Framework Of Quantum Mechanics Research Articles

Statistical properties of the q-deformed relativistic Dirac oscillator in minimal length quantum mechanics

In this article, we introduce a two-dimensional Dirac oscillator in the presence of an external magnetic field in terms of q-deformed creation and annihilation operators in the framework of relativistic quantum mechanics with minimal length. We discuss the eigenvalues of q-deformed Dirac oscillator in two dimensions and report the statistical quantities of the system for a small real q.

Quark-Parton Model and Relativistic Quantum Mechanics

An attempt to treat the asymptotic freedom and the quark confinement as a self-consistent problem in the framework of relativistic quantum mechanics is realized. It is shown that the confinement of quarks induces a change of their helicities together with a simultaneous alteration of orbital momenta, so that the total angular momentum of each quark is conserved. This observation may cast light on the so-called proton spin puzzle after some additional numerical estimations.

Hamiltonian Mechanical System with Split Quaternions

In this article, firstly we study about geometrical applications of split quaternions. Then, we obtain Hamitonian mechanical systems with Split quaternions. Quaternionic and Coquaternionic (split analoque of quaternions) extensions of Hamiltonian mechanics are introduced and are shown as offer a unifying framework for quantum mechanics. This study leads to the possibility of employing algebraic techniques of quaternions and coquaternions to absorbing in quantum mechanics. The founded equations are compared with the Hamiltonian energy equations generally are known and the Hamilton energy equations are obtained in Minkowski space.

CRYPTO-HERMITIAN APPROACH TO THE KLEIN–GORDON EQUATION

We explore the Klein-Gordon equation in the framework of crypto-Hermitian quantum mechanics. Solutions to common problems with probability interpretation and indefinite inner product of the Klein-Gordon equation are proposed.

Bianchi I model as a prototype for a cyclical Universe

We analyze the dynamics of the Bianchi I model in the presence of stiff matter, an ultrarelativistic component and a small negative cosmological constant. We quantize this model in the framework of the polymer quantum mechanics, in order to introduce cut-off features in the minisuperspace dynamics.We then apply to the polymer Wheeler–DeWitt equation, emerging from the Dirac constraint, an adiabatic approximation a la Vilenkin, which treats the Universe volume as a quasi-classical variable, becoming de facto the dynamical clock for the pure quantum degrees of freedom, here identified in the Universe anisotropies.The main issue of the present analysis consists of determining a cyclical evolution for the Bianchi I model, oscillating between the Big-Bounce induced by the cut-off physics and the turning point due to the small cosmological constant. Furthermore, the mean value of the Universe anisotropy variables remains finite during the whole evolution, including the phase across the Big-Bounce. Such a feature, according to a suitable choice of the initial conditions makes the present cosmological paradigm, a viable scenario for the description of a possible primordial and late phases of the actual Universe.

Spin Entanglement Witness for Quantum Gravity.

Understanding gravity in the framework of quantum mechanics is one of the great challenges in modern physics. However, the lack of empirical evidence has lead to a debate on whether gravity is a quantum entity. Despite varied proposed probes for quantum gravity, it is fair to say that there are no feasible ideas yet to test its quantum coherent behavior directly in a laboratory experiment. Here, we introduce an idea for such a test based on the principle that two objects cannot be entangled without a quantum mediator. We show that despite the weakness of gravity, the phase evolution induced by the gravitational interaction of two micron size test masses in adjacent matter-wave interferometers can detectably entangle them even when they are placed far apart enough to keep Casimir-Polder forces at bay. We provide a prescription for witnessing this entanglement, which certifies gravity as a quantum coherent mediator, through simple spin correlation measurements.

Proposed physical explanation for the electron spin and related antisymmetry

We offer a possible physical explanation for the origin of the electron spin and the related antisymmetry of the wave function for a two-electron system, in the framework of nonrelativistic quantum mechanics as provided by linear stochastic electrodynamics. A consideration of the separate coupling of the electron to circularly polarized modes of the random electromagnetic vacuum field, allows to disclose the spin angular momentum and the associated magnetic moment with a $g$-factor 2, and to establish the connection with the usual operator formalism. The spin operator turns out to be the generator of internal rotations, in the corresponding coordinate representation. In a bipartite system, the distinction between exchange of particle coordinates (which include the internal rotation angle) and exchange of states becomes crucial. Following the analysis of the respective symmetry properties, the electrons are shown to couple in antiphase to the same vacuum field modes. This finding, encoded in the antisymmetry of the wave function, provides a physical rationale for the Pauli principle. The extension of our results to a multipartite system is briefly discussed.

