scholarly journals All You Ever Wanted to Know About the Quantum Zeno Effect in 70 Minutes

2014 ◽  
Vol 21 (01n02) ◽  
pp. 1440007 ◽  
Author(s):  
Saverio Pascazio
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Projective Measurement ◽  
Previous Knowledge ◽  
Quantum Zeno Effect ◽  
Von Neumann ◽  
Zeno Effect ◽  
The Subject

This is a primer on the quantum Zeno effect, addressed to students and researchers with no previous knowledge on the subject. The prerequisites are the Schrödinger equation and the von Neumann notion of projective measurement.

GEODESIC FLOWS, VON NEUMANN EQUATION AND QUANTUM MECHANICS ON NONCOMMUTATIVE CYLINDER

2006 ◽  
Vol 21 (28) ◽  
pp. 2151-2160
Author(s):  
PARTHA GUHA
Keyword(s):  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Geodesic Flows ◽  
Von Neumann ◽  
Discrete Schrödinger Equation ◽  
Von Neumann Equation ◽  
Area Preserving

We study quantum mechanics on the noncommutative cylinder via Moyal deformed geodesic flows on the group of area preserving diffeomorphism. This equation coincides exactly with the von Neumann equation. Using discretization techniques of Kemmoku and Saito we obtain the discrete Schrödinger equation on noncommutative cylinder. Thus we reproduce the result of Balachandran et al.1

scholarly journals SYMPLECTIC STRUCTURES AND QUANTUM MECHANICS

1996 ◽  
Vol 10 (12) ◽  
pp. 545-553 ◽  
Author(s):  
GIUSEPPE MARMO ◽  
GAETANO VILASI
Keyword(s):  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Classical Field Theory ◽  
General Setting ◽  
Von Neumann ◽  
Neumann Theorem ◽  
Starting Point ◽  
Good Starting Point ◽  
Von Neumann Theorem

Canonical coordinates for the Schrödinger equation are introduced, making more transparent its Hamiltonian structure. It is shown that the Schrödinger equation, considered as a classical field theory, shares with Liouville completely integrable field theories the existence of a recursion operator which allows for the infinitely many conserved functionals pairwise commuting with respect to the corresponding Poisson bracket. The approach may provide a good starting point to get a clear interpretation of Quantum Mechanics in the general setting, provided by Stone–von Neumann theorem, of Symplectic Mechanics. It may give new tools to solve in the general case the inverse problem of quantum mechanics whose solution is given up to now only for one-dimensional systems by the Gel’fand-Levitan-Marchenko formula.

On the mapping connecting the cylindrical nonlinear von Neumann equation with the standard von Neumann equation

2010 ◽  
Vol 76 (3-4) ◽  
pp. 645-653 ◽  
Author(s):  
RENATO FEDELE ◽  
SERGIO DE NICOLA ◽  
DUSAN JOVANOVIĆ ◽  
DAN GRECU ◽  
ANCA VISINESCU
Keyword(s):  
Phase Space ◽  
Schrödinger Equation ◽  
Wigner Function ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Soliton Solutions ◽  
Nonlinear Schrodinger Equation ◽  
Von Neumann ◽  
Nonlinear Schrödinger ◽  
Von Neumann Equation

AbstractThe Wigner transformation is used to define the quasidistribution (Wigner function) associated with the wave function of the cylindrical nonlinear Schrödinger equation (CNLSE) in a way similar to that of the standard nonlinear Schrödinger equation (NLSE). The phase-space equation, governing the evolution of such quasidistribution, is a sort of nonlinear von Neumann equation (NLvNE), called here the ‘cylindrical nonlinear von Neumann equation’ (CNLvNE). Furthermore, the phase-space transformations, connecting the Wigner function and the NLvNE with the ‘cylindrical Wigner function’ and the CNLvNE, are found by extending the configuration space transformations that connect the NLSE and the CNLSE. Some examples of phase-space soliton solutions are given analytically and evaluated numerically.

scholarly journals Numerical Continuation of Resonances and Bound States in Coupled Channel Schrödinger Equations

2012 ◽  
Vol 11 (2) ◽  
pp. 435-455 ◽  
Author(s):  
Przemysław Kłosiewicz ◽  
Jan Broeckhove ◽  
Wim Vanroose
Keyword(s):  
Schrödinger Equation ◽  
Bifurcation Theory ◽  
Schrodinger Equation ◽  
Bound States ◽  
Numerical Continuation ◽  
Continuation Methods ◽  
Coupled Equations ◽  
Resonant States ◽  
The Subject ◽  
Coupled Channel

AbstractIn this contribution, we introduce numerical continuation methods and bifurcation theory, techniques which find their roots in the study of dynamical systems, to the problem of tracing the parameter dependence of bound and resonant states of the quantum mechanical Schrödinger equation. We extend previous work on the subject [1] to systems of coupled equations.Bound and resonant states of the Schrödinger equation can be determined through the poles of the S-matrix, a quantity that can be derived from the asymptotic form of the wave function. We introduce a regularization procedure that essentially transforms the S-matrix into its inverse and improves its smoothness properties, thus making it amenable to numerical continuation. This allows us to automate the process of tracking bound and resonant states when parameters in the Schrödinger equation are varied. We have applied this approach to a number of model problems with satisfying results.

