Initial Wave Function Research Articles

The Influence of the Symmetry of Identical Particles on Flight Times.

In this work, our purpose is to show how the symmetry of identical particles can influence the time evolution of free particles in the nonrelativistic and relativistic domains as well as in the scattering by a potential -barrier. For this goal, we consider a system of either two distinguishable or indistinguishable (bosons and fermions) particles. Two sets of initial conditions have been studied: different initial locations with the same momenta, and the same locations with different momenta. The flight time distribution of particles arriving at a ‘screen’ is calculated in each case from the density and flux. Fermions display broader distributions as compared with either distinguishable particles or bosons, leading to earlier and later arrivals for all the cases analyzed here. The symmetry of the wave function seems to speed up or slow down the propagation of particles. Due to the cross terms, certain initial conditions lead to bimodality in the fermionic case. Within the nonrelativistic domain, and when the short-time survival probability is analyzed, if the cross term becomes important, one finds that the decay of the overlap of fermions is faster than for distinguishable particles which in turn is faster than for bosons. These results are of interest in the short time limit since they imply that the well-known quantum Zeno effect would be stronger for bosons than for fermions. Fermions also arrive earlier and later than bosons when they are scattered by a -barrier. Although the particle symmetry does affect the mean tunneling flight time, in the limit of narrow in momentum initial Gaussian wave functions, the mean times are not affected by symmetry but tend to the phase time for distinguishable particles.

The NUMEN Technical Design Report

NUMEN proposes an innovative technique to access the nuclear matrix elements entering the expression of the lifetime of the double beta decay by cross-section measurements of heavy-ion induced Double Charge Exchange (DCE) reactions. Despite the fact that the two processes, namely neutrinoless double beta decay and DCE reactions, are triggered by the weak and strong interaction respectively, important analogies are suggested. The basic point is the coincidence of the initial and final state many-body wave functions in the two types of processes and the formal similarity of the transition operators. The main experimental tools for this project are the K800 Superconducting Cyclotron and MAGNEX spectrometer at the INFN-LNS laboratory. However, the tiny values of DCE cross-sections and the resolution requirements demand beam intensities much higher than those manageable with the present facility. The on-going upgrade of the INFN-LNS facilities promoted by the POTLNS a project in this perspective is intimately connected to the NUMEN project. This paper describes the solutions proposed as a result of the R&D activity performed during the recent years. The goal is to develop suitable technologies allowing for the measurements of DCE cross-section under extremely high beam intensities. a PIR01_00005 — potenziamento dell’infrastruttura di ricerca Laboratori Nazionali del Sud per la produzione di fasci di ioni ad alta intensitá.

Revealing the wave-function-dependent zeptosecond birth time delay in molecular photoionization with double-slit interference minima

We study the photoionization of molecule ${\mathrm{H}}_{2}^{+}$ in an XUV pulse by numerically solving the time-dependent Schr\"odinger equation simulation and focus on a zeptosecond birth time delay of a photoelectron from the different cores. We propose a simple and robust method to extract accurately the zeptosecond birth time delay with double-slit interference minima. Based on this extraction method, our results show that the birth time delay is strongly affected by the initial bound-electron wave function due to the deviation of the electron emission position from the central core. Furthermore, an experimental scheme is also proposed to testify this wave-function-dependent zeptosecond birth time delay. Our study sheds more light on the ultrafast molecular photoionization dynamics on the zeptosecond timescale.

Averaging method and coherence applied to Rabi oscillations in a two-level system

We study Rabi oscillations in a two-level system within the semiclassical approximation as an archetype test field of the Averaging Method (AM). The population transfer between the two levels is approached within the first and the second order AM. We systematically compare AM predictions with the rotating wave approximation (RWA) and with the complete numerical solution utilizing standard algorithms (NRWA). We study both the resonance (Δ = 0) and out-of-resonance () cases, where Δ = ω − Ω, and ℏΩ = E 2 − E1 is the two-level energetic separation, while ω is the (cyclic) frequency of the electromagnetic field. We introduce three types of dimensionless factors ϵ, i.e., ΩR/Δ, ΩR/Σ, and ΩR/ω, where ΩR is the Rabi (cyclic) frequency and Σ = ω + Ω and explore the range of ϵ where the AM results are equivalent to NRWA. Finally, by allowing for a phase difference in the initial electron wave functions, we explore the prospects coherence can offer. We illustrate that even with equal initial probabilities at the two levels, but with phase difference, strong oscillations can be generated and manipulated.