New Physical Mechanism for Lightning

The article is devoted to electromagnetic phenomena in the atmosphere. The set of experimental data on the thunderstorm activity is analyzed. It helps to identify a possible physical mechanism of lightning flashes. This mechanism can involve the formation of metallic bonds in thunderclouds. The analysis of the problem is performed at a microphysical level within the framework of quantum mechanics. The mechanism of appearance of metallic conductivity includes the resonant tunneling of electrons along resonance-percolation trajectories. Such bonds allow the charges from the vast cloud charged subsystems concentrate quickly in lightning channel. The formation of metal bonds in the thunderstorm cloudiness is described as the second-order phase transition. A successive mechanism for the process of formation and development of the lightning channel is suggested. This mechanism is associated with the change in the orientation of crystals in growing electric field. Possible consequences of the quantum-mechanical mechanism under discussion are compared with the results of observations.

Non-self-adjoint Schrödinger operators with nonlocal one-point interactions

We generalize and study, within the framework of quantum mechanics and working with 1-dimensional, manifestly non-Hermitian Hamiltonians H=−d2/dx2+V, the traditional class of exactly solvable models with local point interactions V=V(x). We discuss the consequences of the use of nonlocal point interactions such that (Vf)(x)=∫K(x,s)f(s)ds by means of the suitably adapted formalism of boundary triplets.

On the spin-statistics theorem

The possibility of proving the theorem on the connection between spin and statistics in the nonrelativistic quantum mechanical framework is examined.

Emergent Quantum Mechanics and the Origin of Quantum Non-local Correlations

A geometric interpretation for quantum correlations and entanglement according to a particular framework of emergent quantum mechanics is developed. The mechanism described is based on two ingredients: 1. At an hypothetical sub-quantum level description of physical systems, the dynamics has a regime where it is partially ergodic and 2. A formal projection from a two-dimensional time mathematical formalism of the emergent quantum theory to the usual one-dimensional time formalism of quantum dynamics. Observable consequences of the theory are obtained. Among them we show that quantum correlations must be instantaneous from the point of view of the spacetime description, but the spatial distance up to which they can be observed must be bounded. It is argued how our mechanism avoids Bell theorem and Kochen-Specken theorem. Evidence for non-signaling faster than the speed of light in our proposal is discussed.

Radiative corrections to false vacuum decay in quantum mechanics

We consider radiative corrections to false vacuum decay within the framework of quantum mechanics for the general potential of the form 1/2 M q^2 (q-A)(q-B), where M , A and B are arbitrary parameters. For this type of potential we provide analytical results for Green function in the background of corresponding bounce solution together with one loop expression for false vacuum decay rate. Next, we discuss the computation of higher order corrections for false vacuum decay rate and provide numerical expressions for two and three loop contributions.

Quantization, Frobenius and Bi Algebras from the Categorical Framework of Quantum Mechanics to Natural Language Semantics

Compact Closed categories and Frobenius and Bi algebras have been applied to model and reason about Quantum protocols. The same constructions have also been applied to reason about natural language semantics under the name: ``categorical distributional compositional'' semantics, or in short, the ``DisCoCat'' model. This model combines the statistical vector models of word meaning with the compositional models of grammatical structure. It has been applied to natural language tasks such as disambiguation, paraphrasing and entailment of phrases and sentences. The passage from the grammatical structure to vectors is provided by a functor, similar to the Quantization functor of Quantum Field Theory. The original DisCoCat model only used compact closed categories. Later, Frobenius algebras were added to it to model long distance dependancies such as relative pronouns. Recently, bialgebras have been added to the pack to reason about quantifiers. This paper reviews these constructions and their application to natural language semantics. We go over the theory and present some of the core experimental results.

Hydrogen behaviour at twist {110} grain boundaries in α-Fe.

The behaviour of hydrogen at structural defects such as grain boundaries plays a critical role in the phenomenon of hydrogen embrittlement. However, characterization of the energetics and diffusion of hydrogen in the vicinity of such extended defects using conventional ab initio techniques is challenging due to the relatively large system sizes required when dealing with realistic grain boundary geometries. In order to be able to access the required system sizes, as well as high-throughput testing of a large number of configurations, while remaining within a quantum-mechanical framework, an environmental tight-binding model for the iron-hydrogen system has been developed. The resulting model is applied to study the behaviour of hydrogen at a class of low-energy {110}-terminated twist grain boundaries in α-Fe. We find that, for particular Σ values within the coincidence site lattice description, the atomic geometry at the interface plane provides extremely favourable trap sites for H, which also possess high escape barriers for diffusion. By contrast, via simulated tensile testing, weakly trapped hydrogen at the interface plane of the bulk-like Σ3 boundary acts as a 'glue' for the boundary, increasing both the energetic barrier and the elongation to rupture.This article is part of the themed issue 'The challenges of hydrogen and metals'.

