Three-dimensional Quantum Research Articles

Symmetry selected quantum dynamics of few electrons in nanopillar transistors

Study on single electron tunnel using current-voltage characteristics in nanopillar transistors at 298 K show that the mapping between the Nth electron excited in the central box ∼8.5 × 8.5 × 3 nm3 and the Nth tunnel peak is not in the one-to-one correspondence to suggest that the total number N of electrons is not the best quantum number for characterizing the quality of single electron tunnel in a three-dimensional quantum box transistor. Instead, we find that the best number is the sub-quantum number nz of the conduction z channel. When the number of electrons in nz is charged to be even and the number of electrons excited in the nx and ny are also even at two, the adding of the third electron into the easy nx/ny channels creates a weak symmetry breaking in the parity conserved x-y plane to assist the indirect tunnel of electrons. A comprehensive model that incorporates the interactions of electron-electron, spin-spin, electron-phonon, and electron-hole is proposed to explain how the excited even electrons can be stabilized in the electric-field driving channel. Quantum selection rules with hierarchy for the ni (i = x, y, z) and N = Σni are tabulated to prove the superiority of nz over N.

The generalized uncertainty principle with commuting coordinates

In this paper, we present a new D-dimensional generalized uncertainty principle (GUP) algebra with commuting coordinates which recovers [Formula: see text] in one dimension. We find two representations for this GUP: momentum representation and position representation. We discuss the GUP-corrected three-dimensional quantum mechanics in position representation for a small [Formula: see text]. Finally, we discuss the momentum wave function and GUP-corrected Fermi metal theory.

Three-dimensional quantum mechanics in a curved space based on the q-addition

In this paper, we extend the theory of the [Formula: see text]-deformed quantum mechanics in one dimension[Formula: see text] into three-dimensional case. We relate the [Formula: see text]-deformed quantum theory to the quantum theory in a curved space. We discuss the diagonal metric based on [Formula: see text]-addition in the Cartesian coordinate system and core radius of neutron star. We also discuss the diagonal metric based on [Formula: see text]-addition in the spherical coordinate system and [Formula: see text]-deformed Heisenberg atom model.

The Maxwell group in 2+1 dimensions and its infinite-dimensional enhancements

The Maxwell group in 2+1 dimensions is given by a particular extension of a semi-direct product. This mathematical structure provides a sound framework to study different generalizations of the Maxwell symmetry in three space-time dimensions. By giving a general definition of extended semi-direct products, we construct infinite-dimensional enhancements of the Maxwell group that enlarge the ISL(2, ℝ) Kac-Moody group and the {hat{mathrm{BMS}}}_3 group by including non-commutative supertranslations. The coadjoint representation in each case is defined, and the corresponding geometric actions on coadjoint orbits are presented. These actions lead to novel Wess-Zumino terms that naturally realize the aforementioned infinite-dimensional symmetries. We briefly elaborate on potential applications in the contexts of three-dimensional gravity, higher-spin symmetries, and quantum Hall systems.

Synthesis of three-dimensional Au-graphene quantum dots@Pt core–shell dendritic nanoparticles for enhanced methanol electro-oxidation

Au-graphene quantum dots (GQDs)@Pt core–shell nanodendrites are synthesized through a two-step reduction approach, in which Au forms the core, GQDs form an intermediate layer and dendritic Pt forms the shell. Among the above synthesized catalysts, the GQDs can manipulate the binding of reaction intermediates on the Pt surface as well as assemble π–π* conjugate bonds, thus forming a dendritic Pt shell instead of a compact Pt shell. The obtained core–shell structure was characterized by transmission electron microscopy, energy-dispersive x-ray and x-ray photoelectron spectroscopy. The methanol electro-oxidation was investigated in alkaline media on the Au-GQDs@Pt modified electrode via cyclic voltammetry, chronoamperometry and electrochemical impedance spectroscopy analysis. In particular, we discovered that Au–Pt assembled with GQDs could dramatically improve the activity and stability of the catalysts, owing to the synergistic effect raised by the GQDs, which exhibit prominent electron conductivity and great chemical/physical stability. It was also found that the Pt/Au mole ratios could control the Pt shell thickness, which significantly affected the catalytic methanol oxidation activity of the Au-GQDs@Pt nanodendrites. The Au-GQDs@Pt nanodendrites with optimum Pt/Au mole ratios of 1.0 exhibited a 2.5 times increase in electrocatalytic activity toward methanol oxidation compared with the commercial catalyst (Pt/C), and its CO tolerance was also greatly improved. The above results show that the Au-GQDs@Pt nanocatalysts have potential application prospects in direct methanol fuel cells.

