scholarly journals QUANTUM INSTABILITY FOR MIXED STATES

2002 ◽  
Vol 17 (31) ◽  
pp. 2039-2048 ◽  
Author(s):  
MAREK NOWAKOWSKI
Keyword(s):  
Time Evolution ◽  
Neutral Kaon ◽  
Single Step ◽  
Lagrangian Formalism ◽  
Mixed States ◽  
Linear Superposition ◽  
Instability Analysis ◽  
Mass Eigenstates ◽  
Alternative Method ◽  
Unstable States

The analysis of the time evolution of unstable states which are linear superposition of other, observable, states can, in principle, be carried out in two distinct, non-equivalent ways. One of the methods, usually employed for the neutral kaon system, combines the mixing and instability into one single step which then results in unconventional properties of the mass-eigenstates. An alternative method is to remain within the framework of a Lagrangian formalism and to perform the mixing prior to the instability analysis. Staying close to the [Formula: see text] system, we compare both methods pointing out some of their shortcomings and advantages.

scholarly journals Effects of initial coherence on distinguishability of pure/mixed states and chiral stability in an open chiral system

2014 ◽  
Vol 92 (2) ◽  
pp. 112-118 ◽  
Author(s):  
Heekyung Han ◽  
David M. Wardlaw ◽  
Alexei M. Frolov
Keyword(s):  
Analytical Solution ◽  
Time Evolution ◽  
Mixed States ◽  
Position Measurement ◽  
Decay Interaction ◽  
Initial States ◽  
Chiral Systems ◽  
Chiral System ◽  
Dephasing Rate ◽  
Pure Versus

We examine how initial coherences in open chiral systems affect distinguishability of pure versus mixed states and purity decay. Interaction between a system and an environment is modeled by a continuous position measurement and a two-level approximation is taken for the system. The resultant analytical solution is explored for various parameters, with emphasis on the interplay of initial coherences of the system and dephasing rate in determining the purity decay and differences in the time evolution of pure versus mixed initial states. Implications of the results for several fundamental problems are noted.

A MEASURE OF ENTANGLEMENT THROUGH QUANTUM TRAJECTORY APPROACH

2008 ◽  
Vol 06 (02) ◽  
pp. 403-410 ◽  
Author(s):  
X. L. HUANG ◽  
L. C. WANG ◽  
X. X. YI
Keyword(s):  
Master Equation ◽  
Time Evolution ◽  
Physical System ◽  
Quantum Trajectory ◽  
Mixed States ◽  
Trajectory Approach

We propose a measure of entanglement through the quantum trajectory approach. The advantage of this measure is that it can avoid the problem of finding all possible decompositions for mixed states, which is usually complicated. This method can be applied to any physical system whose time evolution is governed by the master equation. As an example, we calculate the entanglement of the following cases: (A) entangled system composed of a pair of two-level atoms coupling to two separate baths and, (B) two entangled modes subjected to two separate baths.

scholarly journals Perturbations and stability of rotating stars. I. Completeness of normal modes

1979 ◽  
Vol 368 (1734) ◽  
pp. 389-410 ◽  
Keyword(s):  
Initial Data ◽  
Eigenvalue Problem ◽  
Time Evolution ◽  
Normal Modes ◽  
Inner Product ◽  
Parallel Projection ◽  
Projection Operators ◽  
Quadratic Eigenvalue Problem ◽  
Linear Superposition ◽  
Quadratic Eigenvalue

Linear adiabatic perturbations of a differentially rotating, axisymmetric, perfect-fluid stellar model have normal modes described by a quadratic eigenvalue problem of the form where A and C are symmetric operators, B antisymmetric, and £ the Lagrangian displacement vector. We study this problem and the associated time evolution equation. We show that, in the Hilbert space H', whose norm is square-integration weighted by A, the operators A~lB and A~XC are anti-selfadjoint and selfadjoint, respectively, when restricted to vectors £ belonging to a particular but arbitrary axial harmonic. We then find bounds on the spectrum of normal modes and show that any initial data in the domain of C leads to a solution whose growth rate is limited by the spectrum and which can be expressed in a certain weak sense as a linear superposition of the normal modes. The normal modes are defined more precisely in terms of parallel projection operators associated with each isolated part of the spectrum. The quadratic eigenvalue problem can be reformulated in the space H' © ' (initial data space, or phase space) as a linear eigenvalue problem for an operator T, the generator of time evolution. This operator is not selfadjoint in H' © H' but it is selfadjoint in a Krein space (an indefinite inner-product space) formed by equipping H' © H' with the symplectic inner product. The normal modes are its eigenvectors and generalized eigenvectors.

