Applications In Molecular Physics Research Articles

Real eigenvalues of non-hermitian operators

ABSTRACT A basic fact, having fundamental significance in quantum mechanics, is that hermitian (or self-adjoint) operators have only real eigenvalues. However, in certain applications in molecular physics, one deals with non-hermitian operators. We discuss a condition for non-hermitian operators to have real eigenvalues, proving that it is the case if and only if it can be decomposed as a product of two, generally non-commuting hermitian operators, one of which is positive definite. The theorem is illustrated on the example of non-hermitian effective Hamiltonians occurring in the non-perturbative form of the Bloch equation.

Three-body harmonic molecule

In this study, the quantum three-body harmonic system with finite rest length R and zero total angular momentum L = 0 is explored. It governs the near-equilibrium S-states eigenfunctions of three identical point particles interacting by means of any pairwise confining potential that entirely depends on the relative distances between particles. At R = 0, the system admits a complete separation of variables in Jacobi-coordinates, it is (maximally) superintegrable and exactly-solvable. The whole spectra of excited states is degenerate, and to analyze it a detailed comparison between two relevant Lie-algebraic representations of the corresponding reduced Hamiltonian is carried out. At R > 0, the problem is not even integrable nor exactly-solvable and the degeneration is partially removed. In this case, no exact solutions of the Schrödinger equation have been found so far whilst its classical counterpart turns out to be a chaotic system. For R > 0, accurate values for the total energy E of the lowest quantum states are obtained using the Lagrange-mesh method. Concrete explicit results with not less than eleven significant digits for the states are presented in the range a.u. In particular, it is shown that (I) the energy curve develops a global minimum as a function of the rest length R, and it tends asymptotically to a finite value at large R, and (II) the degenerate states split into sub-levels. For the ground state, perturbative (small-R) and two-parametric variational results (arbitrary R) are displayed as well. An extension of the model with applications in molecular physics is briefly discussed.

The magnetocaloric effect, thermo-magnetic and transport properties of LiH diatomic molecule

This research article investigates the effects of magnetic and Aharanov-Bohm (AB) fields on the thermo-magnetic and transport properties and magneto-caloric effect (MCE) of Lithium Hydride (LiH) modelled by the Varshni potential. So, the Schrödinger equation in 2D is solved under the influence of external fields and Varshni potential using the functional analysis approach (FAA) to obtain the energy equation and wave function, respectively. The accessible energy levels are summed to obtain the partition function, which is used to obtain the aforementioned properties. The influences of the magnetic and AB fields on the above-mentioned properties have been examined over a broad temperature region. The susceptibility has only positive values in different scenarios analysed, which implies paramagnetism. The temperature dependence of the magnetic entropy (magneto-caloric effect) changes shows a decreasing tendency. This research could find applications in molecular physics and inspire discussions and studies on MCE for several diatomic molecules.

The Schrödinger Equation with Deng-Fan-Eckart Potential (DFEP): Nikiforov-Uvarov-Functional Analysis (NUFA) Method

In this study, the radial part of the Schrödinger equation with the Deng-Fan-Eckart potential (DFEP) is solved analytically by employing the improved Greene and Aldrich approximation to bypass the centrifugal barrier and using the Nikiforov-Uvarov-Functional Analysis method (NUFA). The energy expression and wave function are obtained respectively. The numerical energy spectra for some diatomic molecules have been studied and compared with the findings of earlier studies and it has been found to be in good agreement. The NUFA method used in this study is easy and very less cumbersome compared to other methods that currently exist and it is recommended that researchers in this area adopt this method. The findings of this study will find direct applications in molecular physics.

Kapitza-Dirac Blockade: A Universal Tool for the Deterministic Preparation of Non-Gaussian Oscillator States.

Harmonic oscillators count among the most fundamental quantum systems with important applications in molecular physics, nanoparticle trapping, and quantum information processing. Their equidistant energy level spacing is often a desired feature, but at the same time a challenge if the goal is to deterministically populate specific eigenstates. Here, we show how interference in the transition amplitudes in a bichromatic laser field can suppress the sequential climbing of harmonic oscillator states (Kapitza-Dirac blockade) and achieve selective excitation of energy eigenstates, cat states, and other non-Gaussian states. This technique can transform the harmonic oscillator into a coherent two-level system or be used to build a large-momentum-transfer beam splitter for matter waves. To illustrate the universality of the concept, we discuss feasible experiments that cover many orders of magnitude in mass, from single electrons over large molecules to dielectric nanoparticles.

Molecular applications of attosecond laser pulses

We review the present state of the application of attosecond lasers in molecular physics. Following the first synthesis and characterization of attosecond laser pulses a little more than a decade ago, the first applications in molecular physics have been published only in the last few years. These have yielded new insight into the coupling of multiple electronic degrees of freedom and that of electronic and nuclear degrees of freedom on the attosecond to few-femtosecond timescale. We review these first experiments as well as theoretical work that was carried out during the same period, and sketch some future molecular applications of attosecond pump–probe spectroscopy.

