Three-dimensional Quantum Research Articles

A sensitive Potentiometric resolved ratiometric Photoelectrochemical aptasensor for Escherichia coli detection fabricated with non-metallic nanomaterials

In this work, a sensitive potentiometric resolved ratiometric photoelectrochemical aptasensor for Escherichia coli (E. coli) detection was successfully fabricated with non-metallic nanomaterials. To avoid the use of precious metals or heavy metals, three-dimensional graphene hydrogel-loaded carbon quantum dots (C-dots/3DGH) and graphene-like carbon nitride (g-C3N4) with excellent PEC activity and matched potential were prepared. These two materials were modified onto two adjacent areas on the ITO electrode. By applying different bias voltage, the cathodic current generated by C-dots/3DGH and the anodic current generated by g-C3N4 can be clearly distinguished and would not interfere with one another. Then E. coli aptamer was modified onto the surface of C-dots/3DGH. In the presence of targets, the binding of E. coli with aptamer lead to the steric hindrance greatly increased and the cathodic current decreased significantly. Meanwhile, the anodic current generated by g-C3N4 was not influenced and it can serve as a stable reference to evaluate the environmental factors. Therefore, the concentration of E. coli can be quantified by the ratio of cathodic current to anodic current, which can effectively eliminate these analyte-independent factors and provide a more precise analysis. In addition, this ratiometric PEC biosensor also showed a good sensitivity and a wide linear range (2.9 cfu/mL to 2.9 × 106 cfu/mL).

Constructing three-dimensional porous graphene-carbon quantum dots/g-C3N4 nanosheet aerogel metal-free photocatalyst with enhanced photocatalytic activity

Photocatalysis has been widely considered to be an effective way for solving the worldwide environmental pollution issues. Herein, a new type of three-dimensional (3D) ternary graphene-carbon quantum dots/g-C3N4 nanosheet (GA-CQDs/CNN) aerogel visible-light-driven photocatalyst was synthesized via a two-step hydrothermal method. In this unique ternary photocatalyst, both carbon quantum dots (CQDs) and reduced graphene oxide (rGO) could improve the visible light absorption and promote the charge separation. Furthermore, reduced graphene oxide (rGO) could act as a supportor for the 3D framework. Such a ternary system overcame the drawbacks of bulk g-C3N4 (BCN) and achieved the enhanced photocatalytic activity and long-term stability. As a result, the methyl orange (MO) removal ratio of GA-CQDs/CNN-24% was up to 91.1%, which was about 7.6 times higher than that of bulk g-C3N4 (BCN) under the identical conditions. Moreover that GA-CQDs/CNN-24% exhibited inappreciable loss of photocatalytic activity after four-cycle degradation processes. Finally, the photocatalytic mechanism of GA-CQDs/CNN-24% was interpreted both theoretically and experimentally.

Magnetic monopoles and nonassociative deformations of quantum theory

We examine certain nonassociative deformations of quantum mechanics and gravity in three dimensions related to the dynamics of electrons in uniform distributions of magnetic charge. We describe a quantitative framework for nonassociative quantum mechanics in this setting, which exhibits new effects compared to ordinary quantum mechanics with sourceless magnetic fields, and the extent to which these theoretical consequences may be experimentally testable. We relate this theory to noncommutative Jordanian quantum mechanics, and show that its underlying algebra can be obtained as a contraction of the alternative algebra of octonions. The uncontracted octonion algebra conjecturally describes a nonassociative deformation of three-dimensional quantum gravity induced by magnetic monopoles, which we propose is realised by a non-geometric Kaluza-Klein monopole background in M-theory.