Extended Migdal-Watson formula to evaluate background strength in binary breakup reactions

A new formula to evaluate the nonresonant background for binary breakup is proposed by extending the Migdal-Watson (MW) formula, which was originally developed for $s$-wave breakup in charge neutral systems. The strength of the direct breakup, which is assumed by a one step transition from the initial bound state, is simulated by the complex scaling method (CSM) in binary cluster systems. The extended MW formula is applied to the direct breakup of $^{20}\mathrm{Ne}\phantom{\rule{4pt}{0ex}}\ensuremath{\rightarrow}\phantom{\rule{4pt}{0ex}}\ensuremath{\alpha}+^{16}\mathrm{O}$, and we have found that the formula nicely reproduces the strength of the direct breakup evaluated by CSM. We have demonstrated that new parameters introduced in the extended MW formula have a close connection to the spatial size of the initial wave packet, which is given by the product of the initial wave function and the external field. The application of the new formula to the direct breakup of $^{12}\mathrm{Be}$ into $\ensuremath{\alpha}+^{8}\mathrm{He}$ is also discussed.

4D-imaging of drip-line radioactivity by detecting proton emission from 54mNi pictured with ACTAR TPC

Proton radioactivity was discovered exactly 50 years ago. First, this nuclear decay mode sets the limit of existence on the nuclear landscape on the neutron-deficient side. Second, it comprises fundamental aspects of both quantum tunnelling as well as the coupling of (quasi)bound quantum states with the continuum in mesoscopic systems such as the atomic nucleus. Theoretical approaches can start either from bound-state nuclear shell-model theory or from resonance scattering. Thus, proton-radioactivity guides merging these types of theoretical approaches, which is of broader relevance for any few-body quantum system. Here, we report experimental measurements of proton-emission branches from an isomeric state in 54mNi, which were visualized in four dimensions in a newly developed detector. We show that these decays, which carry an unusually high angular momentum, ℓ = 5 and ℓ = 7, respectively, can be approximated theoretically with a potential model for the proton barrier penetration and a shell-model calculation for the overlap of the initial and final wave functions.

The LISE package: Solvers for static and time-dependent superfluid local density approximation equations in three dimensions

Nuclear implementation of the density functional theory (DFT) is at present the only microscopic framework applicable to the whole nuclear landscape. The extension of DFT to superfluid systems in the spirit of the Kohn-Sham approach, the superfluid local density approximation (SLDA) and its extension to time-dependent situations, time-dependent superfluid local density approximation (TDSLDA), have been extensively used to describe various static and dynamical problems in nuclear physics, neutron star crust, and cold atom systems. In this paper, we present the codes that solve the static and time-dependent SLDA equations in three-dimensional coordinate space without any symmetry restriction. These codes are fully parallelized with the message passing interface (MPI) library and the time-dependent code takes advantage of graphic processing units (GPU) for accelerating execution. The dynamic code has checkpoint/restart capabilities and for initial conditions one can use any generalized Slater determinant type of wave function. By generating the appropriate initial quasi-particle wave-functions in a static calculation only, the time-dependent code can describe a large number of physical problems: nuclear fission, collisions of heavy ions, the interaction of quantized vortices with nuclei in the nuclear star crust, excitation of superfluid fermion systems by time dependent external fields, quantum shock waves, domain wall generation and propagation, the dynamics of the Anderson-Bogoliubov-Higgs mode, dynamics of fragmented condensates, vortex rings dynamics, generation and dynamics of quantized vortices, their crossing and recombinations and the incipient phases of quantum turbulence. Program summaryProgram title: LISECPC library link to program files:https://doi.org/10.17632/mwr7rsxpjw.1Licensing provisions: BSD 3-ClauseProgramming language: C, CUDANature of problem: The description of nuclear fission and nuclear reactions within the mean field approximation in real time within the extension of the density functional theory to superfluid systems is an extremely computationally demanding problem, which requires the solutions of a very large system of nonlinear coupled complex partial differential equations in 3+1 coordinates. Similar problems also appear in the case of cold atoms and in the dynamics of the neutron star crust, which have been tackled within the same framework with the same codes, using appropriate initial quasi-particle wave functions and/or an appropriate time-dependent external potential.Solution method: The evolution equations are discretized on a 3-dimensional spatial lattice and propagated in time. Spatial derivatives are evaluated using the fast Fourier transform technique. The propagation in time is performed using a predictor-modifier-corrector algorithm due to Adams-Bashforth-Milne, which requires only two evaluations of the right hand side of the equations per time step. The numerical accuracy of the time integration is ∼O(Δt)6. This method has a low truncation error, excellent numerical stability, and low roundoff errors.Additional comments including restrictions and unusual features: The code has been implemented on a variety of supercomputers (Jaguar, Titan, Piz Daint, Tsubame, Summit, Sierra) and demonstrates excellent scaling properties. The strong scaling capabilities can be significantly affected if a very large number of GPUs is used, when the communication time between processes overtakes the computation time as the dominant run time cost.

