Supersymmetric quantum mechanics and the equivalent classical transformation

In the usual supersymmetric quantum mechanics, the supercharges change the eigenfunction from the bosonic to fermionic sector and conversely. The classical correspondent of this transformation is shown to be the addition of a total time derivative of a purely imaginary function to the Lagrangian function of the system.

Induced variational method from supersymmetric quantum mechanics and the screened Coulomb potential

The formalism of supersymmetric quantum mechanics supplies a trial wave function to be used in the variational method. The screened Coulomb potential is analyzed within this approach. Numerical and exact results for energy eigenvalues are compared.

Confined systems through variational supersymmetric quantum mechanics

The energy states of the confined harmonic oscillator and the Hulthén potentials are evaluated using the Variational Method associated to Supersymmetric Quantum Mechanics.

Merging higher derivative gravity and quantum mechanics

The most general quantum mechanical wave equation for a massive scalar particle in a metric generated by a spherically symmetric mass distribution is considered within the framework of higher derivative gravity (HDG). The exact effective Hamiltonian is constructed and the significance of the various terms is discussed using the linearized version of the above-mentioned theory. Not only does this analysis shed new light on the long standing problem of quantum gravity concerning the exact nature of the coupling between a massive scalar field and the background geometry, it also greatly improves our understanding of the role of HDG's coupling parameters in semiclassical calculations.

Is the equivalence principle doomed forever to Dante's Inferno on account of quantum mechanics?

It is commonly assumed that the equivalence principle can coexist without conflict with quantum mechanics. We shall argue here that, contrary to popular belief, this principle does not hold in quantum mechanics. We illustrate this point by computing the second-order correction for the scattering of a massive scalar boson by a weak gravitational field, treated as an external field. The resulting cross-section turns out to be mass-dependent. A way out of this dilemma would be, perhaps, to consider gravitation without the equivalence principle. At first sight, this seems to be a too much drastic attitude toward general relativity. Fortunately, the teleparallel version of general relativity - a description of the gravitational interaction by a force similar to the Lorentz force of electromagnetism and that, of course, dispenses with the equivalence principle - is equivalent to general relativity, thus providing a consistent theory for gravitation in the absence of the aforementioned principle. © World Scientific Publishing Company.

Conflict between the classical equivalence principle and quantum mechanics

As far as external gravitational fields described by Newton's theory are concerned, theory shows that there is an unavoidable conflict between the universality of free fall (Galileo's equivalence principle) and quantum mechanics - a result confirmed by experiment. Is this conflict due perhaps to the use of Newton's gravity, instead of general relativity, in the analysis of the external gravitational field? The response is negative. To show this we compute the low corrections to the cross-section for the scattering of different quantum particles by an external gravitational field, treated as an external field, in the framework of Einstein's linearized gravity. To first order the cross-sections are spin-dependent; if the calculations are pushed to the next order they become dependent upon energy as well. Therefore, the Galileo's equivalence and, consequently, the classical equivalence principle, is violated in both cases. We address these issues here.

Aspects of classical and quantum motion on a flux cone

Motion of a nonrelativistic particle on a cone with a magnetic flux running through the cone axis (a flux cone) is studied. It is expressed as the motion of a particle moving on the Euclidean plane under the action of a velocity-dependent force. The probability fluid (quantum flow) associated with a particular stationary state is studied close to the singularity, demonstrating nontrivial Aharonov-Bohm effects. For example, it is shown that, near the singularity, quantum flow departs from classical flow. In the context of the hydrodynamical approach to quantum mechanics, quantum potential due to the conical singularity is determined, and the way it affects quantum flow is analyzed. It is shown that the winding number of classical orbits plays a role in the description of the quantum Bow. The connectivity of the configuration space is also discussed.

Time evolution of the Wigner function in discrete quantum phase space for a soluble quasi-spin model

The discrete phase space approach to quantum mechanics of degrees of freedom without classical counterparts is applied to the many-fermions/quasi-spin Lipkin model. The Wi:ner function is written for some chosen states associated to discrete angle and angular momentum variables, and the rime evolution is numerically calculated using the discrete von Neumnnn-Liouville equation. Direct evidences in the lime evolution of the Wigner function are extracted that identify a tunnelling effect. A connection with a SU(2)-based semiclassical continuous approach to the Lipkin model is also presented.

Quantum topology change and large-N gauge theories

We study a model for dynamical localization of topology using ideas from non-commutative geometry and topology in quantum mechanics. We consider a collection X of N one-dimensional manifolds and the corresponding set of boundary conditions (self-adjoint extensions) of the Dirac operator D. The set of boundary conditions encodes the topology and is parameterized by unitary matrices g. A particular geometry is described by a spectral triple x(g) = (A X, script H sign X, D(g)). We define a partition function for the sum over all g. In this model topology fluctuates but the dimension is kept fixed. We use the spectral principle to obtain an action for the set of boundary conditions. Together with invariance principles the procedure fixes the partition function for fluctuating topologies. The model has one free-parameter β and it is equivalent to a one plaquette gauge theory. We argue that topology becomes localized at β = ∞ for any value of N. Moreover, the system undergoes a third-order phase transition at β = 1 for large-N. We give a topological interpretation of the phase transition by looking how it affects the topology. © SISSA/ISAS 2004.