Three-body problem in d-dimensional space: Ground state, (quasi)-exact-solvability

As a straightforward generalization and extension of our previous paper [A. V. Turbiner et al., “Three-body problem in 3D space: Ground state, (quasi)-exact-solvability,” J. Phys. A: Math. Theor. 50, 215201 (2017)], we study the aspects of the quantum and classical dynamics of a 3-body system with equal masses, each body with d degrees of freedom, with interaction depending only on mutual (relative) distances. The study is restricted to solutions in the space of relative motion which are functions of mutual (relative) distances only. It is shown that the ground state (and some other states) in the quantum case and the planar trajectories (which are in the interaction plane) in the classical case are of this type. The quantum (and classical) Hamiltonian for which these states are eigenfunctions is derived. It corresponds to a three-dimensional quantum particle moving in a curved space with special d-dimension-independent metric in a certain d-dependent singular potential, while at d = 1, it elegantly degenerates to a two-dimensional particle moving in flat space. It admits a description in terms of pure geometrical characteristics of the interaction triangle which is defined by the three relative distances. The kinetic energy of the system is d-independent; it has a hidden sl(4, R) Lie (Poisson) algebra structure, alternatively, the hidden algebra h(3) typical for the H3 Calogero model as in the d = 3 case. We find an exactly solvable three-body S3-permutationally invariant, generalized harmonic oscillator-type potential as well as a quasi-exactly solvable three-body sextic polynomial type potential with singular terms. For both models, an extra first order integral exists. For d = 1, the whole family of 3-body (two-dimensional) Calogero-Moser-Sutherland systems as well as the Tremblay-Turbiner-Winternitz model is reproduced. It is shown that a straightforward generalization of the 3-body (rational) Calogero model to d > 1 leads to two primitive quasi-exactly solvable problems. The extension to the case of non-equal masses is straightforward and is briefly discussed.

Moving Boundary Truncated Grid Method for Wave Packet Dynamics.

The moving boundary truncated grid method is developed to significantly reduce the number of grid points required for wave packet propagation. The time-dependent Schrödinger equation (TDSE) and the imaginary time Schrödinger equation (ITSE) are integrated using an adaptive algorithm which economizes the number of grid points. This method employs a variable number of grid points in the Eulerian frame (grid points fixed in space) and adaptively defines the boundaries of the truncated grid. The truncated grid method is first applied to the time integration of the TDSE for the photodissociation dynamics of NOCl and a three-dimensional quantum barrier scattering problem. The time-dependent truncated grid precisely captures the wave packet evolution for the photodissociation of NOCl and finely adjusts according to the process of the wave packet bifurcation into reflected and transmitted components for the barrier scattering problem. The truncated grid method is also applied to the time integration of the ITSE for the eigenstates of quantum systems. Compared to the full grid calculations, the truncated grid method requires fewer grid points to achieve high accuracy for the stationary state energies and wave functions for a two-dimensional double well potential and the Ar trimer. Therefore, the truncated grid method demonstrates a significant reduction in the number of grid points needed to perform accurate wave packet propagation governed by the TDSE or the ITSE.

Hydrogenic impurity bound polaron in an anisotropic quantum dot

The effect of the electron–phonon interaction on an electron bound to a hydrogenic impurity in a three-dimensional (3D) anisotropic quantum dot (QD) is studied theoretically. We use the Landau–Pekar variational approach to calculate the binding energy of ground state (GS) and first-excited state (ES) with considering electron–phonon interaction. The expressions of the GS and ES energies under investigation depict a rich variety of dependent relationship with the variational parameters in three different limiting cases. Numerical calculations were performed for ZnSe QDs with different confinement lengths in the xy-plane and the z-direction, respectively. It is illustrated that binding energies of impurity polarons corresponding to each level are larger in small QDs. Furthermore, the contribution to binding energy from phonon is about 15% of the total binding energy.

Decay Rates of the Compressible Hall-MHD Equations for Quantum Plasmas

In this paper, we consider the global existence and decay rates of strong solutions to the three-dimensional compressible quantum Hall-magneto-hydrodynamics equations. By combing the Lp-Lq estimates for the linearized equations and a standard energy method, the global existence and its convergence rates are obtained in various norms for the solution to the equilibrium state in the whole space when the initial perturbation of the stationary solution is small in some Sobolev norms. More precisely, the decay rates in time of the solution and its first order derivatives in L2-norm are obtained when the L1-norm of the perturbation is bounded.

