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.

Quantum Mechanics Insight into the Microwave Nucleation of SrTiO3 Nanospheres

An extensive investigation of strontium titanate, SrTiO3 (STO), nanospheres synthesized via a microwave-assisted hydrothermal (MAH) method has been conducted to gain a better insight into thermodynamic, kinetic, and reaction phenomena involved in STO nucleation and crystal growth processes. To this end, quantum chemical modeling based on the density functional theory and periodic super cell models were done. Several experimental techniques were employed to get a deep characterization of structural and optical features of STO nanospheres. A possible formation mechanism was proposed, based on dehydration of titanium and strontium clusters followed by mesoscale transformation and a self-assembly process along an oriented attachment mechanism resulting in spherical like shape. Raman and XANES analysis renders a noncentrosymmetric environment for the octahedral titanium, while infrared and first order Raman modes reveal OH groups which are unsystematically incorporated into uncoordinated superficial sites. These results seem to indicate that the key component is the presence of distorted TiO6 clusters to engender a luminescence property. Analysis of band structure, density Of states, and charge map shows that there is a close relationship among local broken symmetry, polarization, and energy split of the 3d orbitals of titanium. The interplay among these electronic and structural features provides necessary conditions to evaluate its luminescent properties under two energy excitation.

A new simple class of superpotentials in SUSY quantum mechanics

In this work, we introduce the class of quantum mechanics superpotentials W(x) = g epsilon(x)x(2n) and study in detail the cases n = 0 and 1. The n = 0 superpotential is shown to lead to the known problem of two supersymmetrically related Dirac delta potentials (well and barrier). The n = 1 case results in the potentials V+/-(x) = g(2)x(4) +/- 2g|x|. For V-, we present the exact ground-state solution and study the excited states by a variational technique. Starting from the ground state of V- and using logarithmic perturbation theory, we study the ground states of V+ and also of V(x) = g(2)x(4) and compare the result obtained in this new way with other results for this last potential in the literature.

Structure and electronic properties of hydrated mesityl oxide: a sequential quantum mechanics/molecular mechanics approach

The hydration of mesityl oxide (MOx) was investigated through a sequential quantum mechanics/molecular mechanics approach. Emphasis was placed on the analysis of the role played by water in the MOx syn-anti equilibrium and the electronic absorption spectrum. Results for the structure of the MOx-water solution, free energy of solvation and polarization effects are also reported. Our main conclusion was that in gas-phase and in low-polarity solvents, the MOx exists dominantly in syn-form and in aqueous solution in anti-form. This conclusion was supported by Gibbs free energy calculations in gas phase and in-water by quantum mechanical calculations with polarizable continuum model and thermodynamic perturbation theory in Monte Carlo simulations using a polarized MOx model. The consideration of the in-water polarization of the MOx is very important to correctly describe the solute-solvent electrostatic interaction. Our best estimate for the shift of the pi-pi* transition energy of MOx, when it changes from gas-phase to water solvent, shows a red-shift of -2,520 +/- 90 cm(-1), which is only 110 cm(-1) (0.014 eV) below the experimental extrapolation of -2,410 +/- 90 cm(-1). This red-shift of around -2,500 cm(-1) can be divided in two distinct and opposite contributions. One contribution is related to the syn -> anti conformational change leading to a blue-shift of similar to 1,700 cm(-1). Other contribution is the solvent effect on the electronic structure of the MOx leading to a red-shift of around -4,200 cm(-1). Additionally, this red-shift caused by the solvent effect on the electronic structure can by composed by approximately 60 % due to the electrostatic bulk effect, 10 % due to the explicit inclusion of the hydrogen-bonded water molecules and 30 % due to the explicit inclusion of the nearest water molecules.

Structure and thermodynamics of H3O+(H2O)8 clusters: A combined molecular dynamics and quantum mechanics approach

We have studied the structure and stability of (H3O+)(H2O)8 clusters using a combination of molecular dynamics sampling and high-level ab initio calculations. 20 distinct oxygen frameworks are found within 2 kcal/mol of the electronic or standard Gibbs free energy minimum. The impact of quantum zero-point vibrational corrections on the relative stability of these isomers is quite significant. The box-like isomers are favored in terms of electronic energy, but with the inclusion of zero-point vibrational corrections and entropic effects tree-like isomers are favored at higher temperatures. Under conditions from 0 to 298.15 K, the global minimum is predicted to be a tree-like structure with one dangling singly coordinated water molecule. Above 298.15 K, higher entropy tree-like isomers with two or more singly coordinated water molecules are favored. These assignments are generally consistent with experimental IR spectra of (H3O+)(H2O)8 obtained at 150 K.

