Related papers: Time-reversal positivity
In a remarkable development Bender and coworkers have shown that it is possible to formulate quantum mechanics consistently even if the Hamiltonian and other observables are not Hermitian. Their formulation, dubbed PT quantum mechanics,…
While the microscopic laws of physics are often symmetric under time reversal, most natural processes that we observe are not. The emergent asymmetry between typical and time-reversed processes is referred to as the arrow of time. In…
We investigate the statistical arrow of time for a quantum system being monitored by a sequence of measurements. For a continuous qubit measurement example, we demonstrate that time-reversed evolution is always physically possible, provided…
We consider a two dimensional reflecting random walk on the nonnegative integer quadrant. It is assumed that this reflecting random walk has skip free transitions. We are concerned with its time reversed process assuming that the stationary…
Time-reversibility measured by the deviation of the perturbed time-reversed motion from the unperturbed one is examined for normal quantum diffusion exhibited by four classes of quantum maps with contrastive physical nature. Irrespective of…
We consider the time-reversal-invariant Hofstadter-Hubbard model which can be realized in cold atom experiments. In these experiments, an additional staggered potential and an artificial Rashba--type spin-orbit coupling are available.…
Reversal of the time direction in stochastic systems driven by white noise has been central throughout the development of stochastic realization theory, filtering and smoothing. Similar ideas were developed in connection with certain…
It is well known that nonrelativistic quantum mechanics presents a clear asymmetry between space and time. Much of this asymmetry is attributed to the lack of Lorentz invariance of the theory. Nonetheless, a recent work [Phys. Rev. A…
After a synoptic panorama about some still unsolved foundational problems involving time-reversal, we show that the \emph{double time-reversal superselection rule} of Nonrelativistic Quantum Mechanics is redundant. We then analyze which,…
In this article, we consider the diffusion equation with multi-term time-fractional derivatives. We first derive that the solution is positive when the source term is nonpositive by a subordination principle for the solution. As an…
Quantum mechanics still provides new unexpected effects when considering the transport of energy and information. Models of continuous time quantum walks, which implicitly use time-reversal symmetric Hamiltonians, have been intensely used…
This paper is concerned with time reversal in \emph{photoacoustic tomography} (PAT) of dissipative media that are similar to water. Under an appropriate condition, it is shown that the time reversal method in \cite{Wa11,AmBrGaWa11} based on…
Time reversal of vast classes of phenomena has direct implications with predictability, causality and the second principle of thermodynamics. We analyze in detail time reversibility of a paradigmatic dissipative nonlinear dynamical system,…
Directed topology was introduced as a model of concurrent programs, where the flow of time is described by distinguishing certain paths in the topological space representing such a program. Algebraic invariants which respect this…
In this short note we discuss the time-reversal of a quasiprobability distribution of work.
Many financial time series have varying structures at different quantile levels, and also exhibit the phenomenon of conditional heteroscedasticity at the same time. In the meanwhile, it is still lack of a time series model to accommodate…
It is one of the most important and long-standing issues of physics to derive the irreversibility out of a time-reversal symmetric equation of motion. The present paper considers the breaking of the time-reversal symmetry in open quantum…
Open quantum systems are often represented by non-Hermitian effective Hamiltonians that have complex eigenvalues associated with resonances. In previous work we showed that the evolution of tight-binding open systems can be represented by…
Topological phases are enriched in non-equilibrium open systems effectively described by non-Hermitian Hamiltonians. While several properties unique to non-Hermitian topological systems were uncovered, the fundamental role of symmetry in…
We study the time reversal of a general PDMP. The time reversed process is defined as $X_{(T-t)-}$, where $T$ is some given time and $X_t$ is a stationary PDMP. We obtain the parameters of the reversed process, like the jump intensity and…