Long tipping times of a quantum rod

2006 ◽  
Vol 84 (1) ◽  
pp. 19-36 ◽  
Author(s):  
Mark B Lundeberg ◽  
Mark RA Shegelski
Keyword(s):  
Quantum State ◽  
Schrodinger Equation ◽  
Center Of Mass ◽  
Edge Length ◽  
The Other ◽  
Late Time ◽  
Time Behaviour ◽  
Complex Energy ◽  
Energy Eigenstates ◽  
Quantum Rod

We calculate the tipping time of a quantum rod that has a height several times that of the edge length of its square base. We use an expression for the tipping time that has heuristic value, and gives the average time at which, upon measurement, the initially balanced rod is found to tip. We use two methods to calculate the tipping time. One method is to examine the "late time" behaviour of the quantum state of the center of mass of the rod by using an equation that has the form of the time-independent Schrödinger equation except that it involves a "complex energy." The other method uses energy resonances in the eigenstates of the Hamiltonian to determine the tipping time. We use the well-known Wentzel–Kramers–Brillouin approximation to calculate the energy eigenstates. With these methods, we obtain expressions for the tipping time that are valid for very long tipping times. PACS Nos.: 03.65.–w, 03.65.Xp

scholarly journals Jordan products of quantum channels and their compatibility

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Mark Girard ◽  
Martin Plávala ◽  
Jamie Sikora
Keyword(s):  
Quantum State ◽  
Sufficient Conditions ◽  
The Other ◽  
Independent Interest ◽  
Quantum Channels ◽  
Semidefinite Programs ◽  
Jordan Product ◽  
Marginal Problem ◽  
Jordan Products ◽  
Product Of Matrices

AbstractGiven two quantum channels, we examine the task of determining whether they are compatible—meaning that one can perform both channels simultaneously but, in the future, choose exactly one channel whose output is desired (while forfeiting the output of the other channel). Here, we present several results concerning this task. First, we show it is equivalent to the quantum state marginal problem, i.e., every quantum state marginal problem can be recast as the compatibility of two channels, and vice versa. Second, we show that compatible measure-and-prepare channels (i.e., entanglement-breaking channels) do not necessarily have a measure-and-prepare compatibilizing channel. Third, we extend the notion of the Jordan product of matrices to quantum channels and present sufficient conditions for channel compatibility. These Jordan products and their generalizations might be of independent interest. Last, we formulate the different notions of compatibility as semidefinite programs and numerically test when families of partially dephasing-depolarizing channels are compatible.

scholarly journals The late-time behaviour of vortic Bianchi type VIII universes

2006 ◽  
Vol 23 (9) ◽  
pp. 3017-3035 ◽  
Author(s):  
Sigbjørn Hervik ◽  
Woei Chet Lim
Keyword(s):  
Bianchi Type ◽  
Late Time ◽  
Time Behaviour ◽  
Type Viii

scholarly journals Multi-Bloch vector representation of the qutrit

2011 ◽  
Vol 11 (5&6) ◽  
pp. 361-373
Author(s):  
Pawel Kurzynski
Keyword(s):  
Quantum State ◽  
Quantum Systems ◽  
Quantum States ◽  
The Other ◽  
Two Dimensional ◽  
Bloch Vector ◽  
Vector Representation ◽  
Alternative Approach ◽  
Complete Set

An ability to describe quantum states directly by average values of measurement outcomes is provided by the Bloch vector. For an informationally complete set of measurements one can construct unique Bloch vector for any quantum state. However, not every Bloch vector corresponds to a quantum state. It seems that only for two-dimensional quantum systems it is easy to distinguish proper Bloch vectors from improper ones, i.e. the ones corresponding to quantum states from the other ones. I propose an alternative approach to the problem in which more than one vector is used. In particular, I show that a state of the qutrit can be described by the three qubit-like Bloch vectors.

scholarly journals Time Profile of the Neutrino Burst from the Supernova 1987A

1988 ◽  
Vol 108 ◽  
pp. 426-427
Author(s):  
Hideyuki Suzuki ◽  
Katsuhiko Sato
Keyword(s):  
Monte Carlo ◽  
Neutrino Flux ◽  
Supernova Explosion ◽  
Time Profile ◽  
The Other ◽  
Late Time ◽  
The Core ◽  
Supernova 1987A ◽  
Theoretical Predictions ◽  
First Time

SN1987A gave us the first opportunity to study the supernova core directly by providing us the neutrino signal from the core. The observational data of the neutrino flux detected by Kamiokande[1] and IMB[2] show surprisingly good agreements with the theoretical predictions as a whole[3,4]. The fundamental concept of the collapse driven supernova explosion is confirmed for the first time. On the other hand, there are some puzzles. The most peculiar feature of the data is the 7 seconds gap of the Kamiokande data. The first 8 events of Kamiokande were detected in 2 seconds, following the 7 seconds gap and the last 3 events in 4 seconds. Of course just only 7 seconds gap is not unnatural if small neutrino flux come. But there were detected 3 events after the gap. These 3 events may not be produced by the weak flux. We can estimate the time integrated luminosity of corresponding to the last 3 events and get the large value such as 7 · 1052erg [5]. Can we get out of this inconsistency, 3 events after the 7 seconds gap? If not, we may need to consider some nonstandard mechanism of the neutrino emission at the late time. In order to investigate the probability of the case in which there is a 7 seconds gap before 3 events, we have performed Monte Carlo simulations for the simple model of neutrino flux.

