Algebraic function operator expectation value based quantum eigenstate determination: A case of twisted or bent Hamiltonian, or, a spatially univariate quantum system on a curved space

2015 ◽  
Author(s):  
N. A. Baykara
Keyword(s):  
Quantum System ◽  
Algebraic Function ◽  
Curved Space ◽  
Expectation Value

scholarly journals QUANTUM BACKREACTION (CASIMIR) EFFECT WITHOUT INFINITIES: ALGEBRAIC ANALYSIS

2012 ◽  
Vol 14 ◽  
pp. 376-382
Author(s):  
ANDRZEJ HERDEGEN
Keyword(s):  
Hilbert Space ◽  
Quantum Theory ◽  
Quantum System ◽  
Casimir Effect ◽  
Quantum Field ◽  
Expectation Value ◽  
Physical Systems ◽  
Algebra Of Observables ◽  
General Terms ◽  
External Conditions

Casimir effect, in most general terms, is the backreaction of a quantum system responding to an adiabatic change of external conditions. This backreaction is expected to be quantitatively measured by a change in the expectation value of a certain energy observable of the system. However, for this concept to be applicable, the system has to retain its identity in the process. Most prevailing tendencies in the analysis of the effect seem to ignore this question. In general, a quantum theory is defined by an algebra of observables, whose representations by operators in a Hilbert space define concrete physical systems described by the theory. A quantum system retains its identity if both the algebra as well as its representation do not change. We discuss the resulting restrictions for admissible models of changing external conditions. These ideas are applied to quantum field models. No infinities arise, if the algebraic demands are respected.

scholarly journals Entropic Characterization of Quantum States with Maximal Evolution under Given Energy Constraints

Entropy ◽  
2019 ◽  
Vol 21 (8) ◽  
pp. 770 ◽  
Author(s):  
Ana P. Majtey ◽  
Andrea Valdés-Hernández ◽  
César G. Maglione ◽  
Angel R. Plastino
Keyword(s):  
Energy Distribution ◽  
Variational Problem ◽  
Quantum System ◽  
Dynamical Evolution ◽  
Quantum States ◽  
Time Interval ◽  
Expectation Value ◽  
Energy Constraints ◽  
Pure Quantum State

A measure D [ t 1 , t 2 ] for the amount of dynamical evolution exhibited by a quantum system during a time interval [ t 1 , t 2 ] is defined in terms of how distinguishable from each other are, on average, the states of the system at different times. We investigate some properties of the measure D showing that, for increasing values of the interval’s duration, the measure quickly reaches an asymptotic value given by the linear entropy of the energy distribution associated with the system’s (pure) quantum state. This leads to the formulation of an entropic variational problem characterizing the quantum states that exhibit the largest amount of dynamical evolution under energy constraints given by the expectation value of the energy.

Correlation analysis of radiation damage

1978 ◽  
Vol 36 (1) ◽  
pp. 214-215
Author(s):  
R. Hegerl ◽  
A. Feltynowski ◽  
B. Grill
Keyword(s):  
Electron Microscopy ◽  
Independent Random Variables ◽  
Optical Parameters ◽  
Bright Field Image ◽  
Bright Field ◽  
Expectation Value ◽  
All Optical ◽  
Image Element ◽  
Stochastic Series ◽  
The Common

Till now correlation functions have been used in electron microscopy for two purposes: a) to find the common origin of two micrographs representing the same object, b) to check the optical parameters e. g. the focus. There is a third possibility of application, if all optical parameters are constant during a series of exposures. In this case all differences between the micrographs can only be caused by different noise distributions and by modifications of the object induced by radiation.Because of the electron noise, a discrete bright field image can be considered as a stochastic series Pm,where i denotes the number of the image and m (m = 1,.., M) the image element. Assuming a stable object, the expectation value of Pm would be Ηm for all images. The electron noise can be introduced by addition of stationary, mutual independent random variables nm with zero expectation and the variance. It is possible to treat the modifications of the object as a noise, too.

DISORDER AS PROJECTION FROM IDEAL, CURVED SPACE

1985 ◽  
Vol 46 (C8) ◽  
pp. C8-409-C8-413
Author(s):  
N. Rivier ◽  
A. Lawrence
Keyword(s):  
Curved Space

GRAVITY CAN BE OBSERVED IN THE ABSENCE OF CURVED SPACETIME, THUS CURVED SPACETIME IS NOT RESPONCIBLE FOR GRAVITY

2015 ◽  
Vol 8 (1) ◽  
pp. 1976-1981
Author(s):  
Casey McMahon
Keyword(s):  
General Relativity ◽  
Special Relativity ◽  
Relative Position ◽  
Gravitational Force ◽  
Curved Spacetime ◽  
Relative Time ◽  
Curved Space ◽  
Spacetime Curvature ◽  
Equivalence Model ◽  
The Universe

The principle postulate of general relativity appears to be that curved space or curved spacetime is gravitational, in that mass curves the spacetime around it, and that this curved spacetime acts on mass in a manner we call gravity. Here, I use the theory of special relativity to show that curved spacetime can be non-gravitational, by showing that curve-linear space or curved spacetime can be observed without exerting a gravitational force on mass to induce motion- as well as showing gravity can be observed without spacetime curvature. This is done using the principles of special relativity in accordance with Einstein to satisfy the reader, using a gravitational equivalence model. Curved spacetime may appear to affect the apparent relative position and dimensions of a mass, as well as the relative time experienced by a mass, but it does not exert gravitational force (gravity) on mass. Thus, this paper explains why there appears to be more gravity in the universe than mass to account for it, because gravity is not the resultant of the curvature of spacetime on mass, thus the “dark matter” and “dark energy” we are looking for to explain this excess gravity doesn’t exist.

Global symmetries and Noether’s theorem

2018 ◽  
Author(s):  
Michael Kachelriess
Keyword(s):  
Global Symmetries ◽  
Symmetry Transformation ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Quantum Field ◽  
Expectation Value ◽  
Minkowski Space Time ◽  
Integral Measure ◽  
Colour Charge ◽  
Internal Symmetries

Noethers theorem shows that continuous global symmetries lead classically to conservation laws. Such symmetries can be divided into spacetime and internal symmetries. The invariance of Minkowski space-time under global Poincaré transformations leads to the conservation of the four-momentum and the total angular momentum. Examples for conserved charges due to internal symmetries are electric and colour charge. The vacuum expectation value of a Noether current is shown to beconserved in a quantum field theory if the symmetry transformation keeps the path-integral measure invariant.

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