Symmetric Wave Functions Research Articles

Scalar bosons with gravitational effects near Schwarzschild’s black hole: The Rindler recipe

In this study, we explore the quantum effects in the Schwarzschild spacetime for massive and massless scalar particles in the presence of an external gravitational field. The methodology involves the analytical solution of the Klein–Gordon equation for the scalar particles in the near-horizon spacetime limit, using Rindler approximation. The results show that the quantum effects differ significantly for the massive and massless cases, they possess similar characteristics near the event horizon. Bosons without mass that are distant from the event horizon undergo a reduced gravitational impact and possess a symmetric wave function that remains unchanged when they approach the event horizon. However, the symmetry is lost, indicating that the particle strives for a lower energy state and becomes erratic as it nears the event horizon. This aligns with the anticipated behavior of particles within the Schwarzschild horizon. The particles have an energy spectrum even for tremendous values of the Schwarzschild radius, which entails the validity of the Rindler approximation in the near horizon geometry. We have observed that the quantum effects of massive and massless particles differ based on the mass. Specifically, massive and massless scalars behave differently due to their geometric differences, which results in different eigenstates. Although they both tend to seek lower energy levels when they approach the event horizon, their behavior is not the same.

Double parton distributions with flavor interference from lattice QCD

We study double parton distributions with flavor interference in the nucleon and compare them with previous results for the flavor diagonal case. We investigate both unpolarized and polarized partons. We compare our lattice results with those obtained from the simple description of the proton in terms of an SU(6) symmetric three-quark wave function and find that this description fails for both flavor and polarization dependence. We also derive and test a factorization ansatz for the unpolarized flavor interference distribution in terms of single-parton distributions and find that this ansatz fails to a large extent.

Self-purification and entanglement revival in lambda matter

In this study, we explore the dynamics of entanglement in an ensemble of qutrits with a lambda-type level structure interacting with single-mode bosons. Our investigation focuses on zero-energy states within the subspace of totally symmetric wave functions. Remarkably, we observe a universal two-stage dynamics of entanglement with intriguing revival behavior. The revival of entanglement is a consequence of the self-purification process, where the quantum state relaxes and converges universally to a special dark state within the system.

Spin-active single photon emitters in hexagonal boron nitride from carbon-based defects

Most single photon emitters in hexagonal boron nitride have been identified as carbon substitutional defects, forming donor-acceptor systems. Unlike the most studied bulk emitters (i.e. color centers in diamond), these defects have no net spin, or have a single unpaired spin. By means of density functional calculations, we show that two non-adjacent carbon substitutional defects of the same type (i.e. CB-CB, and CN-CN), can have a triplet groundstate. In particular, one of such defects has a zero phonon line energy of 2.5 eV, and its triplet state is nearly 0.5 eV more stable than its singlet. The mechanism behind the destabilization of the singlet state is related to a larger electrostatic repulsion of a symmetric wave function in a charged lattice.

The single- and two-photon scattering in the waveguide QED coupling to a giant atom

The giant atom, which means the nonlocal atom-waveguide coupling, gives lots of newfangled physics. In this paper, we study the single- and two-photon scattering in the waveguide quantum electrodynamics on a two-level giant atom. For single-photon scattering, we find that the transmission rate is dependent on the atomic size. For the two-photon scattering, using a reasonable wave function hypothesis, we can get the two-photon scattering state, which consists of the symmetric and anti-symmetric plane wave functions. The other eigenstate is the two-photon bound state, which is orthogonal to the two-photon scattering state. We find that the spatial extent of the two-photon bound state is related to the detuning between waveguide and atom, which is distinguished from the character of the general atom. Our study is beneficial to photon control and the fundamental research of the two-photon scattering.

