Quantum Mechanical Spectrum Research Articles

Signatures of Exciton Orbits in Quantum Mechanical Recurrence Spectra of Cu_{2}O.

The seminal work by Kazimierczuk etal. [Nature 514, 343 (2014)10.1038/nature13832] has shown the existence of highly excited exciton states in a regime, where the correspondence principle is applicable and quantum mechanics turns into classical mechanics; however, any interpretation of exciton spectra based on a classical approach to excitons is still missing. Here, we close this gap by computing and comparing quantum mechanical and semiclassical recurrence spectra of cuprous oxide. We show that the quantum mechanical recurrence spectra exhibit peaks, which, by application of semiclassical theories and a scaling transformation, can be directly related to classical periodic exciton orbits. The application of semiclassical theories to exciton physics requires the detailed analysis of the classical exciton dynamics, including three-dimensional orbits, which strongly deviate from hydrogenlike Keplerian orbits. Our findings illuminate important aspects of excitons in semiconductors by directly relating the quantum mechanical band structure splittings of excitons to the corresponding classical exciton dynamics.

Thermodynamics and Inflammation: Insights into Quantum Biology and Ageing

Inflammation as a biological concept has been around a long time and derives from the Latin “to set on fire” and refers to the redness and heat, and usually swelling, which accompanies injury and infection. Chronic inflammation is also associated with ageing and is described by the term “inflammaging”. Likewise, the biological concept of hormesis, in the guise of what “does not kill you, makes you stronger”, has long been recognized, but in contrast, seems to have anti-inflammatory and age-slowing characteristics. As both phenomena act to restore homeostasis, they may share some common underlying principles. Thermodynamics describes the relationship between heat and energy, but is also intimately related to quantum mechanics. Life can be viewed as a series of self-renewing dissipative structures existing far from equilibrium as vortexes of “negentropy” that ages and dies; but, through reproduction and speciation, new robust structures are created, enabling life to adapt and continue in response to ever changing environments. In short, life can be viewed as a natural consequence of thermodynamics to dissipate energy to restore equilibrium; each component of this system is replaceable. However, at the molecular level, there is perhaps a deeper question: is life dependent on, or has it enhanced, quantum effects in space and time beyond those normally expected at the atomistic scale and temperatures that life operates at? There is some evidence it has. Certainly, the dissipative adaptive mechanism described by thermodynamics is now being extended into the quantum realm. Fascinating though this topic is, does exploring the relationship between quantum mechanics, thermodynamics, and biology give us a greater insight into ageing and, thus, medicine? It could be said that hormesis and inflammation are expressions of thermodynamic and quantum principles that control ageing via natural selection that could operate at all scales of life. Inflammation could be viewed as a mechanism to remove inefficient systems in response to stress to enable rebuilding of more functional dissipative structures, and hormesis as the process describing the ability to adapt; underlying this is the manipulation of fundamental quantum principles. Defining what “quantum biological normality” is has been a long-term problem, but perhaps we do not need to, as it is simply an expression of one end of the normal quantum mechanical spectrum, implying that biology could inform us as to how we can define the quantum world.

Fast quasi-centroid molecular dynamics.

We describe a fast implementation of the quasi-centroid molecular dynamics (QCMD) method in which the quasi-centroid potential of mean force is approximated as a separable correction to the classical interaction potential. This correction is obtained by first calculating quasi-centroid radial and angular distribution functions in a short path integral molecular dynamics simulation and then using iterative Boltzmann inversion to obtain an effective classical potential that reproduces these distribution functions in a classical NVT simulation. We illustrate this approach with example applications to the vibrational spectra of gas phase molecules, obtaining excellent agreement with QCMD reference calculations for water and ammonia and good agreement with the quantum mechanical vibrational spectrum of methane.

Quantum mechanical reference spectrum simulation for precursors and degradation products of chemicals relevant to the Chemical Weapons Convention.

A selection of acidic, alkaline and neutral degradation products relevant to the Chemical Weapons Convention was studied in wide range of pH conditions to determine their spin systems as well as spectral parameters. The pH dependence of chemical shifts and J couplings was parameterized using Henderson-Hasselbalch-based functions using dichloromethane as additional shift reference in TSP-d4 referenced spectra. The resulting parameters allowed calculation of precise chemical shifts and J coupling constants in arbitrary pH conditions. The validity of the obtained spin system definitions and parameters as a source of quantum mechanically simulated reference data in chemical verification analysis is demonstrated.

