Wigner Theory Research Articles

Statistical description of interacting multistream quantum systems

In this research, the electrostatically coupled multistream quasiparticle excitations are studied in the framework of the Wigner distribution function. It is remarked that the Wigner distribution of coupled multistream collective quantum excitations satisfies a simple Liouville-like evolution equation from which a generalized distribution function for multistream quasiparticle excitations is deduced. The phase-space structure of collective quantum excitations in counter-stream electron and two-stream electron–positron gas with their evolution is calculated and electron/positron hole formation due to the onset of quantum stream instability is studied in connection with the energy band structure of the multistream quantum system, for the first time. The quantum stream instabilities in symmetric and asymmetric stream systems are studied and compared. It is found that the presence of opposite-charge streams leads to overall stability due to lowering the interaction potential effect. The generalized Wigner theory is also applied to study the electron transport in a one-dimensional periodic lattice using the concept of virtual streams. Current generalized statistical formalism may be used to model different quantum phenomena in the linear excitations limit with collective electrostatic interactions. The applications extend to the stream instability in quantum charge transport in metals, semiconductors, plasmonic devices, phase-space structure of charge carriers in periodic lattices interacting with the external potential of arbitrary shape and the dynamic evolution of dense electron–positron jets in active galactic nuclei or within the extremely dense astrophysical objects.

Reconciling Conflicting Approaches for the Tunneling Time Delay in Strong Field Ionization.

Several recent attoclock experiments have investigated the fundamental question of a quantum mechanically induced time delay in tunneling ionization via extremely precise photoelectron momentum spectroscopy. The interpretations of those attoclock experimental results were controversially discussed, because the entanglement of the laser and Coulomb field did not allow for theoretical treatments without undisputed approximations. The method of semiclassical propagation matched with the tunneled wave function, the quasistatic Wigner theory, the analytical R-matrix theory, the backpropagation method, and the under-the-barrier recollision theory are the leading conceptual approaches put forward to treat this problem, however, with seemingly conflicting conclusions on the existence of a tunneling time delay. To resolve the contradicting conclusions of the different approaches, we consider a very simple tunneling scenario which is not plagued with complications stemming from the Coulomb potential of the atomic core, avoids consequent controversial approximations and, therefore, allows us to unequivocally identify the origin of the tunneling time delay.

Formation of the CH/CD molecules through radiative association of C with H/D

ABSTRACT Reaction rate constants have been calculated for the formation of CH and CD molecules through radiative association of C and H/D atoms in their ground states. Quantum mechanical and semiclassical/classical methods were used to obtain the reaction cross-sections. Shape resonances and inverse pre-dissociation are accounted for with Breit–Wigner theory. The potential, permanent/transition dipole moment curves and experimental pre-dissociation widths are taken from the literature. The resulting reaction rate constants were fitted to the Kooij formula for use in astrochemical modelling. Our rate constant is 3.5 × 10−17 cm3 s−1 at 100 K and it peaks at 20 K, where it is 8.0 × 10−17 cm3 s−1. These values are larger than what has been obtained in earlier studies but not large enough to account for the interstellar abundance of CH.

Dynamics of atoms within atoms

Recent experiments with Bose–Einstein condensates have entered a regime in which thousands of ground-state condensate atoms fill the Rydberg-electron orbit. After the excitation of a single atom into a highly excited Rydberg state, scattering off the Rydberg electron sets ground-state atoms into motion, such that one can study the quantum-many-body dynamics of atoms moving within the Rydberg atom. Here we study this many-body dynamics using Gross–Pitaevskii and truncated Wigner theory. Our simulations focus in particular on the scenario of multiple sequential Rydberg excitations on the same rubidium condensate which has become the standard tool to observe quantum impurity dynamics in Rydberg experiments. We investigate to what extent such experiments can be sensitive to details in the electron–atom interaction potential, such as the rapid radial modulation of the Rydberg molecular potential, or p-wave shape resonance. We demonstrate that both effects are crucial for the initial condensate response within the Rydberg orbit, but become less relevant for the density waves emerging outside the Rydberg excitation region at later times. Finally we explore the local dynamics of condensate heating. We find that it provides only minor corrections to the mean-field dynamics. Combining all these insights, our results suggest Bose–Einstein condensates as a viable platform for the in situ and real time interrogation of ultra-cold chemistry dynamics involving Rydberg states.

Sampling initial positions and momenta for nuclear trajectories from quantum mechanical distributions.