Prediction of Optimal Thickness of InAs/InGaAs Quantum Well

In this work, some properties of the InAs/InGaAs quantum well (QW) were calculated, such as the wave functions and the charge density of the 2D free electron gas (2DEG) by solving the Poisson- Schroedinger equation. The thinner capping layer gives charge densities forming inside the QW that are higher than the thicker values. The optimal thickness of the capping layer can be 10 nm due to the most stable charge density and fully symmetrical wave functions. Our result indicates that higher charge densities can be found with higher Si-delta doping concentrations. However, the distance of the Si-delta doping also affects the charge population. The charge density linearly decreases with a higher Si-delta doping spacer; the thickness was chosen as 7nm. We performed the growth with different concentrations of Si with optimal thicknesses and compared them with the calculated values. There is good agreement between the simulations and experiments with the lower Si-doping concentrations.

The exciton spectrum of the cylindrical quantum dot - quantum ring semiconductor nanostructure in an electric field

In the model of effective masses and rectangular potentials for an electron and a hole, the influence of a uniform electric field on the energy spectrum and wave functions of the exciton and the oscillator strengths of interband quantum transitions in the semiconductor (GaAs/AlxGa1-xAs) quantum dot-quantum ring nanostructure is theoretically investigated. The stationary Schrödinger equations for noninteracting quasiparticles in the presence of an electric field cannot be solved analytically. For their approximate solution, the unknown wave functions are sought in the form of an expansion over the complete set of cylindrically symmetric wave functions, and the electron energy is found by solving the corresponding secular equation. The exciton binding energy is found using perturbation theory.
 The dependences of the energy spectra, the wave functions of an electron, hole, and exciton, and the intensity of interband optical quantum transitions on the magnitude of the electric field strength are analyzed.

Anti-Hong–Ou–Mandel interference by coherent perfect absorption of entangled photons

Two-photon interference, known as the Hong–Ou–Mandel effect, has colossal implications for quantum technology. It was observed in 1987 with two photodetectors monitoring outputs of the beamsplitter illuminated by photon pairs: the coincidence rate of the detectors drops to zero when detected photons overlap in time. More broadly, bosons (e.g. photons) coalesce while fermions (e.g. electrons) anti-coalesce when interfering on a lossless beamsplitter. Quantum interference of bosons and fermions can be tested in a single—photonics platform, where bosonic and fermionic states are artificially created as pairs of entangled photons with symmetric and anti-symmetric spatial wavefunctions. We observed that interference on a lossy beamsplitter of a subwavelength thickness, or a coherent perfect absorber, reverses quantum interference in such a way that bosonic states anti-coalesce while fermionic states exhibit coalescent-like behavior. The ability to generate states of light with different statistics and manipulate their interference offers important opportunities for quantum information and metrology.

Impurity effect on the spectral parameters of an electron in a quantum dot–quantum ring semiconductor nanostructure

In the model of effective masses and rectangular potentials, the effect of a hydrogen-like donor impurity on the energy spectrum, electron wave functions and oscillator strengths of intraband quantum transitions in a quantum dot–quantum ring semiconductor nanostructure (GaAs/AlxGa1-xAs) is studied theoretically. The stationary Schrödinger equation for an electron interacting with an impurity cannot be solved analytically exactly. For its approximate solution, the unknown wave functions are sought in the form of an expansion over a complete set of cylindrically symmetric wave functions in the nanostructure without impurity, and the electron energy is found by solving the corresponding secular equation. The dependences of the energy spectrum, the binding energy of the electron with the impurity and the oscillator strengths of the quantum intraband transitions on the geometric parameters of the nanostructure are analyzed.

Supersolidity in the second layer of para-H2adsorbed on graphite

We calculated the phase diagram of the second layer of para-${\mathrm{H}}_{2}$ adsorbed on graphite using quantum Monte Carlo methods. The second layer shows an incommensurate triangular crystal structure. By using a symmetric wave function, which makes possible molecule exchanges, we observed that this nearly two-dimensional crystal shows a finite superfluid density around a total density of 0.1650 \AA{}${}^{\ensuremath{-}2}$. The superfluid fraction of this supersolid phase was found to be small, $(0.41\ifmmode\pm\else\textpm\fi{}0.05)%$, but still experimentally accessible.