Tailored multilevel approaches in vibrational structure theory: A route to quantum mechanical vibrational spectra for complex systems

AbstractVibrational spectroscopies have emerged as important tools to elucidate structures and processes in life sciences. The interpretation of vibrational spectra requires, in most cases, computational assistance and account for anharmonic effects. Pushing the size limitations of anharmonic vibrational structure calculations is therefore of great interest. Fortunately, interpretation of the experimental results often requires only a limited part of the vibrational spectrum. Hence, it can be expected that multilevel approaches, focusing computational effort on the relevant parts, are highly beneficial. Still, such approaches are rather sparse in the field of vibrational structure theory. In this perspective, we outline the present status on multilevel static vibrational wave functions and rectilinear vibrational coordinates. We further foresee how those ingredients can be combined to formulate a comprehensive multilevel vibrational structure framework.

Vibrational coupling to hydration shell - Mechanism to performance enhancement of qualitative analysis in NIR spectroscopy of carbohydrates in aqueous environment.

Vibrational coupling between carbohydrates and the hydration shell is unveiled as the underlying mechanism that improves wavenumber-selectively the carbohydrate discrimination performance by near-infrared (NIR) spectroscopy. The investigation is based on measurement of six carbohydrates (fructose, glucose, mannose, ribose, xylose and sorbitol) in aqueous solution in different concentration levels (5 mg/L, ~0.03 mmol/dm-3 and 20 mg/L, ~0.1 mmol/dm-3). The results of multivariate classification are interpreted by quantum mechanical NIR spectra simulations. The simulation unveils that the phenomenon is vibration-selective and thus wavenumber-selective, and leads to an enhancement of the qualitative information contained in the specific spectral regions. The location of these regions and the related performance correspond fully to the appearance and magnitude of the unveiled cooperative vibration effect.

Supersymmetric Hamiltonian solutions simulated by Andreev bound states

It is argued that an analog of a supersymmetric quantum mechanical spectrum can be realized in a Josephson junction formed by a topological insulator. These Andreev bound states can be studied by means of a circuit quantum electrodynamics setup. At the same time the equilibrium Josephson current has a more complicated analytical structure and is not expressed in terms of the Andreev states by a standard formula.

Heat kernel approach for confined quantum gas

In this paper, based on the heat kernel technique, we calculate equations of state and thermodynamic quantities for ideal quantum gases in confined space with external potential. Concretely, we provide expressions for equations of state and thermodynamic quantities by means of heat kernel coefficients for ideal quantum gases. Especially, using an analytic continuation treatment, we discuss the application of the heat kernel technique to Fermi gases in which the expansion diverges when the fugacity [Formula: see text]. In order to calculate the modification of heat kernel coefficients caused by external potentials, we suggest an approach for calculating the expansion of the global heat kernel of the operator [Formula: see text] based on an approximate method of the calculation of spectrum in quantum mechanics. We discuss the properties of quantum gases under the condition of weak and complete degeneration, respectively. Moreover, we give an expansion of the one-loop effective action in D-dimensional space.

GPU accelerated simulation of channeling radiation of relativistic particles

In this paper we describe and demonstrate a C++ code written to determine the trajectory of particles traversing oriented single crystals and a CUDA code written to evaluate the radiation spectra from charged particles with arbitrary trajectories. The CUDA/C++ code can evaluate both classical and quantum mechanical radiation spectra for spin 0 and 1/2 particles. We include multiple Coulomb scattering and energy loss due to radiation emission which produces radiation spectra in agreement with experimental spectra for both positrons and electrons. We also demonstrate how GPUs can be used to speed up calculations by several orders of magnitude. This will allow research groups with limited funding or sparse access to super computers to do numerical calculations as if it were a super computer. We show that one Titan V GPU can replace up to 100 Xeon 36 core CPUs running in parallel. We also show that choosing a GPU for a specific job will have great impact on the performance, as some GPUs have better double precision performance than others. Program summaryProgram Title: Radiation From Charged Particles Penetrating Oriented CrystalsProgram Files doi:http://dx.doi.org/10.17632/zp9gskrbvg.1Licensing provisions: MIT licenseProgramming language: C++ and CUDANature of problem: Solving the problem of calculating the radiation spectrum emitted from charged particles penetrating oriented single crystals. Exact solutions are not possible analytically, but with Monte Carlo simulations we achieve the closest agreements with experiments. This problem is particularly difficult because of the amount of integrals needed to evaluate the entire radiation spectrum.Solution method: By moving the evaluation of each radiation integral to a thread on a GPU, we are able to parallelize the problem massively, and thereby decrease computation times by several orders of magnitude. Each thread in a Kernel call to the GPU then handles one integral. As Kernel calls can be queued, and the time to evaluate the trajectory of a particle is relatively long, each thread on the CPU evaluates its own trajectory and calls a kernel to evaluate the radiation from that specific particle. In this way we minimize the downtime of the GPU, as there will always be a few CPU threads with a Kernel call ready to be evaluated on the GPU.