We compare algorithms to sample initial positions and momenta of a molecular system for classical trajectory simulations. We aim at reproducing the phase space quantum distribution for a vibrational eigenstate, as in Wigner theory. Moreover, we address the issue of controlling the total energy and the energy partition among the vibrational modes. In fact, Wigner's energy distributions are very broad, quite at variance with quantum eigenenergies. Many molecular processes depend sharply on the available energy, so a better energy definition is important. Two approaches are introduced and tested: the first consists in constraining the total energy of each trajectory to equal the quantum eigenenergy. The second approach modifies the phase space distribution so as to reduce the deviation of the single mode energies from the correct quantum values. A combination of the two approaches is also presented.

Radiative association for the formation of MgO

ABSTRACTThe radiative association process for the formation of magnesium oxide (MgO) may be of great importance due to its frequent occurrence in the low-density and dust-poor astrochemical environments. In this work, the cross-sections and rate coefficients for the A1Π → X1Σ+, ${\rm X}^1\Sigma ^+\, \rightarrow \, {\rm A}^1\Pi$, D1Δ → A1Π, a3Π → e3Σ−, ${\rm X}^1\Sigma ^+\, \rightarrow \, {\rm X}^1\Sigma ^+$, and A1Π → A1Π radiative association processes of forming MgO are theoretically estimated. The cross-sections for the transitions between the different states are obtained by using the semiclassical method for direct contributions and the Breit–Wigner theory as a complement for resonance contributions. For the transitions between the same states, the quantum mechanical method is used. The rate coefficients are then obtained from the cross-sections for the temperatures in the range of 10–10 000 K and the results are found to vary from 4.69 $\times \, 10^{-16}$ to 6.27 $\times \, 10^{-14}$ cm3 s−1. For temperatures lower than around 693 K, the rate coefficients for the A1Π → X1Σ+ process are dominant, which indicates this process is the most efficient way of producing MgO at low temperatures. However, the rate coefficients for the D1Δ → A1Π process go through a rapid increase with increasing temperature and become dominant at higher temperatures. For other processes, their rate coefficients are several orders of magnitude lower than those for the two processes mentioned above. The results can be used to further investigate the formation and evolution of MgO in low density and hot gas close to the photosphere of evolved oxygen-rich stars.

Formation of CO+ by radiative association

ABSTRACT We theoretically estimate formation rate coefficients for CO+ through the radiative association of C+(2P) with O(3P). In 1989, Petuchowski et al. claimed radiative association to be the most important route for CO+ formation in SN 1987A. In 1990, Dalgarno, Du and You challenged this claim. Therefore, in this study, we improve previous estimates of the radiative association rate coefficients for forming CO+ from C+(2P) and O(3P). To do this, we perform quantum mechanically based perturbation theory calculations as well as semiclassical calculations, which are combined with Breit–Wigner theory in order to add the effect of shape resonances. We explicitly include four electronic transitions. The required potential energy and transition dipole-moment curves are obtained through large basis set multireference configuration interaction electronic structure calculations. We report cross-sections and from these we obtain rate coefficients in the range of 10 –10 000 K, finding that the CO+ formation rate coefficient is larger than the previous estimate by Dalgarno et al. Still our results support their claim that in SN 1987A, CO is mainly formed through radiative association and not through the charge transfer reaction CO+ + O → CO + O+ as earlier suggested by Petuchowski et al.

Gene regulatory network stabilized by pervasive weak repressions: microRNA functions revealed by the May-Wigner theory.

Food web and gene regulatory networks (GRNs) are large biological networks, both of which can be analyzed using the May–Wigner theory. According to the theory, networks as large as mammalian GRNs would require dedicated gene products for stabilization. We propose that microRNAs (miRNAs) are those products. More than 30% of genes are repressed by miRNAs, but most repressions are too weak to have a phenotypic consequence. The theory shows that (i) weak repressions cumulatively enhance the stability of GRNs, and (ii) broad and weak repressions confer greater stability than a few strong ones. Hence, the diffuse actions of miRNAs in mammalian cells appear to function mainly in stabilizing GRNs. The postulated link between mRNA repression and GRN stability can be seen in a different light in yeast, which do not have miRNAs. Yeast cells rely on non-specific RNA nucleases to strongly degrade mRNAs for GRN stability. The strategy is suited to GRNs of small and rapidly dividing yeast cells, but not the larger mammalian cells. In conclusion, the May–Wigner theory, supplanting the analysis of small motifs, provides a mathematical solution to GRN stability, thus linking miRNAs explicitly to ‘developmental canalization’.