Thermoeconomic Diagnosis: Zooming Strategy Applied to Highly Complex Energy Systems: Part 1 — Detection and Localization of Anomalies

2002 ◽  
Author(s):  
Vittorio Verda ◽  
Luis Serra ◽  
Antonio Valero
Keyword(s):  
Inverse Problem ◽  
Complex Systems ◽  
Reference Conditions ◽  
Energy Systems ◽  
Combined Cycle ◽  
Operating Conditions ◽  
The Other ◽  
Complex Energy ◽  
Operational Diagnosis ◽  
Detection And Localization

This paper presents a summary of our most recent advances in Thermoeconomic Diagnosis, developed during the last three years [1–3], and how they can be integrated in a zooming strategy oriented towards the operational diagnosis of complex systems. In fact, this paper can be considered a continuation of the work presented at the International Conference ECOS’99 [4–6] in which the concepts of malfunction (intrinsic and induced) and dysfunction [7] were analyzed in detail. These concepts greatly facilitate and simplify the analysis, the understanding and the quantification of how the presence of an anomaly, or malfunction, affects the behavior of the other plant devices and of the whole system. However, what remains unresolved is the so-called inverse problem of diagnosing [3], i.e. given two states of the plant (actual and reference operating conditions), find the causes of deviation of the actual conditions with respect to the reference conditions. The present paper tackles this problem and describes significant advances in addressing how to locate the actual causes of malfunctions, based on the application of procedures for filtering induced effects that hide the real causes of degradation. In this paper a progressive zooming thermoeconomic diagnosis procedure, which allows one to concentrate the analysis in an ever more specific zone is described and applied to a combined cycle. In an accompanying paper (part 2 [8]) the accuracy of the diagnosis results is discussed, depending on choice of the thermoeconomic model.

scholarly journals The Modal-Hamiltonian Interpretation of Quantum Mechanics as a Kind of “Atomic” Interpretation

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Juan Sebastián Ardenghi ◽  
Olimpia Lombardi
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
Quantum State ◽  
The Other ◽  
Interpretation Of Quantum Mechanics ◽  
Modal Interpretation ◽  
Atomic Systems ◽  
Modal Interpretations ◽  
The One ◽  
The Relationship

Modal interpretations are non-collapse interpretations, where the quantum state of a system describes its possible properties rather than the properties that it actually possesses. Among them, the atomic modal interpretation (AMI) assumes the existence of a special set of disjoint systems that fixes the preferred factorization of the Hilbert space. The aim of this paper is to analyze the relationship between the AMI and our recently presented modal-hamiltonian interpretation (MHI), by showing that the MHI can be viewed as a kind of “atomic” interpretation in two different senses. On the one hand, the MHI provides a precise criterion for the preferred factorization of the Hilbert space into factors representing elemental systems. On the other hand, the MHI identifies the atomic systems that represent elemental particles on the basis of the Galilei group. Finally, we will show that the MHI also introduces a decomposition of the Hilbert space of any elemental system, which determines with precision what observables acquire definite actual values.

ASSISTED INFLATION

2002 ◽  
Vol 17 (20) ◽  
pp. 2755-2755
Author(s):  
A. A. COLEY ◽  
R. J. VAN DEN HOOGEN
Keyword(s):  
Perfect Fluid ◽  
Scalar Fields ◽  
Cosmological Models ◽  
Late Time ◽  
Time Behaviour ◽  
Field Curvature ◽  
Scaling Solution ◽  
Dynamical Properties ◽  
Spatially Homogeneous ◽  
Parameter Values

The dynamical properties of spatially homogeneous and isotropic cosmological models containing a barotropic perfect fluid and multiple scalar fields with independent exponential potentials is investigated. It is shown that the assisted inflationary scaling solution is the global late-time attractor for the parameter values for which the model is inflationary, even when curvature and barotropic matter are included. For all other parameter values the multi-field curvature scaling solution is the global late-time attractor (in these solutions the curvature is not dynamically negligible asymptotically). Consequently, in general all of the scalar fields in multi-field models with exponential potentials are non-negligible in late-time behaviour, contrary to what is commonly believed.

Takeoff Mechanics of the Double Backward Somersault

1990 ◽  
Vol 6 (2) ◽  
pp. 177-186 ◽  
Author(s):  
Inseong Hwang ◽  
Gukung Seo ◽  
Zhi Cheng Liu
Keyword(s):  
Angular Momentum ◽  
Total Angular Momentum ◽  
Dominant Role ◽  
Center Of Mass ◽  
Velocity Curve ◽  
The Other ◽  
Transverse Axis ◽  
Angular Momenta ◽  
Total Body ◽  
Direction Opposite

This study examined the biomechanical profiles of the takeoff phase of double backward somersaults in three flight positions: seven layout double backward somersaults (L), seven twisting double backward somersaults (TW), and seven tucked double backward somersaults (TDB). Selected kinematic variables and angular momenta were calculated in order to compare the differences resulting from different aerial maneuvers. The amount of total body angular momentum about the transverse axis through the gymnasts' center of mass progressively increased from TDB to TW to L. The gymnasts performing the skill in the layout position tried to minimize the angle of block in a direction opposite the intended motion by maximizing the angle of touchdown and takeoff. In so doing, the horizontal velocity center-of-mass curve of the L showed a slowly decreasing curve compared with those of the other two somersaults while the vertical velocity curve of the L increased more slowly than the other curves during the takeoff phase. In all cases the legs played the dominant role in contributing to total angular momentum during takeoff.

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