Master equation

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

Fluctuation theorem for transport in mesoscopic systems

Abstract: The fluctuation theorem for currents is applied to several mesoscopic systems on the basis of Schnakenberg's network theory, which allows one to verify its conditions of validity. A graph is associated with the master equation ruling the random process and its cycles can be used to obtain the thermodynamic forces or affinities corresponding to the nonequilibrium constraints. This provides a method of defining the independent currents crossing the system in nonequilibrium steady states and to formulate the fluctuation theorem for the currents. This result is applied to out-of-equilibrium diffusion in a chain, to a biophysical model of ion channels in a membrane, and to electronic transport in mesoscopic circuits made of several tunnel junctions. In this latter, we show that the generalizations of Onsager's reciprocity relations to the nonlinear response coefficients also hold.

Wigner functions, squeezing properties, and slow decoherence of a mesoscopic superposition of two-level atoms

Abstract: Department of Quantum Physics, University of Ulm, D-89069 Ulm, Germany(Submitted to Physical Review A: March 26, 1999.)We consider a class of states in an ensemble of two-level atoms: a superposition of two distinctatomic coherent states, which can be regarded as atomic analogues of the states usually calledSchr¨odinger cat states in quantum optics. According to the relation of the constituents we definepolar and nonpolar cat states. The properties of these are investigated by the aid of the sphericalWigner function. We show that nonpolar cat states generally exhibit squeezing, the measure of whichdepends on the separation of the components of the cat, and also on the number of the constituentatoms. By solving the master equation for the polar cat state embedded in an external environment,we determine the characteristic times of decoherence, dissipation and also the characteristic time ofa new parameter, the non-classicality of the state. This latter one is introduced by the help of theWigner function, which is used also to visualize the process. The dependence of the characteristictimes on the number of atoms of the cat and on the temperature of the environment shows that thedecoherence of polar cat states is surprisingly slow.PACS number(s): 42.50.-p, 42.50.Fx, 03.65.BzI. INTRODUCTION

An Introduction to Operational Quantum Dynamics

Abstract: This special volume celebrates the 40th anniversary of the discovery of the Gorini-Kossakowski-Sudarshan-Lindblad master equation, which is widely used in quantum physics and quantum chemistry. The...

Gauge-Invariant Perturbations in Hybrid Quantum Cosmology

Abstract: We consider cosmological perturbations around homogeneous and isotropic spacetimes minimally coupled to a scalar field and present a formulation which is designed to preserve covariance. We truncate the action at quadratic perturbative order and particularize our analysis to flat compact spatial sections and a field potential given by a mass term, although the formalism can be extended to other topologies and potentials. The perturbations are described in terms of Mukhanov-Sasaki gauge invariants, linear perturbative constraints, and variables canonically conjugate to them. This set is completed into a canonical one for the entire system, including the homogeneous degrees of freedom. We find the global Hamiltonian constraint of the model, in which the contribution of the homogeneous sector is corrected with a term quadratic in the perturbations, that can be identified as the Mukhanov-Sasaki Hamiltonian in our formulation. We then adopt a hybrid approach to quantize the model, combining a quantum representation of the homogeneous sector with a more standard field quantization of the perturbations. Covariance is guaranteed in this approach inasmuch as no gauge fixing is adopted. Next, we adopt a Born-Oppenheimer ansatz for physical states and show how to obtain a Schrodinger-like equation for the quantum evolution of the perturbations. This evolution is governed by the Mukhanov-Sasaki Hamiltonian, with the dependence on the homogeneous geometry evaluated at quantum expectation values, and with a time parameter defined also in terms of suitable expectation values on that geometry. Finally, we derive effective equations for the dynamics of the Mukhanov-Sasaki gauge invariants, that include quantum contributions, but have the same ultraviolet limit as the classical equations. They provide the master equation to extract predictions about the power spectrum of primordial scalar perturbations.

Solvable quantum nonequilibrium model exhibiting a phase transition and a matrix product representation.

Abstract: We study a one-dimensional $\mathit{XX}$ chain under nonequilibrium driving and local dephasing described by the Lindblad master equation. The analytical solution for the nonequilibrium steady state found for particular parameters in a previous study [M. \ifmmode \check{Z}\else \v{Z}\fi{}nidari\ifmmode \check{c}\else \v{c}\fi{} J. Stat. Mech. (2010) L05002] is extended to arbitrary coupling constants, driving, and a homogeneous magnetic field. All one-, two-, and three-point correlation functions are explicitly evaluated. It is shown that the nonequilibrium stationary state is not Gaussian. Nevertheless, in the thermodynamic and weak-driving limit it is only weakly correlated and can be described by a matrix product operator ansatz with matrices of fixed dimension $4$. A nonequilibrium phase transition at zero dephasing is also discussed. It is suggested that the scaling of the relaxation time with the system size can serve as a signature of a nonequilibrium phase transition.