Topological magnon insulator with Dzyaloshinskii–Moriya interaction under the irradiation of light**Project supported by the National Natural Science Foundation of China (Grant No. 61604106) and Shandong Provincial Natural Science Foundation, China (Grant No. ZR2014FL025).

The topological magnon insulator on a honeycomb lattice with Dzyaloshinskii–Moriya interaction (DMI) is studied under the application of a circularly polarized light. At the high-frequency regime, the effective tight-binding model is obtained based on Brillouin–Wigner theory. Then, we study the corresponding Berry curvature and Chern number. In the Dirac model, the interplay between a light-induced handedness-dependent effective DMI and intrinsic DMI is discussed.

Wigner Time Delay Induced by a Single Quantum Dot

Resonant scattering of weak coherent laser pulses on a single two-level system realized in a semiconductor quantum dot is investigated with respect to a time delay between incoming and scattered light. This type of time delay was predicted by Wigner in 1955 for purely coherent scattering and was confirmed for an atomic system in 2013 [R. Bourgain etal., Opt. Lett. 38, 1963 (2013)OPLEDP0146-959210.1364/OL.38.001963]. In the presence of electron-phonon interaction, we observe deviations from Wigner's theory related to incoherent and strongly non-Markovian scattering processes which are hard to quantify via a detuning-independent pure dephasing time. We observe detuning-dependent Wigner delays of up to 530ps in our experiments which are supported quantitatively by microscopic theory allowing for pure dephasing times of up to 950ps.

Wigner equation for general electromagnetic fields: The Weyl-Stratonovich transform

Gauge-invariant Wigner theories are formulated in terms of the kinetic momentum, which---being a physical quantity---is conserved after a change of the gauge. These theories rely on a transform of the density matrix, originally introduced by Stratonovich, which generalizes the Weyl transform by involving the vector potential. We thus present an alternative derivation of the Weyl-Stratonovich transform, which bridges the concepts and notions used by the different, available gauge-invariant approaches and thus links physically intuitive with formal mathematical viewpoints. Furthermore, an explicit form of the Wigner equation, suitable for numerical analysis and corresponding to general, inhomogeneous, and time-dependent electromagnetic conditions, is obtained. For a constant magnetic field, the equation reduces to two models: in the case of a constant electric field, this is the ballistic Boltzmann equation, where classical particles are driven by local forces. The second model, derived for general electrostatic conditions, involves novel physics, where the magnetic field acts locally via the Liouville operator, while the electrostatics is determined by the manifestly nonlocal Wigner potential. A significant consequence of our work is the fact that now the constant magnetic field case can be treated with existing numerical approaches developed for the standard, scalar potential Wigner theory. Therefore, in order to demonstrate the feasibility of the approach, a stochastic method is applied to simulate a physically intuitive evolution problem.

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.

Tunneling Flight Time, Chemistry, and Special Relativity.

Attosecond ionization experiments have not resolved the question "What is the tunneling time?". Different definitions of tunneling time lead to different results. Second, a zero tunneling time for a material particle suggests that the nonrelativistic theory includes speeds greater than the speed of light. Chemical reactions, occurring via tunneling, should then not be considered in terms of a nonrelativistic quantum theory calling into question quantum dynamics computations on tunneling reactions. To answer these questions, we define a new experimentally measurable paradigm, the tunneling flight time, and show that it vanishes for scattering through an Eckart or a square barrier, irrespective of barrier length or height, generalizing the Hartman effect. We explain why this result does not lead to experimental measurement of speeds greater than the speed of light. We show that this tunneling is an incoherent process by comparing a classical Wigner theory with exact quantum mechanical computations.

Thermodynamics of relativistic Newton—Wigner particle in external potential field

Thermodynamic properties of relativistic spinless particle described by the Klein–Gordon equation have been studied using the Newton–Wigner theory of particle in external potential field. Concept of Wiener path integral was extended on relativistic case. A new path integral Monte–Carlo method was developed for relativistic particle in external potential field. The bounds of applicability of available analytical approaches and related results have been specified by comparison with Monte–Carlo calculations. Developed path integral formalism can be directly extended on systems of many identical Newton–Wigner particles, which interact with external field and each other.

