and localization in a nanoscale ring to model light-harvesting systems found in nature

We analyze a 1-d ring structure composed of many two-level systems, in the limit where only one excitation is present. The two-level systems are coupled to a common environment, where the excitation can be lost, which induces super and subradiant behavior, an example of cooperative quantum coherent effect. We consider time-independent random fluctuations of the excitation energies. This static disorder, also called inhomogeneous broadening in literature, induces Anderson localization and is able to quench Superradiance. We identify two different regimes:

Microstructure and thickening of dense suspensions under extensional and shear flows

i)

Solution of the Kirchhoff-Plateau Problem

weak opening, in which Superradiance is quenched at the same critical disorder at which the states of the closed system localize;

Interplay of different environments in open quantum systems: Breakdown of the additive approximation

ii)

Instability Paths in the Kirchhoff–Plateau Problem

strong opening, with a critical disorder strength proportional to both the system size and the degree of opening, displaying robustness of cooperativity to disorder. Relevance to photosynthetic complexes is discussed.

Collective couplings: Rectification and supertransmittance.

Dense suspensions are non-Newtonian fluids which exhibit strong shear thickening and normal stress differences. Using numerical simulation of extensional and shear flows, we investigate how rheological properties are determined by the microstructure which is built under flows and by the interactions between particles. By imposing extensional and shear flows, we can assess the degree of flow-type dependence in regimes below and above thickening. Even when the flow-type dependence is hindered, nondissipative responses, such as normal stress differences, are present and characterise the non-Newtonian behaviour of dense suspensions.

Non-Hermitian Hamiltonian approach to quantum transport in disordered networks with sinks: Validity and effectiveness

The Kirchhoff–Plateau problem concerns the equilibrium shapes of a system in which a flexible filament in the form of a closed loop is spanned by a liquid film, with the filament being modeled as a Kirchhoff rod and the action of the spanning surface being solely due to surface tension. We establish the existence of an equilibrium shape that minimizes the total energy of the system under the physical constraint of noninterpenetration of matter, but allowing for points on the surface of the bounding loop to come into contact. In our treatment, the bounding loop retains a finite cross-sectional thickness and a nonvanishing volume, while the liquid film is represented by a set with finite two-dimensional Hausdorff measure. Moreover, the region where the liquid film touches the surface of the bounding loop is not prescribed a priori. Our mathematical results substantiate the physical relevance of the chosen model. Indeed, no matter how strong is the competition between surface tension and the elastic response of the filament, the system is always able to adjust to achieve a configuration that complies with the physical constraints encountered in experiments.

Slender-body theory for viscous flow via dimensional reduction and hyperviscous regularization

We analyze an open quantum system under the influence of more than one environment: a dephasing bath and a probability-absorbing bath that represents a decay channel, as encountered in many models of quantum networks. In our case, dephasing is modeled by random fluctuations of the site energies, while the absorbing bath is modeled with an external lead attached to the system. We analyze under which conditions the effects of the two baths can enter additively the quantum master equation. When such additivity is legitimate, the reduced master equation corresponds to the evolution generated by an effective non-Hermitian Hamiltonian and a Haken-Strobl dephasing super-operator. We find that the additive decomposition is a good approximation when the strength of dephasing is small compared to the bandwidth of the probability-absorbing bath.

A theoretical framework for steady-state rheometry in generic flow conditions

The Kirchhoff–Plateau problem concerns the equilibrium shapes of a system in which a flexible filament in the form of a closed loop is spanned by a soap film, with the filament being modeled as a Kirchhoff rod and the action of the spanning surface being solely due to surface tension. Adopting a variational approach, we define an energy associated with shape deformations of the system and then derive general equilibrium and (linear) stability conditions by considering the first and second variations of the energy functional. We analyze in detail the transition to instability of flat circular configurations, which are ground states for the system in the absence of surface tension, when the latter is progressively increased. Such a theoretical study is particularly useful here, since the many different perturbations that can lead to instability make it challenging to perform an exhaustive experimental investigation. We generalize previous results, since we allow the filament to possess a curved intrinsic shape and also to display anisotropic flexural properties (as happens when the cross section of the filament is noncircular). This is accomplished by using a rod energy which is familiar from the modeling of DNA filaments. We find that the presence of intrinsic curvature is necessary to obtain a first buckling mode which is not purely tangent to the spanning surface. We also elucidate the role of twisting buckling modes, which become relevant in the presence of flexural anisotropy.

Importance and Effectiveness of Representing the Shapes of Cosserat Rods and Framed Curves as Paths in the Special Euclidean Algebra

We investigate heat transport between two thermal reservoirs that are coupled via a large spin composed of N identical two-level systems. One coupling implements the dissipative Dicke superradiance. The other coupling is locally of the pure-dephasing type and requires to go beyond the standard weak-coupling limit by employing a Bogoliubov mapping in the corresponding reservoir. After the mapping, the large spin is coupled to a collective mode with the original pure-dephasing interaction, but the collective mode is dissipatively coupled to the residual oscillators. Treating the large spin and the collective mode as the system, a standard master equation approach is now able to capture the energy transfer between the two reservoirs. Assuming fast relaxation of the collective mode, we derive a coarse-grained rate equation for the large spin only and discuss how the original Dicke superradiance is affected by the presence of the additional reservoir. Our main finding is a cooperatively enhanced rectification effect due to the interplay of supertransmittant heat currents (scaling quadratically with N) and the asymmetric coupling to both reservoirs. For large N, the system can thus significantly amplify current asymmetries under bias reversal, functioning as a heat diode. We also briefly discuss the case when the couplings of the collective spin are locally dissipative, showing that the heat-diode effect is still present.