A fast spectral method for the Uehling-Uhlenbeck equation for quantum gas mixtures: Homogeneous relaxation and transport coefficients

A fast spectral method (FSM) is developed to solve the Uehling-Uhlenbeck equation for quantum gas mixtures with generalized differential cross-sections. The computational cost of the proposed FSM is O(Mdv−1Ndv+1log⁡N), where dv is the dimension of the problem, Mdv−1 is the number of discrete solid angles, and N is the number of frequency nodes in each direction. Spatially-homogeneous relaxation problems are used to demonstrate that the FSM conserves mass and momentum/energy to the machine and spectral accuracy, respectively. Based on the variational principle, transport coefficients such as the shear viscosity, thermal conductivity, and diffusion are calculated by the FSM, which agree well with the analytical solutions. Then, the FSM is applied to find the accurate transport coefficients through an iterative scheme for the linearized quantum Boltzmann equation. The shear viscosity and thermal conductivity of three-dimensional quantum Fermi and Bose gases interacting through hard-sphere potential are calculated. For Fermi gas, the relative difference between the accurate and variational transport coefficients increases with fugacity; for Bose gas, the relative difference in thermal conductivity has similar behavior as the gas moves from the classical to degenerate limits, but the relative difference in shear viscosity decreases when the fugacity increases. Finally, the viscosity and diffusion coefficients are calculated for a two-dimensional equal-mole mixture of Fermi gases. When the molecular masses of the two components are the same, our numerical results agree with the variational solutions. However, when the molecular mass ratio is not one, large discrepancies between the accurate and variational results are observed; our results are reliable because (i) the method does not rely on any assumption on the form of velocity distribution function and (ii) the ratio between shear viscosity and entropy density satisfies the minimum bound predicted by the string theory.

On a conservative Fourier spectral Galerkin method for cubic nonlinear Schrödinger equation with fractional Laplacian

In this paper, a Crank–Nicolson Fourier spectral Galerkin method is proposed for solving the cubic fractional Schrödinger equation. Firstly, we discuss the mass and energy conservation laws for the nonlinear system and its corresponding fully discrete scheme. Secondly, the convergence with the spectral order accuracy in space and the second order of accuracy in time is exhibited. We perform one-dimensional calculation of the fractional derivative differential equation to verify our theoretical findings. Moreover, the proposed scheme is successfully applied to study two- and three-dimensional fractional quantum mechanics. Numerical results clearly exhibit that the fractional order can affect the shapes of soliton and rogue waves. The evolution of ground state solution can be clearly seen to be non-symmetrically configured when the fractional order becomes smaller.

Universal critical behavior in the ferromagnetic superconductor Eu(Fe0.75Ru0.25)2As2

The study of universal critical behavior is a crucial issue in a continuous phase transition, which groups various critical phenomena into universality classes for revealing microscopic electronic behaviors. The understanding of the nature of magnetism in Eu-based ferromagnetic superconductors is largely impeded by the infeasibility of performing inelastic neutron scattering measurements to deduce the microscopic magnetic behaviors and the effects on the superconductivity, due to the significant neutron absorption effect of natural $^{152}$Eu and unavailability of large single crystals. However, by systematically combining the neutron diffraction experiment, the first-principles calculations, and the quantum Monte Carlo simulations, we have obtained a perfectly consistent universal critical exponent value of $\beta=0.385(13)$ experimentally and theoretically for Eu(Fe$_{0.75}$Ru$_{0.25}$)$_{2}$As$_{2}$, from which the magnetism in the Eu-based ferromagnetic superconductors is identified as the universal class of a three-dimensional anisotropic quantum Heisenberg model with long-range magnetic exchange coupling. This study not only clarifies the nature of microscopic magnetic behaviors in the Eu-based ferromagnetic superconductors, but also opens a new avenue of systemic methodology for studying the universal critical behaviors associated with magnetic phase transitions in the area of magnetism and the spin fluctuations effects on the unconventional superconductivity.

