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Papers by Giuseppe Barbalinardo

2018 IEEE 18th International Conference on Nanotechnology (IEEE-NANO), 2018

Alongside with exceptional electronic and optoelectronic properties, two-dimensional van der Waal... more Alongside with exceptional electronic and optoelectronic properties, two-dimensional van der Waals materials present intriguing heat transport properties, such as ultra-high thermal conductivity. Here we perform molecular simulations to unravel how heat transport in these materials may be tuned upon mechanical strain and chemical transformations. Our study sheds light on the phononic structure and the thermal conductivity of strained and lithium-intercalated MoS2, and on the thermal boundary resistance among graphene layers.

Glasses usually represent the lower limit for the thermal conductivity of solids, but a fundament... more Glasses usually represent the lower limit for the thermal conductivity of solids, but a fundamental understanding of lattice heat transport in amorphous materials can provide design rules to beat such a limit. Here we investigate the role of mass disorder in glasses by studying amorphous silicon-germanium alloy (a-${\mathrm{Si}}_{1\ensuremath{-}x}{\mathrm{Ge}}_{x}$) over the full range of atomic concentration from x=0x=0x=0 to x=1x=1x=1, using molecular dynamics and the quasiharmonic Green-Kubo lattice dynamics formalism. We find that the thermal conductivity of a-${\mathrm{Si}}_{1\ensuremath{-}x}{\mathrm{Ge}}_{x}$ as a function of xxx exhibits a smoother U shape than in crystalline mass-disordered alloys. The main contribution to the initial drop of thermal conductivity at low Ge concentration stems from the localization of otherwise extended modes that make up the lowest 8% of the population by frequency. Contributions from intermediate frequency modes are decreased more gradually with in...

Journal of Applied Physics

Nature Communications

We introduce a novel approach to model heat transport in solids, based on the Green-Kubo theory o... more We introduce a novel approach to model heat transport in solids, based on the Green-Kubo theory of linear response. It naturally bridges the Boltzmann kinetic approach in crystals and the Allen-Feldman model in glasses, leveraging interatomic force constants and normal-mode linewidths computed at mechanical equilibrium. At variance with molecular dynamics, our approach naturally and easily accounts for quantum mechanical effects in energy transport. Our methodology is carefully validated against results for crystalline and amorphous silicon from equilibrium molecular dynamics and, in the former case, from the Boltzmann transport equation.

In this article we illustrate a method to predict a sport competition. In the specific case, data... more In this article we illustrate a method to predict a sport competition. In the specific case, data are referred to the 2014 Soccer World Cup but the method can be applied to any sport. One problem we face in the develop of the strategy, is to take into the account the "luckiness factor". Some teams play easier matches than others and thus most likely will arrive to a better stage. The solution explained is based on the Monte Carlo method. This method is widely used in finance, math, physics and statistics, and has been used in the last century for realizing the first atomic bombs and in the past to empirically find Pi (for some primitive variants).

Graphic Processor Units are becoming more and more important in recent years and are spreading in... more Graphic Processor Units are becoming more and more important in recent years and are spreading into many different fields, some of which include: computational finance, defense and intelligence, machine learning, fluid dynamics, structural mechanics, electronic biology, physics, chemistry, numerical analysis and security. There are many reasons why a person should learn how to write code for a GPU. For example, GPU’s have been used to successfully decrypt passwords (add reference) in record time, a 25-GPU cluster is able to crack any standard Windows password (95^8 combinations) in less than 6 hours. Other applications of the GPU include data mining for Bitcoin and also applying machine learning for sentimental analysis on tweets. In this article I explain how to set up a Monte Carlo simulation on a standard NVidia GPU.

There are many systems in nature that adhere at least approximately to a double well potential. S... more There are many systems in nature that adhere at least approximately to a double well potential. Some examples are the inversion of the ammonia molecule and the localization of the electron in the hydrogen bonding. With little modification this simple model can be used to describe other interesting phenomena like the symmetry breaking in the ”mexican hat” potential (three dimensional double well) or the false vacuum effect (asymmetric double well). What makes this model so interesting is the phenomena of tunneling.
In quantum mechanics it is possible for a particle with an energy lower than the barrier height to exist outside the classical turning points. We call tunneling the process of the particle passing through the barrier, and tunneling time, the time elapsed. We can have tunneling even if the kinetic energy of a particle localized in one minimum is smaller than the barrier height.
In this model the potential is defined by a positive quartic term a negative quadratic term and a negative constant term.
Since the potential is parity invariant we can form a complete basis labelled by the parity and the energy.
The aim of this notes is to show how to calculate the mean tunneling time by three methods. As a demonstration of the physical process we obtain tunneling time directly from the time propagator. Then we will calculate such value accurately with the Monte Carlo method. Finally, we compare the results with the Galerkin’s variational method.

