Quantum Mechanical Perturbation Theory Research Articles

Effect of Environment on Protoporphyrin IX: Absorbance, Fluorescence and Nonlinear Optical Properties.

The present study investiaged the enhancement of nonlinear optical properties of Protoporphyrin IX in photodynamic therapy using nano-droplet. To this end; absorbance, fluorescence, and nonlinear optical properties of Protoporphyrin IX were examined and results showed that dye aggregation and dielectric constant of solvent could change absorbance and fluorescence spectra. According to quantum mechanical perturbation theory, dipole moment of Protoporphyrin IX in solutions of water-ethanol was extracted. The values of nonlinear absorption and nonlinear refractive index of Protoporphyrin IX in AOT/Toluene/H2O were also reproted to be larger than aqueous solutions, due to polarity reduction of solvent as well as discount of Protoporphyrin IX aggregation in AOT/Toluene/H2O. Furthermore, the effect of cell culture media on the nonlinear optical properties of Protoporphyrin IX was analyzed and the results were compared with those of water. The photon correlation spectroscopy of solution also showed a growth in dye-droplet aggregation following the increase of Protoporphyrin IX concentration.

Background gravity correction to the limiting mass of white dwarfs

While computing the Fermi degeneracy pressure of electrons in a white dwarf star within the framework of hydrostatic equilibrium, we depart from the extant practice of treating the electrons as a free fermion gas, by including the effect of the background gravitational potential experienced by the electrons in the star, resulting from the mass of its constituent atoms (being the mass of all nucleons). Modifying the free particle Hamiltonian with this effective potential, we employ first order quantum mechanical perturbation theory to compute the degeneracy pressure, in order to study the effect of inclusion of this self-gravity of the star on the limiting mass. The final effect is found to be non-trivial, but perhaps a shade too small to alter any major observational result.

Mirror deformation affects solid state laser maximum beam quality

The surface micro-deformation of reflector mirrors in the solid-state laser cavity caused by machining accuracy is a key factor affecting the maximum beam quality. The effects of resonator mirror deformation on maximum laser beam quality were calculated in this study as per the perturbation theory of quantum mechanics, wherein mirror deformation is regarded as a perturbation in the light-field motion equation. The maximum beam quality was about 1.26 and 1.06 when the machining accuracy was λ/10 and λ/20, respectively. The influence of mirror deformation on the maximum beam quality is only related to mirror machining accuracy; it is independent of the laser beam radius or random distributions and directions of mirror deformation.

Formation of the NH molecule and its isotopologues through radiative association

The rate coefficients and the cross-sections for the formation of imidogen (NH) molecule (and its isotopologues: 15NH and ND) through radiative association are determined by employing quantum mechanical perturbation theory, classical Larmor formula, and Breit–Wigner theory. We suggest the radiative association process as possible route for NH production in diffuse interstellar clouds.

Gauge invariance and origin independence of electronic charge density and current density induced by optical fields.

Expressions for the first-order polarization charge density ρ (1) and current density J (1) induced in a molecule by a monochromatic plane wave, obtained by time-dependent quantum mechanical perturbation theory, have been investigated to assess their gauge invariance and independence of the coordinate system in passive and active translations. The conditions arrived at show that, within the (long wavelengths) dipole approximation, only the electric contributions to these densities are needed to rationalize the phenomenology. To the next higher quadrupole approximation, assuming that the magnetic field and the electric field gradient are uniform over the molecular dimensions, corresponding contributions to ρ (1) and J (1) are considered. It has been found that total densities are independent of the origin, whereas the contributions from electric and magnetic fields are not separately invariant. A magnetic contribution to J (1), which is by itself origin independent, can be defined by means of an approach based on continuous translation of the origin of the coordinate system.

Heavy quarkonium dissociation by thermal gluons at next-to-leading order in the Quark–Gluon Plasma

Using the chromo-electric dipole coupling Hamiltonian from QCD multipole expansion, we derive the dissociation cross sections of heavy quarkonia by thermal gluons at next-to-leading order (NLO, also known as inelastic parton scattering dissociation) in the Quark–Gluon Plasma (QGP) in the framework of second order quantum mechanical perturbation theory. While suffering divergence (infrared and soft-collinear divergences) in vacuum, the cross sections thus derived become finite in the QGP as rendered by the finite thermal gluon masses. In contrast to the leading order (LO, also known as gluo-dissociation) counterparts rapidly dropping off with increasing incident gluon energy, the NLO cross sections exhibits finite value toward high energies because of new phase space being opened up. We then carry out a full calculation of the dissociation rates for various charmonia and bottomonia within a non-relativistic in-medium potential model. The NLO process is shown to dominate the dissociation rate toward high temperatures when the binding energies of heavy quarkonia become smaller relative to the Debye screening mass.