scholarly journals DISSIPATIVE CONTRIBUTIONS TO ε′/ε

1999 ◽  
Vol 14 (22) ◽  
pp. 1519-1529 ◽  
Author(s):  
F. BENATTI ◽  
R. FLOREANINI
Keyword(s):  
Time Evolution ◽  
Neutral Kaon ◽  
Quantum Dynamical ◽  
Quantum Dynamical Semigroups ◽  
Standard Terms

The time evolution and decay of the neutral kaon system can be described using quantum dynamical semigroups. Non-standard terms appear in the expression of relevant observables; they can be parametrized in terms of six new phenomenological constants. We discuss how the presence of these constants affects the determination of the parameter ε′/ε.

scholarly journals Interplay of gravitation and linear superposition of different mass eigenstates

1998 ◽  
Vol 57 (8) ◽  
pp. 4724-4727 ◽  
Author(s):  
D. V. Ahluwalia ◽  
C. Burgard
Keyword(s):  
Linear Superposition ◽  
Mass Eigenstates

scholarly journals Quantum field-theoretical description of neutrino and neutral kaon oscillations

2018 ◽  
Vol 33 (13) ◽  
pp. 1850075 ◽  
Author(s):  
Igor P. Volobuev
Keyword(s):  
Plane Waves ◽  
Neutral Kaon ◽  
Theoretical Description ◽  
Matrix Formalism ◽  
Quantum Field ◽  
Time Intervals ◽  
Standard Quantum ◽  
Mass Eigenstates ◽  
Quantum Mechanical Description ◽  
S Matrix

It is shown that the neutrino and neutral kaon oscillation processes can be consistently described in quantum field theory using only plane waves of the mass eigenstates of neutrinos and neutral kaons. To this end, the standard perturbative S-matrix formalism is modified so that it can be used for calculating the amplitudes of the processes passing at finite distances and finite time intervals. The distance-dependent and time-dependent parts of the amplitudes of the neutrino and neutral kaon oscillation processes are calculated and the results turn out to be in accordance with those of the standard quantum mechanical description of these processes based on the notion of neutrino flavor states and neutral kaon states with definite strangeness. However, the physical picture of the phenomena changes radically: now, there are no oscillations of flavor or definite strangeness states, but, instead of it, there is interference of amplitudes due to different virtual mass eigenstates.

scholarly journals Depth Biases in XBT Data Diagnosed Using Bathymetry Data

2011 ◽  
Vol 28 (2) ◽  
pp. 287-300 ◽  
Author(s):  
Simon A. Good
Keyword(s):  
Shallow Water ◽  
Time Evolution ◽  
Temporal Variations ◽  
Historical Record ◽  
Depth Information ◽  
Time Varying ◽  
Ocean Temperature ◽  
Alternative Method ◽  
Subsurface Ocean ◽  
Expendable Bathythermograph

Abstract Expendable bathythermograph (XBT) profiles are an important component of the historical record of subsurface ocean temperature. To correct for time-varying biases in these data, adjustments to XBT depths and/or temperatures have been proposed by a number of groups based on comparisons between XBT data and profiles recorded using other types of instruments. In this study, an alternative method for diagnosing biases has been developed that uses ocean depth information from the XBT profiles and from the General Bathymetry Chart of the Oceans (GEBCO) 30-arc-sec gridded bathymetry. This isolates any depth biases from additional, unrelated temperature biases. Corrections to depths obtained with this method for the Sippican T4 XBT follow a time evolution similar to that found in other studies that derived time-varying adjustments, but are relatively large during the 1980s. Similarities in the evolution of Sippican T7 XBT biases were also observed, but with differences in recent years. Corrections from a study that proposed non-time-varying adjustments were found to broadly remove the biases in the T4 depths but overcorrected the T7 data, with temporal variations in the biases remaining. For the Sippican T10 XBT a more detailed time evolution of depth biases has been obtained than was previously possible. Although corrections have also been derived for approximately 50% of the XBTs for which type and manufacturer are unknown, these should only be used with caution as this study necessarily focuses on shallow water and proportions of different XBT types in use there are not typical of the wider ocean.

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