Lajos Diósi

Continuous quantum measurement and itô formalism

Abstract A new quantum-stochastic differential calculus is derived for representing a continuous quantum measurement of the position operator. A closed nonlinear quantum-stochastic differential equation is given for the quantum state of the observed particle. A possible physical realization of a continuous position measurement is constructed.

The non-Markovian stochastic Schrödinger equation for open systems

Abstract We present the non-Markovian generalisation of the widely used stochastic Schrodinger equation. Our result allows one to describe open quantum systems in terms of stochastic state vectors rather than density operators, without Markov approximation. Moreover, it unifies two recent independent attempts towards a stochastic description of non-Markovian open systems, based on path integrals on the one hand and coherent states on the other. The latter approach utilises the analytical properties of coherent states and enables a microscopic interpretation of the stochastic states. The alternative first approach is based on the general description of open systems using path integrals as originated by Feynman and Vernon.

On High-Temperature Markovian Equation for Quantum Brownian Motion

It is shown that a systematic Markovian approximation yields a given new term to the known master equation, ensuring conservation of positivity for arbitrary initial conditions and for all times.

Non-Markovian quantum-state diffusion: Perturbation approach

We present a perturbation theory for non-Markovian quantum state diffusion (QSD), the theory of diffusive quantum trajectories for open systems in a bosonic environment [Physical Review A 58, 1699, (1998)]. We establish a systematic expansion in the ratio between the environmental correlation time and the typical system time scale. The leading order recovers the Markov theory, so here we concentrate on the next-order correction corresponding to first-order non-Markovian master equations. These perturbative equations greatly simplify the general nonMarkovian QSD approach, and allow for efficient numerical simulations beyond the Markov approximation. Furthermore, we show that each perturbative scheme for QSD naturally gives rise to a perturbative scheme for the master equation which we study in some detail. Analytical and numerical examples are presented, including the quantum Brownian motion model.

DECOHERENT HISTORIES AND QUANTUM STATE DIFFUSION

We demonstrate a close connection between the decoherent histories (DH) approach to quantum mechanics and the quantum state diffusion (QSD) picture, for open quantum systems described by a master equation of Lindblad form. The (physically unique) set of variables that localize in the QSD picture also define an approximately decoherent set of histories in the DH approach. The degree of localization is related to the degree of decoherence, and the probabilities for histories prescribed by each approach are essentially the same.

Quantum Stochastic Processes as Models for State Vector Reduction

An elementary introduction of quantum-state-valued Markovian stochastic processes (QSP) for N-state quantum systems is given. It is pointed out that a so-called master constraint must be fulfilled. For a given master equation a continuous and, as a new alternative possibility, a discontinuous QSP are derived. Both are discussed as possible models for state reduction during measurement.

Notes on certain Newton gravity mechanisms of wavefunction localization and decoherence

Both an additional nonlinear term in the Schrodinger equation and an additional non-Hamiltonian term in the von Neumann equation, proposed to ensure localization and decoherence of macro-objects, resp., contain the same Newtonian interaction potential formally. We discuss certain aspects that are common for both equations. In particular, we calculate the enhancement of the proposed localization and/or decoherence effects, which would take place if one could lower the conventional length-cutoff and resolve the mass density on the interatomic scale.

Stochastic pure state representation for open quantum systems

Abstract We show that the usual master equation formalism of markovian open quantum systems is completely equivalent to a certain state vector formalism. The state vector of the system satisfies a given frictional Schrodinger equation except for random instant transitions of discrete nature. Hasses frictional hamiltonian is recovered for the damped harmonic oscillator.

Progressive Decoherence and Total Environmental Disentanglement

The simple stationary decoherence of a two-state quantum system is discussed from a new viewpoint of environmental entanglement. My work emphasizes that an unconditional local state must be totally disentangled from the rest of the universe. It has been known for longthat the loss of coherence within the given local system is gradual. Also the quantum correlations between the local system and the rest of the universe are beingdestro yed gradually. I show that, differently from local decoherence, the process of environmental disentanglement may terminate in finite time. The time of perfect disentanglement turns out to be on the decoherence time scale, and in a simple case we determine the exact value of it.

Quantum approach to coupling classical and quantum dynamics

We present a consistent framework of coupled classical and quantum dynamics. Our result allows us to overcome severe limitations of previous phenomenological approaches, such as evolutions that do not preserve the positivity of quantum states or that allow one to activate quantum nonlocality for superluminal signaling. A ‘‘hybrid’’ quantum-classical density is introduced, and its evolution equation derived. The implications and applications of our result are numerous: it incorporates the back-reaction of quantum on classical variables, and it resolves fundamental problems encountered in standard mean-field theories, and remarkably, also in the quantum measurement process; i.e., the most controversial example of quantum-classical interaction is consistently described within our approach, leading to a theory of dynamical collapse. Opinions vary about the coexistence of and interaction between classical and quantum systems. In orthodox quantum theory, classical macrosystems and quantized microsystems coexist; their interaction is described asymmetrically. The influence of macrovariables upon microsystems is precisely taken into account as external forces. The backreaction of quantized microsystems upon classical macrosystems is largely ignored, except for detector variables which are typically sensitive to certain microvariables. The theory of this specific back-reaction, called measurement theory@1#, predicts the statistics of the final states after the interaction. However, the interpretation of quantized dynamics is exclusively based on this nondynamical model of back-reaction ~cf. collapse of the quantum state!; without it we could not test the validity of quantized dynamics at all. Possibly, quantization extends to macrosystems, indeed the criteria of being macroscopic or microscopic are loosely if ever defined. Contrary to quantized microvariables, quantized macrovariables may have significant back-reactions on generic classical macrovariables as well. This becomes apparent in the widely used mean-field approximation@2# which, however, has several fundamental drawbacks @3#, as we shall recall in this paper. The measurement theory also describes back-reaction, but only for idealized detectors. In some attempts to define quantum gravity, matter and some fields are quantized, while other fields ~gravity in particular! are treated as classical, thus requiring a definite hybrid—i.e., a coupled classical and quantum—dynamics. Thus a general model of the backreaction is desirable. Such a theory would describe the ‘‘collapse’’ of the wave function dynamically @4#, would replace mean-field approximations in a systematic way @5‐7#, and could have deep implications for quantum cosmology. The first conceptual attempts @4‐6# were followed by ups and downs @8#, until severe limitations were clarified @9#. In this paper we use a straightforward transformation of the problem which automatically leads to a consistent model of hybrid dynamics.