Excitations of the nS States of Atomic Hydrogen by Electron Impact, Excitation Rate Coefficients, and Phase Shifts: Comparison with Positron Impact Excitation

The excitation cross-sections of the nS states of atomic hydrogen, n = 2 to 6, by electron impact on the ground state of atomic hydrogen were calculated using the variational polarized-orbital method at various incident electron energies in the range 10 to 122 eV. Converged excitation cross-sections were obtained using sixteen partial waves (L = 0 to 15). Excitation cross-sections to 2S state, calculated earlier, were calculated at higher energies than before. Results obtained using the hybrid theory (variational polarized orbital method) are compared to those obtained using other approaches such as the Born–Oppenheimer, close-coupling, R-matrix, and complex-exterior scaling methods using only the spherical symmetric wave functions. Phase shifts and elastic cross-sections are given at various energies and angular momenta. Excitation rate coefficients were calculated at various electron temperatures, which are required for plasma diagnostics in solar and astrophysics to infer plasma parameters. Excitation cross-sections are compared with those obtained by positron impact excitation.

One-dimensional spin-1/2 fermionic gases with two-body losses: Weak dissipation and spin conservation

We present a theoretical analysis of the dynamics of a one-dimensional spin-1/2 fermionic gas subject to weak two-body losses. Our approach highlights the crucial role played by spin conservation in the determination of the full time evolution. We focus in particular on the dynamics of a gas that is initially prepared in a Dicke state with a fully symmetric spin wave function, in a band insulator, or in a Mott insulator. In the latter case, we investigate the emergence of a steady symmetry-resolved purification of the gas. Our results could help with the modelization and understanding of recent experiments with alkaline-earth(-like) gases like ytterbium and fermionic molecules.

Using a post-version continuum distorted wave formalism for calculation of the fully differential cross section of helium atom single ionization by proton impact

In the present work, the fully differential cross section of single ionization of helium atom is calculated by fast proton impact. The calculations are done as a four-body formalism and by using a post-version continuum distorted wave theory with considering symmetric wave functions in the both initial and final channels. The ionization is considered from the ground and $$2^{1}S$$ excited states of helium atom. In order to investigate the role of the static electronic correlations, the calculations are performed by single-parameter Hylleraas and two-parameter Silverman as the ground state of helium atom wave functions. The results of the present theory are compared with the experiment in 1MeV proton impact energy and various values of the ejected electron energy and momentum transfer in the scattering and azimuthal planes. The results show that the present theory is able to predict the binary and recoil peaks as well as the experiment for ejected electron energies and momentum transfers are discussed in this manuscript.

Modern State of the Pauli Exclusion Principle and the Problems of Its Theoretical Foundation

The Pauli exclusion principle (PEP) can be considered from two aspects. First, it asserts that particles that have half-integer spin (fermions) are described by antisymmetric wave functions, and particles that have integer spin (bosons) are described by symmetric wave functions. It is called spin-statistics connection (SSC). The physical reasons why SSC exists are still unknown. On the other hand, PEP is not reduced to SSC and can be consider from another aspect, according to it, the permutation symmetry of the total wave function can be only of two types: symmetric or antisymmetric. They both belong to one-dimensional representations of the permutation group, while other types of permutation symmetry are forbidden. However, the solution of the Schrödinger equation may have any permutation symmetry. We analyze this second aspect of PEP and demonstrate that proofs of PEP in some wide-spread textbooks on quantum mechanics, basing on the indistinguishability principle, are incorrect. The indistinguishability principle is insensitive to the permutation symmetry of wave function. So, it cannot be used as a criterion for the PEP verification. However, as follows from our analysis of possible scenarios, the permission of states with permutation symmetry more general than symmetric and antisymmetric leads to contradictions with the concepts of particle identity and their independence. Thus, the existence in our Nature particles only in symmetric and antisymmetric permutation states is not accidental, since all symmetry options for the total wave function, except the antisymmetric and symmetric, cannot be realized. From this an important conclusion follows, we may not expect that in future some unknown elementary particles that are not fermions or bosons can be discovered.

