Selected Publications by Marco Tavora
This is a selection of my published works. For the full list you can check my Google Scholar profile.
My Ph.D. thesis can be found at the link below:
My Master's thesis is also available here:
For a selected list of conferences where I presented the work contained in these papers see the next section of this website.
2013-2015
Physical Review B 88, 115144 (09/2013) (link)
Quench dynamics of one-dimensional bosons in a commensurate periodic potential: A quantum kinetic equation approach (Marco Tavora and Aditi Mitra)
We studied a bosonic system after an interaction quench with the simultaneous switching on of a periodic potential. A new quantum kinetic equation is derived and solved, and a 2PI formalism is used to build the energy-momentum tensor. At long times the system is found to thermalize.
Physical Review Letters 113, 010601 (07/2014) (link)
Quench dynamics of one-dimensional interacting bosons in a disordered potential: Elastic dephasing and critical speeding-up of thermalization (Marco Tavora, Achim Rosch, Aditi Mitra)
The dynamics of interacting bosons in one dimension following the sudden switching on of a weak disordered potential is investigated. A novel quantum kinetic equation accounting for both disorder and interactions is employed to study the dynamics. The numerically obtained thermalization times are found to agree well with analytic estimates.
Physical Review B 91, 220302 (R) (06/2015) (link)
Short-time universal scaling in an isolated quantum system after a quench (Alessio Chiocchetta, Marco Tavora, Andrea Gambassi and Aditi Mitra)
Renormalization-group methods provide a viable approach for investigating the emergent collective behavior of classical and quantum statistical systems in both equilibrium and non-equilibrium conditions. Within this approach we investigate the dynamics of an isolated quantum system represented by a scalar quartic theory after a global quench of the potential close to a dynamical critical point.
2016-2017
Physical Review A 94, 012113 (07/2016) (link)
Excited-state quantum phase transitions in many-body systems with infinite-range interaction (Lea F. Santos, Marco Tavora, Francisco Perez Bernal)
Excited state quantum phase transitions (ESQPTs) are generalizations of quantum phase transitions (QPTs) to excited levels. Here, we investigate how the presence of an ESQPT can be detected from the analysis of the structure of the Hamiltonian matrix, the level of localization of the eigenstates, the onset of bifurcation, and the speed of the system evolution.
Entropy 18 (10), 359 - Special Issue "Quantum Information 2016" (editor's special invitation) (09/2016) (link)
Realistic many-body quantum systems vs full random matrices: static and dynamical properties (E.J.T. Herrera, Jonathan Karp, Marco Tavora, Lea F. Santos)
We study the static and dynamical properties of isolated many-body quantum systems and compare them with the results for full random matrices. In doing so, we link concepts from quantum information theory with those from quantum chaos. In particular, we relate the von
Neumann entanglement entropy with the Shannon information entropy and discuss their relevance for the analysis of the degree of complexity of the eigenstates, the behavior of the system at different time scales and the conditions for thermalization.
Physical Review B 94,134311 (10/2016) (link)
Short time universal scaling & lightcone dynamics after a quench in d dimensions (Alessio Chiocchetta, Marco Tavora, Andrea Gambassi, Aditi Mitra)
We investigate the effects of fluctuations on the dynamics of an isolated quantum system represented by a quartic field theory with O(N) symmetry after a quench in d > 2 spatial dimensions. A perturbative renormalization-group approach involving a dimensional expansion in (4-d) is employed in order to study the evolution within a pre-thermal regime controlled by elastic dephasing. In particular, we focus on a quench from a disordered initial state to the critical point, which introduces an effective temporal boundary in the evolution.
Physical Review A 94, 041603(R) (11/2016) (link)
Inevitable power-law behavior of many-body quantum systems & how it anticipates thermalization (Marco Tavora, E.J.T. Herrera, Lea F. Santos)
Despite being ubiquitous, out-of-equilibrium quantum systems are much less understood than systems at equilibrium. Progress in the field has benefited from a symbiotic relationship between theoretical studies and new experiments on coherent dynamics. The present work strengthens this connection by providing a general picture of the relaxation process of isolated lattice many-body quantum systems that are routinely studied in experiments with cold atoms, ions traps, and nuclear magnetic resonance. We show numerically and analytically that the long-time decay of the probability for finding the system in its initial state necessarily shows a power-law behavior. This happens independently of the details of the system, such as integrability, level repulsion, and the presence or absence of disorder. Information about the spectrum, the structure of the initial state, and the number of particles that interact simultaneously is contained in the value of the decay exponent. From it, we can anticipate whether the initial state will or will not thermalize.
Physical Review A 95, 013604 (12/2016) (link)
Power-law Decay Exponents: a Dynamical Criterion for Predicting Thermalization (Marco Tavora, E.J.T. Herrera, Lea F. Santos)
From the analysis of the relaxation process of isolated lattice many-body quantum systems quenched far from equilibrium, we deduce a criterion for predicting when they are certain to thermalize. It is based on the algebraic behavior of the survival probability at long times. We show that the value of the power-law exponent γdepends on the shape and filling of the weighted energy distribution of the initial state. Two scenarios are explored in details: γ ≥ 2 and γ < 1. Exponents γ ≥ 2 imply that the energy distribution of the initial state is ergodically filled and the eigenstates are uncorrelated, so thermalization is guaranteed to happen. In this case, the power-law behavior is caused by bounds in the energy spectrum. Decays with γ < 1 emerge when the energy eigenstates are correlated and signal lack of ergodicity. They are typical of systems undergoing localization due to strong onsite disorder and are found also in clean integrable systems.
2018-Present
Quantum Science and Technology Volume 3, Number 4 (link)
From few- to many-body quantum systems (Mauro Schiulaz, Marco Tavora and Lea F. Santos)
How many particles are necessary to make a quantum system many-body? To answer this question, we take as reference for the many-body limit a quantum system at half-filling and compare its properties with those of a system with N particles, gradually increasing N from 1. We show that convergence for the static properties of the system with few particles to the many-body limit is fast. For N>4, the density of states is already very close to Gaussian and signatures of many-body quantum chaos, such as level repulsion and fully extended eigenstates, become evident. The dynamics, on the other hand, depend on the initial state and time scale. In dilute systems, as the particles move away from each other, the entropy growth changes in time from linear, as typical for many-body systems, to logarithmic.