Finite Quantum Research Articles

Analysis of Electron Penetration into the Insulator in Finite Quantum Wells for Nanosheet MOSFETs

Analysis of Electron Penetration into the Insulator in Finite Quantum Wells for Nanosheet MOSFETs

Divergence of thermalization rates driven by the competition between finite temperature and quantum coherence

The thermalization of an isolated quantum system is described by quantum mechanics and thermodynamics, while these two subjects are still not fully consistent with each other. This leaves a less-explored region where both quantum and thermal effects cannot be neglected, and the ultracold-atom platform provides a suitable and versatile testbed to experimentally investigate these complex phenomena. Here we perform experiments based on ultracold atoms in optical lattices and observe a divergence of thermalization rates of quantum matters when the temperature approaches zero. By ramping an external parameter in the Hamiltonian, we observe the time delay between the internal relaxation and the external ramping. This provides us with a direct comparison of the thermalization rates of different quantum phases. We find that the quantum coherence and bosonic stimulation of superfluid induces the divergence while the finite temperature and the many-body interactions are suppressing the divergence. The quantum coherence and the thermal effects are competing with each other in this isolated thermal quantum system, which leads to the transition of thermalization rate from divergence to convergence.

Localized electronic states induced by the presence of two defective resonators in electronic comb-like waveguides structure

Abstract In this paper, we use the transfer matrix method to determine the band structure and electrical transmission rate of a one-dimensional electronic comb-like waveguide system. This structure is made up of the periodicity of finite GaAs quantum wire (QWR) (segment) grafted in its extremity by a vertical Ga 1 − x Al x As QWR (resonator). In this perfect structure, we replace the resonator situated in the middle of the periodic structure by a composed resonator made of vertical superposition of two resonators of different Al concentrations (x 01 and x 02). These defective resonators induce electronic localized states, inside the electronic band gaps of the perfect structure, with higher energy values depending on the geometrical (lengths) and the physical (x 01, x 02) parameters of the defective resonators. When the length d 02 of the upper resonator composed of Al concentration x 02 = 0.3 increases, these localized electronic states move to lower energies; conversely, when the concentration x 02 increases, they move to higher energies. We also show that there is an important effect of changing the localized states of two resonators connected in cascade with different concentrations. Our results may be relevant to the design of electronic guidance, filtering, and detection systems.

CONSTRUCTING QUANTUM ANGULAR MOMENTUM L3 IN SPECIFIC DIRECTION BY USING U(1) GROUP

The purpose of this work is to investigate the mathematical structure of finite quantum angular momentum in a specific direction L3 which can be constructed from the representation of the U(1) group. The angular momentum eigenstate is invariant under Abelian rotation symmetry. The character group of U(1) is constructed to show that there exists an additive unitary operator for the angular momentum eigenstate, and the rotation eigenstate is invariant under it. The Weyl relation is proved by showing that the angle and angular momentum L3 are the canonical conjugate pair of observables.

Evanescent Electron Wave-Spin.

This study demonstrates the existence of an evanescent electron wave outside both finite and infinite quantum wells by solving the Dirac equation and ensuring the continuity of the spinor wavefunction at the boundaries. We show that this evanescent wave shares the spin characteristics of the wave confined within the well, as indicated by analytical expressions for the current density across all regions. Our findings suggest that the electron cannot be confined to a mathematical singularity and that quantum information, or quantum entropy, can leak through any quantum confinement. These results emphasize that the electron wave, fully characterized by Lorentz-invariant charge and current densities, should be considered the true and sole entity of the electron.

