Search results for "Master"
showing 10 items of 340 documents
Positioning in a flat two-dimensional space-time: the delay master equation
2010
The basic theory on relativistic positioning systems in a two-dimensional space-time has been presented in two previous papers [Phys. Rev. D {\bf 73}, 084017 (2006); {\bf 74}, 104003 (2006)], where the possibility of making relativistic gravimetry with these systems has been analyzed by considering specific examples. Here we study generic relativistic positioning systems in the Minkowski plane. We analyze the information that can be obtained from the data received by a user of the positioning system. We show that the accelerations of the emitters and of the user along their trajectories are determined by the sole knowledge of the emitter positioning data and of the acceleration of only one …
Trajectory Statistics of Confined L\'evy Flights and Boltzmann-type Equilibria
2013
We analyze a specific class of random systems that are driven by a symmetric L\'{e}vy stable noise, where Langevin representation is absent. In view of the L\'{e}vy noise sensitivity to environmental inhomogeneities, the pertinent random motion asymptotically sets down at the Boltzmann-type equilibrium, represented by a probability density function (pdf) $\rho_*(x) \sim \exp [-\Phi (x)]$. Here, we infer pdf $\rho (x,t)$ based on numerical path-wise simulation of the underlying jump-type process. A priori given data are jump transition rates entering the master equation for $\rho (x,t)$ and its target pdf $\rho_*(x)$. To simulate the above processes, we construct a suitable modification of t…
Application of thermodynamics to driven systems
2007
Application of thermodynamics to driven systems is discussed. As particular examples, simple traffic flow models are considered. On a microscopic level, traffic flow is described by Bando's optimal velocity model in terms of accelerating and decelerating forces. It allows to introduce kinetic, potential, as well as total energy, which is the internal energy of the car system in view of thermodynamics. The latter is not conserved, although it has certain value in any of two possible stationary states corresponding either to fixed point or to limit cycle in the space of headways and velocities. On a mesoscopic level of description, the size n of car cluster is considered as a stochastic varia…
Loss induced collective subradiant Dicke behaviour in a multiatom sample
2005
The exact dynamics of $N$ two-level atoms coupled to a common electromagnetic bath and closely located inside a lossy cavity is reported. Stationary radiation trapping effects are found and very transparently interpreted in the context of our approach. We prove that initially injecting one excitation only in the $N$ atoms-cavity system, loss mechanisms asymptotically drive the matter sample toward a long-lived collective subradiant Dicke state. The role played by the closeness of the $N$ atoms with respect to such a cooperative behavior is brought to light and carefully discussed.
Master equation approach to the three-state open Majorana model
2019
The three-state Majorana model in the presence of dissipation is considered. Different models of system-environment interaction are explored, ranging from a situation where dissipation is the main effect to regimes where dephasing is mainly produced. It is shown that the detrimental effects of the noise are stronger in the presence of dissipation than in the presence of dephasing. The role of temperature is also discussed.
Effective Landau-Zener transitions in circuit dynamical Casimir effect with time-varying modulation frequency
2016
We consider the dissipative single-qubit circuit QED architecture in which the atomic transition frequency undergoes a weak external time-modulation. For sinusoidal modulation with linearly varying frequency we derive effective Hamiltonians that resemble the Landau-Zener problem of finite duration associated to a two- or multi-level systems. The corresponding off-diagonal coupling coefficients originate either from the rotating or the counter-rotating terms in the Rabi Hamiltonian, depending on the values of the modulation frequency. It is demonstrated that in the dissipation less case one can accomplish almost complete transitions between the eigenstates of the bare Rabi Hamiltonian even f…
Class of exact memory-kernel master equations
2016
A well-known situation in which a non-Markovian dynamics of an open quantum system $S$ arises is when this is coherently coupled to an auxiliary system $M$ in contact with a Markovian bath. In such cases, while the joint dynamics of $S$-$M$ is Markovian and obeys a standard (bipartite) Lindblad-type master equation (ME), this is in general not true for the reduced dynamics of $S$. Furthermore, there are several instances (\eg the dissipative Jaynes-Cummings model) in which a {\it closed} ME for the $S$'s state {\it cannot} even be worked out. Here, we find a class of bipartite Lindblad-type MEs such that the reduced ME of $S$ can be derived exactly and in a closed form for any initial produ…
Microscopic derivation of the Jaynes-Cummings model with cavity losses
2006
In this paper we provide a microscopic derivation of the master equation for the Jaynes-Cummings model with cavity losses. We single out both the differences with the phenomenological master equation used in the literature and the approximations under which the phenomenological model correctly describes the dynamics of the atom-cavity system. Some examples wherein the phenomenological and the microscopic master equations give rise to different predictions are discussed in detail.
Non-Markovian dissipative dynamics of two coupled qubits in independent reservoirs: a comparison between exact solutions and master equation approach…
2009
The reduced dynamics of two interacting qubits coupled to two independent bosonic baths is investigated. The one-excitation dynamics is derived and compared with that based on the resolution of appropriate non-Markovian master equations. The Nakajima-Zwanzig and the time-convolutionless projection operator techniques are exploited to provide a description of the non-Markovian features of the dynamics of the two-qubits system. The validity of such approximate methods and their range of validity in correspondence to different choices of the parameters describing the system are brought to light.
Collision-model-based approach to non-Markovian quantum dynamics
2013
We present a theoretical framework to tackle quantum non-Markovian dynamics based on a microscopic collision model (CM), where the bath consists of a large collection of initially uncorrelated ancillas. Unlike standard memoryless CMs, we endow the bath with memory by introducing inter-ancillary collisions between next system-ancilla interactions. Our model interpolates between a fully Markovian dynamics and the continuous interaction of the system with a single ancilla, i.e., a strongly non-Markovian process. We show that in the continuos limit one can derive a general master equation, which while keeping such features is guaranteed to describe an unconditionally completely positive and tra…