108,308 research outputs found
New Perspectives on the Aharonov-Bohm Effect
No full textThe Aharonov-Bohm effect is a quantum mechanical effect, that is, has no classical counterpart. The effect was predicted in 1959 in a seminal paper of Y. Aharonov and D. Bohm [AB59] in which they demonstrated that a beam of electrons is affected by the existence of the electric/magnetic field even though electrons travel through field-free regions. Aharonov and Bohm carried out two hypothetical experiments to support their claim that potentials are more fundamental than fields and they are responsible of the effect. Since then, the debate has arisen around whether potentials are mathematical tools or fundamental entities in physics. Different arguments have been set to explain the results predicted by Aharonov and Bohm and experimentally confirmed. Amongst these arguments, the first argument adopted by Aharonov and Bohm was that potentials are physically significant. Many have claimed that fields do have non-local features, i.e. action at a distance. Others have claimed that topological effects
may interpret the effect in which potentials are modeled as connections in higher-dimensional fiber bundle geometries. The most recent argument has been proposed by Vaidman [Vai12] who claimed that the the composite system is represented by one state, an entangled state, and due to the electromagnetic interactions part of this state is changed, hence, the total state. In the present essay, I will discuss the latter argument as well as reviewing some other arguments
Locality, Lorentz invariance and the Bohm model
No full textNon-local forces exist in nature for two reasons. First that the recent experiments on locality are supposed to be accurate enough. Second that there is no local theory that can reproduce all the predictions of orthodox quantum theory which, almost for about a century, have been proved to be correct experimentally again and again. This thesis concerns both of these. A brief discussion of the measurement in quantum theory is followed by two comments which show that the quantum description is frame dependent and that the collapse of the wave-function of a system may occur without the relevant measurement being performed. After this the Bohm model and a modified version of the Bohm model are described. Next we introduce a new method for obtaining the Bell-type inequalities which can be used for testing locality. We derive more inequalities by this method than obtained by other existing procedures. Using Projection Valued(PV) and Positive Operator Valued Measures(POVM) measurements we have designed experiments which violates one of the Bell inequalities by a larger factor than existing violations which in turn could increase the accuracy of experiments to test for non-locality. This is our first result. After discussing the non-locality and non-Lorentz invariant features of the Bohm model, its retarded version, namely Squires' model - which is local and Lorentz invariant - is introduced. A problem with this model, that is the ambiguity in the cases where the wave-function depends on time, is removed by using the multiple-time wave-function. Finally, we apply the model to one of the experiments of locality and prove that it is in good agreement with the orthodox quantum theory
Why the De Broglie-Bohm Theory Goes Astray
No full textWe show that the de Broglie-Bohm theory is inconsistent with the established parts of quantum mechanics concerning its physical content. According to the de Broglie-Bohm theory, the mass and charge of an electron are localized in a position where its Bohmian particle is. However, protective measurement implies that they are not localized in one position but distributed throughout space, and the mass and charge density of the electron in each position is proportional to the modulus square of its wave function there
Solving the measurement problem: de Broglie-Bohm loses out to Everett
No full textThe quantum theory of de Broglie and Bohm solves the measurement problem, but the hypothetical corpuscles play no role in the argument. The solution finds a more natural home in the Everett interpretation
Is the electron's charge 2e? A problem of the de Broglie-Bohm theory
No full textIt is shown that the de Broglie-Bohm theory has a potential problem concerning the charge distribution of a quantum system such as an electron. According to the guidance equation of the theory, the electron's charge is localized in a position where its Bohmian particle is. But according to the Schrödinger equation of the theory, the electron's charge is not localized in one position but distributed throughout space, and the charge density in each position is proportional to the modulus square of the wave function of the electron there. Although this tension may be resolved by assuming that the electron's charge is not e but 2e, one for its Bohmian particle and the other for its wave function, the resolution will introduce more serious problems
Protective measurements and the meaning of the wave function in the de Broglie-Bohm theory
No full textThere are three possible interpretations of the wave function in the de Broglie-Bohm theory: taking the wave function as corresponding to a physical entity or a property of the Bohmian particles or a law. In this paper, we argue that the first interpretation is favored by an analysis of protective measurements
Chiral solitons with bohm potential using G' /G method and exp-function method
No full textThis paper studies the chiral nonlinear Schrödinger's equation with Bohm potential. There are two approaches that are used to carry out the integration of the governing equation. They are the G' /G method and the exp-function method. Finally the traveling wave hypothesis is used to obtain solution in terms of doubly periodic function where in the limiting case topological soliton solutions are retrieved
Aharonov–Bohm superselection sectors
No full textWe show that the Aharonov–Bohm effect finds a natural description in the setting of QFT on curved spacetimes in terms of superselection sectors of local observables. The extension of the analysis of superselection sectors from Minkowski spacetime to an arbitrary globally hyperbolic spacetime unveils the presence of a new quantum number labelling charged superselection sectors. In the present paper, we show that this “topological” quantum number amounts to the presence of a background flat potential which rules the behaviour of charges when transported along paths as in the Aharonov–Bohm effect. To confirm these abstract results, we quantize the Dirac field in the presence of a background flat potential and show that the Aharonov–Bohm phase gives an irreducible representation of the fundamental group of the spacetime labelling the charged sectors of the Dirac field. We also show that non-Abelian generalizations of this effect are possible only on spacetimes with a non-Abelian fundamental group
CHIRAL SOLITONS WITH BOHM POTENTIAL USING G '/G METHOD AND EXP-FUNCTION METHOD
No full textThis paper studies the chiral nonlinear Schrodinger's equation with Bohm potential. There are two approaches that are used to carry out the integration of the governing equation. They are the G'/G method and the exp-function method. Finally the traveling wave hypothesis is used to obtain solution in terms of doubly periodic function where in the limiting case topological soliton solutions are retrieved
Pre-torsors and Galois comodules over mixed distributive laws
No full textWe study comodule functors for comonads arising from mixed distributive laws. Their Galois property is reformulated in terms of a (so-called) regular arrow in Street's bicategory of comonads. Between categories possessing equalizers, we introduce the notion of a regular adjunction. An equivalence is proven between the category of pre-torsors over two regular adjunctions (N A, RA) and (NB, RB) on one hand, and the category of regular comonad arrows (RA, ξ) from some equalizer preserving comonad C to NBRB on the other. This generalizes a known relationship between pre-torsors over equal commutative rings and Galois objects of coalgebras. Developing a bi-Galois theory of comonads, we show that a pre-torsor over regular adjunctions determines also a second (equalizer preserving) comonad D and a coregular comonad arrow from D to NARA, such that the comodule categories of C and D are equivalent. © 2009 Springer Science + Business Media B.V
- …