Controlled information transfer in continuous-time chiral quantum walks

In this paper we investigate properties of continuous time chiral quantum walks, which possess complex valued edge weights in the underlying graph structure, together with an initial Gaussian wavefunction spread over a number of vertices. We demonstrate that, for certain graph topology and phase matching conditions, we are able to direct the flow of probability amplitudes in a specific direction inside the graph network. We design a quantum walk graph analogue of an optical circulator which is a combination of a cycle and semi-infinite chain graphs. Excitations input into the circulator from a semi-infinite chain are routed in a directionally biased fashion to output to a different semi-infinite chain. We examine in detail a two port circulator graph which spatially separates excitations flowing back in forth between the two semi-finite chains to directionally occupy the top or bottom half of the cycle portion of the circulator. This setup can be used, for example, to detect non-Markovian processes, which leads to information and energy back-flow from the bath back into the system.

Construction and evolution of knotted vortex tubes in incompressible Schrödinger flow

We propose a theoretical method for constructing an initial two-component wave function that can be transformed into a knotted velocity field with finite kinetic energy and enstrophy. The wave function is constructed using two complex-valued polynomials, with one determining the desired shape of the knotted central axis and the other encoding the twisting nature of vortex lines, which facilitates the study of helicity conversions. We construct six knotted vortex fields with various centerline and twist helicity as initial conditions for direct numerical simulation of incompressible Schrödinger flow (ISF) in a periodic box. Although the evolution of morphological structure is similar for ISF and classical viscous flow, with all the knots becoming untied after a short time to form one or more separate vortex rings, their statistics are quite different. During the critical period of vortex reconnection, the increase in enstrophy is much more moderate in ISF than in viscous flow, indicating that the Landau–Lifshitz term in ISF inhibits the energy cascade from large to small scales. We also find that the centerline helicity changes dramatically during reconnection, which is consistent with the evolution of the geometrical shape of vortex lines.

Consistency Proof for Multi-time Schr\xf6dinger Equations with Particle Creation and Ultraviolet Cut-Off

For multi-time wave functions, which naturally arise as the relativistic particle-position representation of the quantum state vector, the analog of the Schrödinger equation consists of several equations, one for each time variable. This leads to the question of how to prove the consistency of such a system of PDEs. The question becomes more difficult for theories with particle creation, as then different sectors of the wave function have different numbers of time variables. Petrat and Tumulka (2014) gave an example of such a model and a non-rigorous argument for its consistency. We give here a rigorous version of the argument after introducing an ultraviolet cut-off into the creation and annihilation terms of the multi-time evolution equations. These equations form an infinite system of coupled PDEs; they are based on the Dirac equation but are not fully relativistic (in part because of the cut-off). We prove the existence and uniqueness of a smooth solution to this system for every initial wave function from a certain class that corresponds to a dense subspace in the appropriate Hilbert space.

Inflationary dynamics and particle production in a toroidal Bose-Einstein condensate

We present a theoretical study of the dynamics of a Bose-Einstein condensate (BEC) trapped inside an expanding toroid that can realize an analogue inflationary universe. As the system expands, we find that phonons in the BEC undergo redshift and damping due to quantum pressure effects. We predict that rapidly expanding toroidal BEC's can exhibit spontaneous particle creation, and study this phenomenon in the context of an initial coherent state wavefunction. We show how particle creation would be revealed in the atom density and density correlations, and discuss connections to the cosmological theory of inflation.

On the Quantum Mechanical Measurement Process

The quantum mechanical measurement process is analyzed by means of an explicit generic model describing the interaction between object and measuring device. The solution of the Schrodinger equation for the whole system reflects the ‘collapse’ of the object wave function. A necessary condition is a sufficiently sharply peaked initial measurement device wave function, which is guaranteed in its classical limit. With this assumption, it is in particular proven that the off-diagonal elements of the object density matrix vanish. This study therefore shows the reduction of the object state to be a consequence of Hamiltonian evolution of the total system.

