Master equation

About: Master equation is a research topic. Over the lifetime, 10541 publications have been published within this topic receiving 276095 citations.

Killing vector fields in self-dual, Euclidean Einstein spaces with Λ¬=;0

Abstract: Killing equations for self‐dual, Euclidean Einstein spaces with nonvanishing cosmological term Λ are considered. It is shown that in this case one can reduce ten Killing equations to one master equation. Some important solutions of the master equation are found and one of these solutions is analyzed in detail as it leads to metrics defined by the field equation well known in Euclidean or complex relativity. Ernst potentials for the solutions considered are found.

Hybrid-Liouvillian formalism connecting exceptional points of non-Hermitian Hamiltonians and Liouvillians via postselection of quantum trajectories

Abstract: Exceptional points (EPs) are degeneracies of classical and quantum open systems, which are studied in many areas of physics including optics, optoelectronics, plasmonics, and condensed matter physics. In the semiclassical regime, open systems can be described by phenomenological effective non-Hermitian Hamiltonians (NHHs) capturing the effects of gain and loss in terms of imaginary fields. The EPs that characterize the spectra of such Hamiltonians (HEPs) describe the time evolution of a system without quantum jumps. It is well known that a full quantum treatment describing more generic dynamics must crucially take into account such quantum jumps. In a recent paper [F. Minganti et al., Phys. Rev. A 100, 062131 (2019)], we generalized the notion of EPs to the spectra of Liouvillian superoperators governing open system dynamics described by Lindblad master equations. Intriguingly, we found that in situations where a classical-to-quantum correspondence exists, the two types of dynamics can yield different EPs. In a recent experimental work [M. Naghiloo et al., Nat. Phys. 15, 1232 (2019)], it was shown that one can engineer a non-Hermitian Hamiltonian in the quantum limit by postselecting on certain quantum jump trajectories. This raises an interesting question concerning the relation between Hamiltonian and Lindbladian EPs, and quantum trajectories. We discuss these connections by introducing a hybrid-Liouvillian superoperator, capable of describing the passage from an NHH (when one postselects only those trajectories without quantum jumps) to a true Liouvillian including quantum jumps (without postselection). Beyond its fundamental interest, our approach allows to intuitively relate the effects of postselection and finite-efficiency detectors.

Nakajima-Zwanzig versus time-convolutionless master equation for the non-Markovian dynamics of a two-level system

Abstract: We consider the exact reduced dynamics of a two-level system coupled to a bosonic reservoir, further obtaining the exact time-convolutionless and Nakajima-Zwanzig non-Markovian equations of motion. The system considered includes the damped and undamped Jaynes-Cummings model. The result is obtained by exploiting an expression of quantum maps in terms of matrices and a simple relation between the time evolution map and the time-convolutionless generator as well as the Nakajima-Zwanzig memory kernel. This nonperturbative treatment shows that each operator contribution in Lindblad form appearing in the exact time-convolutionless master equation is multiplied by a different time-dependent function. Similarly, in the Nakajima-Zwanzig master equation each such contribution is convoluted with a different memory kernel. It appears that, depending on the state of the environment, the operator structures of the two sets of equations of motion can exhibit important differences.

Impact of receptor-ligand distance on adhesion cluster stability.

Abstract: Cells in multicellular organisms adhere to the extracellular matrix through two-dimensional clusters spanning a size range from very few to thousands of adhesion bonds. For many common receptor-ligand systems, the ligands are tethered to a surface via polymeric spacers with finite binding range, thus adhesion cluster stability crucially depends on receptor-ligand distance. We introduce a one-step master equation which incorporates the effect of cooperative binding through a finite number of polymeric ligand tethers. We also derive Fokker-Planck and mean field equations as continuum limits of the master equation. Polymers are modeled either as harmonic springs or as worm-like chains. In both cases, we find bistability between bound and unbound states for intermediate values of receptor-ligand distance and calculate the corresponding switching times. For small cluster sizes, stochastic effects destabilize the clusters at large separation, as shown by a detailed analysis of the stochastic potential resulting from the Fokker-Planck equation.

Quantum theory of nonconservative systems

Abstract: We present here in a systematic way a reformulation and a generalization of a quantum theory of nonconservative (dissipative and antidissipative) systems already outlined by us many years ago. In particular, following a procedure first introduced by Levi Civita we give a detailed formulation of the corresponding classical Lagrangian and Hamiltonian treatments and consequently we show that quantum nonconservative systems can be equivalently described by the Schrodinger or Heisenberg picture. Furthermore, a detailed discussion of uncertainty rules for nonconservative systems is developed. By means of such a formulation it is possible to overcome easily criticisms raised against the so-called Caldirola-Kanai equation. Finally the connection between the Schrodinger equation for nonservative systems and the master equation is shortly discussed and some new possible developments of the theory are suggested.