Topological Lifshitz transitions and Fermi arc manipulation in Weyl semimetal NbAs

Surface Fermi arcs (SFAs), the unique open Fermi-surfaces (FSs) discovered recently in topological Weyl semimetals (TWSs), are unlike closed FSs in conventional materials and can give rise to many exotic phenomena, such as anomalous SFA-mediated quantum oscillations, chiral magnetic effects, three-dimensional quantum Hall effect, non-local voltage generation and anomalous electromagnetic wave transmission. Here, by using in-situ surface decoration, we demonstrate successful manipulation of the shape, size and even the connections of SFAs in a model TWS, NbAs, and observe their evolution that leads to an unusual topological Lifshitz transition not caused by the change of the carrier concentration. The phase transition teleports the SFAs between different parts of the surface Brillouin zone. Despite the dramatic surface evolution, the existence of SFAs is robust and each SFA remains tied to a pair of Weyl points of opposite chirality, as dictated by the bulk topology.

Laser-driven vacuum breakdown waves

It is demonstrated by three-dimensional quantum electrodynamics — particle-in-cell (QED-PIC) simulations that vacuum breakdown wave in the form of QED cascade front can propagate in an extremely intense plane electromagnetic wave. The result disproves the statement that the self-sustained cascading is not possible in a plane wave configuration. In the simulations the cascade is initiated during laser-foil interaction in the light sail regime. As a result, a constantly growing electron-positron plasma cushion is formed between the foil and laser radiation. The cushion plasma efficiently absorbs the laser energy and decouples the radiation from the moving foil thereby interrupting the ion acceleration. The models describing propagation of the cascade front and electrodynamics of the cushion plasma are presented and their predictions are in a qualitative agreement with the results of numerical simulations.

Experimental signatures of a three-dimensional quantum spin liquid in effective spin-1/2 Ce2Zr2O7 pyrochlore

A quantum spin liquid is a state of matter where unpaired electrons’ spins, although entangled, do not show magnetic order even at the zero temperature. The realization of a quantum spin liquid is a long-sought goal in condensed-matter physics. Although neutron scattering experiments on the two-dimensional spin-1/2 kagome lattice ZnCu3(OD)6Cl2 and triangular lattice YbMgGaO4 have found evidence for the hallmark of a quantum spin liquid at very low temperature (a continuum of magnetic excitations), the presence of magnetic and non-magnetic site chemical disorder complicates the interpretation of the data. Recently, the three-dimensional Ce3+ pyrochlore lattice Ce2Sn2O7 has been suggested as a clean, effective spin-1/2 quantum spin liquid candidate, but evidence of a spin excitation continuum is still missing. Here, we use thermodynamic, muon spin relaxation and neutron scattering experiments on single crystals of Ce2Zr2O7, a compound isostructural to Ce2Sn2O7, to demonstrate the absence of magnetic ordering and the presence of a spin excitation continuum at 35 mK. With no evidence of oxygen deficiency and magnetic/non-magnetic ion disorder seen by neutron diffraction and diffuse scattering measurements, Ce2Zr2O7 may be a three-dimensional pyrochlore lattice quantum spin liquid material with minimum magnetic and non-magnetic chemical disorder. A detailed neutron scattering and muon spin relaxation study uncovers a continuum of magnetic excitations down to 35 mK in the pyrochlore lattice compound Ce2Zr2O7 with minimum chemical disorder, consistent with quantum spin liquid behaviour.

Orientational relaxation of a quantum linear rotor in a dissipative environment: Simulations with the hierarchical equations-of-motion method.

We study the effect of a dissipative environment on the orientational relaxation of a three-dimensional quantum linear rotor. We provide a derivation of the Hamiltonian of a linear rotor coupled to a harmonic bath from first principles, confirming earlier conjectures. The dynamics generated by this Hamiltonian is investigated by the hierarchical equations-of-motion method assuming a Drude spectral density of the bath. We perform numerically accurate simulations and analyze the behavior of orientational correlation functions and the rotational structures of infrared absorption and Raman scattering spectra. We explore the features of orientational correlation functions and their spectra for a wide range of system-bath couplings, bath memory times, and temperatures. We discuss the signatures of the orientational relaxation in the underdamped regime, the strongly damped regime, and the librational regime. We show that the behavior of orientational correlation functions and their spectra can conveniently be analyzed in terms of three characteristic times, which are explicitly expressed in terms of the parameters of the Hamiltonian.