Position-dependent oscillated decay of a two-level atom immersed in a two-dimensional photon fluid

A Weisskopf–Wigner theory has been used to investigate the spontaneous emission of a two-level atom placed in a photon superfluid. It is found that the atom decays exponentially. However, the atomic decay rate changes periodically with the position of the atom and it is minimal when the atom is located at the wave nodes. The largest decay rate of the atom in photon superfluid has the same order of magnitude as it is in vacuum of free space. Moreover, the analytical result shows that the decay of an atom in photon superfluid, compared with that in planar cavity without photon superfluid, will be inhibited. The physical origin of atomic decay inhibition is also discussed.

Semiclassical Wigner theory of photodissociation in three dimensions: Shedding light on its basis

The semiclassical Wigner theory (SCWT) of photodissociation dynamics, initially proposed by Brown and Heller [J. Chem. Phys. 75, 186 (1981)] in order to describe state distributions in the products of direct collinear photodissociations, was recently extended to realistic three-dimensional triatomic processes of the same type [Arbelo-González et al., Phys. Chem. Chem. Phys. 15, 9994 (2013)]. The resulting approach, which takes into account rotational motions in addition to vibrational and translational ones, was applied to a triatomic-like model of methyl iodide photodissociation and its predictions were found to be in nearly quantitative agreement with rigorous quantum results, but at a much lower computational cost, making thereby SCWT a potential tool for the study of polyatomic reaction dynamics. Here, we analyse the main reasons for this agreement by means of an elementary model of fragmentation explicitly dealing with the rotational motion only. We show that our formulation of SCWT makes it a semiclassical approximation to an approximate planar quantum treatment of the dynamics, both of sufficient quality for the whole treatment to be satisfying.

Phenomenological theory of echo poles

Abstract In scattering theory the effect associated with the downward crossing of the phase-shift δ l ( k ) ( l being the orbital angular momentum and k the momentum) through δ l = π / 2 (mod π ) is called echo . In the standard nuclear theory (Breit–Wigner theory) the echo is described and evaluated in terms of scattering by an impenetrable sphere. However, this model holds only at sufficiently high energy, while it is inadequate at low energy. In this paper we show that the echo effect can be associated with two different regimes acting at low and high energy, respectively. At high energy the hard-sphere scattering model seems to describe appropriately the phenomenon. At low energy we propose a mechanism due to the exchange forces induced by the Pauli exclusion principle in the fermionic interaction, which leads to nonlocal potentials. These potentials admit for the scattering amplitude pole singularities in the fourth quadrant of the complex angular momentum plane. This paper analyzes the role played by this class of poles in the description of the low energy regime of echoes. A specific phenomenological analysis is performed, taking as typical example the α – α elastic scattering.

Interaction of H2@C60 and Nitroxide through Conformationally Constrained Peptide Bridges

We synthesized two molecular systems, in which an endofullerene C60 , incarcerating one hydrogen molecule (H2 @C60 ) and a nitroxide radical are connected by a folded 310 -helical peptide. The difference between the two molecules is the direction of the peptide orientation. The nuclear spin relaxation rates and the para → ortho conversion rate of the incarcerated hydrogen molecule were determined by (1) H NMR spectroscopy. The experimental results were analyzed using DFT-optimized molecular models. The relaxation rates and the conversion rates of the two peptides fall in the expected distance range. One of the two peptides is particularly rigid and thus ideal to keep the H2 @C60 /nitroxide separation, r, as large and controlled as possible, which results in particularly low relaxation and conversion rates. Despite the very similar optimized distance, however, the rates measured with the other peptide are considerably higher and thus are compatible with a shorter effective distance. The results strengthen the outcome of previous investigations that while the para → ortho conversion rates satisfactorily obey the Wigner's theory, the nuclear spin relaxation rates are in excellent agreement with the Solomon-Bloembergen equation predicting a 1/r(6) dependence.

Formation of the SiP Radical through Radiative Association

Formation of the SiP radical through radiative association of Si((3)P) and P((4)S) atoms is studied using classical and quantum dynamics. Rate coefficients for formation in the two lowest doublet states and the two lowest quartet states are calculated for T = 10-20,000 K. Breit-Wigner theory is used to properly account for contribution from quantum mechanical resonances.

Scalar Wigner theory for polarized light in nonlinear Kerr media

A scalar Wigner distribution function for describing polarized light is proposed in analogy with the treatment of spin variables in quantum kinetic theory. The formalism is applied to the propagation of circularly polarized light in nonlinear Kerr media and an extended phase space evolution equation is derived along with invariant quantities. We further consider modulation instability as well as the extension to partially coherent fields.