On the equations governing the perturbations of the Schwarzschild black hole

1975 ◽  
Vol 343 (1634) ◽  
pp. 289-298 ◽  
Keyword(s):  
Black Hole ◽  
Schrödinger Equation ◽  
Time Dependence ◽  
Spherical Harmonics ◽  
Schrodinger Equation ◽  
Schwarzschild Black Hole ◽  
Schwarzschild Metric ◽  
One Dimensional ◽  
The Subject

A coherent self-contained account of the equations governing the perturbations of the Schwarzschild black hole is given. In particular, the relations between the equations of Bardeen & Press, of Zerilli and of Regge & Wheeler are explicitly established. The equations governing the perturbations of the vacuum Schwarzschild metric - the Schwarzschild black hole-have been the subject of many investigations (Regge & Wheeler 1957; Vishveshwara 1970; Edelstein & Vishveshwara 1970; Zerilli 1970 a, b ; Fackerell 1971; Bardeen & Press 1972; Friedman 1973). Nevertheless, there continues to be some elements of mystery shrouding the subject. Thus, Zerilli (1970a) showed that the equations governing the perturbation, properly analysed into spherical harmonics (belonging to the different l values) and with a time dependence iot , can be reduced to a one dimensional Schrodinger equation of the form

scholarly journals Consciousnes and the Problem of Quantum Measurement.

2019 ◽  
Author(s):  
Chris Broka
Keyword(s):  
Fock Space ◽  
Proper Time ◽  
Physical World ◽  
The State ◽  
Quantum Zeno Effect ◽  
Von Neumann ◽  
Zeno Effect ◽  
States Of Consciousness ◽  
The World ◽  
Points Of View

A variant of the von Neumann-Wigner Interpretation is proposed. It does not make use of the familiar language of wave functionsand observers. Instead it pictures the state of the physical world as a vector in a Fock space and, therefore not, literally, a functionof any spacetime coordinates. And, rather than segregating consciousness into individual points of view (each carrying with it asense of its proper time), this model proposes only unitary states of consciousness, Q(t), where t represents a fiducial time withrespect to which both the state of the physical world and the state of consciousness evolve. States in our world's Fock space areclassified as either 'admissible' (meaning they correspond to definite states of consciousness) or 'inadmissible' (meaning they donot). The evolution of the state vector of the world is such as to always keep it restricted to 'admissible' states. Consciousness istreated very much like what Chalmers calls an "M-Property." But we try to show that problems with the quantum Zeno effect do not arise from this model.

scholarly journals Monte Carlo simulation of quantum Zeno effect in the brain

2015 ◽  
Vol 29 (07) ◽  
pp. 1550039 ◽  
Author(s):  
Danko Georgiev
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Von Neumann Entropy ◽  
Quantum Zeno Effect ◽  
Von Neumann ◽  
Zeno Effect ◽  
Brain Entropy ◽  
The Mind ◽  
Local Projections ◽  
The Brain

Environmental decoherence appears to be the biggest obstacle for successful construction of quantum mind theories. Nevertheless, the quantum physicist Henry Stapp promoted the view that the mind could utilize quantum Zeno effect to influence brain dynamics and that the efficacy of such mental efforts would not be undermined by environmental decoherence of the brain. To address the physical plausibility of Stapp's claim, we modeled the brain using quantum tunneling of an electron in a multiple-well structure such as the voltage sensor in neuronal ion channels and performed Monte Carlo simulations of quantum Zeno effect exerted by the mind upon the brain in the presence or absence of environmental decoherence. The simulations unambiguously showed that the quantum Zeno effect breaks down for timescales greater than the brain decoherence time. To generalize the Monte Carlo simulation results for any n-level quantum system, we further analyzed the change of brain entropy due to the mind probing actions and proved a theorem according to which local projections cannot decrease the von Neumann entropy of the unconditional brain density matrix. The latter theorem establishes that Stapp's model is physically implausible but leaves a door open for future development of quantum mind theories provided the brain has a decoherence-free subspace.

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