Fourth-order spin correlation function in the extended central spin model

Spin-noise spectroscopy has developed into a very powerful tool to access the electron spin dynamics. While the spin-noise power spectrum in an ensemble of quantum dots in a magnetic field is essentially understood, we argue that the investigation of the higher-order cumulants promises to provide additional information not accessible by the conventional power-noise spectrum. We present a quantum-mechanical approach to the correlation function of the spin-noise power operators at two different frequencies for small spin bath sizes and compare the results with a simulation obtained from the classical spin dynamics for large number of nuclear spins. This bispectrum is defined as a two-dimensional frequency cut in the parameter space of the fourth-order spin correlation function. It reveals information on the influence of the nuclear-electric quadrupolar interactions on the long-time electron spin dynamics dominated by a magnetic field. For large bath sizes and spin lengths the quantum-mechanical spectra converge to those of the classical simulations. The broadening of the bispectrum across the diagonal in the frequency space is a direct measure of the quadrupolar interaction strength. A narrowing is found with increasing magnetic field indicating a suppression of the influence of quadrupolar interactions in favor of the nuclear Zeeman effect.

High Temperature Optical Spectra of Diatomic Molecules at Local Thermodynamic Equilibrium

In the paper, several theoretical approaches to the determination of the reduced absorption and emission coefficients under local thermodynamic equilibrium conditions were exposed and discussed. The full quantum-mechanical procedure based on the Fourier grid Hamiltonian method was numerically robust but time consuming. In that method, all transitions between the bound, free, and quasi-bound states were treated as bound–bound transitions. The semi-classical method assumed continuous energies of ro-vibrational states, so it did not give the ro-vibrational structure of the molecular bands. That approach neglected the effects of turning points but agreed with the averaged-out quantum-mechanical spectra and it was computer time efficient. In the semi-quantum approximation, summing over the rotational quantum number J was done analytically using the classical Franck–Condon principle and the stationary–phase approximation and its consumption of computer time was lower by a few orders of magnitude than the case of the full quantum-mechanical approach. The approximation described well the vibrational but not the rotational structure of the molecular bands. All the above methods were compared and discussed in the case of a visible and near infrared spectrum of LiHe, Li2, and Cs2 molecules in the high temperature range.

Scattering off PT -symmetric upside-down potentials

The upside-down $\ensuremath{-}{x}^{4}$, $\ensuremath{-}{x}^{6}$, and $\ensuremath{-}{x}^{8}$ potentials with appropriate $\mathcal{PT}$-symmetric boundary conditions have real, positive, and discrete quantum-mechanical spectra. This paper proposes a macroscopic quantum-mechanical scattering experiment in which one can observe and measure these bound-state energies directly. An important subtlety of the scattering experiment is that the incoming (and outgoing) waves are not plane waves but rather must be carefully engineered so as to enforce the $\mathcal{PT}$-symmetry of the potential.

Perturbative/nonperturbative aspects of Bloch electrons in a honeycomb lattice

We revisit the spectral problem for Bloch electrons in a two-dimensional bipartite honeycomb lattice under a uniform magnetic field. It is well-known that such a honeycomb structure is realized in graphene. We present a systematic framework to compute the perturbative magnetic flux expansions near two distinct band edges. We then analyze the nonperturbative bandwidth of the spectrum. It turns out that there is a novel similarity between the spectrum near the Dirac point in the honeycomb lattice and the spectrum in the supersymmetric sine-Gordon quantum mechanics. We finally confirm a nontrivial vacuum-instanton-bion threesome relationship. Our analysis heavily relies on numerical experiments.

Ratio between Monomer and Dimer Absorption in Water Vapor within the H2O Rotational Band

Spectral line shape derived using the asymptotic line wing theory (ALWT) with parameters obtained from fitting to experiment in the 8–12-μm spectral region, which describes the spectral and temperature behavior of water vapor absorption in this region, is used to calculate absorption in the longwave wing of the H2O rotational band. The absorption coefficient calculated with the ALWT takes into account absorption by any colliding molecular pairs, except for the absorption due to stable dimers. Application of this line shape to calculation of the absorption coefficient in the region 14–200 cm−1 allows us to extract the stable dimer absorption from the absorption measured with a special-resonator spectrometer. The dimer absorption spectrum derived shows consistency with the spectra from quantum-mechanical calculations and spectra measured in other experiments.