Asymptotic freedom, dimensional transmutation, and an infrared conformal fixed point for the δ-function potential in one-dimensional relativistic quantum mechanics

We consider the Schrödinger equation for a relativistic point particle in an external one-dimensional δ-function potential. Using dimensional regularization, we investigate both bound and scattering states, and we obtain results that are consistent with the abstract mathematical theory of self-adjoint extensions of the pseudodifferential operator H=p2+m2−−−−−−−√. Interestingly, this relatively simple system is asymptotically free. In the massless limit, it undergoes dimensional transmutation and it possesses an infrared conformal fixed point. Thus it can be used to illustrate nontrivial concepts of quantum field theory in the simpler framework of relativistic quantum mechanics.

Loop formulation of supersymmetric Yang-Mills quantum mechanics

We derive the fermion loop formulation of N=4 supersymmetric SU(N) Yang-Mills quantum mechanics on the lattice. The loop formulation naturally separates the contributions to the partition function into its bosonic and fermionic parts with fixed fermion number and provides a way to control potential fermion sign problems arising in numerical simulations of the theory. Furthermore, we present a reduced fermion matrix determinant which allows the projection into the canonical sectors of the theory and hence constitutes an alternative approach to simulate the theory on the lattice.

Supersymmetric quantum mechanics on the lattice: II. Exact results

Simulations of supersymmetric field theories with spontaneously broken supersymmetry require in addition to the ultraviolet regularisation also an infrared one, due to the emergence of the massless Goldstino. The intricate interplay between ultraviolet and infrared effects towards the continuum and infinite volume limit demands careful investigations to avoid potential problems. In this paper – the second in a series of three – we present such an investigation for N=2 supersymmetric quantum mechanics formulated on the lattice in terms of bosonic and fermionic bonds. In one dimension, the bond formulation allows to solve the system exactly, even at finite lattice spacing, through the construction and analysis of transfer matrices. In the present paper we elaborate on this approach and discuss a range of exact results for observables such as the Witten index, the mass spectra and Ward identities.

Supersymmetric quantum mechanics on the lattice: III. Simulations and algorithms

In the fermion loop formulation the contributions to the partition function naturally separate into topological equivalence classes with a definite sign. This separation forms the basis for an efficient fermion simulation algorithm using a fluctuating open fermion string. It guarantees sufficient tunnelling between the topological sectors, and hence provides a solution to the fermion sign problem affecting systems with broken supersymmetry. Moreover, the algorithm shows no critical slowing down even in the massless limit and can hence handle the massless Goldstino mode emerging in the supersymmetry broken phase. In this paper – the third in a series of three – we present the details of the simulation algorithm and demonstrate its efficiency by means of a few examples.

Pseudospectra in non-Hermitian quantum mechanics

We propose giving the mathematical concept of the pseudospectrum a central role in quantum mechanics with non-Hermitian operators. We relate pseudospectral properties to quasi-Hermiticity, similarity to self-adjoint operators, and basis properties of eigenfunctions. The abstract results are illustrated by unexpected wild properties of operators familiar from PT -symmetric quantum mechanics.

The Harmonic Oscillator, a Review of Classical and Elementary Quantum Mechanics

The classical harmonic oscillator and an elementary discussion of the quantum mechanical solutions for the harmonic oscillator are discussed.

From ab initio quantum mechanics to molecular neurobiology: A cation–π binding site in the nicotinic receptor

The nicotinic acetylcholine receptor is the prototype ligand-gated ion channel. A number of aromatic amino acids have been identified as contributing to the agonist binding site, suggesting that cation–π interactions may be involved in binding the quaternary ammonium group of the agonist, acetylcholine. Here we show a compelling correlation between: (i) ab initio quantum mechanical predictions of cation–π binding abilities and (ii) EC50 values for acetylcholine at the receptor for a series of tryptophan derivatives that were incorporated into the receptor by using the in vivo nonsense-suppression method for unnatural amino acid incorporation. Such a correlation is seen at one, and only one, of the aromatic residues—tryptophan-149 of the α subunit. This finding indicates that, on binding, the cationic, quaternary ammonium group of acetylcholine makes van der Waals contact with the indole side chain of α tryptophan-149, providing the most precise structural information to date on this receptor. Consistent with this model, a tethered quaternary ammonium group emanating from position α149 produces a constitutively active receptor.