BCS thermal vacuum of fermionic superfluids and its perturbation theory

The thermal field theory is applied to fermionic superfluids by doubling the degrees of freedom of the BCS theory. We construct the two-mode states and the corresponding Bogoliubov transformation to obtain the BCS thermal vacuum. The expectation values with respect to the BCS thermal vacuum produce the statistical average of the thermodynamic quantities. The BCS thermal vacuum allows a quantum-mechanical perturbation theory with the BCS theory serving as the unperturbed state. We evaluate the leading-order corrections to the order parameter and other physical quantities from the perturbation theory. A direct evaluation of the pairing correlation as a function of temperature shows the pseudogap phenomenon, where the pairing persists when the order parameter vanishes, emerges from the perturbation theory. The correspondence between the thermal vacuum and purification of the density matrix allows a unitary transformation, and we found the geometric phase associated with the transformation in the parameter space.

Magnon-induced non-Markovian friction of a domain wall in a ferromagnet

Motivated by the recent study on the quasiparticle-induced friction of solitons in superfluids, we theoretically study magnon-induced intrinsic friction of a domain wall in a one-dimensional ferromagnet. To this end, we start by obtaining the hitherto overlooked dissipative interaction of a domain wall and its quantum magnon bath to linear order in the domain-wall velocity and to quadratic order in magnon fields. An exact expression for the pertinent scattering matrix is obtained with the aid of supersymmetric quantum mechanics. We then derive the magnon-induced frictional force on a domain wall in two different frameworks: time-dependent perturbation theory in quantum mechanics and the Keldysh formalism, which yield identical results. The latter, in particular, allows us to verify the fluctuation-dissipation theorem explicitly by providing both the frictional force and the correlator of the associated stochastic Langevin force. The potential for magnons induced by a domain wall is reflectionless, and thus the resultant frictional force is non-Markovian similarly to the case of solitons in superfluids. They share an intriguing connection to the Abraham-Lorentz force that is well-known for its causality paradox. The dynamical responses of a domain wall are studied under a few simple circumstances, where the non-Markovian nature of the frictional force can be probed experimentally. Our work, in conjunction with the previous study on solitons in superfluids, shows that the macroscopic frictional force on solitons can serve as an effective probe of the microscopic degrees of freedom of the system.

Absorption coefficients of silicon: A theoretical treatment

A theoretical model with explicit formulas for calculating the optical absorption and gain coefficients of silicon is presented. It incorporates direct and indirect interband transitions and considers the effects of occupied/unoccupied carrier states. The indirect interband transition is calculated from the second-order time-independent perturbation theory of quantum mechanics by incorporating all eight possible routes of absorption or emission of photons and phonons. Absorption coefficients of silicon are calculated from these formulas. The agreements and discrepancies among the calculated results, the Rajkanan-Singh-Shewchun (RSS) formula, and Green's data are investigated and discussed. For example, the RSS formula tends to overestimate the contributions of indirect transitions for cases with high photon energy. The results show that the state occupied/unoccupied effect is almost negligible for silicon absorption coefficients up to the onset of the optical gain condition where the energy separation of Quasi-Femi levels between electrons and holes is larger than the band-gap energy. The usefulness of using the physics-based formulas, rather than semi-empirical fitting ones, for absorption coefficients in theoretical studies of photovoltaic devices is also discussed.

Optical gain coefficients of silicon: a theoretical study

A theoretical model is presented and an explicit formula is derived for calculating the optical gain coefficients of indirect band-gap semiconductors. This model is based on the second-order time-dependent perturbation theory of quantum mechanics by incorporating all the eight processes of photon/phonon emission and absorption between the band edges of the conduction and valence bands. Numerical calculation results are given for Si. The calculated absorption coefficients agree well with the existing fitting formula of experiment data with two modes of phonons: optical phonons with energy of 57.73 meV and acoustic phonons with energy of 18.27 meV near (but not exactly at) the zone edge of the X-point in the dispersion relation of phonons. These closely match with existing data of 57.5 meV transverse optical (TO) phonons at the X4-point and 18.6 meV transverse acoustic (TA) phonons at the X3-point of the zone edge. The calculated results show that the material optical gain of Si will overcome free-carrier absorption if the energy separation of quasi-Fermi levels between electrons and holes exceeds 1.15 eV.