Simple anisotropic three-dimensional quantum spin liquid with fractonlike topological order

We present a three-dimensional cubic lattice spin model, anisotropic in the $\hat{z}$ direction, that exhibits fracton topological order. The latter is a novel type of topological order characterized by the presence of immobile pointlike excitations, named fractons, residing at the corners of an operator with two-dimensional support. As other recent fracton models, ours exhibits a subextensive ground state degeneracy: On an $L_x\times L_y\times L_z$ three-torus, it has a $2^{2L_z}$ topological degeneracy, and an additional non-topological degeneracy equal to $2^{L_xL_y-2}$. The fractons can be combined into composite excitations that move either in a straight line along the $\hat{z}$ direction, or freely in the $xy$ plane at a given height $z$. While our model draws inspiration from the toric code, we demonstrate that it cannot be adiabatically connected to a layered toric code construction. Additionally, we investigate the effects of imposing open boundary conditions on our system. We find zero energy modes on the surfaces perpendicular to either the $\hat{x}$ or $\hat{y}$ directions, and their absence on the surfaces normal to $\hat{z}$. This result can be explained using the properties of the two kinds of composite two-fracton mobile excitations.

Signatures of a gearwheel quantum spin liquid in a spin- 12 pyrochlore molybdate Heisenberg antiferromagnet

We theoretically investigate the low-temperature phase of the recently synthesized Lu$_2$Mo$_2$O$_5$N$_2$ material, an extraordinarily rare realization of a $S=1/2$ three-dimensional pyrochlore Heisenberg antiferromagnet in which Mo$^{5+}$ are the $S=1/2$ magnetic species. Despite a Curie-Weiss temperature ($\Theta_{\rm CW}$) of $-121(1)$ K, experiments have found no signature of magnetic ordering $or$ spin freezing down to $T^*\approx0.5$ K. Using density functional theory, we find that the compound is well described by a Heisenberg model with exchange parameters up to third nearest neighbors. The analysis of this model via the pseudofermion functional renormalization group method reveals paramagnetic behavior down to a temperature of at least $T=|\Theta_{\rm CW}|/100$, in agreement with the experimental findings hinting at a possible three-dimensional quantum spin liquid. The spin susceptibility profile in reciprocal space shows momentum-dependent features forming a "gearwheel" pattern, characterizing what may be viewed as a molten version of a chiral noncoplanar incommensurate spiral order under the action of quantum fluctuations. Our calculated reciprocal space susceptibility maps provide benchmarks for future neutron scattering experiments on single crystals of Lu$_2$Mo$_2$O$_5$N$_2$.

Quantum criticality among entangled spin chains

An important challenge in magnetism is the unambiguous identification of a quantum spin liquid 1,2 , of potential importance for quantum computing. In such a material, the magnetic spins should be fluctuating in the quantum regime, instead of frozen in a classical long-range-ordered state. While this requirement dictates systems 3,4 wherein classical order is suppressed by a frustrating lattice 5 , an ideal system would allow tuning of quantum fluctuations by an external parameter. Conventional three-dimensional antiferromagnets can be tuned through a quantum critical point—a region of highly fluctuating spins—by an applied magnetic field. Such systems suffer from a weak specific-heat peak at the quantum critical point, with little entropy available for quantum fluctuations 6 . Here we study a different type of antiferromagnet, comprised of weakly coupled antiferromagnetic spin-1/2 chains as realized in the molecular salt K2PbCu(NO2)6. Across the temperature–magnetic field boundary between three-dimensional order and the paramagnetic phase, the specific heat exhibits a large peak whose magnitude approaches a value suggestive of the spinon Sommerfeld coefficient of isolated quantum spin chains. These results demonstrate an alternative approach for producing quantum matter via a magnetic-field-induced shift of entropy from one-dimensional short-range order to a three-dimensional quantum critical point. Exploiting the magnetic field-induced shift of entropy in certain molecular salts when going from 1D short-range ordering to a 3D quantum critical point could provide a route for producing strongly fluctuating quantum materials.