Heat capacity and quantum compressibility of dynamical spacetimes with thermal particle creation

This work continues the investigation in two recent papers on the quantum thermodynamics of spacetimes, (1) placing what was studied in [] for thermal quantum fields in the context of early universe cosmology, and (2) extending the considerations of vacuum compressibility of dynamical spaces treated in [] to dynamical spacetimes with thermal quantum fields. We begin with a warning that thermal equilibrium condition is not guaranteed to exist or maintained in a dynamical setting and thus finite temperature quantum field theory in cosmological spacetimes needs more careful considerations than what is often described in textbooks. A full description requires nonequilibrium quantum field theory in dynamical spacetimes using “in-in” techniques. A more manageable subclass of dynamics is where thermal equilibrium conditions are established at both the beginning and the end of evolution, where the in-thermal state and the out-thermal state are both well defined. Particle creation in the full history can then be calculated in this in-out asymptotically-stationary setup via the S-matrix transition amplitudes. Here we shall assume an in-vacuum state. It has been shown that if the intervening dynamics has an initial period of exponential expansion, such as in inflationary cosmology, particles created from the parametric amplification of the vacuum fluctuations in the initial vacuum will have a thermal spectrum measured at the out-state. Under these conditions finite temperature field theory can be applied to calculate the quantum thermodynamic quantities. Here we consider a massive conformal scalar field in a closed four-dimensional Friedmann-Lemaître-Robertson-Walker universe based on the simple analytically solvable Bernard-Duncan model. We calculate the energy density of particles created from an in-vacuum and derive the partition function. From the free energy we then derive the heat capacity and the quantum compressibility of these spacetimes with thermal particle creation. We end with some discussions and suggestions for further work in this program of studies. Published by the American Physical Society 2024

Bipolar topological spin diode and topological spin transistor in finite size quantum spin Hall insulators

Abstract The miniaturization and stability of electronic devices are becoming increasingly important today. We attempt to provide the theoretical support for designing spintronic devices by numerically investigating spin transport in finite size quantum spin Hall insulators (QSHI) under a perpendicular weak magnetic field. By modifying magnetic field strength, we find the gapped spin up and spin down bands are split to realize a half-metal phase which is a promising candidate for designing an efficient spin filter. Moreover, one of the two energy gaps becomes larger and the other smaller due to the weakened or enhanced coupling between two edge states. Here we propose and demonstrate the spin filter based on a finite size QSHI junction under a magnetic field and the polarity can be inverted by a bias voltage or magnetic field. Interestingly, we find a bipolar spin diode effect that only one spin channel is opened and the other spin channel is closed at positive bias, and the opposite spin electron can be transmitted with negative bias. Two spin filters in series can be a spin transistor, the on and off states can be controlled by spin polarization of one spin filter. We show that the topological spin transistor can be controlled by the gate voltage, and it survives in moderate disorder.

Information scrambling and chaos induced by a Hermitian matrix

Abstract Given an
arbitrary \(V \times V\) Hermitian matrix,
considered as a finite discrete quantum Hamiltonian,
we use methods from graph and
ergodic theories to
construct a \textit{quantum Poincar'e map} at energy \(E\) and a
corresponding stochastic
\textit{classical Poincar'e-Markov map} at the same energy
on an appropriate
discrete
\textit{phase space}.
This phase space
consists of the directed edges of a
graph with \(V\) vertices that are in one-to-one correspondence with the
non-vanishing off-diagonal elements of \(H\).
The correspondence between quantum Poincar'e map and classical
Poincar'e-Markov map is
an alternative to the standard quantum-classical
correspondence based on a classical limit \(\hbar \to 0\). Most
importantly it can be constructed where no such limit exists.
Using standard methods from ergodic theory
we then proceed to define
an expression for the
\textit{Lyapunov exponent} \(\Lambda(E)\) of the classical map.
It measures the rate of loss of classical information in the dynamics
and relates it to the separation of stochastic \textit{classical
trajectories} in the phase space. We suggest that
 loss of information in the underlying
classical dynamics is an indicator for quantum information scrambling.