Sum rules for zeros and intersections of Bessel functions from quantum mechanical perturbation theory

Bessel functions play an important role for quantum states in spherical and cylindrical geometries. In cases of perfect confinement, the energy of Schrödinger and massless Dirac fermions is determined by the zeros and intersections of Bessel functions, respectively. In an external electric field, standard perturbation theory therefore expresses the polarizability as a sum over these zeros or intersections. Both non-relativistic and relativistic polarizabilities can be calculated analytically, however. Hence, by equating analytical expressions to perturbation expansions, several sum rules for the zeros and intersections of Bessel functions emerge.

Wetting under Electromagnetic Resonance Irradiation

The influence of the resonance electromagnetic irradiation on the wetting of a solid surface by liquid has been discussed. A simple model of a fluid consisting of two-level atoms, for which changes in their interaction due to a resonance irradiation can be found in the framework of the quantum-mechanical perturbation theory is considered, and the corresponding functional for the grand thermodynamic potential is found. The density functional method is used to calculate the surface tension at the liquid–vapor, solid–liquid, and solid–vapor interfaces, and the Young equation is applied to determine the wetting angle. It is shown that the resonance irradiation can significantly increase the latter parameter.

Aspects of perturbation theory in quantum mechanics: The BenderWuMathematica® package

We discuss a general setup which allows the study of the perturbation theory of an arbitrary, locally harmonic 1D quantum mechanical potential as well as its multi-variable (many-body) generalization. The latter may form a prototype for regularized quantum field theory. We first generalize the method of Bender–Wu,and derive exact recursion relations which allow the determination of the perturbative wave-function and energy corrections to an arbitrary order, at least in principle. For 1D systems, we implement these equations in an easy to use Mathematica® package we call BenderWu. Our package enables quick home-computer computation of high orders of perturbation theory (about 100 orders in 10–30 s, and 250 orders in 1–2 h) and enables practical study of a large class of problems in Quantum Mechanics. We have two hopes concerning the BenderWu package. One is that due to resurgence, large amount of non-perturbative information, such as non-perturbative energies and wave-functions (e.g. WKB wave functions), can in principle be extracted from the perturbative data. We also hope that the package may be used as a teaching tool, providing an effective bridge between perturbation theory and non-perturbative physics in textbooks. Finally, we show that for the multi-variable case, the recursion relation acquires a geometric character, and has a structure which allows parallelization to computer clusters. Program summaryProgram Title: BenderWuProgram Files doi:http://dx.doi.org/10.17632/vpg2zsbryc.1Licensing provisions: CC By 4.0Programming language: Wolfram MathematicaNature of problem: In 1D quantum mechanics, a perturbative expansions are known to generically be divergent. An analysis of such problems was so far limited to a case-by-case basis. The Mathematica package presented here allows a quick computation and analysis of all such 1D quantum mechanical problems.Solution method: The program uses a general recursive relation, inspired by the works of Bender and Wu [1], which allows quick computation of the perturbative data.

Simulations of the Electron Spectrum of Quantum Wires in <i>n</i>-Si of Arbitrarily Doping Profile by Thomas-Fermi Method

Electron spectrum in doped n-Si quantum wires is calculated by the Thomas-Fermi (TF) method under finite temperatures. The many-body exchange corrections are taken into account. The doping profile is arbitrary. At the first stage, the electron potential energy is calculated from a simple two-dimensional equation. The effective iteration scheme is proposed there that is valid for multidimensional problems. Then the energy levels and wave functions of this quantum well are simulated from the Schrodinger equations. The expansion by the full set of eigenfunctions of the linear harmonic oscillator is used. The quantum mechanical perturbation theory can be utilized to compute the energy levels. Generally, the perturbation theory for degenerate energy levels should be used.

Ultra-strong nonlinear optical processes and trigonal warping in MoS2 layers

Nonlinear optical processes, such as harmonic generation, are of great interest for various applications, e.g., microscopy, therapy, and frequency conversion. However, high-order harmonic conversion is typically much less efficient than low-order, due to the weak intrinsic response of the higher-order nonlinear processes. Here we report ultra-strong optical nonlinearities in monolayer MoS2 (1L-MoS2): the third harmonic is 30 times stronger than the second, and the fourth is comparable to the second. The third harmonic generation efficiency for 1L-MoS2 is approximately three times higher than that for graphene, which was reported to have a large χ(3). We explain this by calculating the nonlinear response functions of 1L-MoS2 with a continuum-model Hamiltonian and quantum mechanical diagrammatic perturbation theory, highlighting the role of trigonal warping. A similar effect is expected in all other transition-metal dichalcogenides. Our results pave the way for efficient harmonic generation based on layered materials for applications such as microscopy and imaging.

A surface-hopping method for semiclassical calculations of cross sections for radiative association with electronic transitions.