The Pauli Exclusion Principle and the Problems of its Theoretical Substantiation1

The modern state of the Pauli Exclusion Principle (PEP) is discussed. PEP can be considered from two viewpoints. On the one hand, it asserts that particles with half-integer spin (fermions) are described by antisymmetric wave functions, and particles with integer spin (bosons) are described by symmetric wave functions. This is the so-called spin-statistics connection (SSC). As we will discuss, the physical reasons why SSC exists are still unknown. On the other hand, according to PEP, the permutation symmetry of the total wave functions can be only of two types: symmetric or antisymmetric, both belong to one-dimensional representations of the permutation group, all other types of permutation symmetry are forbidden; whereas the solution of the Schrodinger equation may have any permutation symmetry. It is demonstrated that the proof in some textbooks on quantum mechanics that only symmetric and antisymmetric states can exist is wrong. However, the scenarios, in which arbitrary permutation symmetry (degenerate permutation states) is permitted, lead to contradictions with the concepts of particle identity and their independence. Thus, the existence in our Nature of particles only in nondegenerate permutation states (symmetric and antisymmetric) is not accidental and so-called symmetrization postulate should not be considered as a postulate, since all other symmetry options for the total wave function may not be realized. From this an important conclusion follows: we may not expect that in the future some unknown elementary particles can be discovered that are not fermions or bosons.

Two-component axionic dark matter halos

We consider a two-component dark matter halo (DMH) of a galaxy containing ultra-light axions (ULA) of different mass. The DMH is described as a Bose–Einstein condensate (BEC) in its ground state. In the mean-field (MF) limit, we have derived the integro-differential equations for the spherically symmetrical wave functions of the two DMH components. We studied, numerically, the radial distribution of the mass density of ULA and constructed the parameters which could be used to distinguish between the two- and one-component DMH. We also discuss an interesting connection between the BEC ground state of a one-component DMH and Black Hole temperature and entropy, and Unruh temperature.

Axionic dark matter halos in the gravitational field of baryonic matter

We consider a dark matter halo (DMH) of a spherical galaxy as a Bose–Einstein condensate (BEC) of the ultra-light axions (ULA) interacting with the baryonic matter. In the mean-field (MF) limit, we have derived the integro-differential equation of the Hartree–Fock type for the spherically symmetrical wave function of the DMH component. This equation includes two independent dimensionless parameters: (i) [Formula: see text] is the ratio of baryon and axion total mases and (ii) [Formula: see text] is the ratio of characteristic baryon and axion spatial parameters. We extended our “dissipation algorithm” for studying numerically the ground state of the axion halo in the gravitational field produced by the baryonic component. We calculated the characteristic size, [Formula: see text] of DMH as a function of [Formula: see text] and [Formula: see text] and obtained an analytical approximation for [Formula: see text].

Minimally entangled state preparation of localized wave functions on quantum computers