Generalized entanglement capacity of de Sitter space

Near horizons, quantum fields of low spin exhibit densities of states that behave asymptotically like 1+1 dimensional conformal field theories. In effective field theory, imposing some short-distance cutoff, one can compute thermodynamic quantities associated with the horizon, and the leading cutoff sensitivity of the heat capacity is found to equal to the leading cutoff sensitivity of the entropy. One can also compute contributions to the thermodynamic quantities from the gravitational path integral. For the cosmological horizon of the static patch of de Sitter space, a natural conjecture for the relevant heat capacity is shown to equal the Bekenstein-Hawking entropy. These observations allow us to extend the well-known notion of the generalized entropy to a generalized heat capacity for the static patch of de Sitter (dS). The finiteness of the entropy and the nonvanishing of the generalized heat capacity suggest it is useful to think about dS as a state in a finite dimensional quantum gravity model that is not maximally uncertain. Published by the American Physical Society 2024

Early universe in quantum gravity

We present a new picture of the early universe in finite nonlocal quantum gravity, which is Weyl invariant at the classical and quantum levels. The high-energy regime of the theory consists of two phases, a Weyl invariant trans-Planckian phase and a post-Planckian or Higgs phase described by an action quadratic in the Ricci tensor and where the cosmos evolves according to the standard radiation-dominated model. In the first phase, all the issues of the hot big bang such as the singularity, flatness, and horizon problems find a universal and simple non-inflationary solution by means of Weyl invariance, regardless of the microscopic details of the theory. In the second phase, once Weyl symmetry is spontaneously broken, primordial perturbations are generated around a background that asymptotically evolves as a radiation-dominated flat Friedmann-Lemaître-Robertson-Walker universe.

Tilted-Plane Structure of the Energy of Finite Quantum Systems.

The piecewise linearity condition on the total energy with respect to the total magnetization of finite quantum systems is derived using the infinite-separation-limit technique. This generalizes the well-known constancy condition, related to static correlation error, in approximate density functional theory. The magnetic analog of Koopmans' theorem in density functional theory is also derived. Moving to fractional electron count, the tilted-plane condition is derived, lifting certain assumptions in previous works. This generalization of the flat-plane condition characterizes the total energy surface of a finite system for all values of electron count N and magnetization M. This result is used in combination with tabulated spectroscopic data to show the flat-plane structure of the oxygen atom, among others. We find that derivative discontinuities with respect to electron count sometimes occur at noninteger values. A diverse set of tilted-plane structures is shown to occur in d-orbital subspaces, depending on chemical coordination. General occupancy-based total-energy expressions are demonstrated thereby to be necessarily dependent on the symmetry-imposed degeneracies.

Time-Dependent Variational Principle with Controlled Bond Expansion for Matrix Product States.

We present a controlled bond expansion (CBE) approach to simulate quantum dynamics based on the time-dependent variational principle (TDVP) for matrix product states. Our method alleviates the numerical difficulties of the standard, fixed-rank one-site TDVP integrator by increasing bond dimensions on the fly to reduce the projection error. This is achieved in an economical, local fashion, requiring only minor modifications of standard one-site TDVP implementations. We illustrate the performance and accuracy of CBE-TDVP with several numerical examples on finite quantum lattices, including new results on bipolaron formation in the Peierls-Hubbard model and spin pumping via adiabatic flux insertion in a chiral spin liquid.

Generation of Narrow Beams of Super High-Energy Gamma Quanta in the Resonant Compton Effect in the Field of a Strong X-ray Wave

The article presents a theoretical study of Oleinik resonances in the process of scattering a gamma quantum by an ultrarelativistic electron in the field of a strong electromagnetic wave with intensities up to 1027Wcm−2. The resonant kinematics for three possible resonant reaction channels in a strong external field have been studied in detail. It is shown that under resonant conditions, the scattering channels of the reaction effectively split into two first-order processes according to the fine structure constant, such as the external field-stimulated Compton effect. The annihilation channel of the reaction effectively decays into direct and reverse the external field-stimulated Breit–Wheeler processes. In the absence of interference from the reaction channels, a resonant differential cross-section was obtained in a strong external electromagnetic field. The cases when the energy of the initial electrons significantly exceeds the energy of the initial gamma quanta have been studied. At the same time, all particles (initial and final) fly in a narrow cone away from the direction of wave propagation. The conditions under which the energy of ultrarelativistic initial electrons is converted into the energy of a finite gamma quantum are studied. It is shown that the resonant differential cross-section of such a process significantly (by several orders of magnitude) exceeds the corresponding nonresonant cross-section. This theoretical study predicts a number of new physical effects that may explain the high-energy fluxes of gamma quanta produced near neutron stars and magnetars.