A semiclassical method based on surface-hopping techniques is developed to model the dynamics of radiative association with electronic transitions. It can be proven that this method is an extension of the established semiclassical formula used in the characterization of diatomic molecule-formation. Our method is tested for diatomic molecules. It gives the same cross sections as the former semiclassical formula but, contrary to the former method, it allows us to follow the fate of the trajectories after the emission of a photon. This means that we can characterize the rovibrational states of the stabilized molecules. Using semiclassical quantization, we can obtain quantum state-resolved cross sections or emission spectra for the radiative association process. The calculated semiclassical state-resolved spectra show general agreement with the result of quantum mechanical perturbation theory. Furthermore, our surface-hopping model is not only applicable for the description of radiative association but it can be used for semiclassical characterization of any molecular process where spontaneous emission occurs.

Non-Hermitian time-dependent perturbation theory: Asymmetric transitions and transitionless interactions

The ordinary time-dependent perturbation theory of quantum mechanics, that describes the interaction of a stationary system with a time-dependent perturbation, predicts that the transition probabilities induced by the perturbation are symmetric with respect to the initial and final states. Here we extend time-dependent perturbation theory into the non-Hermitian realm and consider the transitions in a stationary Hermitian system, described by a self-adjoint Hamiltonian Hˆ0, induced by a time-dependent non-Hermitian interaction f(t)Hˆ1. In the weak interaction (perturbative) limit, the transition probabilities generally turn out to be asymmetric for exchange of initial and final states. In particular, for a temporal shape f(t) of the perturbation with one-sided Fourier spectrum, i.e. with only positive (or negative) frequency components, transitions are fully unidirectional, a result that holds even in the strong interaction regime. Interestingly, we show that non-Hermitian perturbations can be tailored to be transitionless, i.e. the perturbation leaves the system unchanged as if the interaction had not occurred at all, regardless the form of Hˆ0 and Hˆ1. As an application of our results, we provide important physical insights into the asymmetric (chiral) behavior of dynamical encircling of an exceptional point in two- and three-level non-Hermitian systems.

Time evolution in deparametrized models of loop quantum gravity

An important aspect in understanding the dynamics in the context of deparametrized models of LQG is to obtain a sufficient control on the quantum evolution generated by a given Hamiltonian operator. More specifically, we need to be able to compute the evolution of relevant physical states and observables with a relatively good precision. In this article, we introduce an approximation method to deal with the physical Hamiltonian operators in deparametrized LQG models, and apply it to models in which a free Klein-Gordon scalar field or a non-rotational dust field is taken as the physical time variable. This method is based on using standard time-independent perturbation theory of quantum mechanics to define a perturbative expansion of the Hamiltonian operator, the small perturbation parameter being determined by the Barbero-Immirzi parameter $\beta$. This method allows us to define an approximate spectral decomposition of the Hamiltonian operators and hence to compute the evolution over a certain time interval. As a specific example, we analyze the evolution of expectation values of the volume and curvature operators starting with certain physical initial states, using both the perturbative method and a straightforward expansion of the expectation value in powers of the time variable. This work represents a first step towards achieving the goal of understanding and controlling the new dynamics developed in [25, 26].

Decoherence of the quantum logic gate implemented with the Jaynes–Cummings model: A semiclassical approach

In this paper, we investigate decoherence of Knill, Laflamme, and Milburn's nonlinear sign-shift gate that is implemented with the Jaynes-Cummings model. Introducing a stochastic variable as an external electric field, we let it couple with a dipole moment of a two-level atom. We examine this model using a semiclassical theory. Results of the Monte Carlo simulations under the semiclassical approximation correspond well with those obtained with the quantum mechanical perturbation theory for the stochastic process. In the results of the simulations, we observe both the $\mbox{T}_{1}$ and $\mbox{T}_{2}$ decays. This paper is a sequel to the reference [H.~Azuma, Prog. Theor. Phys. {\bf 126}, 369 (2011)].

Optical study of xanthene-type dyes in nano-confined liquid

The optical activity of dye molecules in different environments is of great interest for many applications such as laser system or biological imaging. We investigate the fluorescence and absorption spectrum of nano-confined xanthene dyes (RhB and fluorescein sodium salt) in a two-phase liquid. Each show very distinct optical behavior in the water phase of a reverse microemulsion. Their optical properties such as absorption and fluorescence for different concentrations of dye and nanodroplets are investigated. We show that for the same concentration of dye in the microemulsion the peak of fluorescence intensity is varied by altering the concentration of nanodroplets. However, the trend of the change is widely different depending on the hydrophobicity of dyes. Quantum-mechanical second order perturbation theory is used to calculate the ratio of dipole moments in the ground and excited states, which accounts for the Stokes shift in fluorescence peak. Photon correlation spectroscopy is employed to check the trace of the dye in the oil phase of the microemulsion.