Derived by economists Fischer Black, Myron Scholes and Robert Merton in 1973, the Black- Scholes ... more Derived by economists Fischer Black, Myron Scholes and Robert Merton in 1973, the Black- Scholes formula is a way to determine how much an european call option is worth at any given time. This formula led to a boom in options trading and legitimized scientifically the activities of the Chicago Board Options Exchange (CBOE) and other options markets around the world.
In this report we present how the formula is obtained from a stochastic differential equation describing a geometric brownian motion. In the appendix, we present an analytic solution, setting up the boundary conditions and exploiting the analogies between the BS-model and the theory of diffusive processes.

In this notes we explore several fundamental issues related to the interaction between an atom an... more In this notes we explore several fundamental issues related to the interaction between an atom and an electromagnetic field. We show how the spontaneous decay naturally arise in the second quantization framework. At a later stage we include the effect of a classical monochromatic field showing how the population of the atom accomplish the so called Rabi oscillation. Finally we consider the spectra of resonance fluorescence and show the Mollow peaks in the spectra.

In principle, quantum computer can be made by any physical system, however there are several prop... more In principle, quantum computer can be made by any physical system, however there are several properties we want a system own in order to realize an effective quantum computer. For this reason much effort is being putted in the physical implementation of them in the last decades. The list of the properties a system should have, collected under the name of DiVincenzo criteria, is the following
• identification of well-defined qubits;
• reliable state preparation;
• low decoherence;
• accurate quantum gate operations and • strong quantum measurements.

Examples of systems took into account by scientist are: nuclear spin in liquids, trapped ions and trapped atoms, atoms in optical lattices, photons, superconducting circuits, electron suspended over liquid helium surfaces, molecular magnets, nuclear spins in solid, electron spins in semiconductor quantum dots (QD), hole spins in QD, electron spins in impurity centres in semiconductors (such as, phosphorus donors in silicon and nitrogen-vacancy centres in diamond) and non-Abelian anyon excitations in quantum matters with topological orders.
Solid-state systems have the advantage of stability and integrability, however they often have short coherence time due to the interaction with the complex environment. On the other hand, a complication of quantum computing with single atoms in vacuum is the necessity of cooling and trapping them. Large arrays of qubits may be easier to assemble and cool if the atoms are integrated into a solid-state host.

In this paper we want to focus on QD, a promising candidate to use in solid-state quan- tum computation. With several entangled QDs, which are directly related to qubits, plus a way of performing operations, quantum calculations and computers might be possible. The qubit carriers is the electron spin. Compared to superconducting qubit where the carrier may be lost during the measurement or the control process, spin is an elementary degree of freedom, which always exists until the particle (the electron) disappear, thus this kind of qubit is very stable.

We provide a quantum theoretical description of the magnetic polarization induced by intense circ... more We provide a quantum theoretical description of the magnetic polarization induced by intense circularly polarized light in a material. Such effect—commonly referred to as the inverse Faraday effect—is treated using beyond-linear response theory, considering the applied electromagnetic field as external perturbation. An analytical time-dependent solution of the Liouville–von Neumann equation to second order is obtained for the density matrix and used to derive expressions for the optomagnetic polarization. Two distinct cases are treated, the long-time adiabatic limit of polarization imparted by continuous wave irradiation, and the full temporal shape of the transient magnetic polarization induced by a short laser pulse. We further derive expressions for the Verdet constants for the inverse, optomagnetic Faraday effect and for the conventional, magneto-optical Faraday effect and show that they are in general different. Additionally, we derive expressions for the Faraday and inverse Faraday effects within the Drude-Lorentz theory and demonstrate that their equality does not hold in general, but only for dissipationless media. As an example, we perform initial quantum mechanical calculations of the two Verdet constants for a hydrogenlike atom and we extract the trends. We observe that one reason for a large inverse Faraday effect in heavy atoms is the spatial extension of the wave functions rather than the spin-orbit interaction, which nonetheless contributes positively.