Towards background independent quantum gravity with tensor models

We explore whether the phase diagram of tensor models could feature a pregeometric, discrete and a geometric, continuum phase for the building blocks of space. The latter are associated to rank d tensors of size N. We search for a universal large N scaling limit in a rank-3 model with real tensors that could be linked to a transition between the two phases. We extend the conceptual development and practical implementation of the flow equation for the pregeometric setting. This provides a pregeometric ‘coarse-graining’ by going from many microscopic to few effective degrees of freedom by lowering N. We discover several candidates for fixed points of this coarse graining procedure, and specifically explore the impact of a novel class of interactions allowed in the real rank-3 model. In particular, we explain how most universality classes feature dimensional reduction, while one candidate, involving a tetrahedral interaction, might potentially be of relevance for three-dimensional quantum gravity.

QMBlender: Particle-based visualization of 3D quantum wave function dynamics

Simulated three-dimensional quantum wave functions (or probability density distributions, in general), Ψ(x, t), are often represented graphically as smooth isocontours or with 2-dimensional cross-sectional plots. As such, neither the full wave dynamics nor the true stochastic interpretation are captured adequately in a single representation. Moreover, the dynamics are often provided as videos, so that posterior interaction with the solution by other researchers is not possible. Here, we describe a software tool, called QMBlender, that produces 3D models of Ψ(x, t) at each time as a collection of Monte Carlo sampled coordinates represented by graphics primitives, or particles. QMBlender is a plugin to the popular open source Blender editor, which takes advantage of all its 3D editing, I/O, materials/lighting, and rendering capabilities. The resulting 3D models allow for posterior web-based interactive exploration, which we describe and argue could be a new paradigm for communicating and sharing results of numerical simulations. QMBlender can also be executed in a batch pipeline for producing 3D models, without the need for using the Blender GUI. We also implemented the particle sampling and visualization method using the VTK library for a side-by-side comparison with QMBlender. Here algorithms, implementation details, comparison with other similar systems, and examples from simulation of the Schrodinger equation are provided to show the utility of this software tool.

Three-Dimensional Cadmium Telluride Quantum Dots-DNA Nanoreticulation as a Highly Efficient Electrochemiluminescent Emitter for Ultrasensitive Detection of MicroRNA from Cancer Cells.

In this work, a novel three-dimensional cadmium telluride quantum dots-DNA nanoreticulation (3D CdTe QDs-DNA-NR) was used as a signal probe with the dual-legged DNA walker circular amplification as target conversion strategy to establish a pioneering electrochemiluminescence (ECL) biosensing strategy for ultrasensitive detection of microRNA-21 form cancer cells. Herein, such a 3D luminous nanomaterial with reticular structure not only supported abundant CdTe QDs to avoid the inner filter effect for obtaining a high ECL efficiency but also contained the hemin/G-quadruplex as coreaction accelerator in the 3D CdTe QDs-DNA-NR/S2O82- system for the enhancement of ECL intensity. Furthermore, with the target-induced dual-legged DNA walker circular amplification strategy, a mass of output DNA was produced to connect with the 3D CdTe QDs-DNA-NR for the construction of the ECL biosensor, which realized the ultrasensitive detection of microRNA-21 from 100 aM to 100 pM and the detection limit down to 34 aM. Significantly, this work could be readily extended for the detection of other biomolecules to provide a neoteric channel for disease diagnosis.

On the Zeros of a Class of Modular Functions

We generalize a number of works on the zeros of certain level 1 modular forms to a class of weakly holomorphic modular functions whose q-expansions satisfy the following: $$\begin{aligned} f_k(A; \tau )\, {:}{=}\,q^{-k}(1+a(1)q+a(2)q^2+\cdots ) + O(q), \end{aligned}$$ where a(n) are numbers satisfying a certain analytic condition. We show that the zeros of such $$f_k(\tau )$$ in the fundamental domain of $$\text {SL}_2(\mathbb {Z})$$ lie on $$|\tau |=1$$ and are transcendental. We recover as a special case earlier work of Witten on extremal “partition” functions $$Z_k(\tau )$$ . These functions were originally conceived as possible generalizations of constructions in three-dimensional quantum gravity.