Optimal control theory – closing the gap between theory and experiment

Optimal control theory and optimal control experiments are state-of-the-art tools to control quantum systems. Both methods have been demonstrated successfully for numerous applications in molecular physics, chemistry and biology. Modulated light pulses could be realized, driving these various control processes. Next to the control efficiency, a key issue is the understanding of the control mechanism. An obvious way is to seek support from theory. However, the underlying search strategies in theory and experiment towards the optimal laser field differ. While the optimal control theory operates in the time domain, optimal control experiments optimize the laser fields in the frequency domain. This also implies that both search procedures experience a different bias and follow different pathways on the search landscape. In this perspective we review our recent developments in optimal control theory and their applications. Especially, we focus on approaches, which close the gap between theory and experiment. To this extent we followed two ways. One uses sophisticated optimization algorithms, which enhance the capabilities of optimal control experiments. The other is to extend and modify the optimal control theory formalism in order to mimic the experimental conditions.

An alternative multipolar expansion for intermolecular potential functions.

We have derived a new multipolar expansion for intermolecular potential-energy functions with applications in molecular physics, theoretical chemistry, and mathematical physics. The new formulation employs a separation of radial and angular terms with a simple index structure that leads to computational efficiency and ease of physical interpretation. For the case of the Coulomb interaction, we compare the present formulation with two conventional multipole expansions: the Cartesian tensor and the irreducible spherical tensor expansions. The new formalism leads to efficient numerical algorithms that are useful for general applications beyond intermolecular potentials. In addition to the electrostatic Coulomb interaction, we illustrate the formalism with applications to special function theory and a bipolar expansion involved in potential theory.

Pattern Search Methods for User-Provided Points: Application to Molecular Geometry Problems

This paper deals with the application of pattern search methods to the numerical solution of a class of molecular geometry problems with important applications in molecular physics and chemistry. The goal is to find a configuration of a cluster or a molecule with minimum total energy. The minimization problems in this class of molecular geometry problems have no constraints, and the objective function is smooth. The difficulties arise from the existence of several local minima and, especially, from the expensive function evaluation (total energy) and the possible nonavailability of first-order derivatives. We introduce a pattern search approach that attempts to exploit the physical nature of the problem by using energy lowering geometrical transformations and to take advantage of parallelism without the use of derivatives. Numerical results for a particular instance of this new class of pattern search methods are presented, showing the promise of our approach. The new pattern search methods can be used in any other context where there is a user-provided scheme to generate points leading to a potential objective function decrease.

EIGENVALUES AND MAGNETISM OF ELECTRONS ON AN ARTIFICIAL MOLECULE

We discuss the spontaneous magnetism of electrons constrained to the corners of a square plaquette, with a view to applications in molecular physics and nanotechnology. The special cases of three or five electrons have a ground-state level-crossing in strong-coupling, U > 18t, where the ground-state of maximal spin (S = 3/2) overtakes that of minimum spin (S = 1/2).

Two-dimensional theory of chirality. I. Absolute chirality

Chirality is a notion already familiar to undergraduates as the fact that an object is not superposable to its mirror image. Its dichotomous or “yes/no” character, implicit in this definition due to Lord Kelvin, has always been considered self-evident. We prove here and in the companion article that in two dimensions chirality—the very concept of chirality—is a continuous phenomenon in the special case of square-integrable wave functions. This conception of chirality is to Kelvin’s definition what the continuous conception of door opening is to the closed/nonclosed dichotomy; hence it provides a continuous description of the discrete achiral symmetry breaking. This result is first extended to three and higher dimensions, then to the whole nonrelativistic quantum description of matter. Thus molecules are more or less chiral just as doors are more or less open, and molecular chirality changes continuously during chemical reactions. Chirality splits into two complementary forms—absolute and relative chirality. We present here the theory of absolute chirality. More generally, this unexpected and paradoxical breakthrough in symmetry theory is based on a geometrical description of wave functions that should find broad applications in molecular physics and in stereochemistry, where the notion of chirality has an overwhelming importance since long ago.

Expansions for the eigenvalues of three-term recurrence relations. Two applications in molecular physics

Approximate expressions for the eigenvalue of a three-term recurrence relation with a general form describing various physical problems are proposed. Their range of availability is examined by comparison with exact values for two different problems: the bound and continuum states of monoelectronic diatomic ions and the Schrodinger equation describing molecular alignment in intense laser fields. For each case, very good predictions have been obtained, which may be useful as initial values in iterative procedures for deriving exact solutions.

Second International Symposium on Ultrafast Phenomena in Spectroscopy, Reinhardsbrunn, East Germany, October 30–November 5, 1980

Papers presented at the Second International Symposium on Ultrafast Phenomena in Spectroscopy are reviewed. The Symposium dealt with instruments and techniques used in picosecond spectroscopy and their applications in molecular physics, photochemical reactions, solid state physics, and photobiology.

Numerical quantities theory and its application in molecular physics

Numerical quantities theory and its application in molecular physics