Symmetry breaking, Josephson oscillation and self-trapping in a self-bound three-dimensional quantum ball

We study spontaneous symmetry breaking (SSB), Josephson oscillation, and self-trapping in a stable, mobile, three-dimensional matter-wave spherical quantum ball self-bound by attractive two-body and repulsive three-body interactions. The SSB is realized by a parity-symmetric (a) one-dimensional (1D) double-well potential or (b) a 1D Gaussian potential, both along the z axis and no potential along the x and y axes. In the presence of each of these potentials, the symmetric ground state dynamically evolves into a doubly-degenerate SSB ground state. If the SSB ground state in the double well, predominantly located in the first well (z > 0), is given a small displacement, the quantum ball oscillates with a self-trapping in the first well. For a medium displacement one encounters an asymmetric Josephson oscillation. The asymmetric oscillation is a consequence of SSB. The study is performed by a variational and a numerical solution of a non-linear mean-field model with 1D parity-symmetric perturbations.

Phase Diagrams of Three-Dimensional Anderson and Quantum Percolation Models Using Deep Three-Dimensional Convolutional Neural Network

The three-dimensional Anderson model is a well-studied model of disordered electron systems that shows the delocalization--localization transition. As in our previous papers on two- and three-dimensional (2D, 3D) quantum phase transitions [J. Phys. Soc. Jpn. {\bf 85}, 123706 (2016), {\bf 86}, 044708 (2017)], we used an image recognition algorithm based on a multilayered convolutional neural network. However, in contrast to previous papers in which 2D image recognition was used, we applied 3D image recognition to analyze entire 3D wave functions. We show that a full phase diagram of the disorder-energy plane is obtained once the 3D convolutional neural network has been trained at the band center. We further demonstrate that the full phase diagram for 3D quantum bond and site percolations can be drawn by training the 3D Anderson model at the band center.

Unifying static and dynamic properties in three-dimensional quantum antiferromagnets

Quantum Monte Carlo simulations offer an unbiased means to study the static and dynamic properties of quantum critical systems, while quantum field theory provides direct analytical results. We study three dimensional, critical quantum antiferromagnets by performing a combined analysis using both quantum field theory calculations and quantum Monte Carlo data. Explicitly, we analyze the order parameter (staggered magnetization), N\'eel temperature, quasiparticle gaps, and the susceptibilities in the scalar and vector channels. We connect the two approaches by deriving descriptions of the quantum Monte Carlo observables in terms of the quasiparticle excitations of the field theory. The remarkable agreement not only unifies the description of the static and dynamic properties of the system, but also constitutes a thorough test of perturbative O(3) quantum field theory and opens new avenues for the analytical guidance of detailed numerical studies.

Ground state of an exciton in a three-dimensional parabolic quantum dot: Convergent perturbative calculation

Working in the effective-mass approximation, we apply a powerful convergent perturbative technique of Turbiner's to the calculation of the ground state energy and the wave function of an exciton confined to a three-dimensional parabolic quantum dot. Unlike the usual Rayleigh–Schrödinger perturbation theory, Turbiner's approach works well even in the regime of strong coupling and does not require the knowledge of the full solution to the undisturbed problem. The second-order convergent calculation presented below is in excellent agreement with the results of exact numerical simulations for a wide range of system's confinement parameters.

Development of polychromatic ultraviolet light-emitting diodes based on three-dimensional AlGaN quantum wells

We present polychromatic ultraviolet (UV) spectra from electrically driven light-emitting diodes (LEDs) based on three-dimensional (3D) AlGaN quantum wells (QWs). The LED structure is fabricated on AlN composed of (0001) facets, facets, and vicinal (0001) facets with bunched steps. Although subsequent n-AlGaN growth tends to eliminate step bunching, appropriate design of the growth procedures preserves the 3D structure of AlN even in the LED structure. Because the QWs on the (0001) facets and bunched steps emit different colors, the fabricated LED exhibits polychromatic deep UV emission.