Electronic transport properties in GaAs/AlGaAs finite superlattice of cylindrical quantum wires

In this paper, we have studied a theoretical and numerical investigation of the electronic properties of finite cylindrical quantum wires (CQWRs), constituted by the periodic alteration of two semiconductor materials of CQWRs GaAs/AlGaAs in the axial direction, the structure sandwiched between two substrates GaAs. The electronic band structure and the electronic transmission spectrum are obtained by means of Green’s function approach, taking into account the impact of connection barriers. Our results reveal that the electronic energy levels of CQWRs consist of alternating passbands and bandgaps. The coincidence of incoming electronic waves with these discrete electronic energy levels leads to electron transport during the CQWRs superlattice. We employed an effective mass model dependent on the cell position in the axial direction to solve the Schrodinger equation. This model was adjusted to reflect variations in the confining potentials while accounting for changes in the radial direction. When the radius of the structure is relatively small the electronic states tend towards higher energies due to geometrical confinement. On the other hand, as the radius increases, the passbands and bandgaps move to lower energies. Similarly, the pseudogaps turn into full gaps, and their width increases, and this feature is also observed when the number of cells increases. This property is due to the interaction between the neighboring electrons and the eigenstates of the CQWRs. In addition, the passbands and band gaps shift to high energy when the barrier concentration increases, and the width of band gaps increases also. Finally, we have demonstrated the theoretical design of an optoelectronic device for filtering electronic waves by geometrical and physical parameters, whose electronic band structure of this finite CQWRs superlattice can be controlled.

Solutions of the Schrödinger equation with velocity-dependent potentials:a study on Kratzer, Mie and Hulthen potentials

The effect of isotropic velocity-dependent potentials on the bound state energy eigenvalues of the Kratzer, Mie and Hulthen potentials is obtained for any quantum states in the presence of constant form factor εr=γρ0. The corresponding energy eigenvalues and eigenfunctions are determined and tabulated for a set of finite quantum numbers n and l in the framework of the well-known Nikiforov-Uvarov method.

On complementarity and distribution of imaginarity in finite dimensions

We investigate the complementarity relation among the l1 norm of imaginarity, linear entropy and the Brukner–Zeilinger invariant information in the presence of conjugate symmetry. By using an equality derived from the complementarity relation, we define a quantity named index of imaginarity distribution with respect to the imaginarity, linear entropy and invariant information in finite dimensional quantum systems. We show that the index of imaginarity distribution is nonnegative and upper bounded by the square of the l1 norm of imaginarity, and serves as an invaluable tool in characterizing effectively the imaginarity distribution. Detailed examples are presented to illustrate our theoretical analysis.

The automatic imprimitivity for Gq

Let Gq be the Drinfeld-Jimbo deformation of a connected simply-connected compact Lie group and T be its maximal torus. We show that the induction functors from the categories of T-equivariant correspondences to the categories of Gq-equivariant correspondences give equivalences of these categories under the existence of tracial states. As its application, we show some automatic imprimitivity results and classification results for extensions, subalgebras and finite index discrete quantum subgroups of Gqˆ.