Gravity and the quantum: Are they reconcilable?

General relativity and quantum mechanics are not consistent with each other. This conflict stems from the very fundamental principles on which these theories are grounded. General relativity, on one hand, is based on the equivalence principle, whose strong version establishes the local equivalence between gravitation and inertia. Quantum mechanics, on the other hand, is fundamentally based on the uncertainty principle, which is essentially nonlocal. This difference precludes the existence of a quantum version of the strong equivalence principle, and consequently of a quantum version of general relativity. Furthermore, there are compelling experimental evidences that a quantum object in the presence of a gravitational field violates the weak equivalence principle. Now it so happens that, in addition to general relativity, gravitation has an alternative, though equivalent, description, given by teleparallel gravity, a gauge theory for the translation group. In this theory torsion, instead of curvature, is assumed to represent the gravitational field. These two descriptions lead to the same classical results, but are conceptually different. In general relativity, curvature geometrizes the interaction while torsion, in teleparallel gravity, acts as a force, similar to the Lorentz force of electrodynamics. Because of this peculiar property, teleparallel gravity describes the gravitational interaction without requiring any of the equivalence principle versions. The replacement of general relativity by teleparallel gravity may, in consequence, lead to a conceptual reconciliation of gravitation with quantum mechanics. © 2006 American Institute of Physics.

De Sitter relativity and quantum physics

In the presence of a cosmological constant, interpreted as a purely geometric entity, absence of matter is represented by a de Sitter spacetime. As a consequence, ordinary Poincaré special relativity is no longer valid and must be replaced by a de Sitter special relativity. By considering the kinematics of a spinless particle in a de Sitter spacetime, we study the geodesics of this spacetime, the ensuing definitions of canonical momenta, and explore possible implications for quantum mechanics. © 2007 American Institute of Physics.

Non-Markovian expansion in quantum Brownian motion

We consider the non-Markovian Langevin evolution of a dissipative dynamical system in quantum mechanics in the path integral formalism. After discussing the role of the frequency cutoff for the interaction of the system with the heat bath and the kernel and noise correlator that follow from the most common choices, we derive an analytic expansion for the exact non-Markovian dissipation kernel and the corresponding colored noise in the general case that is consistent with the fluctuation-dissipation theorem and incorporates systematically non-local corrections. We illustrate the modifications to results obtained using the traditional (Markovian) Langevin approach in the case of the exponential kernel and analyze the case of the non-Markovian Brownian motion. We present detailed results for the free and the quadratic cases, which can be compared to exact solutions to test the convergence of the method, and discuss potentials of a general nonlinear form. © 2013 Elsevier B.V. All rights reserved.

Entropy effect in quantum computing and information: an open-source environment simulation

The technologies are rapidly developing, but some of them present in the computers, as for instance their processing capacity, are reaching their physical limits. It is up to quantum computation offer solutions to these limitations and issues that may arise. In the field of information security, encryption is of paramount importance, being then the development of quantum methods instead of the classics, given the computational power offered by quantum computing. In the quantum world, the physical states are interrelated, thus occurring phenomenon called entanglement. This study presents both a theoretical essay on the merits of quantum mechanics, computing, information, cryptography and quantum entropy, and some simulations, implementing in C language the effects of entropy of entanglement of photons in a data transmission, using Von Neumann entropy and Tsallis entropy.

Quantum confinement in hydrogen bond

In this work, the quantum confinement effect is proposed as the cause of the displacement of the vibrational spectrum of molecular groups that involve hydrogen bonds. In this approach, the hydrogen bond imposes a space barrier to hydrogen and constrains its oscillatory motion. We studied the vibrational transitions through the Morse potential, for the NH and OH molecular groups inside macromolecules in situation of confinement (when hydrogen bonding is formed) and nonconfinement (when there is no hydrogen bonding). The energies were obtained through the variational method with the trial wave functions obtained from supersymmetric quantum mechanics formalism. The results indicate that it is possible to distinguish the emission peaks related to the existence of the hydrogen bonds. These analytical results were satisfactorily compared with experimental results obtained from infrared spectroscopy. (c) 2015 Wiley Periodicals, Inc.

Quantum confinement in hydrogen bond of DNA and RNA

The hydrogen bond is a fundamental ingredient to stabilize the DNA and RNA macromolecules. The main contribution of this work is to describe quantitatively this interaction as a consequence of the quantum confinement of the hydrogen. The results for the free and confined system are compared with experimental data. The formalism to compute the energy gap of the vibration motion used to identify the spectrum lines is the Variational Method allied to Supersymmetric Quantum Mechanics.