
Williamson theorem in classical, quantum, and statistical physics
F. NicacioThe objective of this text is to present (and encourage the use of) the Williamson theorem and its consequences in several contexts in physics. The demonstration of the theorem is performed using only basic concepts of linear algebra and symplectic matrices. The immediate application is to place the study of small oscillations in the Hamiltonian scenario, where the theorem shows itself as a useful and practical tool for revealing the normalmode coordinates and frequencies of the system. A modest introduction of the symplectic formalism in quantum mechanics is presented, which consequently opens up the use of the theorem to study quantum normal modes and quantum small oscillations, allowing the theorem to be applied to the canonical distribution of thermodynamically stable systems described by quadratic Hamiltonians. As a last example, a more advanced topic concerning uncertainty relations is developed to show once more its utility in a distinct and modern perspective.

Weyl–Wigner representation of canonical equilibrium states
F NicacioThe WeylWigner representations for canonical thermal equilibrium quantum states are obtained for the whole class of quadratic Hamiltonians through a Wick rotation of the WeylWigner symbols of Heisenberg and metaplectic operators. The behavior of classical structures inherently associated to these unitaries is described under the Wick mapping, unveiling that a thermal equilibrium state is fully determined by a complex symplectic matrix, which sets all of its thermodynamical properties. The four categories of Hamiltonian dynamics (Parabolic, Elliptic, Hyperbolic, and Loxodromic) are analyzed. Semiclassical and high temperature approximations are derived and compared to the classical and/or quadratic behavior.

Mean value of the quantum potential and uncertainty relations
F. Nicacio, F. T. FalcianoIn this work we determine a lower bound to the mean value of the quantum potential for an arbitrary state. Furthermore, we derive a generalized uncertainty relation that is stronger than the RobertsonSchrödinger inequality and hence also stronger than the Heisenberg uncertainty principle. The mean value is then associated to the nonclassical part of the covariances of the momenta operator. This imposes a minimum bound for the nonclassical correlations of momenta and gives a physical characterization of the classical and semiclassical limits of quantum systems. The results obtained primarily for pure states are then generalized for density matrices describing mixed states.

Continuous monitoring of energy in quantum open systems
G. P. Martins, N. K. Bernardes, M. F. SantosWe propose a method to continually monitor the energy of a quantum system. We show that by having some previous knowledge of the system’s dynamics, but not all of it, one can use the measured energy to determine many other quantities, such as the work performed on the system, the heat exchanged between the system and a thermal reservoir, the time dependence of the Hamiltonian of the system as well as the total entropy produced by its dynamics. We have also analyzed how this method is dependent on the quality factor of the measurements employed.

Inducing nontrivial qubit coherence through a controlled dispersive environment
Wallace S. Teixeira, Fernando Nicacio, Fernando L. SemiãoWe show how the dispersive regime of the JaynesCummings model may serve as a valuable tool to the study of open quantum systems. We employ it in a bottomup approach to build an environment that preserves qubit energy and induces varied coherence dynamics. We then present the derivation of a compact expression for the qubit coherence, applied here to the case of a finite number of thermally populated modes in the environment. We also discuss how the model parameters can be adjusted to facilitate the production of shorttime monotonic decay (STMD) of the qubit coherence. Our results provide a broadly applicable platform for the investigation of energyconserving open system dynamics which is fully within the grasp of current quantum technologies.

Steady State Entanglement beyond Thermal Limits
F. Tacchino, A. Auffèves, M. F. Santos, D. GeraceClassical engines turn thermal resources into work, which is maximized for reversible operations. The quantum realm has expanded the range of useful operations beyond energy conversion, and incoherent resources beyond thermal reservoirs. This is the case of entanglement generation in a drivendissipative protocol, which we hereby analyze as a continuous quantum machine. We show that for such machines the more irreversible the process, the larger the concurrence. Maximal concurrence and entropy production are reached for the hot reservoir being at negative effective temperature, beating the limits set by classic thermal operations on an equivalent system.

Relative phase shifts for metaplectic isotopies acting on mixed Gaussian states
Maurice A. de Gosson, Fernando NicacioWe address in this paper the notion of relative phase shift for mixed quantum systems. We study the PancharatnamSjoeqvist phase shift for metaplectic isotopies acting on Gaussian mixed states. We complete and generalize previous results obtained by one of us while giving rigorous proofs. This gives us the opportunity to review and complement the theory of the ConleyZehnder index which plays an essential role in the determination of phase shifts.

Noncontextual Wirings
Barbara Amaral, Adán Cabello, Marcelo Terra Cunha, Leandro Aolita 
Probing quantum fluctuation theorems in engineered reservoirs
C Elouard, N K Bernardes, A R R Carvalho, M F Santos, A Auffèves 
Energy, momentum and production rate of photonic Cooper pairs
Filomeno S. de Aguiar Junior, Andre Saraiva, Marcelo F. Santos, Belita Koiller, Reinaldo de Melo e Souza, Arthur Patrocinio Pena, Raigna A. Silva, Carlos H. Monken, Ado Jorio 
Photonic Counterparts of Cooper Pairs
André Saraiva, Filomeno S. de Aguiar Júnior, Reinaldo de Melo e Souza, Arthur Patrocínio Pena, Carlos H. Monken, Marcelo F. Santos, Belita Koiller, Ado JorioThe microscopic theory of superconductivity raised the disruptive idea that electrons couple through the elusive exchange of virtual phonons, overcoming the strong Coulomb repulsion to form Cooper pairs. Light is also known to interact with atomic vibrations, as, for example, in the Raman effect. We show that photon pairs exchange virtual vibrations in transparent media, leading to an effective photonphoton interaction identical to that for electrons in the BCS theory of superconductivity, in spite of the fact that photons are bosons. In this scenario, photons may exchange energy without matching a quantum of vibration of the medium. As a result, pair correlations for photons scattered away from the Raman resonances are expected to be enhanced. An experimental demonstration of this effect is provided here by timecorrelated Raman measurements in different media. The experimental data confirm our theoretical interpretation of a photonic Cooper pairing, without the need for any fitting parameters.

Unified framework to determine Gaussian states in continuousvariable systems
Fernando Nicacio, Andrea ValdésHernández, Ana P. Majtey, Fabricio Toscano 
Coarse graining a nonMarkovian collisional model
Nadja K. Bernardes, Andre R. R. Carvalho, C. H. Monken, Marcelo F. Santos 
Determining stationarystate quantum properties directly from systemenvironment interactions
F. Nicacio, M. Paternostro, A. Ferraro 
High Resolution nonMarkovianity in NMR
Nadja K. Bernardes, John P. S. Peterson, Roberto S. Sarthour, Alexandre M. Souza, C. H. Monken, Itzhak Roditi, Ivan S. Oliveira, Marcelo F. Santos
1 a 15 de 24 Preprints encontradas Grupo(s): GOIQ  UFRJ