Quantum Operation Time Reversal

The dynamics of an open quantum system can be described by a quantum operation, a linear, complete positive map of operators. Here, I exhibit a compact expression for the time reversal of a quantum operation, which is closely analogous to the time reversal of a classical Markov transition matrix. Since open quantum dynamics are stochastic, and not, in general, deterministic, the time reversal is not, in general, an inversion of the dynamics. Rather, the system relaxes towards equilibrium in both the forward and reverse time directions. The probability of a quantum trajectory and the conjugate, time reversed trajectory are related by the heat exchanged with the environment.Comment: 4 page

Time-reversal symmetry breaking versus chiral symmetry breaking in twisted bilayer graphene

6 pags., 3 figs.By applying a self-consistent Hartree-Fock approximation, we show that the mechanism of dynamical symmetry breaking can account for the insulating phase that develops about the charge neutrality point of twisted bilayer graphene around the magic angle. (i) If the Coulomb interaction is screened by metallic gates, the opening of a gap between the lowest-energy valence and conduction bands proceeds through the breakdown of chiral symmetry at strong coupling. Increasing the dielectric screening, however, we find a critical coupling at which chiral symmetry breaking is suppressed, triggering a very strong signal for time-reversal symmetry breaking with Haldane mass. (ii) If the long-range tail of the Coulomb interaction is not screened, we see the appearance of yet a different dominant pattern at strong coupling, which is characterized by breaking the time-reversal invariance but with opposite flux in the two sublattices of each carbon layer, with the consequent valley symmetry breaking. In this case a gap is also opened in the Dirac cones, but superposed to the splitting of the degeneracy of the low-energy bands at the K points of the moiré Brillouin zone.This work has been supported by Spain’s MINECO under Grant No. FIS2017-82260-P as well as by the CSIC Research Platform on Quantum Technologies PTI-001. Access to the computational resources of CESGA (Centro de Supercomputación de Galicia) is also gratefully acknowledged

Time reversal method with stabilizing boundary conditions for Photoacoustic tomography

We study an inverse initial source problem that models photoacoustic tomo- graphy measurements with array detectors, and introduce a method that can be viewed as a modi fi cation of the so called back and forth nudging method. We show that the method converges at an exponential rate under a natural visibility condition, with data given only on a part of the boundary of the domain of wave propagation. In this paper we consider the case of noiseless measurements

Time Reversal and Exceptional Points

Eigenvectors of decaying quantum systems are studied at exceptional points of the Hamiltonian. Special attention is paid to the properties of the system under time reversal symmetry breaking. At the exceptional point the chiral character of the system -- found for time reversal symmetry -- generically persists. It is, however, no longer circular but rather elliptic.Comment: submitted for publicatio

Time reversal symmetry breaking superconductivity

We study time reversal symmetry breaking superconductivity with $\Delta_k = \Delta_{x^2-y^2} (k) +e^{i\theta} \Delta_{\alpha}$ ($\alpha = s$ or $d_{xy}$) symmetries. It is shown that the behavior of such superconductors could be {\em qualitatively} different depending on the minor components ($\alpha$) and its phase at lower temperatures. It is argued that such {\em qualitatively different} behaviors in thermal as well as in angular dependencies could be a {\em source} of consequences in transport and Josephson physics. Orthorhombicity is found to be a strong mechanism for mixed phase (in case of $\alpha = s$). We show that due to electron correlation the order parameter is more like a pure $d_{x^2-y^2}$ symmetry near optimum doping.Comment: 5 pages, 5 figures (attached), to be published in Physical Review