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Master equation
About: Master equation is a research topic. Over the lifetime, 10541 publications have been published within this topic receiving 276095 citations.
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TL;DR: In this paper, a deterministic nonlinear Schrodinger equation for quantum systems is presented. But it is not the master equation for mixed states used to describe the evolution of open quantum systems.
Abstract: First, we summarize the argument against deterministic nonlinear Schrodinger equations. We recall that any such equation activates quantum nonlocality in the sense that that information could be signalled in a finite time over arbitrarily large distances. Next we introduce a deterministic nonlinear Schrodinger equation. We justify it by showing that it is closest, in a precise sense, to the master equations for mixed states used to describe the evolution of open quantum systems. We also illustrate some interesting properties of this equation. Finally, we show that this equation can avoid the signalling problem if one adds noise to it in a precise way. Cases of both discrete and continuous noise are introduced explicitly and related to the density operator evolution. The relevance for the classical limit of the obtained stochastic equations is illustrated on a classically chaotic kicked anharmonic oscillator.
89 citations
TL;DR: A Markovian master equation in the Lindblad form is developed that enables the efficient study of a wide range of open quantum many-body systems that would be inaccessible with existing methods and ensures preservation of the positivity of the density matrix.
Abstract: We develop a Markovian master equation in the Lindblad form that enables the efficient study of a wide range of open quantum many-body systems that would be inaccessible with existing methods. The validity of the master equation is based entirely on properties of the bath and the system-bath coupling, without any requirements on the level structure within the system itself. The master equation is derived using a Markov approximation that is distinct from that used in earlier approaches. We provide a rigorous bound for the error induced by this Markov approximation; the error is controlled by a dimensionless combination of intrinsic correlation and relaxation timescales of the bath. Our master equation is accurate on the same level of approximation as the Bloch-Redfield equation. In contrast to the Bloch-Redfield approach, our approach ensures preservation of the positivity of the density matrix. As a result, our method is robust, and can be solved efficiently using stochastic evolution of pure states (rather than density matrices). We discuss how our method can be applied to static or driven quantum many-body systems, and illustrate its power through numerical simulation of a spin chain that would be challenging to treat by existing methods.
89 citations
89 citations
TL;DR: In this paper, a strongly Bose-condensed atomic vapor in a trap is considered, where the majority of the vapor is not condensed, and acts as a bath of heat and atoms for the condensate.
Abstract: We extend quantum kinetic theory to deal with a strongly Bose-condensed atomic vapor in a trap. The method assumes that the majority of the vapor is not condensed, and acts as a bath of heat and atoms for the condensate. The condensate is described by the particle-number-conserving Bogoliubov method developed by one of the authors. We derive equations which describe the fluctuations of particle number and phase, and the growth of the Bose-Einstein condensate. The equilibrium state of the condensate is a mixture of states with different numbers of particles and quasiparticles. It is not a quantum superposition of states with different numbers of particles---nevertheless, the stationary state exhibits the property of off-diagonal long-range order, to the extent that this concept makes sense in a tightly trapped condensate.
89 citations
TL;DR: In this article, a collision-like model was proposed to describe the evolution of open quantum systems that are completely positive and simultaneously have a semigroup property, and the possibility to derive this type of master equations from an intrinsically discrete dynamics that is modelled as a sequence of collisions between a given quantum system (a qubit) with particles that form the environment.
Abstract: Master equations in the Lindblad form describe evolution of open quantum systems that are completely positive and simultaneously have a semigroup property. We analyze the possibility to derive this type of master equations from an intrinsically discrete dynamics that is modelled as a sequence of collisions between a given quantum system (a qubit) with particles that form the environment. In order to illustrate our approach we analyze in detail how the process of an exponential decay and the process of decoherence can be derived from a collision-like model in which particular collisions are described by SWAP and controlled-NOT interactions, respectively.
89 citations