Multi-scale theoretical approach to X-ray absorption spectra in disordered systems: an application to the study of Zn(ii) in water.

We develop a multi-scale theoretical approach aimed at calculating from first principles X-ray absorption spectra of liquid solutions and disordered systems. We test the method by considering the paradigmatic case of Zn(ii) in water which, besides being relevant in itself, is also of interest for biology. With the help of classical molecular dynamics simulations we start by producing bunches of configurations differing for the Zn(ii)-water coordination mode. Different coordination modes are obtained by making use of the so-called dummy atoms method. From the collected molecular dynamics trajectories, snapshots of a more manageable subsystem encompassing the metal site and two solvation layers are cut out. Density functional theory is used to optimize and relax these reduced system configurations employing a uniform dielectric to mimic the surrounding bulk liquid water. On the resulting structures, fully quantum mechanical X-ray absorption spectra calculations are performed by including core-hole effects and core-level shifts. The proposed approach does not rely on any guessing or fitting of the force field or of the atomic positions of the system. The comparison of the theoretically computed spectrum with the experimental Zn K-edge XANES data unambiguously demonstrates that among the different a priori possible geometries, Zn(ii) in water lives in an octahedral coordination mode.

Integrable systems, symmetries, and quantization

These notes correspond to a mini-course given at the Poisson 2016 conference in Geneva. Starting from classical integrable systems in the sense of Liouville, we explore the notion of non-degenerate singularity and expose recent research in connection with semi-toric systems. The quantum and semiclassical counterpart will also be presented, in the viewpoint of the inverse question: from the quantum mechanical spectrum, can you recover the classical system?

Spectrum of the hydrogen atom in Snyder space in a semiclassical approximation

We study the spectrum of the hydrogen atom in Snyder space in a semiclassical approximation based on a generalization of the Born-Sommerfeld quantization rule. While the corrections to the standard quantum mechanical spectrum arise at first order in the Snyder parameter for the $l=0$ states, they are of second order for $l\neq 0$. This can be understood as due to the different topology of the regions of integration in phase space.

Low-energy QCD in the delta regime

We investigate properties of low-energy QCD in a finite spatial volume, but with arbitrary temperature. In the limit of small temperature and small cube size compared to the pion Compton wavelength, Leutwyler has shown that the effective theory describing low-energy QCD reduces to that of quantum mechanics on the coset manifold, which is the so-called delta regime of chiral perturbation theory. We solve this quantum mechanics analytically for the case of a $U(1)_L \times U(1)_R$ subgroup of chiral symmetry, and numerically for the case of $SU(2)_L \times SU(2)_R$. We utilize the quantum mechanical spectrum to compute the mass gap and chiral condensate, and investigate symmetry restoration in a finite spatial volume as a function of temperature. Because we obtain the spectrum for non-zero values of the quark mass, we are able to interpolate between the rigid rotor limit, which emerges at vanishing quark mass, and the harmonic approximation, which is referred to as the p-regime. We find that the applicability of perturbation theory about the rotor limit largely requires lighter-than-physical quarks. As a stringent check of our results, we raise the temperature to that of the inverse cube size. When this condition is met, the quantum mechanics reduces to a matrix model. The condensate we obtain in this limit agrees with that determined analytically in the epsilon regime.

Charge-vortex interplay in a superconducting Coulomb-blockaded island

The angular momentum or vorticity of Cooper pairs is shown to affect strongly the charge transfer through a small superconducting (S) island of a single electron transistor. This interplay of charge and rotational degrees of freedom in a mesoscopic superconductor occurs through the effect of vorticity on the quantum mechanical spectrum of electron-hole excitations. The subgap quasiparticle levels in vortices can host an additional electron, thus, suppressing the so-called parity effect in the S island. We propose to measure this interaction between the quantized vorticity and electric charge via the charge pumping effect caused by alternating vortex entry and exit controlled by a periodic magnetic field.

Re-examining the value of old quantization and the Bohr atom approach

We use old quantization to predict features of the energy spectrum for bound states in spherically symmetric potentials. We review the application of this method to simple quantum mechanical systems with known analytic results and show that old quantization, while not generally capable of predicting the exact quantum-mechanical spectrum, does consistently give useful information. We then apply the method to a logarithmic potential and compare the results with a numerically calculated spectrum. Finally, we use these techniques to predict the number of bound states in the Yukawa potential and again compare the results with those obtained numerically. In all cases old quantization provides good predictive power for the main features of the true quantum-mechanical problem, and thus can serve as a “back-of-the-envelope” technique for providing rough, qualitative information about the system.