Recently constructed radiation sources deliver brilliant, ultrashort coherent radiation fields wi... more Recently constructed radiation sources deliver brilliant, ultrashort coherent radiation fields with which the material's response can be investigated on the femtosecond to attosecond time scale. Here, we develop a theoretical framework for the interaction of the material's electrons with such intensive, short radiation pulses. Our theory is based on the time evolution of the electron density matrix, as defined through the Liouville-von Neumann equation. The latter equation is solved here within the framework of the response theory, incorporating the perturbing field in higher orders. An analytical tool, called the order notation, is developed, which permits the explicit calculation of the arising nth-order operatorial convolutions. As examples of the formalism, explicit expressions for several optical phenomena are worked out. Through the developed theory presented here, two fundamental results are achieved: first, the perturbing field to higher than linear orders is included in an elegant and compact way, allowing to treat highly brilliant light, and, second, the complete transient time response on the subfemtosecond scale is analytically provided, thus dropping the adiabatic approximation commonly made in standard linear response theory.

Thesis Chapters by Giuseppe Barbalinardo

More than hundred-fifty years ago Michael Faraday observed that a direct influence of the magneti... more More than hundred-fifty years ago Michael Faraday observed that a direct influence of the magnetic polarization of a material on the polarization of the light occours; after propagating through the material, the light polarization plane is rotated over an angle proportional to the induced magnetization.
The inverse effect, the influence of circularly polarized light on the mag- netic polarization of a material, was originally observed in 1965 by van der Ziel et al., who introduced the name the "inverse Faraday effect", to express that, instead of magnetism influencing light (as in the Faraday effect), the light was influencing the magnetism, i.e. a material irradiated by circularly polarized light can display an induced static magnetization. This was considered to be an interesting discovery in the nineteen sixties, but without any technological significance. However, this opinion changed with the advent of brilliant, fem- tosecond lasers during the last decade. The observation of Kimel et al. and subsequent recent studies demonstrated that ultrashort intensive, cir- cularly polarized laser pulses can be used to reverse, with unprecedented speed, magnetic bits in magnetic films made of typical recording materials.
How can circularly polarized light directly change the magnetic polarization in a material within the femtosecond time-scale? The answer to this question is not well know, but the inverse Faraday effect is expected to play a crucial role. However a fundamental understanding of the inverse Faraday effect is lacking. As the first observations of the inverse Faraday effect date back to the early nineteen sixties several theoretical models have already been proposed. These theories are based on classical or semi-classical models and do not allow any material specific predictions. Moreover no quantum mechanical features could be taken into account, for example, only the orbital part of the magnetization could be described preventing any possible evaluation of the spin contribution to this effect. The objective of this thesis is the development of a quantum-theoretical description of the inverse Faraday effect for ultrafast magneto-optics.
The time-response of a system to an external perturbation consists of a complex superposition of several contributions coming from different physical effects. It is of great importance for the understanding and for the optimization of the inverse Faraday effect to be able to isolate its contribution. The focus of this work is not only to study the complete response of the material to a femtosecond laser pulse but also to identify and analyze optical, magneto-optical and opto-magnetic effects.
A quantum-mechanical system evolving from thermodynamic equilibrium is best described within the density matrix formalism. The equation that deter- mines the dynamics of the density matrix is the Liouville-von Neumann equation. A standard perturbative approach to solve it is the response theory, that has been already successfully applied at first order to the calculation of the conductivity leading to the widely known Kubo formula [14]. Unfortunately, already the second order becomes practically untreatable preventing symbolic calculation and further extensions of the theory and thereby greatly concealing the physics. To obviate this difficulty the main contribution of this thesis is the development of a new mathematical tool: the order notation. This approach is able to extend the response theory to treat also the transient behaviors and high order responses. Using the newly developed mathematical tool, a quantum- mechanical description of the inverse Faraday effect is given in this thesis. It is shown that the second-order response in the density matrix is required to obtain the static magnetization induced in a material by light. Expressions for the inverse Faraday effect have been derived which could be evaluated using density-functional theory-based electronic structure calculations. Within such computational approach first-principles predictions of the inverse Faraday effect in real materials could become possible in the near future.

2018 IEEE 18th International Conference on Nanotechnology (IEEE-NANO), 2018

Journal of Applied Physics

Nature Communications