Theory Of Continuous Quantum Measurements Research Articles

Computer Simulation of Charge Transfer In a DNA Molecule within a Simple Model of an Open Quantum System

The quantum-statistical model proposed earlier by Skourtis and Nitzan to describe a charge (hole) propagation in a fragment of artificial DNA molecule has been generalized and further investigated. A numerical simulation of a charge transport was carried out taking into account two different dissipative processes, including the capture of the charged carrier by the environment and the decoherence of its quantum wave properties due to the influence of stochastic fields of the environment. The interaction of the carrier with the environment is regulated by a small set of phenomenological parameters whose values vary in the process of simulation. Within this model, the propagation of a hole carrier in DNA is described by solving the quantum Franke-Kossakovski–Lindblad–Glauber–Sudarshan equation (hereinafter referred to as the Lindblad equation) for the carrier density matrix using the Lindblad MPO Solver program. Results of numerical analysis of the model are in a good agreement with experimental observations and demonstrate two different types of the charged carrier motion, presumably tunneling and incoherent hopping. The model is put in more general context and non-unitary dynamics of the hole carrier is treated within the framework of a theory of continuous quantum measurements by the environment in an open quantum system. The main concepts of the theory of decoherence and superselection for open quantum systems and the prospects for their application for further study of various mechanisms of motion of a charged carrier in DNA are briefly discussed.

Перенос заряда в молекуле ДНК в рамках простой модели открытой квантовой системы

The quantum-mechanical model proposed earlier by Skourtis and Nitzan (J. of Chem. Phys. 119, (2003) 6271) to describe a charge transfer in a fragment of artificial DNA molecule has been numerically investigated. The current rationale for the model is carried out and values of its parameters are indicated. Within this model, the description of the transport of a hole carrier in DNA is based on solutions to the time-dependent Schrödinger equation including damping effects. The non-unitary dynamics of the hole carrier is treated by us within the framework of a theory of continuous quantum measurements by the environment in an open quantum system. Results of numerical analysis of the model are in a good agreement with experimental observations and demonstrate two different types of the charged carrier motion, presumably tunneling and incoherent hopping. The main concepts of the theory of decoherence and superselection for open quantum systems and the prospects for their application for further study of various mechanisms of motion of a charged carrier in DNA are briefly discussed.

Notes on the Cauchy problem for the self-adjoint and non-self-adjoint Schrödinger equations with polynomially growing potentials

The Cauchy problem is studied for the self-adjoint and non-self-adjoint Schrodinger equations. We first prove the existence and uniqueness of solutions in the weighted Sobolev spaces. Secondly we prove that if potentials are depending continuously and differentiably on a parameter, so are the solutions, respectively. The non-self-adjoint Schrodinger equations that we study are those used in the theory of continuous quantum measurements. The results on the existence and uniqueness of solutions in the weighted Sobolev spaces will play a crucial role in the proof for the convergence of the Feynman path integrals in the theories of quantum mechanics and continuous quantum measurements.

Two approaches to coupling classical and quantum variables

We address the issue of coupling variables whichare essentially classical to variables that are quantum.Two approaches are discussed. In the first, continuousquantum measurement theory is used to construct a phenomenological description of theinteraction of a quasiclassical variable X with aquantum variable x, where the quasiclassical nature ofX is assumed to have come about as a result ofdecoherence. The state of the quantum subsystem evolvesaccording to the stochastic nonlinear Schrodingerequation of a continuously measured system, and theclassical system couples to a stochastic c-number\(\overline x \left( t \right)\) representing the imprecisely measured value of x. The theorygives intuitively sensible results even when the quantumsystem starts out in a superposition of well-separatedlocalized states. The second approach involves a derivation of an effective theory from theunderlying quantum theory of the combinedquasiclassical-quantum system, and uses the decoherenthistories approach to quantum theory.

Coupling Classical and Quantum Variables using Continuous Quantum Measurement Theory

We propose a system of equations to describe the interaction of a quasiclassical variable $X$ with a set of quantum variables $x$ that goes beyond the usual mean field approximation. The idea is to regard the quantum system as continuously and imprecisely measured by the classical system. The effective equations of motion for the classical system therefore consist of treating the quantum variable $x$ as a stochastic c-number $\x (t) $ the probability distibution for which is given by the theory of continuous quantum measurements. The resulting theory is similar to the usual mean field equations (in which $x$ is replaced by its quantum expectation value) but with two differences: a noise term, and more importantly, the state of the quantum subsystem evolves according to the stochastic non-linear Schrodinger equation of a continuously measured system. In the case in which the quantum system starts out in a superposition of well-separated localized states, the classical system goes into a statistical mixture of trajectories, one trajectory for each individual localized state.

Yavlenie dekogerentsii i teoriya nepreryvnykh kvantovykh izmerenii

Yavlenie dekogerentsii i teoriya nepreryvnykh kvantovykh izmerenii

Continuous QND measurements: no quantum noise

Monitoring an arbitrary observable is analyzed in the framework of Restricted-Path-Integral (RPI) theory of continuous quantum measurements. While in an usual (quantum-demolition) continuous measurement the measurement noise contains both classical and quantum parts, only the classical noise is shown to be present in a quantum nondemolition (QND) continuous measurement. As a result, no absolute restrictions exist on measurability of a QND observable and the measurement output satisfies the classical equation of motion. Monitoring the energy gives an example of a discrete-spectrum observable.

Continuous quantum measurements: Restricted path integrals and master equations

The relation between two mathematical techniques in the theory of continuous quantum measurements is considered, one of them based on restricted path integrals (RPI) and the other one on master equations (ME). A typical continuous quantum measurement, monitoring an arbitrary observable, is presented for both techniques. This demonstrates mathematical equivalence of RPI and ME methods. Efficiency (reducibility to imaginary terms in a Hamiltonian) and generality (independence of the model of the RPI method) are argued.

Continuous quantum measurements: Restricted path integrals and master equations

The relation between two mathematical techniques in the theory of continuous quantum measurements is considered, one of them based on restricted path integrals (RPI) and the other one on master equations (ME). A typical continuous quantum measurement, monitoring an arbitary observable, is presented for both techniques. This demonstrates mathematical equivalence of RPI and ME methods. Efficiency (reducibility to imaginary terms in a Hamiltonian) and generality (independence of the model of the RPI method) are argued.

The difficulties in the mathematical definition of path integrals are overcome in the theory of continuous quantum measurements

Any real physical process takes place in an external (with respect to the investigated system) medium whose state reflects in one form or another information about the behavior of the system. Therefore, a real model of any process must include a description of the measurement process. This has the consequence that the dynamics of a real system contains both quantum and classical elements. Mathematically, a quantum system subject to continuous measurement can be described by a restricted path integral. The Feynman path integral that is usually employed is an idealization that is not correct in all cases. In a real situation in which the path integral is restricted, the difficulties associated with the mathematical definition of the path integral disappear. These difficulties are in fact a consequence of an unphysical idealization — the neglect of the fact that some information about the behavior of the quantum system remains in classical form in the environment.