Insights into the Electronic, Optical, and Anti-Corrosion Properties of Two-Dimensional ZnO: First-Principles Study

The electronic, optical, and anticorrosion properties of planer ZnO crystal and quantum dots are explored using density functional theory calculations. The calculations for the finite ZnO quantum dots were performed in Gaussian 16 using the B3LYP/6-31g level of theory. The periodic calculations were carried out using VASP with the plane wave basis set and the PBE functional. The subsequent band structure calculations were performed using the hybrid B3LYP functional that shows accurate results and is also consistent with the finite calculations. The considered ZnO nanodots have planer hexagonal shapes with zigzag and armchair terminations. The binding energy calculations show that both structures are stable with negligible deformation at the edges. The ZnO nanodots are semiconductors with a moderate energy gap that decreases when increasing the size, making them potential materials for anticorrosion applications. The values of the electronic energy gaps of ZnO nanodots are confirmed by their UV-Vis spectra, with a wide optical energy gap for the small structures. Additionally, the calculated positive fraction of transferred electrons implies that electron transfer occurs from the inhibitor (ZnO) to the metal surface to passivate their vacant d-orbitals, and eventually prevent corrosion. The best anti-corrosion performance was observed in the periodic ZnO crystal with a suitable energy gap, electronegativity, and fraction of electron transfer. The effects of size and periodicity on the electronic and anticorrosion properties are also here investigated. The findings show that the anticorrosion properties were significantly enhanced by increasing the size of the quantum dot. Periodic ZnO crystals with an appropriate energy gap, electronegativity, and fraction of electron transfer exhibited the optimum anticorrosion performance. Thus, the preferable energy gap in addition to the most promising anticorrosion parameters imply that the monolayer ZnO is a potential candidate for coating and corrosion inhibitors.

Exploring the Quantum Spectral Curve for AdS3/CFT2

Despite the rich and fruitful history of the integrability approach to string theory on the AdS3 × S3 × T4 background, it has not been possible to extract many concrete predictions from integrability, except in a strict asymptotic regime of large quantum numbers, due to the severity of wrapping effects. The situation changed radically with two independent and identical proposals for the Quantum Spectral Curve (QSC) for this system in a background of pure Ramond-Ramond flux. In other integrable superstring backgrounds there is compelling evidence that this formulation captures all wrapping effects exactly and describes the full planar spectrum. This great success motivates us to study the new proposed QSC and develop methods to extract from it concrete predictions for spectral data. The AdS3 × S3 × T4 case presents a significant novel feature and challenge compared to its higher-dimensional analogues — massless modes. It has been conjectured that these manifest themselves in a new property of this QSC: the non-quadratic nature of the branch-cut singularities of the QSC Q-functions. This feature implies new technical challenges in solving the QSC equations as compared to the well-studied case of N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 SYM. In this paper we resolve these difficulties and obtain the first ever predictions for unprotected string excitations in the planar limit with finite quantum numbers and RR flux. We explain how to extract a systematic expansion around the analogue of the weak ’t Hooft coupling limit in N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 SYM and also obtain high-precision numerical results. These concrete data and others obtainable from the QSC could help to identify the so-far mysterious dual CFT.

Topological Properties of a Non‐Hermitian Quasi‐1D Chain with a Flat Band

AbstractThe spectral properties of a non‐Hermitian quasi‐1D lattice in two of the possible dimerization configurations are investigated. Specifically, it focuses on a non‐Hermitian diamond chain that presents a zero‐energy flat band. The flat band originates from wave interference and results in eigenstates with a finite contribution only on two sites of the unit cell. To achieve the non‐Hermitian characteristics, the system under study presents non‐reciprocal hopping terms in the chain. This leads to the accumulation of eigenstates on the boundary of the system, known as the non‐Hermitian skin effect. Despite this accumulation of eigenstates, for one of the two considered configurations, it is possible to characterize the presence of non‐trivial edge states at zero energy by a real‐space topological invariant known as the biorthogonal polarization. This work shows that this invariant, evaluated using the destructive interference method, characterizes the non‐trivial phase of the non‐Hermitian diamond chain. For the second non‐Hermitian configuration, there is a finite quantum metric associated with the flat band. Additionally, the system presents the skin effect despite the system having a purely real or imaginary spectrum. The two non‐Hermitian diamond chains can be mapped into two models of the Su‐Schrieffer‐Heeger chains, either non‐Hermitian, and Hermitian, both in the presence of a flat band. This mapping allows to draw valuable insights into the behavior and properties of these systems.