Relativistic Hydrogen-Like Atom on a Noncommutative Phase Space

The energy levels of hydrogen-like atom on a noncommutative phase space were studied in the framework of relativistic quantum mechanics. The leading order corrections to energy levels 2S 1/2, 2P 1/2 and 2P 3/2 were obtained by using the 𝜃 and the $\bar \theta $ modified Dirac Hamiltonian of hydrogen-like atom on a noncommutative phase space. The degeneracy of the energy levels 2P 1/2 and 2P 3/2 were removed completely by 𝜃-correction. And the $\bar \theta $ -correction shifts these energy levels.

Time fractional quantum mechanics

A time fractional quantum framework has been introduced into quantum mechanics. A new version of the space-time fractional Schrödinger equation has been launched. The introduced space-time fractional Schrödinger equation has a new scale parameter, which is a time fractional generalization of Planck’s constant in quantum physics.It has been shown that the presence of a fractional time derivative in the space-time fractional Schrödinger equation significantly impacts quantum mechanical fundamentals.Time fractional quantum mechanical operators of coordinate, momentum and angular momentum were defined and their commutation relationships were established. The pseudo-Hamilton operator was introduced and its Hermicity has been proven.Two new functions related to the Mittag-Leffler function have been introduced to solve the space-time fractional Schrödinger equation. Energy of a time fractional quantum system has been defined and calculated in terms of the newly introduced functions. It has been found that in the framework of time fractional quantum mechanics there are no stationary states, and the eigenvalues of the pseudo-Hamilton operator are not the energy levels of the time fractional quantum system.A free particle solution to the space-time fractional Schrödinger equation was found. A free particle space-time fractional quantum mechanical kernel has been found and expressed in terms of the H-function. Renormalization properties of a free particle solution and the space-time fractional quantum kernel were established.Some particular cases of time fractional quantum mechanics have been analyzed and discussed.

Rapidly oscillating scatteringless non-Hermitian potentials and the absence of Kapitza stabilization

In the framework of the ordinary non-relativistic quantum mechanics, it is known that a quantum particle in a rapidly oscillating bound potential with vanishing time average can be scattered off or even trapped owing to the phenomenon of dynamical (Kapitza) stabilization. A similar phenomenon occurs for scattering and trapping of optical waves. Such a remarkable result stems from the fact that, even though the particle is not able to follow the rapid external oscillations of the potential, these are still able to affect the average dynamics by means of an effective —albeit small— nonvanishing potential contribution. Here we consider the scattering and dynamical stabilization problem for matter or classical waves by a bound potential with oscillating ac amplitude f(t) in the framework of a non-Hermitian extension of the Schrödinger equation, and predict that for a wide class of imaginary amplitude modulations f(t) possessing a one-sided Fourier spectrum, the oscillating potential is effectively canceled, i.e., it does not have any effect on the particle dynamics, contrary to what happens in the Hermitian case.

Obtaining tight bounds on higher-order interferences with a 5-path interferometer

Within the established theoretical framework of quantum mechanics, interference always occurs between pairs of paths through an interferometer. Higher order interferences with multiple constituents are excluded by Born’s rule and can only exist in generalized probabilistic theories. Thus, high-precision experiments searching for such higher order interferences are a powerful method to distinguish between quantum mechanics and more general theories. Here, we perform such a test in an optical multi-path interferometer, which avoids crucial systematic errors, has access to the entire phase space and is more stable than previous experiments. Our results are in accordance with quantum mechanics and rule out the existence of higher order interference terms in optical interferometry to an extent that is more than four orders of magnitude smaller than the expected pairwise interference, refining previous bounds by two orders of magnitude.

Interpreting Quantum Logic as a Pragmatic Structure

Scholars have wondered for a long time whether the language of quantum mechanics introduces a quantum notion of truth which is formalized by quantum logic (QL) and is incompatible with the classical (Tarskian) notion. We show that QL can be interpreted as a pragmatic language of assertive formulas which formalize statements about physical systems that are empirically justified or unjustified in the framework of quantum mechanics. According to this interpretation, QL formalizes properties of the metalinguistic notion of empirical justification within quantum mechanics rather than properties of a quantum notion of truth. This conclusion agrees with a general integrationist perspective that interprets nonstandard logics as theories of metalinguistic notions different from truth, thus avoiding incompatibility with classical notions and preserving the globality of logic. By the way, some elucidations of the standard notion of quantum truth are also obtained. Key words: pragmatics, quantum logic, quantum mechanics, justifiability, global pluralism.

Quantum particle probe of the Kerr naked singularity

We investigate Kerr’s timelike naked singularity within the framework of quantum mechanics. A quantum particle in the form of a massive boson is sent in the plane \(\theta = \pi/2\) to the naked ring singularity of Kerr which develops for the overspinning case \((a>M)\) to test it from a quantum picture. This singularity is analysed in two different coordinate systems. We show that the spatial operator of the Klein-Gordon equation both in Boyer-Lindquist and in the dragging coordinate systems has a unique self-adjoint extension. As a result, the classical Kerr’s ring singularity becomes quantum regular, if it is probed with massive bosonic particles obeying the Klein-Gordon equation.