Initializing a single site of a lattice scalar field theory into an arbitrary state with support throughout the quantum register requires $O({2}^{{n}_{Q}})$ entangling gates on a quantum computer with ${n}_{Q}$ qubits per site. It is conceivable that instead initializing to functions that are good approximations to states may have utility in reducing the number of required entangling gates. In the case of a single site of a noninteracting scalar field theory, initializing to a symmetric exponential wave function requires ${n}_{Q}\ensuremath{-}1$ entangling gates, the minimal number necessary to create an entangled state of all ${n}_{Q}$ qubits. This is compared with the ${2}^{{n}_{Q}\ensuremath{-}1}+{n}_{Q}\ensuremath{-}3+{\ensuremath{\delta}}_{{n}_{Q},1}$ required for a symmetric Gaussian wave function. In this work, we explore the initialization of one-site (${n}_{Q}=4$), two-site (${n}_{Q}=3$), and three-site (${n}_{Q}=3$) noninteracting scalar field theories with symmetric exponential wave functions using IBM's quantum simulators and quantum devices (Poughkeepsie and Tokyo). With the digitizations attainable with ${n}_{Q}=3,4$, these tensor-product wave functions are found to have large overlap with a Gaussian wave function and provide a suitable low-noise initialization for improvement and Somma inflation. In performing these simulations, we have employed a workflow that interleaves calibrations to mitigate systematic errors in production. The calibrations allow tolerance cuts on gate performance including the fidelity of the symmetrizing Hadamard gate, both in vacuum (${|\mathbf{0}\ensuremath{\rangle}}^{\ensuremath{\bigotimes}{n}_{Q}}$) and in medium (${n}_{Q}\ensuremath{-}1$ qubits initialized to an exponential function). The results obtained in this work are relevant to systems beyond scalar field theories, such as the deuteron radial wave function, two- and three-dimensional Cartesian-space wave functions, and nonrelativistic multinucleon systems built on a localized eigenbasis.

Counterintuitive effects of isotopic doping on the phase diagram of H2–HD–D2 molecular alloy

Molecular hydrogen forms the archetypical quantum solid. Its quantum nature is revealed by behavior which is classically impossible and by very strong isotope effects. Isotope effects between [Formula: see text], [Formula: see text], and HD molecules come from mass difference and the different quantum exchange effects: fermionic [Formula: see text] molecules have antisymmetric wavefunctions, while bosonic [Formula: see text] molecules have symmetric wavefunctions, and HD molecules have no exchange symmetry. To investigate how the phase diagram depends on quantum-nuclear effects, we use high-pressure and low-temperature in situ Raman spectroscopy to map out the phase diagrams of [Formula: see text]-HD-[Formula: see text] with various isotope concentrations over a wide pressure-temperature (P-T) range. We find that mixtures of [Formula: see text], HD, and [Formula: see text] behave as an isotopic molecular alloy (ideal solution) and exhibit symmetry-breaking phase transitions between phases I and II and phase III. Surprisingly, all transitions occur at higher pressures for the alloys than either pure [Formula: see text] or [Formula: see text] This runs counter to any quantum effects based on isotope mass but can be explained by quantum trapping of high-kinetic energy states by the exchange interaction.

Nonlinear absorption coefficient and refractive index changes of two-dimensional two-electron quantum dot in rigid confinement

The Hamiltonian and wavefunctions describing two-dimensional (2D) two-electron ZnO quantum dot in rigid confinement are developed. Then the Schrödinger equation is solved analytically and numerically for determining the ground and excited state energies. The ground state energy of 2D two-electron ZnO quantum dot (QD) in rigid confinement is studied using perturbation and variational methods. The obtained result show that our trial wavefunction is good enough to describe the 2D two-electron QD in rigid confinement. The wavefunction describing the ground state is the combination of symmetric spatial wavefunction and antisymmetric spin wavefunction which is a para-state. The ground state energy eigenvalue obtained by variational technique is a little above that of a perturbation technique. Based on this; the trial wavefunction for the excited state is developed. The excited state energy of 2D two-electron ZnO QD in rigid confinement is studied computationally using variational method. The wavefunction describing the excited state is the combination of symmetric spatial wavefunction with antisymmetric spin wavefunction (para-state) or vice versa (ortho-state). The para and ortho-state energies of the first excited state are calculated and their difference is twice of the exchange energy. Based on the obtained energy eigenvalues of the ground and the first excited state at the value of the coupling constant [Formula: see text] [Formula: see text] 1, the third-order nonlinear absorption coefficient and refractive index changes are investigated. The optical transition is only considered between the two lowest para states.