Photoluminescent Colloidal Nanohelices Self-Assembled from CdSe Magic-Size Clusters via Nanoplatelets.

Reports on photoluminescent colloidal semiconductor two-dimensional (2D) helical nanostructures with one-dimensional quantum confinement are relatively rare. Here, we discuss the formation of such photoluminescent nanostructures for CdSe. We show that when as-synthesized unpurified zero-dimensional (0D) CdSe magic-size clusters (MSCs) (passivated by carboxylate ligands with three-dimensional quantum confinement) are dispersed in a solvent (such as toluene or chloroform) containing hexadecylamine and then subjected to sonication, helical nanostructures are obtained, as observed by transmission electron microscopy. We demonstrate that the formation involves the self-assembly of 0D MSCs into 2D nanoplatelets, which act as intermediates. The CdSe MSCs and their self-assembled 2D nanostructures display almost identical static optical properties, namely, a sharp absorption doublet with peaks at 433 and 460 nm and a narrow emission peak at 465 nm; this is a subject for further study. This study introduces new methods for fabricating photoluminescent helical nanostructures via the self-assembly of photoluminescent MSCs.

Elastic gauge fields and zero-field three-dimensional quantum Hall effect in hyperhoneycomb lattices

Dirac materials respond to lattice deformations as if the electrons were coupled to gauge fields. We derive the elastic gauge fields in the hyperhoneycomb lattice, a three dimensional (3D) structure with trigonally connected sites. In its semimetallic form, this lattice is a nodal-line semimetal with a closed loop of Dirac nodes. Using strain engineering, we find a whole family of strain deformations that create uniform nearly flat Landau levels in 3D. We propose that those Landau levels can be created and tuned in metamaterials with the application of a simple uniaxial temperature gradient. In the 3D quantum anomalous Hall phase, which is topological, we show that the components of the elastic Hall viscosity tensor are multiples of $\eta_{H}=\beta^{2}\sqrt{3}/\left(8\pi a^{3}\right)$, where $\beta$ is an elastic parameter and $a$ is the lattice constant.

Secure Transmission of 3D-QRMW Quantum Images via Quantum Fourier Transform in Blind Cloud

This study explores three-dimensional multi-channel quantum image representation model (3D-QRMW) which can be used in many fields such as three-dimensional medical imaging, atomic imaging, and infrared images. Quantum images are transmited between participants by Quantum Fourier Transform (QFT) in which output qubits are reordered by blind Cloud with permutation. Also key with length K=16N is applied to share signature for recipients. This allows all members to know only their signature information. Security analyzes show that quantum images in the model of 3D-QRMW are transmitted safely. Keywords : 3D quantum image, Security of 3D quantum image, Blind Cloud, Quantum Fourier. DOI : 10.7176/JSTR/5-5-12

Three-dimensional quantum Hall effect and metal-insulator transition in ZrTe5.

The discovery of the quantum Hall effect (QHE)1,2 in two-dimensional electronic systems has given topology a central role in condensed matter physics. Although the possibility of generalizing the QHE to three-dimensional (3D) electronic systems3,4 was proposed decades ago, it has not been demonstrated experimentally. Here we report the experimental realization of the 3D QHE in bulk zirconium pentatelluride (ZrTe5) crystals. We perform low-temperature electric-transport measurements on bulk ZrTe5 crystals under a magnetic field and achieve the extreme quantum limit, where only the lowest Landau level is occupied, at relatively low magnetic fields. In this regime, we observe a dissipationless longitudinal resistivity close to zero, accompanied by a well-developed Hall resistivity plateau proportional to half of the Fermi wavelength along the field direction. This response is the signature of the 3D QHE and strongly suggests a Fermi surface instability driven by enhanced interaction effects in the extreme quantum limit. By further increasing the magnetic field, both the longitudinal and Hall resistivity increase considerably and display a metal-insulator transition, which represents another magnetic-field-driven quantum phase transition. Our findings provide experimental evidence of the 3D QHE and a promising platform for further exploration of exotic quantum phases and transitions in 3D systems.