Quantum Transport Simulation of Nanowire Resonant Tunneling Diodes Based on a Wigner Function Model With Spatially Dependent Effective Masses

We present a self-consistent and three-dimensional quantum simulation for nanowire resonant tunneling diodes (RTDs) based on the Wigner transport equation with spatially dependent effective masses (SDEM), which is discretized by a third-order upwind difference scheme for high-accuracy calculation. Our calculation shows that the current density/voltage ( $J\text{--}V$ ) characteristics of nanowire RTDs with a radius ( $R$ ) $ 5 nm largely deviate from those of the one-dimensional RTDs. As $R$ decreases below 5 nm, the peak-to-valley ratio (PVR) of the low- $V$ negative differential resistance (NDR) decreases rapidly, and the high- $V$ NDR peak shifts sensitively to lower $V$ and becomes sharper. In this study, these results are shown to be closely related to the SDEM. According to our analysis, the SDEM along the transport direction contributes to the formation of an ‘effective double barrier’ in the energy subbands that is higher than the double barrier expected by the band offset, and the SDEM along the confinement direction reduces the height of the effective double barrier. The performance of nanowire RTDs with $R 5 nm was proven to be highly dependent on $R$ because of the SDEM along the confinement direction.

The Effect of Temperature and Electric Field on a Quantum Pseudodot Qubit

The electron’s probability density (EPD) and the oscillating period (OP) of an electron confined by a three-dimensional RbCl quantum pseudodot (QPD) are studied. Calculations are performed by employing variational method of Pekar type (VMPT) and the quantum statistics theory (QST).The influences of the temperature and electric field on the EPD and the OP of the RbCl QPD qubit have been derived in detail. According to the obtained results, it is observed that the EPD and the OP increase (decrease) with raising temperature at lower (higher) temperature region. They are decaying functions of the electric field.

Conformal QED in two-dimensional topological insulators

It has been shown that local four-fermion interactions on the edges of two-dimensional time-reversal-invariant topological insulators give rise to a new non-Fermi-liquid phase, called helical Luttinger liquid (HLL). Here, we provide a first-principle derivation of this HLL based on the gauge-theory approach. We start by considering massless Dirac fermions confined on the one-dimensional boundary of the topological insulator and interacting through a three-dimensional quantum dynamical electromagnetic field. Within these assumptions, through a dimensional-reduction procedure, we derive the effective 1 + 1-dimensional interacting fermionic theory and reveal its underlying gauge theory. In the low-energy regime, the gauge theory that describes the edge states is given by a conformal quantum electrodynamics (CQED), which can be mapped exactly into a HLL with a Luttinger parameter and a renormalized Fermi velocity that depend on the value of the fine-structure constant α.

On the Asymptotic Behavior of Eigenfunctions of the Continuous Spectrum at Infinity in Configuration Space for the System of Three Three-Dimensional Like-Charged Quantum Particles

To our knowledge there are no complete results, even not rigorously mathematically justified, related to a system of three and more quantum particles, interacting by Coulomb pair potentials, and expressed in terms of eigenfunctions. For the system of three such identical particles, asymptotic formulas describing the behavior of eigenfunctions at infinity in configuration space are suggested.

Three-dimensional Dirac semimetal and magnetic quantum oscillations in Cd3As2

Single crystals of topological Dirac semimetal Cd3As2 were synthesized using a modified vapour transport technique. The magnetization of Cd3As2 single crystals was measured in the temperature range from 4.2-300 K and magnetic field up to 5 T along [001] and [100] directions. In the low temperature region we observed the de Haas van Alphen (dHvA) oscillations which allow us to characterize the three dimensional Fermi surface by extracting its relevant parameters. The dHvA oscillations show the existence of two different Fermi surface cross sections and nontrivial Berry’s phase, which is the signature of Dirac fermion in Cd3As2.