A strong-field approach with realistic wave functions to the above-threshold ionization of Ba+

We study the above-threshold ionization of atoms in intense circularly polarized laser pulses. In order to compute photoelectron energy spectra, we apply the strong-field approximation with different models for the initial state wave function. Specifically, we compare the spectra for singly ionized Barium (Ba+) using hydrogenic wave functions and realistic one-particle wave functions obtained by multiconfiguration Dirac–Hartree–Fock computations, respectively. As a particular example, we discuss the dependence of the photoelectron spectra on the magnetic quantum number m of the initial state and we reproduce the well known m-selectivity in strong-field ionization. Here, we show that the photoelectron spectra exhibit noticeable differences for the two models of the initial state and that the m-selectivity is enhanced when realistic wave functions are used. We conclude that the description of strong-field processes within the strong-field approximation will benefit from a realistic description of the initial atomic state.

Transient Quantum Beat Oscillations in Extreme-Relativistic Diffraction in Time

In the solution of the Klein-Gordon equation for the shutter problem, we prove that, at internuclear distances, a relativistic beam of Pi-mesons has a probability density which oscillates in time in a similar way to the spatial dependence in optical Fresnel diffraction from a straight edge. However, for an extreme-relativistic beam, the Fresnel oscillations turn into quantum damped beat oscillations. We prove that quantum beat oscillations are the consequence, at extreme-relativistic velocities, of the interference between the initial incident wave function, and the Green’s function in the relativistic shutter problem. This is a pure quantum relativistic phenomenon.

The dynamics of the early universe in a model with radiation and a generalized Chaplygin gas

The early universe is modeled through the quantization of a Friedmann-Robertson-Walker model with positive curvature of the spatial hypersurfaces. In this model, the universe is filled by two fluids: radiation and a generalized Chaplygin gas. The quantization of this model is made following the prescriptions due to J. A. Wheeler and B. DeWitt. Using the Schutz's formalism, the time notion is recovered and the Wheeler-DeWitt equation transforms into a time dependent Schr\"{o}dinger equation, which rules the dynamics of the early universe, under the action of an effective potential $V_{eff}$. That potential, depends on three parameters. Depending on the values of these parameters, $V_{eff}$ may have two different shapes. $V_{eff}(a)$ may have the shape of a barrier or the shape of a well followed by a barrier. We solve, numerically, the appropriate time dependent Schr\"{o}dinger equation and obtain the time evolution of an initial wave function, for both cases. These wave functions satisfy suitable boundary conditions. For both shapes of $V_{eff}$, we compute the tunneling probability, which is a function of the mean kinetic energy associated to the radiation energy $E_m$ and of the three parameters of the generalized Chaplygin gas: $\alpha$, $A$ and $B$. The tunneling probabilities, for both shapes of $V_{eff}$, indicates that the universe should nucleate with the highest possible values of $E_m$, $\alpha$, $A$ and $B$. Finally, we study the classical universe evolution after the wavefunction has tunneled $V_{eff}$. The calculations show that the universe may emerge from the Planck era in an inflationary phase.

Bootstrap embedding with an unrestricted mean-field bath.

A suite of quantum embedding methods have recently been developed where the Schmidt decomposition is applied to the full system wavefunction to derive basis states that preserve the entanglement between the fragment and the bath. The quality of these methods can depend heavily on the quality of the initial full system wavefunction. Most of these methods, including bootstrap embedding (BE) [M. Welborn et al; J. Chem. Phys. 145, 074102 (2016)], start from a spin-restricted mean-field wavefunction [call this restricted BE (RBE)]. Given that spin-unrestricted wavefunctions can capture a significant amount of strong correlation at the mean-field level, we suspect that starting from a spin-unrestricted mean-field wavefunction will improve these embedding methods for strongly correlated systems. In this work, BE is generalized to an unrestricted Hartree-Fock bath [call this unrestricted BE (UBE)], and UBE is applied to model hydrogen ring systems. UBE's improved versatility over RBE is utilized to calculate high spin symmetry states that were previously unattainable with RBE. Ionization potentials, electron affinities, and spin-splittings are computed using UBE with accuracy on par with spin-unrestricted coupled cluster singles and doubles. Even for cases where RBE is viable, UBE converges more reliably. We discuss the limitations or weaknesses of each calculation and how improvements to RBE and density matrix embedding theory these past few years can also improve UBE.

Probing short-range correlations in the deuteron via incoherent diffractive J/ψ production with spectator tagging at the EIC

Understanding the role of Quantum Chromodynamics in generating nuclear forces is important for uncovering the mechanism of short-ranged nuclear interactions and their manifestation in short range correlations (SRC). The future Electron-Ion-Collider (EIC) at Brookhaven National Laboratory in the US will provide an unprecedented opportunity to systematically investigate the underlying physics of SRC for energies and kinematic regions that are otherwise impossible to reach. We study SRCs in electron-deuteron scattering events using the Monte Carlo event generator BeAGLE. Specifically, we investigate the sensitivity of observables to high internal nucleon momentum in incoherent diffractive J/ψ vector meson production. In a plane wave impulse approximation, the initial state deuteron wave function can be accessed directly from the four-momentum of the spectator nucleon. We use realistic physics estimates and a conceptual far-forward detector simulations of the EIC to fully reveal the potential of this exclusive process. In particular, we provide the luminosity and detector requirements necessary to study SRCs in the deuteron at an EIC.

Proton-transfer dynamics in ionized water chains using real-time time-dependent density functional theory

In density functional-theoretic studies of photoionized water-based systems, the role of charge localization in proton-transfer dynamics is not well understood. This is due to the inherent complexity in extracting the contributions of coupled electron-nuclear non-adiabatic dynamics in the presence of exchange and correlation functional errors. In this work, we address this problem by simulating a model system of ionized linear H-bonded water clusters using real-time Time Dependent Density Functional Theory (rt-TDDFT)-based Ehrenfest dynamics. Our aim is to understand how self-interaction error in semilocal exchange and correlation functionals affects the probability of proton transfer. In particular, we show that for H-bonded (H$_2$O)$_n^+$ chains (with $n>3$), the proton-transfer probability attains a maximum, becoming comparable to that predicted by hybrid functionals. This is because the formation of hemibonded-type geometries is largely suppressed in extended H-bonded structures. We also show how the degree of localization of the initial photo-hole is connected to the probability of a proton-transfer reaction, as well as to the separation between electronic and nuclear charge. These results are compared to those obtained with adiabatic dynamics where the initial wavefunction is allowed to relax to the ground state of the ion cluster, explaining why different functionals and dynamical approaches lead to quantitatively different results.

Understanding the deconfinement process with the infinite square wall model

The infinite square wall model is one of the simplest models to have been introduced in quantum mechanics. We employ this model to illustrate the quantum transitions of particles due to the deconfinement process. With the infinite square wall, we propose that a shift of the wall to a larger x position corresponds to the process of deconfinement with strong interaction. Two limits of the wall’s movement are considered: extremely slow and fast. Particle transitions between different eigenstates are calculated in this changing potential. We extend these conclusions in the infinite wall model to the field of heavy-ion collisions where a fireball like our early universe is generated. The magnitude of particle quantum transitions between different states can be used to quantify the difference between its initial and final wave functions in the fireball. A larger transition rate corresponds with a higher fireball temperature. This can help to extract the initial temperature of the fireball to determine whether the deconfined medium (also called ‘small universe’) is produced in the heavy-ion collisions. This manuscript is intended for college-level use, to help students understand the concepts of quantum transitions and the deconfinement process. The potential readers of this manuscript are those who are familiar with quantum mechanics and particle physics.

Time-dependent relaxation of observables in complex quantum systems

We consider time-dependent relaxation of observables in quantum systems of chaotic and regular type. Using statistical arguments and exact numerical solutions we show that the spread of the initial wave function in the Hilbert space and the main characteristics of evolution of observables have certain generic features. The study compares examples of regular dynamics, a completely chaotic case of the Gaussian orthogonal ensemble, a bosonic system with random interactions, and a fully realistic case of the time evolution of various initial non-stationary states in the nuclear shell model. In the case of the Gaussian orthogonal ensemble we show that the survival probability obtained analytically also fully defines the relaxation timescale of observables. This is not the case in general. Using the realistic nuclear shell model and the quadrupole moment as an observable we demonstrate that the relaxation time is significantly longer than defined by the survival probability of the initial state. The full analysis does not show the presence of an analog of the Lyapunov exponent characteristic for examples of classical chaos.